waveguide photodiodes - kuhij/public/master thesis.pdfwaveguide photodiodes { with high mode overlap...

Master of Science in Physics Thesis

Waveguide Photodiodes– with high mode overlap and sensitivity

Henrik Ingerslev

April 12, 2004

ii

The front page shows an electrical eye diagram for a 10QW SOA-PD device with a 320µm

long SOA. The input power is −12dBm, it is modulated at 10Gb/s, with a pseudo random

bit sequence of 107 − 1, 85mA is applied to the SOA, and −1volt to the PD.

This measurement shows an interesting effect of the history of the bits (section 3.4.2).

Abstract

Characterization and optimization of two different types of photodiodes, for usein optical fiber communication systems, are presented. The first type is a PINwaveguide photodiode, with a bulk active layer of InGaAs. The second type is aPIN waveguide photodiode, with an integrated semiconductor optical amplifier,and it has an active layer of InGaAsP quantum wells.For the first photodiode a total of 22 different designs are characterized, and inthe light of this characterization the best design is chosen. The mode overlap isfurthermore optimized from among different optical fibers, and a maximum of∼ 95% is achieved.For the second photodiode three different heterostructures, with 3, 8, and 10quantum wells, each with several different lengths of the semiconductor opticalamplifier, is characterized. A maximum sensitivity of ∼ −24dBm is achievedby optimizing the length of the semiconductor optical amplifier.

iii

Preface

The work presented in this master of science (M.Sc.) in physics thesis was car-ried out at the Research Center COM, Technical University of Denmark, in theoptoelectronic group, and at GiGA, an Intel company.The work was supervised by Professor Jørn M. Hvam, head of the optoelectronicgroup at COM, Assistant Professor Kresten Yvind, COM, and Poul Erik Lin-delof, vice chairman of the Nanoscience Center at Copenhagen University. I amvery grateful for the support and guidance given by Jørn M. Hvam, and KrestenYvind, and I would also like to thank Ph.D. Jesper Hanberg, GiGA-Intel, forgrowing the first type of photodiode.This thesis presents characterization and optimization of two types of waveguidephotodiodes, for use in an optical fiber communications system.The project began in January 2003, and in the spring term I had a course onthe physics of diode lasers (5 ECTS), and as part of my master education I alsomade a presentation on photonic crystals (5 ECTS) in the fall term.

COM, DTUApril 2004

Henrik [email protected]

[email protected]

v

Contents

1 Introduction 11.1 Optical fiber communication . . . . . . . . . . . . . . . . . . . . . 11.2 Project description . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Structure of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Bulk Photodiode 52.1 Device design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2 PIN Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Bandstructure . . . . . . . . . . . . . . . . . . . . . . . . 82.2.2 I-V curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3 Light absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.4 Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.5 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.5.1 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . 312.5.2 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.6.1 Comparison of devices . . . . . . . . . . . . . . . . . . . . 432.6.2 Improvements . . . . . . . . . . . . . . . . . . . . . . . . . 46

3 Photodiode with integrated SOA 493.1 Device design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.1.1 Quantum wells . . . . . . . . . . . . . . . . . . . . . . . . 513.2 QW Photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.2.1 PIN Junction . . . . . . . . . . . . . . . . . . . . . . . . . 533.2.2 Light absorption . . . . . . . . . . . . . . . . . . . . . . . 553.2.3 Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . 56

3.3 QW SOA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 583.3.1 Optical gain in semiconductor material . . . . . . . . . . 583.3.2 Amplifying cavity . . . . . . . . . . . . . . . . . . . . . . 633.3.3 Total amplification . . . . . . . . . . . . . . . . . . . . . . 65

3.4 SOA-Photodiode . . . . . . . . . . . . . . . . . . . . . . . . . . . 703.4.1 Bandwidth . . . . . . . . . . . . . . . . . . . . . . . . . . 713.4.2 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.5 Summary and discussion . . . . . . . . . . . . . . . . . . . . . . . 77

vii

viii CONTENTS

4 Conclusion 81

Abbreviations 83

Bibliography 85

List of Figures

1.1 Block diagram if a receiver. . . . . . . . . . . . . . . . . . . . . . 2

2.1 Schematic figure of the PIN WGPD . . . . . . . . . . . . . . . . 62.2 Density of occupied states for an intrinsic and doped semiconductor 82.3 Depletion approximation for the electrical potential . . . . . . . . 102.4 Bandstructure for PIN5 . . . . . . . . . . . . . . . . . . . . . . . 122.5 I-V curves for all devices (no incident light) . . . . . . . . . . . . 132.6 Absorption and emission processes . . . . . . . . . . . . . . . . . 162.7 Calculated absorption coefficient . . . . . . . . . . . . . . . . . . 172.8 Quantum efficiency versus incident wavelength for PIN5 . . . . . 182.9 I-V curves for all devices with optical input powers . . . . . . . . 212.10 Photocurrent for PIN8, at two different wavelengths . . . . . . . 242.11 Schematic of the refractive index in the PD . . . . . . . . . . . . 262.12 Effective index method calculation of the mode in PIN6 . . . . . 272.13 Farfields of three different optical fibers . . . . . . . . . . . . . . 302.14 Schematic of the electrical setup for dynamical measurements . . 322.15 Model used to calculate the bandwidth of the PDs . . . . . . . . 332.16 Block diagram of the setup for measuring the bandwidth. . . . . 362.17 Bandwidth: Responsivity versus modulation frequency . . . . . . 372.18 Block diagram of the setup for the sensitivity measurements . . . 402.19 Optical and electrical eye diagrams . . . . . . . . . . . . . . . . . 402.20 Sensitivity: BER versus optical input power . . . . . . . . . . . . 422.21 New diagram of external components . . . . . . . . . . . . . . . . 46

3.1 Schematic figure of the SOA-PD devices . . . . . . . . . . . . . . 513.2 Structure of bandgap through one QW from the 10QW device . 523.3 I-V curves for all QW PDs, with different optical input power . 543.4 Bandstructure of the 8QW device . . . . . . . . . . . . . . . . . . 563.5 Photocurrent versus incident optical wavelength . . . . . . . . . . 573.6 Schematic illustration of the integrated SOA-PD device . . . . . 583.7 Calculated gain spectrum . . . . . . . . . . . . . . . . . . . . . . 593.8 Optical output spectrum from an AR coated 10QW SOA . . . . 613.9 Photocurrent from the PD versus incident wavelength, and SOA-

current, for three different SOA-PDs . . . . . . . . . . . . . . . . 62

ix

x LIST OF FIGURES

3.10 I-V curves of the PD at different SOA-currents . . . . . . . . . . 643.11 Photocurrent from PD versus SOA-current . . . . . . . . . . . . 663.12 Amplification of seven different SOAs versus SOA-current, and

incident optical power . . . . . . . . . . . . . . . . . . . . . . . . 683.13 Bandwidth: Responsivity versus modulation frequency . . . . . . 723.14 Sensitivity: BER versus optical input power . . . . . . . . . . . . 763.15 Sensitivity versus length of SOA . . . . . . . . . . . . . . . . . . 77

List of Tables

2.1 Growth data for all bulk WGPDs. . . . . . . . . . . . . . . . . . 72.2 Breakdown voltages, and breakdown fields . . . . . . . . . . . . . 132.3 Responsivity of all bulk PDs . . . . . . . . . . . . . . . . . . . . . 192.4 Key parameters of the modes in the bulk PD waveguides . . . . . 292.5 Measured and calculated bandwidths of the bulk PDs . . . . . . 342.6 Calculated and measured sensitivity for five bulk PDs . . . . . . 432.7 Data sheet for all the bulk PDs . . . . . . . . . . . . . . . . . . . 442.8 Key parameters for six PDs including PIN5 from GiGA . . . . . 45

3.1 Growth data for the three different SOA-PDs . . . . . . . . . . . 503.2 Calculated parameters for the QW material . . . . . . . . . . . . 523.3 Key parameters of the modes in the SOA-PD waveguides . . . . 573.4 Measured and calculated bandwidths of the SOA-PDs . . . . . . 743.5 Data sheet for the SOA-PDs . . . . . . . . . . . . . . . . . . . . . 78

xi

xii LIST OF TABLES

Chapter 1

Introduction

1.1 Optical fiber communication

An optical fiber communication system consists basically of a transmitter, anoptical fiber, and a receiver. The transmitter converts the data from electricalform to optical form, and couples the optical data into the optical fiber. Theoptical fiber then transfers the data over long distances to the receiver, thatconverts the data from optical form back to electrical form.There are two modulations formats for the optical data signal, either return tozero (RZ), or non return to zero (NRZ). As the name implies; in the RZ formatthe optical signal goes to zero between each bit (binary digit) even if there aremultiple bit1’s after each other, whereas in the NRZ format the optical signalwill stay at the bit1 level between multiple bit1’s.The transmitter part consists of a laser (light amplification by stimulated emis-sion of radiation), and for bit rates up to 10Gb/s direct modulation of the laseris commonly used. But, if the bit rate has to be higher for example 40Gb/s,external modulation is used, with a Mach-Zehnder modulator, or an electro ab-sorption modulator (EAM) as the external modulator.An optical fiber are today made with a core and cladding layer of silica glass,because this material has a very low loss of about 0.2dB/km for light at a wave-length of 1550nm [5]. The core and cladding layer are doped differently so thatthe core have the highest refractive index, and the guiding mechanism in thefiber is total internal reflection. There is another important quantity to considerfor optical fibers, besides loss, namely dispersion. Dispersion is caused by effectslike 1) the refractive index of silica depends on the optical wavelength, and 2)core and the cladding layer has different refractive index. And by engineeringthe optical fiber in a certain way the dispersion minimum can be made to coin-cide with the loss minimum, namely at 1550nm. An optical mode at 1550nmis therefore widely used in optical fiber communication today. But even thouloss and dispersion is being minimized in optical fibers today, regeneration andamplification of the optical signal along the optical fiber will still be needed for

1

2 CHAPTER 1. INTRODUCTION

Figure 1.1: Block diagram if a receiver.

very long transfer distances (> 100km) [5].Figure 1.1 shows a block diagram of a receiver, and the components of such areceiver can be arranged in three sections; a front end, a linear channel, and adata recovery section.The front end consists of a photodiode (PD) possibly with an integrated semi-conductor optical amplifier (SOA) (see section 3.4), and an electrical preampli-fier that amplifies the electrical signal for further processing.The linear channel consists of an amplifier and a low pass filter. The amplifiergain is controlled automatically to fix the average output voltage to a specificlevel, irrespective of the input voltage from the front end. The purpose of thelow pass filter is to cut off high frequency noise.The data recovery section consists of a decision circuit, and a clock recovery cir-cuit. The latter finds the bit rate of the received signal, which gives informationabout the time period of the bit slot. The decision circuit compares the outputfrom the linear channel to a threshold value at sampling times determined bythe clock recovery circuit, and decides whether the signal corresponds to a bit1or a bit0.To increase the total bit rate in an optical fiber communication network, twomethods are developed; optical time division multiplexing (OTDM), and wave-length division multiplexing (WDM). In WDM systems several different baserate channels, each at a different wavelength, are coupled into one fiber. TheOTDM systems works by delaying each of the base rate channels (each at thesame wavelength), by a certain amount of time with respect to the next channel,and then couple all of the channels into one fiber.

This thesis will be dealing with the PD and the SOA from the receiver. Thereare a number of ways to make a PD that can absorb photons at a wavelengthof 1550nm, both Ge and InP/InGaAs materials can be used. The junction canbe either PN or PIN (see section 2.2), and the light can be incident either ontothe surface (called a surface PD), or into a waveguide1 from the facet (called awaveguide photodiode (WGPD)).The InP/InGaAs material has the advantage over Ge that InGaAs has a di-

1The waveguide will be introduced in section 2.4

1.2. PROJECT DESCRIPTION 3

rect bandgap, whereas Ge has an indirect bandgap, so the absorption i muchhigher for InGaAs then for Ge. Another advantage is that InGaAs tends to havesmaller dark current, which is due to a smaller intrinsic carrier concentration(see equation 2.4). The PIN junction has the advantage over a PN junctionthat we can control the size of the depletion layer, which is used to optimize keytime parameters for the PD (see section 2.5.1). The surface PD and the WGPDeach have their advantages; the surface PD has a large area for the incidentlight to hit, whereas for the WGPD the incident light has to be aligned verycarefully to the waveguide, which makes it hard to fabricate. But, the largearea of the surface PD also results in large capacitance, which in turn gives alarge RC time and consequently a low bandwidth (see section 2.5.1). So, forhigh bit rates at 1550nm the PIN WGPD made from InP/InGaAs are preferable.

1.2 Project description

The work presented in this thesis focuses on the PD part of a receiver. Specifi-cally on two different types of PDs:

1) A PIN WGPD made with a bulk absorbing layer of InGaAs, which islattice matched to an InP substrate.

2) A PIN WGPD with an integrated SOA, made with a number of InGaAsPquantum wells as the active layer, which are strained to an InP substrate.

At GiGA-Intel they have designed a receiver unit, and the bulk PD is designedto be the PD part of this receiver.The PD with integrated SOA is made from materials that are not specificallydesigned for this purpose. The materials are made by COM, for mode-lockedlasers [15].The fabrication part of this project is to cleave the ready-made wafers into dies,for the second type of PD this involves cleaving the SOAs with different lengths.Then mount the dies onto a substrate, for either DC or AC measurements, andbond gold wires from the die to the substrate.

The goal of the project is to characterize and optimize the two differenttypes of PDs, for use in optical fiber communication systems, and to find waysto improve them.Intel made the following requirements on the PD before they began developingit (at an incident Wavelength of 1550nm):

• Responsivity ≥ 1A/W (see section 2.3)

• Bandwidth ≥ 10Gb/s (see section 2.5.1)

• Dark current ≤ 1nA (see section 2.2)

• Bias voltage = 3− 5volt (see section 2.2)

4 CHAPTER 1. INTRODUCTION

To verify if these requirements has been met, the characterization of the bulkPD involves measurements like; current voltage graphs with different opticalinput powers, photocurrent versus incident wavelength, breakdown voltages,dark currents, bandwidths, and sensitivities.The optimization part for the bulk PD consists of optimizing the responsivity2,be using many different optical fibers to couple the light into the PD.For the PD with integrated SOA, the characterization involves the same thingsas for the bulk PD, but also measurements on the SOA that shows the gainspectrum, total power amplification at 1550nm, and threshold level (which iswhere it starts to lase, see section 3.3).The optimization part of the PD with integrated SOA consists, like the bulkPD, of finding an optimal optical fiber, but more importantly it also consists ofoptimizing the length of the SOA, so that the integrated device gives a maximumsensitivity3.I have developed several different LabVIEW4 programs from scratch, for makingall these measurements, which includes programs to make surface plots (seefigure 3.9 and 3.12).

1.3 Structure of thesis

After this introduction chapter, the thesis is divided into two main chapters;chapter 2 is devoted to the bulk PD, and chapter 3 is devoted to the PD withintegrated SOA.In chapter 4 we summarizes what has been made, emphasizes the advantagesand disadvantages of the two types of PDs, and concludes wether the goals fromthe project description has been met.

2The responsivity will be defined in equation 2.113The sensitivity will be defines in section 3.4.24LabVIEW is a graphical development software for test, measurement, and control, pro-

vided by National Instruments Corporation

Chapter 2

Bulk Photodiode

In this chapter we will be dealing with the first PD, namely the bulk PIN WGPDmade from InGaAs/InP.The chapter starts with a description of a number of different heterostructurematerials that the devices are made from. The PIN junction is first charac-terized electrically in section 2.2, and then with absorption of incident light insection 2.3. The waveguide in the device, and mode overlap, is considered insection 2.4. Then we turn to dynamical measurements of bandwidth and sensi-tivity in section 2.5. And the chapter finishes with a comparison of the differentdesigns, and some ideas on how to improve it.

2.1 Device design

A total of twelve different designs of the bulk PIN WGPD have been made.They are named PIN1 through PIN10, PIN12 and PIN13, PIN11 does not ex-ist!, and measurements are performed on all except PIN1 because it were thefirst design and did not work well.The overall design of all these devices are similar, and consist from top to bot-tom of a top contact layer, which is designed to give good electrical contactto the metal leads. Down through the device we then have a layer of positivedoped (P-doped) InP, then a smaller layer of undoped InP, called a standofflayer. After that we have three small undoped layers of InGaAsP with decreas-ing bandgap, which are called grading layers. Then we reaches the layer thatabsorbs the incoming light, it is made of In0.53Ga0.47As and is called the activelayer. Then we again have three layers of InGaAsP, also called grading layers,now with increasing bandgap. After that we reaches the last layer, which is anegatively doped (N-doped) InP layer.All these layers are lattice matched to InP, and grown in the 100 direction on aN-doped InP Wafer. The structure can be seen schematic in figure 2.1, wherethe length of the device is cleaved to about 200µm. The P-doping is made with

5

6 CHAPTER 2. BULK PHOTODIODE

Figure 2.1: Schematic figure of the PIN WGPD with light incident onto thefacet from an optical fiber. To the left is a zoom-in around the active layer.

with Zn atoms, and the N-doping is made with Si atoms.A ridge is made by lithography, and on both sides of the ridge an insulating ma-terial called BCB (benzocyclobutene), is filled. The ridge is made in two designs;one with a width of 1.5µm and another with a width of 2.0µm. The differencesbetween the eleven designs are the thickness of the active layer, standoff layer,and grading layers, height of ridge, and the doping concentration of the P-side.A summary of all these parameters for the eleven devices, are listed in table 2.1.

2.2 PIN Junction

A junction with a P-doped region followed by a N-doped region is called a P-Njunction, and by introducing an intrinsic (undoped) region between the P andN side we have a PIN junction. If the materials in the junction are the same,the junction is called a homojunction, and if there are involved different ma-terials in the junction, it is called a heterojunction. Since all devices in thisproject have P-doped, N-doped, and intrinsic regions, and made from differentInGaAsP alloys, these junctions are all PIN heterojunctions.

2.2. PIN JUNCTION 7

PIN

2P

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PIN

4P

IN5

PIN

6P

IN7

PIN

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Figure 2.2: (a) Fermi’s distribution function for an intrinsic semiconductor at300K, (b) density of states (3D), (c) density of occupied states for the intrinsicsemiconductor, and (d) shows the density of occupied stated for an n-dopedsemiconductor

2.2.1 Bandstructure

Before vi collect the P, I and N materials to a junction, let’s first look at eachmaterial separately. The energy distribution for electrons and holes (absenceof an electron in an otherwise filled band) are governed by Fermi’s distributionfunction (see figure 2.2(a)), and the density of states can be calculated on thebasis of our knowledge of the crystal (see figure 2.2(b)). These two functionsmultiplied give us the density of occupied states (see figure 2.2(c)) [1]. In intrin-sic materials there are equal densities of electrons and holes, which is obtainedthrough the Fermi energy from Fermi’s distribution function. That is, the Fermienergy adjusts the ratio between electrons and holes.If we introduce doping, lets say donor atoms in the crystal, we will have moreelectrons and fewer holes (though the product of electron and hole densities arestill the same), this will make the Fermi energy shift upwards as can be seen infigure 2.2(d).Now lets look at what happens when we combine P, I, and N materials in thePIN junction. There will be a large carrier concentration gradient across thejunction, which will make the free electrons from the N-side diffuse across theintrinsic region into the P-side, and free holes from the P-side will diffuse acrossthe intrinsic region into the N-side. So, this process will lower the Fermi energyof the N-side, and raise the Fermi energy of the P-side. As this process con-tinues, the diffused carriers will cause an electric field to be built up, called abuilt-in electric field, and this electric field will counteract the diffusion.Current due to a carrier concentration gradient is called diffusion current, andcurrent due to an electric field is called drift current. After some time a steadystate situation will be reached where the diffusion current, and the drift current

2.2. PIN JUNCTION 9

are in equilibrium. In this steady state the Fermi energy of the two materialswill have reached the same level.In the steady state situation the electrons that have diffused from the N-side tothe P-side will be trapped at acceptor atoms, and holes that have diffused fromthe P-side to the N-side will be trapped at donor atoms. (An electron/hole thatare not trapped at an acceptor/donor atom will be free to move, and will bedrifted back to the N-side/P-side by the built-in electric field).There are two important quantities connected with the junction; the depletionregion with width wdep, and the built in potential Vbi. The depletion region isthe entire I region, and the region of the the P and N materials where there areno more free carriers. The built-in potential across the depletion region, whichis caused by the diffused carriers, is equal to the difference in Fermi energy ofthe P-side and N-side, before they were combined.Because there are no free carriers in the depletion region it is highly insulating,and by applying an external potential (bias voltage V0) to the junction, the po-tential will lay mainly across the depletion region. The total potential across thejunction will now be a combination of built-in potential, and external appliedpotential (Vbi + V0). The Fermi energy will now be different on either side ofthe depletion region, with a difference equal to the applied bias. The two Fermienergies are called quasi Fermi levels (see figure 2.4).

We here define the bandstructure as the position of the valence, and con-duction band through the junction. To plot a bandstructure we need to findthe electrical potential through the junction (from poisson’s equation)[6]:

∇2V = ρ/ε , where ρ = e(p− n + N+D −N−

A ) (2.1)

where V is the electric potential, ρ the total charge density, ε the dielectricconstant, p and n are densities of free electrons and holes, and N+

D and N−A are

doping concentrations of the ionized donors and the acceptors.Since we know the total charge density (due to diffusion of carriers) is positiveon the N-side, and negative on the P-side, we will approximate the electric field(E = −∇V ) to a scalar one dimensional problem, where the electric field isperpendicular to the junction interface (lateral x-direction).The electrical potential, and the electric field has to satisfy the boundary con-ditions [6]:

∆V = 0 ε∆E = 0 (2.2)

To find the electrical potential V we need the total charge density ρ, and basedon the discussion above we can approximate it with a step function which is−|N−

A | at the P-side, +|N+D | in the N-side, and zero in the I region and else-

where, see figure 2.3(a). This is called the depletion approximation[3]. Thewidth of the depletion region must subsequently be adjusted to match the totalpotential (Vbi + V0).The solution to poisson’s equation, and the resulting electric field are shown infigure 2.3 (b) and (c).


Figure 2.3: In (a) the assumed total charge density across the depletion region,in (b) the magnitude of the electric field, where the direction is vertical upthrough the device, and in (c) the electrical potential, is shown. A reverse biasV0 = −5volt is applied to the junction.

2.2. PIN JUNCTION 11

From the electrical potential in figure 2.3(c) it is now fairly easy to constructthe bandstructure through the device. The bandstructure represents the energyof the electrons in the valence band, and in the conduction band, so we have tomultiply the potential (in figure 2.3(c)) with −|e|, and at the interface betweentwo materials we have a discontinuity in energy according to the bandgap dif-ference. In figure 2.4 the bandstructure for PIN5 at minus one, zero, and plusone volt bias is shown. The two quasi Fermi levels are the Fermi energy of theP- and N-side.

2.2.2 I-V curves

In figure 2.5 measured currents versus applied voltage (I-V curves) for all de-vices are shown, except PIN9, and PIN10 because in DC measurements theyare like PIN8 and PIN5 respectively.These I-V curves can be divided into three important regimes, starting fromthe right, we see a sudden increase in current at small forward bias (positiveto P-side and negative to N-side) around 0.6volt to 0.8volt. Then we have asection with almost no current, called dark current in a PD. This regime ends atsome reverse bias (positive to N-side and negative to P-side), where the currentagain suddenly increases, this is called break down of the diode, and the reversevoltage at which it happens is called the breakdown voltage.Breakdown can be attributed to two mechanisms, called Zener breakdown, andavalanche breakdown. Zener breakdown is caused by tunnelling of the carriersthrough the junction, and happens for heavily doped > 1017cm−3 PN (not PIN)junctions where the conduction and valence band at reverse bias can get veryclose.For PIN junctions, or lightly doped PN junctions tunnelling is negligible becausethe depletion region is much wider. In such devices the breakdown is caused byinfinite avalanche multiplication, called avalanche breakdown. Avalanche mul-tiplication will occur in junctions with a high electric field and a large depletionlayer, where the carriers can gain enough kinetic energy to excite new carriersby impact. These new carriers will also gain kinetic energy and by impact excitenew carriers and so forth. (This process can, if it can be controlled, be used tomake gain in a PD, such a PD is called an avalanche photodiode (APD)). Butif the electric field gets high enough, the avalanche multiplication gets infinite,and the junctions breaks down[4].All devices in this project are PIN junctions, and based on the discussion abovethe breakdown mechanism must be avalanche breakdown. In table 2.2 the mea-sured breakdown voltages, and corresponding calculated maximum electric fields(called the break down fields Ebd) are listed. This maximum electric field is inthe intrinsic region (see figure 2.3(b)), and the width of the intrinsic regions aretherefore also listed in table 2.2.By looking at table 2.2 we see that for all devices, except PIN12 and 13, thebreakdown field is inverse proportional to the width of the intrinsic region, andthis corresponds well with the breakdown being caused by avalanche multipli-


Figure 2.4: Structure of the bandgap through device PIN5 at (a) -1volt bias,(b) 0 volt bias, and (c) +1 volt bias. Based on the depletion approximation [3].

2.2. PIN JUNCTION 13

Figure 2.5: I-V curves for all devices. The inset is a close up of the forwardcurrent, where the solid black line is equation 2.6.

PIN2 PIN3 PIN4 PIN5 PIN6Vbd [volt] 25 13 8 12.5 14wi [nm] 712 262 110 260 290Ebd [kV/cm] 355 474 586 462 466

PIN7 PIN8 PIN12 PIN13Vbd [volt] 13.5 35 11 6wi [nm] 240 1060 260 260Ebd [kV/cm] 522 334 375 275

Table 2.2: Lists the breakdown voltages (Vbd), breakdown electric fields (Ebd),and the width of the intrinsic regions.


cation. Because the number of impact ionization must depend on both themagnitude of the electric field, and also on the length at which the ionizationscan occur.The reason that PIN12 and 13 do not follow this pattern is probably becausethey are P-doped so highly, that the doping ions begins to diffuse into the in-trinsic layer[14], causing the intrinsic region to decrease and the electric field toincrease.

At reverse bias, from the breakdown voltage up to zero volt we have thedark current regime.When we set reverse bias to the junction, we increase the potential across thedepletion region (which also increases the width of the depletion region), this willincrease the drift current in comparison to the diffusion current. We thereforehave a net drift current of holes from the N-side to the P-side, and a net currentof electrons from the P-side to the N-side. This gives givers a very small current,called the saturation current, and according [3] it is given by:

Is = eAn2iInP

(√Dp

τp

1N+

D

+√

Dn

τn

1N−

A

)(2.3)

where A is the current cross section area, niInPis the intrinsic carrier concen-

tration of InP, τp is the life time of a hole in N-side, and τn is the life time ofan electron in P-side.Using A = 2µm × 200µm (ridge width times length of device), niInP = 1.3 ·107cm−3 [11], τp = 1ns, τn = 5ns [9], Dn = 100cm2/s, and Dp = 3cm2/s[4], acurrent of about ∼ 10−23A is obtained.A larger term contributing to the dark current is thermal generation of carriers.Each time an electron hole pair (EHP) is generated thermally in the depletionregion, the electric field will separate them, and pull the hole to the P-side, andthe electron the to N-side. The rate of generation will depend on the intrinsiccarrier concentration ni, and the generation rate per volume is approximatedby ni/τ , where τ is the life time of the carriers in intrinsic material [3]:

Ithermal =e VInGaAs niInGaAs

τInGaAs(2.4)

where VInGaAs is the volume of the active layer, and τInGaAs is the life timeof carriers in intrinsic In0.53Ga0.47As. The grading layers and standoff layerare also part of the intrinsic region, so there should also be a similar term forthose layers. But since they have lower intrinsic carrier concentrations, theygive negligible thermal currents compared to the active region. The intrinsiccarrier concentration of InGaAs is niInGaAs

= 1012cm−3 [8], and the lifetime isτInGaAs = 15ns [11].For PIN2 this gives about 2nA, and because the rest of the devices has aboutthe same volume of the active layer they all give about 0.2nA. So accordingto these calculations the dark current Idark = Is + Ithermal stems from thermalgeneration of carriers.

2.3. LIGHT ABSORPTION 15

Measurements of the dark current is hard because it is so low, and because thedevice has to be in complete darkness, but at GiGA they have measurementequipment for doing this. We measured the dark current on several differentPIN5 devices, and they all gave a dark current about ∼ 0.5nA. Since this re-sult matches fairly well with the calculated value above, I think it is reasonablyto assume that the dark current stems from thermal generated carriers in theactive layer, and has a value Idark < 1nA for all devices (except PIN2).

The last section of the I-V curve is at forward bias. When we set forwardbias on the junction we reduce the potential across the depletion region (whichin turn also will reduce the width of the depletion region), this will reduce thedrift current in comparison the the diffusion current. Therefore we have a netdiffusion current of holes from the P-side to the N-side, and electron from theN-side the P-side, this is called minority carrier injection. This diffusion currentis according to [3] given by:

I(V ) = Is

(ee V/kT − 1

)(2.5)

where V is forward applied bias, k Boltzmann’s constant and T is the temper-ature. This is called the ideal diode characteristic [3].Because of the the small Is, this gives only about 1nA at 0.8volt, which is muchsmaller then what we measure in figure 2.5.Another term attributing to the forward current is recombination current. Whenthe applied forward bias is equal to the bandgap of the active layer, the minoritycarrier injection starts to fill the conduction band, and valence band of the activelayer with electrons, and holes respectively. This will lead to recombinations inthe active layer, which according to [3] is given by:

I(V ) =e Vactive niInGaAs

2τree V/2kT (2.6)

where τr is the recombination lifetime of the electrostatic doped InGaAs. Thislifetime should intuitive be shorter then for intrinsic InGaAs (τInGaAs) fromabove, and it is found to be τr ∼ 1ns for a doping concentration of 1016cm−3[10].This equation, gives a much larger current then equation 2.5, and is plotted inthe insert of figure 2.5, where it fits quit well to the measured I-V curves.

To summarize the electrical PIN junction; breakdown occurs because of in-finite avalanche multiplication, dark current is due to thermal generation ofcarriers in the active layer, and forward current is a recombination current i theactive layer.

2.3 Light absorption

From figure 2.4(a) it is very intuitive how a PD works, an incoming photon willexcite an electron from the valence band to the conduction band, and leave a


Figure 2.6: Stimulated absorption and emission, and spontaneous emission (atsmall forward bias), f1 and f2 are Fermi distribution functions for the two quasiFermi levels.

hole in the valence band. The electron will then be pulled to the N-side becauseof the lower electron energy there, and the hole (which has a positive charge) willbe pulled to the P-side. The generated electrons and holes can now be measuredas a current. For this process to occur we need a high electron density in thevalence band, and a high hole density in the conduction band. This is bestobtained at reverse bias as can be seen in figure 2.4 (a) to (c).Besides absorption, we can also have emission of light, and in figure 2.6 theprocesses that can occur when light interacts with matter is sketched; stimulatedabsorption, stimulated emission, and spontaneous emission (which is stimulatedby the vacuum field).The transition rate of these three processes can be quantified using Fermi’sdistribution function for the two quasi Fermi levels, the density of transitionpairs ρr(E21) (reduced density of states), and a transition probability, where thetwo last contributions often is collected in the famous ”Fermi’s golden rule”[2]:

Rr =2π

~|H ′

21|2ρr(E21) (2.7)

where H′21 is a transition matrix element.

To get the transition rates for the three processes we now only need to includeFermi’s distribution function for the two quasi Fermi levels; f1 and f2:

R12 = Rrf1(1− f2)R21 = Rrf2(1− f1) (2.8)

Rsp′21 = Rvf

r f2(1− f1)


Figure 2.7: Absorption coefficient for bulk In53Ga47As (bandgap at 1676nm,0.74eV), and for InGaAsP quantum well material (effective bandgap at1585nm). Calculated on the basis of [2] chapter 4. A Lorentzian lineshapebroadening with 13meV broadening of the energy levels is included [2].

Where Rsp′21 is the transition rate of spontaneous emission from one pair of

transition levels, R12 and R21 are the transition rates for stimulated absorptionand emission. The latter can be used to find the absorption per length, calledthe absorption coefficient α:

α ≡ −1Np

dNp

dz=

−1Npvg

dNp

dt=

1Npvg

(R12 −R21) =1

NpvgRr (f1 − f2) (2.9)

Where Np is the density of photons, and it can be shown that[2]:

α(E21) =πe2~

nε0cm20E21

|MT |2ρr(E21)(f1 − f2) (2.10)

where MT stems from the matrix element, and is tabulated in [2] for bulkIn0.53Ga0.47As to be |MT |2 ' 4m0, where m0 is the free electron mass. In thisway the absorption coefficient as function of the photon energy is calculated, andplotted in figure 2.7. At 1550nm the absorption coefficient can be estimated toabout 0.5µm−1, and if 5 % of the light is confined in the active region (dependingon the device see table 2.4) we need the length of the device to be a few times1/(5%0.5µm−1) = 40µm for all the light to be absorbed. The length of alldevices is about ∼ 200µm, so all light will be absorbed (at appropriate reversebias).The generated EHPs can, if they do not recombine, be detected as current, calledphotocurrent. To quantify this process we define two very important parameter,


Figure 2.8: Measurement of quantum efficiency η versus incident wavelengthfor PIN5, at 5volt reverse bias, and 1mW optical input power. At each mea-surement point the optical fiber was aligned to the device for optimal coupling.

called the responsivity and the quantum efficiency. The responsivity (R):

R =Current generated

Power of incident light(2.11)

tells us how many ampere of current we will get per watt incident light.The quantum efficiency (η):

η =Number of detected carriersNumber af incident photons

(2.12)

tells us how many of the incident photons that will generate detectable carriersto the photocurrent. The quantum efficiency is a number between 0 and 1, andincludes all kinds of loss.In figure 2.8 a measurement of the quantum efficiency versus incident wave-length, is shown. The graph is made by measuring the photocurrent at eachwavelength, and then divide it by eP/hν, where P is the incident optical power,and hν is the photon energy.The graph shows that the quantum efficiency is highest for the lower wave-lengths. There are a number of ways to explain this, which we will look at alittle later.

We know that each photon has an energy hν, and that each generated carrierhas a charge e, so we can express the the responsivity in terms of the quantumefficiency:

R =ηe

hν(2.13)


PIN2 PIN3 PIN4 PIN5 PIN62µm ridge [A/W ] 0.520 0.657 0.722 0.745 0.7121.5µm ridge [A/W ] 0.505 0.634 0.711 0.719 0.683

PIN7 PIN8 PIN12 PIN132µm ridge [A/W ] 0.640 0.750 0.745 0.7481.5µm ridge [A/W ] 0.617 0.710 0.687 0.699

Table 2.3: Responsivity measurements on the bulk PDs, all with the sameoptical fiber, no AR coating, and reverse bias −5volt, except PIN8 at −15voltbias. All numbers are the average of measurements on at least 3 different devices.

For the perfect PD η will be equal to 1, which means that every incident pho-ton generate one detectable EHP. Thus for the perfect PD the responsivity at1550nm will be 1.25A/W . This is the absolute maximum responsivity we canget from the PDs (without amplification).Measurements of the responsivity of the PDs are listed in table 2.3. The bestobserved responsivity is about 0.75A/W , so this device has a quantum efficiencyof η = 0.75/1.25 = 60%. At the facet 27% of the incident light is being reflected(see section 2.4), so if the device were antireflection (AR) coated it could givea responsivity of about 1A/W and have a quantum efficiency of 80%. The re-maining loss, which we will look at later, can be attributed to effects like; 1) lossthrough the optical fiber (section 2.4), 2) mode overlap between the incomingmode from the fiber, and the mode sustained in the waveguide (section 2.4),3) absorption outside the active region, due to free carrier loss (later in thissection), and 4) recombinations of the generated EHPs before they are detected(section 2.4).

When we send a continuous wave (CW) beam of light into the device, it willbe absorbed and generate EHPs, which will change the I-V curves from figure2.5. The photocurrent at reverse bias is simply given by the responsivity:

Iphoto = R P (2.14)

However as we increase the bias from reverse to forward we inject more and moreminority carriers; electrons from the N-side into the conduction band, and holesfrom the P-side into the valence band, especially into the active layer becauseit has the lowest bandgap. So as we increase bias (from reverse to forward)we begin to fill the conduction band of the active layer with electron, and thevalence band with holes, which is called band filling. This will cause two things;1) a reduction of the absorption coefficient, because the injected minority car-riers induces a higher effective bandgap of the active layer, and 2) an increasedEHP recombination rate, because of the increased carrier density. As bias isincreased, the I-V curves will therefore gradually return to equation 2.6.In figure 2.9 I-V curves for all devices at different input powers are shown, the


input powers for PIN number 3, 4, 5, 7, 8 are Pin = 0, 1, 3, 5, and 7 mW withone optical fiber, and for the rest of the devices the input powers are Pin = 0,0.25, 0.75, 1.25, and 1.75 mW, because for those measurements a better opticalfiber, that couples more of the light into the device, is used. But the step wiseincrease in input power are maintained, so the qualitatively features of the plotscan be compared between all devices.The first thing to note is the change in current at reverse bias, compared to fig-ure 2.5. The magnitude of the current at reverse bias is linear with the incidentoptical power, which agrees with equation 2.14.

Here we will look at free carrier loss. Absorption of light by free electronsin the conduction band, or free holes in valence band do not generate EHPs,and is therefore considered as loss (called free carrier loss). Because there arehigh densities of free carriers in doped materials compared to intrinsic materials,doped materials will give rise to far most free carriers loss. Furthermore becausethere are three hole bands (heavy hole, light hole, and split off), and only oneelectron band, P-type material give rise to most free carrier loss.If we compare device PIN5 and PIN8, where the only difference is that PIN8has a 950nm standoff layer on the P-side, and PIN5 has 150nm standoff layer.We see that PIN8 needs more reverse bias to pull out all the generated carriers,but PIN8 does not give more photo current than PIN5. The large standoff layerof PIN8 will ”shield” the light mode in the waveguide so that no light is in theP-doped layer, where free carrier absorption could occur. This suggests thatfree carrier loss is negligible for these devices.But by comparing PIN4 and PIN5, where the only difference is that PIN5 hasa 150nm standoff layer and PIN4 have none, we see that PIN5 has the highestresponsivity. The optical power in the optical mode in the waveguide is centeredin the active layer (see section 2.4), so the closer the P-doped material is to theactive material, the more free carrier loss it could induce. This can explain whyPIN5 have a higher responsivity that PIN4.From the last section we know that it is reasonable to assume that the Zn-ionsfrom the P-doped layer will diffuse into the intrinsic layers, which will make theZn-atoms get even closer to the active layer. And the standoff layer is intendedto keep the P-doped atoms away from the active region.On the basis of this discussion it seems that a small standoff layer, of 150nm orless, makes free carrier loss negligible.

Another thing to note is that some of the I-V curves have one bend, and somehave two bends, in the transition from photo current in reverse to recombina-tion current i forward. PIN number 2, 3, 4, 12, and 13 goes very abruptly fromabsorbing the incoming light, to generate recombination current and have onlyone bend. The other devices, PIN number 5, 6, 7, and especially 8, decrease thephoto current to zero, and then as bias is increased further the recombinationcurrent begins.This transition region is actually very interesting, because in this region we haveband filling. And band filling causes, as discussed above, two effects; a reduction


Figure 2.9: I-V curves for all devices, with different optical input powers asindicated on each graph.


Caption: Same as previous page.


Figure 2.10: (a) Photocurrent at reverse bias for device PIN8, at two differ-ent wavelengths (1530nm and 1610nm), with the same photon current Nph,measured at four different photon currents. (b) Magnitude of the 1530nm pho-tocurrent minus the magnitude of the 1610nm photocurrent.

in absorption coefficient α, and an increased EHP recombination rate. Thesetwo effects can actually be probed by making an I-V plot at two different wave-lengths with the same photon current Nph. In figure 2.10(a) this is shown forPIN8 at two wavelengths; 1530nm and 1610nm, each with a photon current ofNph =1, 2, 3, and 5·1016photons/second. In figure 2.10(b) the magnitude of thecurrent from the more energetic photons (1530nm), are subtracted the magni-tude of the current from the less energetic photons (1610nm). It can be seenthat at small reverse bias, the more energetic photons (1530nm) results in mostcurrent. Then, from a few volt reverse bias to about 8 volt reverse bias, it is theless energetic photons that gives the most current. And finally at even higherreverse bias it again is the more energetic photons that gives most current.The same effect can be seen for PIN5, though the effect is much harder to seebecause it all happens around ±0.5V .The effect seen in figure 2.10(b) can be explained in the following way: As thereverse bias is increased the absorption also increases (band filling decreases),and from zero to a few volts not all light is absorbed (the absorption length islonger then the length of the device ), therefore it is favorable with more ener-getic photons that have a higher absorption coefficient (see figure 2.7). Whenthe curve crosses the y-axis both wavelength generate equal amount of current,so about at this point all light is being absorbed in the waveguide. When we in-crease the reverse bias further (∼ −4volt to ∼ −8volt)) all light will be absorbed,but the more energetic photons (that has the highest absorption coefficient) arejust using a smaller portion of the waveguide to be absorbed, and hence thegenerated carrier density will be higher. This higher carrier density generatedby the energetic photons will lead to more recombinations and therefore less

2.4. WAVEGUIDE 25

detectable current.In the last section of the graph there is no more bandfilling i.e. the depletionregion is really depleted of carriers, and the more energetic photons again givesthe most current.PIN5 also gives more photo current at shorter wavelengths, which we saw infigure 2.8 for the quantum efficiency. There are a number of ways to explainthis: 1) The more energetic photons will give an extra kick to the generatedEHPs, and therefore help the EHPs over the barriers at the grading layers,which in turn gives less recombination loss, 2) the mode overlap will depend onwavelength, or 3) the mode in the waveguide are more confined for the shorterwavelengths, which will lower free carrier loss in the P-side. However, we knowthat free carrier loss is negligible for PIN5, so this is most likely not the reason.There are three grading layers with four steps at both the valence and conductionband, which gives an average barrier height of (1.35eV −0.74eV )/8 = 75meV ateach step. 75meV is three times higher then the thermal energy, so these stepsare indeed barriers for the carriers. It therefore seems likely that recombinationsof the EHPs will contribute to loss of electrons.

To summarize this section, we have seen that the material absorption co-efficient for InGaAs is α = 0.5µm−1 at 1550nm. The best responsivity wasmeasured to be R = 0.75A/W , which corresponds to a quantum efficiency ofη = 60%, (or if AR was used; R = 1A/W , and η = 80%). We have also seenthat free carrier loss are negligible, when a small standoff layer of 150nm or lessare used, but that recombinations of the generated EHPs still can give loss.

2.4 Waveguide

The incident light comes from an optical fiber where it is confined in the trans-verse plan, and has some transverse mode profile. At the end of the fiber thereis a lens that focuses the light onto the facet of the device (see figure 2.1). Aswe will see later in this section, 27% of the incident light will be reflected at thefacet, but this effect can be eliminated by AR coating the device, which we willsee in section 3.2.Inside the device the light will be guided by total internal reflection, becausethe active layer has a higher refractive index than InP and BCB, forming aso-called waveguide. The waveguide guides the light through the device withsome transverse mode profile, and keeps the light centered in the active layer.The amount of incoming light that will be guided by the waveguide depend onhow well the mode profile of the incoming light from the optical fiber, matchesthe mode profile in the waveguide.The waveguide in the device is centered around the absorbing layer, and in fig-ure 2.11 a simplified schematic of the different refractive indices in the device,as seen from the facet, is shown.

The equations governing the photon mode in the waveguide is Maxwell’s


Figure 2.11: The refractive indexes in the device as seen from the facet, andthe predominant directions for the electric field and magnetic field for the twopolarization modes.

equations, and by combining them the right way we reach two important waveequations:

∇2E =n2

c2

∂2E∂t2

∇2H =n2

c2

∂2H∂t2

(2.15)

for the electric field E, and the magnetic field H, where the refractive index ndepend on space coordinate according to figure 2.11. To solve these equationswe need approximations, and the first approximation comes from a guess on thesolution of the form:

E(x, y, z, t) = eE0U(x, y)eikz−iωt (2.16)

and equivalently for the magnetic field. The polarization e is approximatedto be independent of the space coordinates. Then we have an amplitude E0,a mode profile in the transverse plane U(x, y), and a plan wave eikz−iωt, thatmakes the mode travel down the waveguide. The polarization e of the light canhave two directions, see figure 2.11: 1) E is predominantly in the transversedirection, and H is predominantly in the lateral direction, called TransverseElectric (TE), or 2) H is predominantly in the transverse direction and E ispredominantly in the lateral direction, called Transverse Magnetic (TM).By inserting equation 2.16 into equation the wave equation 2.15 we get:

(∂2

∂x2+

∂2

∂y2+ k2 − n2k2

0

)U(x, y) = 0 (2.17)

where we use k to denote the wave vector in the medium, and k0 = ω/c todenote the free space wavevector. For the magnetic field we would get the exactsame equation, so we need only to solve this equation.To solve equation 2.17 we need another approximation, and a widely used ap-proximation is the effective index method [2], which first uses separation of

2.4. WAVEGUIDE 27

Figure 2.12: Effective index method calculation of the mode in PIN6

variables U(x, y) = U(x)U(y), then defines an effective refractive index neff ineach of the three vertical regions 1, 2, 3 of figure 2.11: neff,i ≡ k/k0 wherei = 1, 2, 3, this gives:

1U(x) · ∂2U(x)

∂x2 = −k2x

1U(y) · ∂2U(y)

∂y2 = −k2y

where − k2

x − k2y + k2

0 n2eff,i = n2k2

0 (2.18)

The next part of the effective index method is to have a thin slap, which meansthe central rectangle in figure 2.11 has to be much wider then its height, so thatU(y) changes slowly compared to U(x), and we can approximate ky = 0.The boundary conditions can to a good approximation be set to be continuousand differentiable, (the discontinuity that arises when the electric field is perpen-dicular to the interface will only give a small correction to to this approximation,because the differences in refractive index are small). This approximation makesboth TE and TM modes the same.This approximation turns equation 2.18 into a 1D problem in each of the threelateral x-direction (1,2,3 in figure 2.11), which results in an effective refractiveindex in each of the three regions; neff,i (n = 1, 2, 3). The final part of the effec-tive index method is to use these three effective indices to a final one-dimensionalequation in the transverse direction (y-direction), which results in a mode pro-file and a ”total” effective refractive index neff . This has been performed ondevices PIN6, and the result can be seen in figure 2.12.For more accurate calculations of the mode in the waveguide, I have used acomputer program called Selene, and not the simplified structure in figure 2.11,but the true structure from figure 2.1 and table 2.1. Selene uses a numerical


method called ”multi grid finite difference” (MGFD). This program has beenused on all devices that have different modes; PIN number 2, 3, 5, 6, and 7,with ridge widths of 1.5µm and 2µm, see table 2.4. The program is used tocalculate the confinement factor Γ, which is the fraction of optical power thatis confined within the active layer. From the confinement factor we calculatethe absorption length, which is the length at which the power of the light hasdropped to 1/e, as (αΓ)−1. Selene is also used to find the effective refractiveindex, and some characteristic field dimensions such as full width at half maxi-mum (FWHM) waist, and the 1/e waist.

Now that we know the mode inside the waveguide, we need to find what theincoming mode that hits the facet looks like. Because, then we can find theoverlap of the two modes, which tells us how much of the incoming light couplesinto the waveguide. This mode overlap give rise to another loss term, and isincluded in the quantum efficiency with a factor ηmo.The responsivity depends strongly on what optical fiber is used, responsivity aslow as 0.14A/W for PIN5 has been measured, and all the way up to 0.75A/Wwith the best fiber. In figure 2.13 measured far fields from three different opticalfibers, and the corresponding responsivities when they are used to couple lightinto PIN5, are shown. A far field is optical intensity as function of a transverseangle and a lateral angel. The best fiber, which is named A4-2, is used for therest of the measurements in the report.The farfield will hit the facet of the PD, and the amount that will be transmit-ted through the facet depends on the angle of incident according to Fresnel’sequations[6]. For the best fiber (A4-2, figure 2.13 right) the FWHM angularwidth, and 13.5% angular width is measured to be ±15deg, and ±26deg respec-tively. Therefore the polarization of the incoming light, whether it is TE orTM, will be polarized predominant parallel to the facet. According to Fresnel’sequations the transmission is reduced 1.2%, and 3.7% for light polarized parallelto the facet, at the FWHM angular width (15deg), and at the 13.5% angularwidth (26deg) respectively.We therefore, to a good approximation, say that all of the light in the modefrom the fiber will bee transmitted through the facet with the same coefficientηfacet = 1 − ((neff − nair)/(neff + nair))2. The factor ηfacet is part of thequantum efficiency, and is listed in table 2.4.With this approximation we also say that the mode that enters through thefacet, is the measured farfield projected onto the facet. So to quantify the modeoverlap, the mode inside the waveguide (calculated by Selene), and the modefrom the measurement farfield projected onto the facet, is used. Mode overlapsfrom such calculations are also part of the quantum efficiency, and is called ηmo.The factor ηmo is listed in table 2.4, and for comparison a mode overlap with aspherical symmetrical gauss mode, is also included.

There is also measured loss in the optical fiber A4-2. With a surface PDwith known quantum efficiency, there is measured a loss of 8% through the fiber.When we send 1mW into the fiber, only 0.92mW comes out at the end of the

2.4. WAVEGUIDE 29

2µm

Rid

ge1.

5µm

Rid

geP

IN2

PIN

3P

IN5

PIN

6P

IN7

PIN

2P

IN3

PIN

5P

IN6

PIN

7C

onfin

emen

tΓ

65%

23%

6.9

%15

%2.

0%

56%

22%

4.8

%14

%-

Abs

orpt

ion

leng

th(α

Γ)−

1[µ

m]

3.2

8.8

2813

.610

43.

69.

242

15-

Effe

ctiv

ere

frac

tive

Inde

x3.

423.

253.

183.

203.

173.

413.

243.

173.

19-

Tra

nsm

issi

on;η f

acet

70%

72%

73%

73%

73%

70%

72%

73%

73%

-FW

HM

tran

sver

se[µ

m]

1.63

1.24

1.18

1.18

1.20

1.45

1.01

0.94

0.94

-FW

HM

late

ral[µ

m]

0.40

0.33

0.47

0.38

0.62

0.40

0.33

0.49

0.38

-1/

etr

ansv

erse

[µm

]1.

400.

970.

900.

900.

911.

360.

810.

730.

73-

1/e

late

ral[µ

m]

0.33

0.37

0.64

0.49

0.96

0.33

0.37

0.72

0.49

-M

ode

over

lap

wit

hG

auss

ian

65%

85%

94%

92%

72%

65%

88%

80%

93%

-1/

eof

gaus

sG

auss

ian∗

[µm

]0.

70.

70.

90.

81.

50.

70.

61.

10.

7-

Mod

eov

erla

pw

ith

A4-

2;η m

o71

%88

%95

%95

%77

%74

%92

%84

%96

%-

Res

pons

ivity

[A/W

]C

alcu

late

d∗∗

0.57

0.73

0.80

0.80

0.65

0.60

0.76

0.71

0.81

-M

easu

red

wit

hA

4-2

0.51

0.66

0.75

0.71

0.64

0.51

0.63

0.72

0.68

0.62

Tab

le2.

4:C

alcu

lati

ons

ofim

port

ant

para

met

ers

for

the

mod

ein

the

wav

egui

de,do

neby

the

com

pute

rpr

ogra

mSe

lene

.P

INnu

mbe

r4,

8,9,

10,

12,

and

13ha

sth

esa

me

mod

eas

PIN

5.∗ W

aist

ofth

esp

heri

cal

sym

met

ric

gaus

sm

ode,

that

give

sth

em

axim

umm

ode

over

lap.

∗∗ca

lcul

ated

as1.

25A

/W

η fib

erη f

acetη m

o


Figure 2.13: Farfield measurements on three different optical fibers, and thecorresponding responsivity measured when the fiber is used to couple the lightinto PIN5. The farfield to the right is from fiber A4-2, and this fiber is used farmost.

fiber. This loss in the optical fiber is also included in the quantum efficiencywith a factor ηfiber = 92%.

So far we have discussed loss effects like, loss through the optical fiber,reflection at the facet, mode overlap, free carrier loss, and recombination ofthe generated carriers. Loss thorough the fiber ηfiber, transmission through thefacet ηfacet, and mode overlap ηmo are known (see table 2.4). We also know thatdevices with a standoff layer has negligible free carrier loss, which all devicesin table 2.4 except PIN2 has. Therefore only loss due to recombinations ofgenerated carriers is left unknown.By setting the quantum efficiency η from equation 2.12 equal to the knownloss terms: η = ηfiber ηfacet ηmo, we can calculate the responsivity as R =η 1.25A/W . This calculated responsivity is listed table 2.4, together with themeasured responsivity for comparison.We see that the measured responsivity matches fairly well with the calculatedresponsivity, there only seems to be an additional loss raging from 0% to about15%, with an average of 8%. Since the only loss term that are not accountedfor, is loss due to recombinations of generated carriers, these last ∼ 8% losscould be due to that.

2.5 Dynamics

Up until now we have looked at the detector in DC measurements and withCW light input. But, when we start to modulate the light input we also geta modulated electrical output, and it is of course in such a setup the detectoris intended to work. In this section we will look at what happens when wemodulate the input signal, and how fast we can modulate it, while still being

2.5. DYNAMICS 31

able to retrieve the information in the output signal.There are two ways to modulate the light input; either with a sinusoidal fre-quency (done with a network analyzer), or with information in the form of bits(done with a bit error rate test-set).If we modulate the light input with a sinusoidal frequency, we can measurethe AC responsivity, as function of the this modulation frequency. The ACresponsivity is the amplitude of the modulated optical power input, divided bythe amplitude of the electrical current output. The frequency where the ACresponsivity has dropped to the half (-3dB), is defined as the bandwidth of thePD.If we modulate the light input signal with information in the form of bits, wesimulate a real environment for detector. In such a measurement we need tocompare each optical input bit with the electrical output bit, and measure therate of errors, called the bit error rate (BER). The BER is an important quan-tity for a detector and will depend on the power of the input light, and howwe modulate of the light input. There are three important quantities connectedwith how to modulate the light input; (1) The number of bits per second, calledthe bitrate B, the bulk PDs are intended to work at B = 10Gb/s so all mea-surements are performed at this bitrate. (2) The bit sequence, called pseudorandom bit sequence (PRBS), it is the number of bits that are repeatedly beingsend into the PD, typically from 27 − 1 (all possible combinations of 7 bits mi-nus one) up to 231− 1 (all possible combinations of 31 bits minus one), where aPRBS length of 231 − 1 is used. (3) the format of the bits can either be RZ, orNRZ, where the NRZ format is used, because it seems to be the most commonlyused format.With a bitrate of B = 10Gb/s, and a PRBS length of 231−1 in the NRZ format,we can measure the BER as function of the light input power. As we increasethe optical power, the BER will decrease, and the optical power at which theBER is 10−9, is defined as the sensitivity of the detector (The sensitivity issometimes defined at BER = 10−10 or lower).So with a network analyzer, and a BER test-set we can measure two importantquantities for the PD, namely the bandwidth and the sensitivity.

2.5.1 Bandwidth

To determine the bandwidth of the device there are some key time parameterswhich we will describe here. These key time parameters are connected with themovement of the electrons. When an incident photon is absorbed and an EHPis generated, the EHP is pulled out of the depletion region, and this takes acertain time called the transit time τtr. When the EHP is outside the depletionregion there are two capacitors, the first is the parallel plate capacitor acrossthe depletion region, called diode capacitance Cd. The second is between thebonding pad, and the bottom of the depletion layer, called the bonding padcapacitance Cb. Each of these capacitors has a time constant.An equivalent circuit diagram for the diode, together with the rest of the electri-


Figure 2.14: A schematic diagram of the electrical setup for dynamical measure-ments, with a equivalence diagram for the diode, a 50Ω load resistor Rl, and abias tee.

cal setup for dynamical measurements, are shown in figure 2.14. The diode canbe represented by a current source, two capacitors as just described, a resistorRpn originating from the doped P- and N-side, called the contact resistance,and a large resistor accounting for the small dark current Rdark.The two capacitors, and the resistor Rpn, can be estimated from the design ofthe device. The resistance for a doped semiconductor is given by:

Rn =Ln

N+DeµnAn

Rp =Lp

N−A eµpAp

(2.19)

for electrons and holes respectively (holes are pulled out through the P-side,and electron are pulled out through the N-side), where L and A are the lengthand the cross section area of the region. Equation 2.19 gives about Rp ' 5Ωand Rn ' 0.1Ω, therefore the total resistance is Rpn ' 5Ω.The contact resistance is measured as the differential resistance at high forwardcurrent where the slope of the I-V curve is constant. At 60mA forward currentthe resistance is about ∼ 7Ω, so this matches well with the calculation.The diode capacitance is through the depletion region, which is made up of InP(standoff layer) with dielectric constant of 12.4, InGaAs with dielectric constantof 13.9, and 6 layers of InGaAsP with a dielectric constant set to the averageof the two. The area of the plates A are set to the width of the ridge (2µm)multiplied by the absorption length (see table 2.4), and the capacitance is givenby:

C = A

(∑

i

(εi

wi

)−1)−1

(2.20)

where ε and w are the dielectric constant, and the width of each of the layersthrough the depletion region.

2.5. DYNAMICS 33

Figure 2.15: Model used to calculate the bandwidth of the PDs

The bonding capacitance is calculated in the same way, where the area of thebonding pads are 50µm×50µm, and the dielectric materials are BCB (ε = 2.7),and the depletion layer (ε is set to 13). The thickness of the BCB is equal tothe hight of the P-side from table 2.1. The calculated diode and bonding capac-itances for all devices are shown in table 2.5. Because Rpn is much smaller thanthe load resistor Rl, which is 50Ω, the discharging time of these two capacitorscan be approximated by τRC = (C−1

d + C−1b )−1 · Rl, which also is written into

table 2.5.The transit time τtr can be estimated the following way; the maximum elec-tric field is so high that electrons and holes for all devices reaches the satu-ration velocity1. So the transit time is calculated as τtr = wdep/vsat, wherevsat ' 107cm/s is the saturation velocity for both InP[12], and InGaAs[13].

Now that we have an estimate of the RC discharge time, and transit time,we can calculate the the bandwidth of the devices, to compare with the mea-surements.In figure 2.15 a model to calculate the bandwidth, with three reservoirs and flowrates between, is shown. A similar modal for a diode laser can be found in [2].The three reservoirs are; a photon reservoir with Np photons, a carrier reservoirin the active region with Na carriers, and a carrier reservoir of detectable car-riers (carriers on the two capacitors) with N carriers.The incoming photon rate is the incident power divided by the energy of eachphoton, and here we have loss due to reflection at the facet, mode overlap,and loss through the optical fiber, which collected is designated η0 (η0 =ηfiber + ηfacet + ηmo). From the photons in the device we could have freecarrier loss, but that is negligible as discussed, instead we have stimulated ab-

1the velocity where the kinetic energy and the thermal energy is about the same


PIN

2P

IN3

PIN

4P

IN5

PIN

6P

IN7

PIN

8P

IN9

PIN

10P

IN12

PIN

13E

max

[kV

/cm

]87

224432

226205

242152

152226

235239

Depletion

region[n

m]

728303

190302

328285

10881088

302281

273D

iodecapacitance

[fF

]1

735

219

796

621

2324

Pad

capacitance[f

F]

2224

2424

2424

2217

1824

24R

Ctim

eτR

C[p

s] ∗1.2

1.63.0

2.31.7

5.21.4

1.22.0

2.42.4

Transit

time

τtr

[ps]

7.33.0

1.93.0

3.32.9

10.910.9

3.02.8

2.7B

andwidth

[GH

z]C

alculated ∗∗18.8

34.632.5

30.031.8

19.712.9

13.231.8

30.631.2

Measured

--

3234

--

1811

29-

-

Table

2.5:M

easuredand

calculatedbandw

idths,and

correspondingestim

ateddynam

icalparam

eters.C

alculationsare

made

at-5

voltbias

forall

exceptfor

PIN

8and

PIN

9at

-15voltbias.

∗Bonding

padcapacitance

anddiode

capacitancein

parallelm

ultipliedw

itha

50Ωload

resistor.∗∗C

alculatedbandw

idthaccording

toequation

(2.24).

2.5. DYNAMICS 35

sorption R12 and stimulated emission R21. This absorption takes place in theactive region, so the generated carriers are also in the active region.The carriers generated in the active region can give spontaneous emission, butthat is negligible because the device works with about 5 volt reverse bias, andhence the region is depleted of free carriers. The major flow rate of carriersout from the active region is into the P- and N-side, which happens with therate Na/τtr. But because of the barriers at the grading layers, recombinationscould occur, which is included with a loss (Na/τtr)(1 − ηRec) . From the P-and N-side the flow of carriers can be seen as discharging of the two capacitors,diode capacitor and bond capacitor, which is done with the rate N/τRC .So to calculate the number of detectable carriers N(t), generated from a modu-lated input power P (t), we can make a set of three coupled differential equations,called rate equations:

dNp(t)dt

=η0P (t)

hν− (R12 −R21)

dNa(t)dt

= (R12 −R21)− Na(t)τtr

(2.21)

dN(t)dt

=Na(t)τtr

· ηRec − N(t)τRC

From equation 2.9 we have (R12−R21) = Np(t)Γαvg, and by modulating the in-put power with a specific angular frequency ω, amplitude P1 around a DC valueP0; P (t) = P0 + P1e

iωt and using Fourier analysis we can find the detectablenumber of particles as function of the modulation frequency:

N(ω) =η0ηRecτRC

hν

(P0 +

P1

(1− iωτRC)(1− iωτtr)(1− iω(Γαvg)−1)

)(2.22)

We see that it has at constant DC term and a varying AC term, and for thebandwidth we are only interested in the varying AC term. The AC responsivityfrom the AC term in equation 2.22 will then be given by.

R(ω) =η0ηRece

hν

(1

(1− iωτRC)(1− iωτtr)(1− iω(Γαvg)−1)

)(2.23)

To find the bandwidth ∆f we need to find the frequency where the responsivityhas dropped to the half (-3dB), that is to solve 0.5 · R(0) = R(∆f 2π) for ∆f(ω in the equations above is the angular frequency). The result can to a goodapproximation be estimated by:

∆f =1

2π(τRC + τtr)(2.24)

which also is seen in textbooks[5]. Calculated values for all devices are shownin table 2.5.


Figure 2.16: Block diagram of the setup for measuring the bandwidth.

To measure the bandwidth we need to measure the responsivity as functionof the modulation frequency. This is done on five of the most interesting devices,namely PIN number 4, 5, 8, 9 and, 10. They all have the same active layer andsame grading layers, and therefore also the high DC responsivity (∼ 0.75A/W ).However, they differ a lot in the RC time and transit time, because they havedifferent standoff layer and ridge height, so therefore these five devices havebeen chosen for the bandwidth measurements.In figure 2.16 a block diagram of the measurement setup for the bandwidth mea-surements, is shown. The network analyzer has an electrical output and input.The output is a modulated electrical signal from 50MHz to 40GHz, and at theinput an electrical signal at the same frequency is detected. The network ana-lyzer sweeps the output from 50MHz to 40GHz, measure the input, and givesthe input output ratio in decibel units as function of the modulation frequency.I want to measure on a PD, therefore I need to convert the electrical outputfrom the network analyzer to an optical signal, this is done with a CW laserand an electro absorption modulator (EAM). The measured input output ratioas function of the modulation frequency is then the responsivity of both theEAM and the PD, we therefore need to calibrate out the response curve of theEAM. This is done by inserting a commercial PD with a known response curve,and then calibrate the network analyzer to give zero decibel at all frequencies.When we then insert my PD, the measured response curve will then be relativeto the response curve of the commercial PD, and we therefore need to subtractthe response curve of the commercial PD from the measured response curve ofmy PD, to get the real response curve of my PD.

The measured (and calibrated) response curves are shown in figure 2.17,where each curve represents a measurement on a different device. The band-width can now be read of the curves for each device, as the point where thecurve crosses -3dB, and this is written into table 2.5.The measured bandwidth matches quit well with the calculated bandwidth, ex-cept for PIN8 which has a discrepancy of almost 40%. This discrepancy is thesame for both devices that are measured on, and since the limiting factor forPIN8 is the transit time (τtr À τRC), the discrepancy might be due to an error

2.5. DYNAMICS 37

Figure 2.17: Responsivity (in dB units) versus modulation frequency, for the-3dB bandwidth measurement. The different curves in the same plot are mea-surements on different devices.

2.5. DYNAMICS 39

in growing the high standoff layer. I have no better explanation!

An increase in standoff layer gives lower diode capacitance and thereforelower RC time, but a larger transit time. The change in standoff layer fromPIN4 to PIN5 that according to the calculations should make PIN4 the fastest,can not bee seen in the measurements. Probably because the change in totaltime (τtr + τRC) according to the calculations only is 0.4ps, which must be con-sidered small compared to the uncertainty in the estimated τtr, and τRC , andalso compared to the uncertainty in the bandwidth measurement. But the bigchange in standoff layer from PIN5 to PIN8, which according to the calculationsshould make PIN5 the fastest, matches well with the measurements.An increase in ridge height gives lower bond capacitance and therefore lowerRC time. The change in ridge height from PIN5 to PIN10, and from PIN8 toPIN9, which should make PIN10 and PIN9 the fastest can not be seen in themeasurements either. Again probably because the change in RC time (0.3ps),is to small to be verified by the measurement.

To summarize the bandwidth measurements; the most noticeable differenceis that PIN number 4, 5, and 10 are relatively good with a bandwidth about& 30GHz, and that PIN8 and 9 has a lower bandwidth of about 11 to ∼ 18GHz.

2.5.2 Sensitivity

To measure the sensitivity we need to measure the BER as function of the inci-dent power, and the sensitivity is in this project defined as the power where theBER is 10−9. Sensitivity measurements are performed on the same 5 devicesas for the bandwidth measurements, namely PIN number 4, 5, 8, 9, and 10,because they have the largest changes in RC time and transit time.A block diagram of the electrical setup for the sensitivity measurements is shownin figure 2.18. It starts with a CW laser and a erbium doped optical fiber am-plifier (EDFA) that gives 12.5 dBm optical power at 1550nm, followed by apolarization controller, and a Mach-Zehnder modulator. The polarization con-troller is used because the Mach-Zehnder modulator depends on polarization.The Mach-Zehnder modulator is controlled by the BER test-set with a PRBSof 231 − 1, at B = 10Gb/s, and its output can be seen on an oscilloscope. Theoutput from the Mach-Zehnder is also send into another EDFA, because theMach-Zehnder modulator has a high loss (∼ 7dB), and then into an attenuator,and a power-meter so we can measure the average optical power that we sendinto the PD. After the PD we insert an electrical preamplifier, whose output issend into the BER test-set, to measure the BER, and into the oscilloscope, tomeasure an electrical eye.The oscilloscope is triggered at a much lower frequency than the B = 10Gb/s,but it measures a lot of data points from different bit sequences and plots themon the same plot. So, the plot from the oscilloscope has bit1’s, and bit0’s withall different kinds of histories (the history of a bit is the bit sequence that laysbefore the bit). Such a plot from the oscilloscope looks like an eye (see figure


Figure 2.18: Block diagram of the setup for measuring the sensitivity, and theeye diagrams (optical and electrical). The Photodiode box is equivalent to theentire figure 2.14 (including load resistor, and bias tee)

Figure 2.19: The optical eye diagram of the Mach-Zehnder modulator, and threedifferent electrical eye diagrams of PIN8 at different optical input powers.

2.19), which is why it is called an eye diagram.Figure 2.19 shows the optical eye diagram, and three different electrical eye di-agrams obtained from PIN8, at different optical input powers; Pin = −5dBm,−7dBm, −9dBm.As can be seen in figure 2.19 there are noise on the bit1, and bit0, and the noiseto eye-opening ratio increases as the optical power decreases. This noise makesit difficult to determine whether a bit is a bit1, or a bit0, and there will thereforebe some error readings which is measured as the BER.

There are two terms of noise in a PD; shot noise, and thermal noise. Shotnoise is a manifestation of the fact that current is a stream of electrons that aregenerated at random times, and is given by[5]:

σs =√

2eI∆fn (2.25)

where I is the current, and ∆fn is the bandwidth of the (white) noise, which isexperimentally set by a low pass filter (in this case the bias tee; 12.5GHz). Byfar the largest current in this receiver is the current in the 50Ω load resistor,

2.5. DYNAMICS 41

for PIN4, 5, and 10 the current is about 100mA (at 5volt reverse bias), and forPIN8, and 9 it is about 300mA (at 15volt reverse bias).The thermal noise stems from the fact that electrons in a conductor, at finitetemperature, moves randomly. In this receiver we have a 50Ω load resistor RL

that gives the following thermal noise [5]:

σT =√

4kBT∆fnFn/RL (2.26)

where kB is Boltzmanns constant, T is the temperature, and Fn is a noisefigure of the electrical preamplifier. The electrical preamplifier used in thesemeasurements has a noise figure of 4.A very important parameter connected with the eye-diagram is the Q-factor [5]:

Q =I1 − I0

σ1 + σ0(2.27)

where I1, and I0 are the currents of the bit1, and bit0, and σ1, and σ0 are thestandard deviations of the bit1, and bit0. The standard deviations are for thesedevices given by σ2

0 = σ21 = σ2

s + σ2T . The Q-factor for an eye diagram is the

opening of the eye, divided by standard deviations for the top and bottom of theeye. The eye opening can be related to the average optical power; by lookingat figure 2.19 (left), we can see that the eye opening is equal to ∼ 1.3 times theaverage optical power. This means: I1 − I0 ' 1.3PR, where P is the averageoptical input power (measured by the power meter) and R is the responsivity.There are an approximate relation between the Q-factor and the BER [5]

BER ' exp(−Q2/2)Q√

2π(2.28)

By combining the equations above we can calculate BER as function of the aver-age optical input power. The power at which the BER is 10−9 (the sensitivity)is −6.5dBm for PIN4, 5, and 10, and for PIN8, and 9 it is −4dBm.

The measured BER versus the average optical input power is shown in figure2.20, including an electrical eye diagram at the sensitivity power. We know thatPIN5 has RC- and transit-time of a few ps, and in the eye diagrams in figure2.20 we can see the the rise and fall times are about 50ps. However, in thesemeasurements the time constants are not limited by the PD, but by the electricalbias tee that cuts off at about 12.5GHz. This is also the reason why all eyediagrams in figure 2.20 has about the same up and down times, even though weknow that the devices has different bandwidth.The measured and calculated sensitivity are listed in table 2.6. The measuredsensitivity matches very well with the calculated sensitivity for PIN4, 5, and 10.The measured sensitivity for PIN8, and 9 are smaller than for PIN4, 5, and 10,though not as much as the calculations indicate.


Figure 2.20: Measured BER versus optical input power, and electrical eye dia-grams at the sensitivity power.

2.6. SUMMARY 43

PIN4 PIN5 PIN8 PIN9 PIN10 UnitCalculated -6.5 -6.5 -4 -4 -6.5 dBmMeasured -7 -6.5 -5 -5.8 -6.5 dBm

Table 2.6: Calculated and measured sensitivity for five devices.

2.6 Summary

In this section I will compare the different PDs and try to find the best, then Iwill compare this best PD with other commercial diodes, and at last I will givesome ideas on how to improve the PD.

2.6.1 Comparison of devices

Key parameters we can use to compare the PDs are; responsivity, dark current,bandwidth, sensitivity, and to some degree also the breakdown voltage. Param-eters like the total capacitance, and RC- and transit-time constants are includedin the bandwidth parameter. All these parameters are listed in table 2.7 underelectrical characteristics, and they are measured with the optical fiber, A4-2.We also need to have some optical characteristics of the mode in the waveguide,in case another optical fiber is used. Optical characteristics of the PD are there-fore also included in table 2.7, where important parameters, calculated by theprogram Selene, are listed. The most important optical parameter is the modeoverlap, and from section 2.4 the mode overlap with the mode from the goodoptical fiber A4-2, and from a perfect spherical gaussian mode was found. Fora general parameter of the mode overlap, the gaussian mode overlap is listed intable 2.7. The optical characteristic part of table 2.7 also include the materialabsorption coefficient of the active layer, the 1/e waist (transverse/lateral) ofthe mode in the waveguide, the confinement factor, and effective refractive in-dex.

To decide which device is the best, I will start by comparing the responsiv-ity, and a high responsivity of about 1A/W (with AR coating) is seen for PINnumber 4, 5, 6, 8, 9, 10, 12, and 13 (because they all have about the samemode overlap). The dark current is < 1nA for all these devices. The Band-width of these devices is & 30GHz except PIN8, and 9 which has a somewhatlower bandwidth (because for the large transit time). The sensitivity of thedevices are limited by the shot noise of the current in the load resistor, and isthe same for all devices, except PIN8 and 9 that has a slightly lower sensitivity.A commonly used reverse bias voltage is 5volt, and since this is very close thebreakdown voltage of PIN13, we have to exclude this device.On the basis of this discussion the best devices are PIN number 4, 5, 6, 10, and12, which only have small differences in responsivity and bandwidth. Lookingat these five devices from a production point of view PIN10 must be somewhat


Electrical

characteristics

PIN

2P

IN3

PIN

4P

IN5

PIN

6P

IN7

PIN

8P

IN9

PIN

10P

IN12

PIN

13B

iasvoltage

[volt]

2–232–11

2–62–10

2–122–11

12–3012–30

2–102–7

2–4R

esponsivity ∗[A

/W]

0.880.90

0.991.02

0.980.88

1.031.03

1.021.02

1.03D

arkcurrent

[nA

]∼

2<

1<

1<

1<

1<

1<

1<

1<

1<

1<

1B

reakdown

voltage[v

olt]25

138

12.514

13.5∼

35∼

3512.5

96

Contact

resistance[Ω

]∼

7∼

7∼

7∼

7∼

7∼

7∼

7∼

7∼

7∼

5∼

3C

apacitance[f

F]

2331

5945

33103

2823

3947

48R

Ctim

e[p

s]1.2

1.63.0

2.31.7

5.21.4

1.22.0

2.42.4

Transit

time

[ps]

7.33.0

1.93.0

3.32.9

10.910.9

3.02.8

2.7B

andwidth

[GH

z]-

-32

34-

-(18)

1129

--

Sensitivity ∗∗[d

Bm

]-

--7

-6.5-

--5

-5.8-6.5

--

Optical

characteristics

PIN

2P

IN3

PIN

4P

IN5

PIN

6P

IN7

PIN

8P

IN9

PIN

10P

IN12

PIN

13M

odeoverlap

with

Gauss

65%

85%

94%

92%

72%94

%A

bsorptioncoeffi

cient[µ

m−

1]0.5

0.50.5

0.50.5

0.51/e

lateral[µ

m]

1.400.97

0.900.90

0.910.90

1/etransverse

[µm

]0.33

0.370.64

0.490.96

0.64C

onfinement

65%

23%

6.9%

15%

2%

6.9%

Effective

refractiveindex

3.423.25

3.183.20

3.173.18

Table

2.7:D

atasheet

forall

thebulk

PD

s.T

hetable

issectioned

inelectrical

andoptical

characteristics.∗w

ithA

Rcoating,

and@

1550nm

.∗∗

With

anexternal

electricalam

plifier.

2.6. SUMMARY 45

GiGA U2T XL Thor- metro- OEC Unit(PIN5) labs tek

Responsivity 1 0.65 0.8 1 0.9 0.95 A/WDark current < 1 . 50 . 1 1.5 . 1 . 0.8 nABandwidth & 30 > 50 > 12 > 5 2.5 2.5 GHzCapacitance 45 - . 200 300 600 500 fFSensitivity -6.5 - - - - - dBmLight area Ø (∼ 1) (∼ 1) 20 80 60 60 µmNote waveguide surface

Table 2.8: A collection of key parameters for six PDs including PIN5 fromGiGA. They are all made with bulk InGaAs active layer and a PIN junction,GiGA and U2T are waveguide PDs whereas the rest are surface PDs.

more expensive to produce then PIN4, 5, and 6, because it has a 800nm higherZn-doped InP layer in the ridge. And since the three times higher P-doping ofPIN12 does not give any significant changes, the best devices are PIN4, PIN5and PIN6.Among these three devices the differences are negligible, but theoretically thestandoff layer should give less diffusion of the Zn-doped ions, which should giveless free carrier loss. Furthermore a longer absorption length should give lessrecombinations of generated carriers.Therefore the best devices are PIN4, PIN5 and PIN6, with PIN5 being the oneto choose.

To compare PIN5 with other commercial PDs, table 2.8 lists key parametersfor five other PDs, all of them with an InGaAs active layer, and a PIN junction,just like PIN5. One of them (U2T) is made with a waveguide, like PIN5, theothers are surface PDs.The responsivity of PIN5 is some what higher then the other waveguide PD(U2T), and slightly higher then the surface PDs. This is probably becausea surface PD is not sensitive to the alignment of the optical fiber, whereas awaveguide PD is very sensitive. The measured responsivity of 1A/W for PIN5is with a perfectly aligned optical fiber, which has a very high mode overlap of∼ 95%, whereas the other PDs are packed in a box with the optical fiber weldedor soldered, so the alignment for those PDs are most likely not perfect.The Bandwidth is smaller than the other waveguide PD, but higher than thesurface PDs. A surface diode will always have a lower bandwidth, because ofthe larger light sensitive area which gives a larger capacitance and RC time.The dark current for PIN5 is among the best. And the sensitivity could not befound for any of the other devices.


Figure 2.21: New diagram of external components, which improves the sensi-tivity. Compared with figure 2.14 there are here included a capacitor in serieswith the load resistor.

2.6.2 Improvements

An obvious improvement is to use an AR coating, which, as we will see in sec-tion 3.2, can eliminate the reflection at the facet.

The sensitivity can be improved by including a capacitor in series with theload resistor, see figure 2.21. This will eliminate the large current in the loadresistor, which gave a large shot noise. The shot noise will in this new configu-ration originate from photo current and dark current for a bit1, and only darkcurrent for a bit0. By using the equations from section 2.5.2 we can calculatethat the sensitivity should drop to about −14dBm (@ BER = 10−9), and thatthe shot noise now should be smaller then the thermal noise.

The responsivity should be able to get as high as 1.25A/W , but we onlymeasure 1A/W , that is a 20% loss. We know the mode overlap gives about 5%loss (see table 2.4), and loss through the optical fiber gives about 8% loss, sothere are still about 7% loss. As discussed this last loss seems to come fromrecombinations of the generated carriers at the grading barriers. The averagebarrier height at each step is ∼ 75meV , which is more then the thermal energy(25meV ). This suggests that the four steps for electrons and holes are indeedlarge barriers, which leads to recombinations. So two ways to improve the re-sponsivity is to use a better optical fiber, that do not have loss through it, andto make many grading layers, so that each step is small compared to the thermalenergy.

Bandwidth seems to be hard to improve, according to table 2.5 the tansit-and RC-time are about the same. If we decrease the depletion layer to decrease

2.6. SUMMARY 47

the transit time, we also increase the diode capacitance and vice versa. A freeparameter we can optimize is the bond capacitance, but the bonding pads, whichare 50µm× 50µm, are already difficult to make a good bond on.

Chapter 3

Photodiode with integratedsemiconductor opticalamplifier

In this chapter we will be dealing with a PIN WGPD with an integrated semi-conductor optical amplifier (SOA), where the active region consists of a numberof quantum wells (QW).The chapter starts with a description of the design of the devices, and a bitof theory of the QW. Then there are three sections, the first is devoted to thePD alone (section 3.2), the next to the SOA alone (section 3.3), and the thirdto the PD with integrated SOA (section 3.4). Section 3.2 is much like chapter2, and will therefore be a short treatment of the PDs. Section 3.3 is dealingwith DC and CW measurements on the SOAs, and in section 3.4 we will look atdynamical measurements on the PD with integrated SOA. The chapter finishesin section 3.5, with a summary that emphasizes the most important measure-ments, and suggests some improvements.

3.1 Device design

The devices are made up of a SOA and a PIN WGPD integrated along onecontinuous waveguide, which we will call a SOA-PD. The active material in thewaveguide (the same for both SOA and PD) is a heterostructure made up of anumber of QWs. A schematic illustration of the structure, as seen from one ofthe facets is shown in figure 3.1.The Ridge is made by UV-lithography and etching, the width of the ridge is2µm, and etching of the ridge stops at the ”etch stop” layer (see table 3.1). TheSOA- and PD-section are separated by etching, a few µm wide trench, in theridge. This electrically isolates the two sections, so that we can set different bias

49

50 CHAPTER 3. PHOTODIODE WITH INTEGRATED SOA

3QW

8QW

10QW

Doping

Height

Doping

Height

Doping

Height

Note

[cm−

3][n

m]

[cm−

3][n

m]

[cm−

3][n

m]

Contact

layerInP

:Zn

∼10

18

1600InP

:Zn

∼10

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1000InP

:Zn

∼10

18

1000U

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n1·10

17

200InP

:Zn

9·1017

700InP

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3.1. DEVICE DESIGN 51

Figure 3.1: Schematic figure of the heterostructure used for the SOA-PD de-vices’s, with etched ridge. To the right is a zoom-in of the QWs, where therecan be either 3, 8, or 10 QWs. All numbers are approximate. (Figure adoptedfrom [15])

voltages on them (there are about 2kΩ between the two sections). So the onlydifference between the SOA, and the PD, is that the SOA is forward biased,and the PD is reversed biased.Three different heterostructures were grown, where the main difference is thenumber of QWs; 3, 8, or 10, and the devices are therefore named 3QW, 8QW,and 10QW SOA-PD. The growth data for the three different heterostructures islisted table 3.1. The heterostructures were designed to be used as mode lockedlasers [15], thus they are not optimized for a PD with integrated SOA.

3.1.1 Quantum wells

Figure 3.2 shows the structure for the heavy hole (hh) band, light hole (lh) band,and the electron band, through one of the QWs in a 10QW device (without anyelectric field). The active material is strained with respect to the substrate,with compressive strain in the well material, and tensile strain in the barriermaterial. Strain splits up the hh band, and the lh band. Compressive strainraises the energy of the hh band compared to the lh band, and tensile strainraises the energy of the lh band compared to the hh band. This makes the QWdeeper for the hh, and for the lh there are no QW in the well material (see figure3.2).Bandgap for barrier and well material, the depth of the QWs in the conductionband, and in the hh band, the effective masses for electrons, and hh’s in well,and barrier materials, are listed in table 3.2. These parameters are calculatedfrom the growth data in table 3.1, on the basis of [17], by Kresten Yvind [15].


Figure 3.2: Structure of bandgap through one QW in the 10QW device, withoutany electric field. The lowest energy level and corresponding wavefunction forthe electron and hh is also shown. (Part of the figure is adopted from [15])

Parameter Name 3QW 8QW 10QW UnitQW width LQW 7.2 7.2 8.0 nmBand gap barrier Egb 958.1 939.5 956.1 meVBand gap well Egw 754.3 746.8 762.4 meVConduction band offset ∆Ec/∆Eg 0.447 0.457 0.454QW depth for electrons Ve 91.1 88.1 88.0 meVQW depth for heavy holes Vhh 112.6 104.6 105.7 meVElectron eff. mass in well mw

e 0.041 0.040 0.041hh eff. mass in well mw

hh 0.372 0.372 0.373Electron eff. mass in barrier mb

e 0.050 0.049 0.050hh eff. mass in barrier mb

hh 0.374 0.375 0.375Lowest electron QW energy E0

e 45.0 44.6 40.1 meVLowest hh QW energy E0

hh 12.1 11.9 10.1 meVEffective energy gap in QW EgQW 811.4 803.3 812.6 meV

1528 1544 1526 nm

Table 3.2: In the first section of the table are parameters for the for the QWs,calculated from the growth data, on the basis of [17], by Kresten Yvind [15]. Inthe bottom section, the lowest energy level of the electron and hh, and effectivebandgap, are calculated.

3.2. QW PHOTODIODE 53

We now have both the width and depth of the QWs for the electrons in theconduction band, and the hh’s in the heavy hole band. To find the energy levelsin these QWs we need to solve schrodingers equation in one dimension for afinite depth QW, it results in the equations (see ex. [7] or [2]):

√2mw

e Ee · tan

(√2mw

e Ee

~LQW

2

)=

√2mb

e(Ve − Ee)

√2mw

hhEhh · tan

(√2mw

hhEhh

~LQW

2

)=

√2mb

hh(Vhh − Ehh)(3.1)

where Ee, and Ehh is the energy eigenvalues of electrons and hh respectively,~ is Planck’s constant divided by 2π, and all the other parameters are listedin table 3.2. The first equation is for symmetric modes of an electron in theconduction band, and the second equation is for symmetric modes of a hh inthe valence band. For antisymmetric modes we just need to include a factor−π/2 in the tangens parenthesis. For the electrons in the conduction band thereis only one confined state, whereas for the heavy holes the are a few confinedstates. But due to orthogonality between the electron and hh wavefunction inthe QWs, the transition matrix element is close to zero for all transitions, exceptbetween states with the same level number. We are therefore only interested inthe lowest symmetric level, and numerical solutions to the two equations 3.1 forthe lowest energy levels are listed in table 3.2. The corresponding wavefunctionsof the lowest electron, and hh state, are shown in figure 3.2.The effective bandgap of a QW material is the bandgap of the bulk material,plus the lowest energy level of the electron, and the hh; EgQW = Ew

g +E0e +E0

hh.This parameter is listed in the bottom of table 3.2, in units of both nm and meV .

3.2 QW Photodiode

In this section we will look at the three different QW PDs without SOA. Thissection is similar to chapter 2, and is therefore a short treatment of the QWPDs, with references to chapter 2 for more thorough explanations.An important difference compared to the bulk PD from last chapter is that allthese QW PDs are AR coated.

3.2.1 PIN Junction

The I-V curves of the PDs can be seen in figure 3.3, where the topmost solidred curves are without incident light. We can see that these I-V curves looksvery similar to the I-V curves for the bulk PD.Starting from the left (at high reverse bias) they have a break down, then alow dark current region, and at small forward bias there is a sharp increase incurrent.Breakdown occurs at ∼ −30volt for the 3QW PD, and at ∼ −7volt for the 8QW


Figure 3.3: I-V curves for the three different QW PDs, with no optical inputpower and with 0.25, 0.75, 1.25, and 1.75mW optical input power. (Adoptedfrom [15])


and 10QW PDs, and since the junction is a PIN junction, the breakdown mustbe avalanche breakdown (see section 2.2.2).

The dark current region of the I-V curves should according to equation 2.4from chapter 2 give about Idark ∼ 0.05nA depending on the length of the waveg-uide. To measure so low currents are hard, and the measurement equipmentused for the bulk PDs were, at this point in the project, no longer available atGiGA. So I have only been able to measure the dark current for these deviceswith an uncertainty of about 1µA, and for the 3 and 8 QW PD the dark currentwas below 1µA, probably also well below 1nA according to the calculation. Forthe 10QW PD there is a large ”dark current”, but because it is relatively largeand because it is linear in the bias voltage, it must be a leak current. This leakcurrent was seen for all the 10QW PDs, and therefore probably originates fromdefects in the epitaxial material, or a processing error.At forward bias these PDs also increases sharply at about 0.6volt to 0.8volt andequation 2.6 from last chapter fits fine with the measured curves, so the forwardcurrent are also for these QW PDs, a recombination current.

3.2.2 Light absorption

In figure 3.4(a) the structure of the bandgap through the junction of the 8QWPD with 1 volt reverse bias is shown. The absorption coefficient is given byequation 2.10, where ρr(E21) now is the 2D reduced density of states, which isa stepfunction. It is zero up to the effective bandgap of the QWs, where it stepsup to some value, and is constant up to the bandgap of the barrier. It onlysteps one time because, as discussed above, only one pair of levels are allowedfor transitions.The matrix element |MT | for a QW depends on the polarization of the light;TE or TM, and on transition type; heavy hole-conduction (hh-c) or light hole-conduction (lh-c). Since we only have hh-c transitions, and because the transi-tion matrix element for the hh-c transition is |MT |2 ' 6m0 for TE polarization,and |MT |2 = 0 for TM polarization, the devices are very polarizations depended.If the material were not strained we would also have a confined light hole modein the valence band, which has a non zero transition matrix element for TMpolarization, and the PD could therefore be made less polarization dependent.This polarization dependence is an unwanted effect because it can reduce bothabsorption in the PD, but also the amplification in the SOA. We therefore inserta polarizations controller just before the device, that changes the polarizationof all the incoming light to TE.The absorption coefficient for QW material is shown in figure 2.7, which sug-gests that the absorption coefficient, and thereby the photocurrent will dependstrongly on wavelength around 1550nm. In figure 3.5 a measurement of the pho-tocurrent versus incident wavelength, for the three different devices at constantphoton current, is shown. According to this measurement the effective bandgapfor the 3QW device is at ∼ 1575nm, and for the 8QW, and 10QW devices the


Figure 3.4: (a) Band structure of the 8QW device at 1V reverse bias. The firstfew nanometers up until the first red dotted vertical line is the depleted regionin the P-side, and the last few nanometers after the second red dotted verticalline is the depleted region in the N-side. (b) The same at 1V forward bias.

effective bandgap is located at & 1610nm.We can also see that the effective bandgap of the 3QW PD, is shifting towardshigher wavelengths when we increase the reverse bias. This shift of bandgap asfunction of reverse bias voltage is due to quantum confinement stark effect[18].

Because figure 3.5 suggests that we at 1550nm is passed the step in the ab-sorption spectrum from figure 2.7, we approximate the absorption coefficient toα = 1µm−1 at 1550nm, for all three devices.

3.2.3 Waveguide

The waveguide is centered around the QW material, and according to [15] thebarrier and well materials has an average refractive index of 3.45. The numer-ical computer program Selene is again used to calculate the transverse modeprofile in the waveguide, and also to calculate the confinement factor, effectiverefractive index, mode size, and mode overlap with fiber A4-2, which all is listedin table 3.3.Since these devices are AR coated we can calculate a responsivity as R =1.25A/W ηfiber ηmo, which also is listed table 3.3, together with the measuredresponsivity.We see that there is a very fine agreement between the measured, and the cal-culated responsivity.


Figure 3.5: Photocurrent versus incident optical wavelength for the three differ-ent PDs, at constant photon current Nph = 1016s−1. The bias voltage is -2V,-5V, and -10V for the 3QW device, and -2V for 8QW, and 10QW.

3QW 8QW 10QW UnitConfinement, Γ 7.3% 16.8% 17.1%Absorption length 13.7 6.1 5.8 µmEffective refractive 3.24 3.20 3.21FWHM transverse 1.49 1.71 1.72 µmFWHM lateral 0.46 0.41 0.40 µm1/e transverse 1.25 1.55 1.56 µm1/e lateral 0.45 0.50 0.49 µmMode overlap with Gauss 81% 79% 78%1/e of gauss Gauss∗ 0.8 1 1 µmMode overlap with A4-2; ηmo 84% 83% 82%ResponsivityCalculated ∗∗ 0.97 0.95 0.94 A/WMeasured with A4-2 0.94 0.95 0.95 A/W

Table 3.3: Calculations of important parameters for the mode in the waveg-uide, done by the computer program Selene. ∗Waist of the spherical sym-metric gauss mode, that gives the maximum mode overlap. ∗∗ calculated as:1.25A/W ηfiber ηmo


Figure 3.6: Schematic illustration of the integrated SOA-PD device as seen fromabove.

3.3 QW SOA

In this section we will look at the SOA part of the integrated SOA-PD. Someof the measurements in subsection 3.3.1 are performed on the SOA alone, i.e.without a PD section. The rest of the measurements in this section are per-formed on the integrated SOA-PD devices, but focuses on the SOA section. TheSOA is made from the same material as the PD (see table 3.1), and the onlydifference compared to the PD is that we set forward bias on the SOA. The totalamplification in the SOA will, as we shall see, depend strongly on its length.Therefore the SOA will be designated with both its number of QWs, but alsowith it’s length.The SOA is an angled facet travelling wave SOA[5], (see figure 3.6). It consistsof a waveguide which is tilted 7o compared to the normal of the facet, and thefacet where the light is injected, is AR coated.

3.3.1 Optical gain in semiconductor material

At the SOA section we apply forward bias, and as we saw in the I-V curves, infigure 3.3, we get a sharp increase in current at about 0.7volt, which is caused byrecombinations of injected minority carriers. In figure 3.4(b) the band structureof the 8QW device with 1volt forward bias is shown, and we can see that thequasi fermi levels are raised so that we have a lot of electrons in the conductionband, and a lot of holes in the valence band. This situation is called populationinversion. When we send light into such a forward biased diode, we will initiatestimulated emission, and because there are very few electrons in the valenceband, there will be very little absorption. This causes R21 > R12 from equation2.8, and the incident light will therefore be amplified.In equation 2.10 we have the material absorption coefficient α, and the materialgain g is simply given by g(E21) = −α(E21) [2]. In figure 3.7 the calculatedg(E21) as function of the incident photon wavelength, is shown, which is called

3.3. QW SOA 59

Figure 3.7: Calculated material gain versus incident photon wavelength, calledgain spectrum. It is calculated for QW material with an effective bandgap at1585nm, and at different ∆Ef (energy difference of the two quasi fermi levels).A Lorentzian lineshape broadening with energy broadening of the energy levelsof 13meV is included [2].

the gain spectrum. The gain spectrum is shown at different ∆Ef , which is theenergy difference between the two quasi Fermi levels, and it is shown for QWmaterial with an effective bandgap of 1585nm. A lorentz lineshape broadeningwith energy broadening of the energy levels of 13meV , is included [2].The gain of the mode in the waveguide is called the modal gain 〈g〉, and is givenby 〈g〉 = Γg, where g is the material gain, and Γ is the confinement from table3.3.The difference in the two quasi fermi levels ∆Ef is to a good approximationequal to the external applied bias, as long as the voltage drop across the junctionis larger then the voltage drop across the P and N side Rpn (Rpn is measuredto about Rpn ∼ 2.5Ω for a 800µm long 8QW SOA).From figure 3.7 there are three important things to note; 1) as we increase biasthe overall gain increases, 2) as we increase bias the wavelength at which wehave the maximum gain decreases, and 3) there are only a small change from1.05volt to 2volt applied bias, which is because we at such high ∆Ef have com-plete inversion of carriers, which means that f1 = 0 (Fermi function for thevalence band), and f2 = 1 (Fermi function for the conduction band), and in-creasing bias will not change this.


It can be shown that when ∆Ff > Eg the gain spectrum starts to be positiveat some wavelength interval [2].

We have now discussed gain in the SOA, but since the reflections at theboundaries of the SOA are finite, a photon cavity will be formed. This cavitywill have a high loss of light, both through the AR coated facet, and due toabsorption in the PD section.At some point, as we increase bias, the gain might become as high as the loss,and at this point the SOA will starts to lase. Therefore the SOA might turninto a laser, if the gain becomes as high as the loss, and we shall see later thatthis can happen. The point where lasing is initiated is called the threshold level.Threshold level refers both to a threshold gain gth, a threshold current Ith, andother parameters at threshold.Lasing is reached the following way; as we increase bias voltage (or current) thecarrier density in the active region will increase, this will increase ∆Ef , and gain(see e.g. figure 3.4). If the gain at some applied current reaches a level slightlylarger than the loss, an avalanche process is triggered that amplifies the lightby stimulated emission, called lasing. As the process continues the number ofphotons (and optical power) inside the cavity increases, so this process cannotcontinue forever. Each stimulated emission process is caused by an electronhole recombination, and as the number of photons increases so does the rate ofrecombinations. This will decrease the number of carriers, which also decreasesthe gain.If we still keep the applied current constant the gain will not decreases belowthe level of loss either. Because in that case the number of photons will begin todecrease, this will decrease the rate of stimulated emission, which will increasethe number carriers, and gain will again increase.A steady state situation will in this manner be reached, where the gain is fixedand equal to the loss, and gain can not increase any more. An increase in biaswill still increase the current, which increases the rate of carrier injection, but itwill not increase the carrier density and thereby ∆Ef , and gain. It will insteadincrease the rate of stimulated emission, and in this manner keep the carrierdensity constant. So, after the threshold level is reached, the optical outputpower will be proportional to the applied current.

The threshold level can be seen in figure 3.8(c) for a 900µm long 10QWSOA, where we increase current, and at some point the optical output powerstarts to increase linear with applied current. The laser effect is shown for adevice without AR (just angeled facets), and a device with AR, and we see thatthe threshold level is increased as AR is introduced, because AR gives a higherloss through the facet.The laser effect can also be seen in figure 3.8(a) where the optical output spec-trum of a AR coated 10QW SOA (without the PD section) is measured atdifferent applied currents from 20mA to 70mA. A ∼ 20dB increase in opticalpower is seen from 60mA to 70mA, which is caused by the initiation of lasing.A closeup of the lasing peak is shown in figure 3.8(b), and we see that there

3.3. QW SOA 61

Figure 3.8: (a) Optical output spectrum from an AR coated 10QW SOA, for-ward biased with 20, 30,...,70mA, (b) a closeup of the lasing peak showing theFabry Perot modes, and (c) a plot of Pout vs current showing the threshold levelwith and without AR.

are many smaller peaks. Each peak is called a Fabry Perot mode and has awavelength λm that satisfies (λmm)/(2neff ) = L, where m is an integer, neff

is the effective refractive index, and L is the length of the cavity.

Before threshold, the output spectrum in figure 3.8(a), is just amplified spon-taneous emission (ASE), and from these curves we can demonstrate the gainspectrum. As we increase current the overall gain should increases, which wouldgive more ASE at all wavelengths, and this effect can clearly be seen in figure3.8(a). We also see the peak in the ASE is shifting towards larger photon en-ergies as we increase the current, which matches well with the theoretical gainspectrum in figure 3.7.Another way to demonstrate the gain spectrum of the SOA is to send light withdifferent wavelengths into the integrated SOA-PD, and measure the photocur-rent of the PD as function of the current on the SOA (ISOA), and incidentwavelength. In this way the measured current will originate from a backgroundof ASE, the amplified input signal, and a small leakage current from the SOA.Such measurements are shown in figure 3.9 for a 3QW device with length of theSOA LSOA = 800µm, and for two 8QW devices with lengths LSOA = 250µm,and 800µm. The 3QW SOA-PD, and the LSOA = 250µm long 8QW SOA-PDcannot lase, they do not have enough gain to compensate for the loss. Howeverthe LSOA = 800µm 8QW SOA-PD will begin to lase at about Ith = 70mA.In these measurements we again see that the overall gain increases, and that thegain peak is shifting toward higher photon energy, as ISOA is increased, but wealso see three other effects. (1) In figure 3.9(a) and (b) we have a 3QW deviceand a 8QW device that can not lase, and the approximative position of thebandgap is different. An approximative position of the bandgap is according to


Figure 3.9: The surface plots to the left are measurements of the photocurrentin the PD as function of the incident wavelength, and current on the SOA,at constant photon current Nph. The graphs to the right are intersectionsof the surface plots at specific SOA currents. (a) 3QW device with LSOA =800µm, Nph = 8 · 1015s−1, and −2volt bias on the PD (b) 8QW device withLSOA = 250µm, Nph = 8 · 1015s−1, and 0volt bias on the PD, and (c) 8QWdevice with LSOA = 800µm, Nph = 1 ·1015s−1, and −1volt bias on the PD. Themaximum SOA currents are chosen to be as large as possible without destroyingthe devices.

3.3. QW SOA 63

the gain spectrum in figure 3.7 at the middle of the increasing slope. The 3QWdevice has the bandgap at a lower wavelength than the 8QW device, which wealso saw in the measurements in figure 3.5 of the photo current versus incidentwavelengths.(2) The next effect is seen from figure 3.9(b) to (c), which both are for the 8QWdevice but for two different lengths of the SOA section, the long 800µm SOA-PD will start to lase at Ith = 70mA, the other will not. For both devices thegain peak shifts towards higher energy as the gain current increases. However atabout 1550nm the gain peak for the long device do not shift any more, whereasfor the short device the gain peak shifts further. This is because lasing startsin the long SOA-PD, and as discussed above, gain cannot increase beyond thethreshold level.(3) The third effect is that the (energy) distance from the approximative po-sition of the bandgap, to the gain peak, is different for the 3QW device, andthe LSOA = 250µm 8QW device. The distance from the bandgap to gain peak,in the QW gain spectrum, depend solely on the lineshape broadening function.If there were no lineshape broadening, the gain peak would coincide with thebandgap. The lineshape broadening accounts for broadening of the energy lev-els, which can be caused by temperature, finite lifetime of carriers [2], and inthis case where we have more then one QW it will depend on how precisely alikethe QWs are grown. So the larger lineshape broadening of the 8QW device thenthe 3QW device, is probably caused by the higher number of QW, because eachQW are not precisely alike.

3.3.2 Amplifying cavity

For a SOA with length L, and modal gain 〈g〉, we define the (modal) poweramplification as:

G = exp(〈g〉L) (3.2)

The SOA is intended to amplify the optical signal before it is detected in thePD, and we would therefore like it to have a high amplification with little noiseat 1550nm. The amplification can be increased by making the SOA longer, andjust by increasing the current to the SOA. But, as discussed in the last section,when we reach the threshold level, the device will begin to lase, and the gain cannot increase beyond this level. Furthermore, the optical power from the lasingwill also be detected in the PD, which will introduce a lot of noise. Thereforewe would like the SOA to be operated close to threshold, where it has a highgain g, and therefore also a high amplification G, and no lasing.The device is shown in figure 3.6, and because we apply different bias voltageson the SOA, and the PD, we will introduce a small change in refractive indexbetween the SOA- and PD-section. This will give a small reflection between theSOA and the PD, which we will denote r2 (field amplitude reflection). The fieldamplitude reflection at the AR coated facet, and cleaved facet will be denotedr1, and r3 respectively. Therefore two cavities can be formed; in the SOA section


Figure 3.10: I-V curves of the PD section of a 8QW SOA-PD, with LSOA =800µm, at different currents on the SOA section, and with no incident light.The slope of the curves at reverse bias is due the 2KΩ between the SOA andPD section.

alone with r1 and r2 as boundaries, or in both SOA and PD with boundaries r1

and r3.The modal threshold gain of the SOA section is given by [2]:

〈g〉SOAth =

1LSOA

· ln(

1r1r2

)+ αint (3.3)

and the modal threshold gain of the SOA and PD is given by [2]:

〈g〉SOA−PDth = Γα

LPD

L+

1L· ln

(1

r1r3

)+ αint (3.4)

Where αint is internal loss in the SOA section, due to effects like free carrierloss, and absorption. But SOAs has low reflection facets, and internal loss istherefore negligible[2].The field amplitude reflection r2 is given by r2 ' ∆n/2neff , where ∆n is thechange in refractive index from SOA to PD. And according to [19], which con-siders changes in refractive index due to carrier injection, we can approximatethe field amplitude reflection by r2 ∼

√2 · 10−3 (where an injected carrier den-

sity of 1018cm−3, are used, which seems reasonable according to [2] page 170).The field amplitude reflections r1, and r3 are about r1 ∼

√10−3 [15], and

r3 ∼√

0.01 [16]. As we will see in section 3.4.2, the devices with the best sensi-tivity has a SOA length of about LSOA ∼ 500µm and PD length of LPD ∼ 50to 100µm. By inserting this, and Γ = 17% (8QW or 10QW devices), the modalthreshold gain of the SOA-PD is gSOA−PD

th & 260cm−1, and for the SOA it isgSOA

th ∼ 130cm−1. The laser cavity must therefore be in the SOA section.In figure 3.10 I-V curves of the PD section of an 8QW SOA-PD device (LSOA =800µm), with different current on the SOA section (there are no incident light),are shown.We see that the threshold level is reached at about 60mA current on the SOA

3.3. QW SOA 65

section, and more importantly we also see that the lasing is not suppressed atreverse bias. Which shows that the device can lase even at reverse bias, proba-bly originating from the SOA cavity.

3.3.3 Total amplification

Since the cavity in the SOA section starts to lase first, it is equation 3.3 thatdetermines the threshold gain. And from that equation we can see that thetotal (power) amplification G at threshold is given by:

Gth =1

r1r2(3.5)

Since the amplitude reflection r1 enters in this equation, and r3 do not, we onlyAR coat the incident facet.As discussed we can approximate r1 ∼

√10−3[15], and r2 ∼

√2 · 10−3[19], which

gives a total threshold amplification of about Gth = 700 or 28dB .

Just before the threshold level we have the maximum amplification in the de-vice without lasing, but not all SOAs can reach the threshold level. For examplea 100µm long SOA with confinement factor Γ = 17% (8QW or 10QW device),has according to equation 3.3 a material threshold gain of gth = 0.95µm−1. Thisis just about the maximum possible gain at the right wavelength (see figure 3.7),and it can therefore be hard to reach.Another effect that can keep the device from reaching threshold, is if Rpn is sohigh (more than a few ohms) that the voltage drop across the junction, as weincrease forward bias, becomes small compared to the voltage drop across theP- and N-side. Because in that case an increase in bias will not increase thevoltage across the junction, but across the P- and N-side, which means that∆Ef , and gain will not increase.Both decreasing the threshold gain from equation 3.3, and decreasing the resis-tance of the P- and N-side, can be done by increasing the length of the SOA.And increasing the length of the SOA will according to equation 3.5 not affectthe threshold amplification, which we are trying to reach. So, to get close tothreshold, and thereby getting the maximum amplification without lasing, dif-ferent devices with increasing length of the SOA section, are made.In figure 3.11 measurements on seven 8QW SOA-PDs with different length ofthe SOA, are shown. The graph shows the measured current from the PD, asfunction of the applied current on the SOA (where the maximum applied cur-rent is about the maximum we can apply, without destroying it). Since thereis no incident light in these measurements, all the photocurrent is originatingfrom ASE and/or lasing generated in the SOA. We see that the first five devicescannot lase, whereas the devices with the 700µm and 760µm long SOA can.This means that threshold can be reached for the 8QW SOAs, when it’s lengthis somewhere between LSOA = 620µm and LSOA = 700µm.Similar measurements are performed on the 10QW devices, where threshold can


Figure 3.11: Measured photocurrent in the PD as function of applied current tothe SOA, on seven 8QW devices with different lengths of the SOA. There areno incident light, and there are zero volt applied to the PD.

be reached when the length of the SOA is somewhere between LSOA = 530µmand LSOA = 580µm.The 3QW SOA is amplifying the signal very little; in figure 3.9(a) about 1mWoptical power is send into a 800µm 3QW SOA, and the measured photocurrentin the PD, which is a combination of ASE and amplified signal, is maximum2mA. With a responsivity of about 1A/W without the SOA, see table 3.3, thiscorresponds to an amplification of less the 2. We will therefore discard the 3QWSOA-PDs, and only look at the 8QW and 10QW SOA-PD devices. The smallamplification could be due to a low confinement factor, which in turn gives alow modal amplification. Or if we look at figure 3.9(a) we can see that the gainpeak is relatively sharp defined around 1520nm (not 1550nm).

When we send light into the SOA-PD, the measured photocurrent in thePD is due to a combination of ASE, and amplified incident signal, and theresponsivity of the SOA-PD is therefore defined as:

RSOA−PD =Photocurrent in PD due to amplified incident signal

Incident optical power(3.6)

From this definition the amplification of the SOA can be approximated by:

G ' RSOA−PD

R' RSOA−PD

1A/W(3.7)

3.3. QW SOA 67

where R is the responsivity of the PD alone (without SOA). We can make thisapproximation because we still have loss through the optical fiber (ηfiber), andeven though the mode overlap between the SOA and PD is perfect, we also stillhave a mode overlap at the incident facet of the SOA, which is identical to themode overlap for the PD alone (except for a small change in refractive indexdue to carrier injection [19]). So by measuring the responsivity of the SOA-PD,we immediately also get the amplification of SOA.The responsivity of the SOA-PD will of course depend on ISOA, but also on theoptical power of the incident light. Measured amplification of the SOA (respon-sivity of the SOA-PD), as function of ISOA, and incident optical power, for thesame seven SOA-PD devices as in figure 3.11, is shown in figure 3.12.Current in the PD due to ASE, and due to the small leakage current from SOAto PD, is measured (figure 3.11) and subtracted, so figure 3.12 represents thetrue amplification of the SOA.

We know, from figure 3.11, that the LSOA = 700µm, and LSOA = 760µmSOA-PD devices have a current threshold at Ith ' 75mA, and Ith ' 65mArespectively, whereas the five other devices in figure 3.12 can not lase. Weclearly see that the amplification is increasing with the length of the SOA uptill LSOA = 620µm, after which the amplification decreases.The LSOA = 620µm device has the largest amplification of about G = 450(26.5dB), which matches well with the approximated threshold amplificationfrom above; Gth = 700 (28dB). Similar measurements on the 10QW SOA-PDdevices showed a maximum gain of about 500 (27dB), for a SOA-PD with a530µm long SOA.We also see that the amplification depends on the incident optical power. Thisis probably because the incident signal to some degree is drowning in ASE. Forthe LSOA = 620µm device at ISOA = 150mA there is 3mA photocurrent inthe PD due to ASE (see figure 3.11), which corresponds to about 3mW opticalpower. The incident power is only about 1 to 10µW , and at a very narrowwavelength range around 1550nm, whereas the 3mW optical power from ASEcomes from a wide range of wavelengths, as can be seen in figure 3.8(a).The decrease in amplification when lasing is initiated is probably because theincident optical signal now is drowning in optical lasing power. From figure3.8(a) we know that when lasing is initiated, the optical power at 1550nm inthe SOA is increasing much more than before lasing.

To summarize this section we have looked at the gain spectrum, to try andlocate the wavelength that has the highest gain, we have looked at the transi-tion from ASE to lasing, to try and find the maximum length the SOA can havewithout lasing, and we have looked at the total power amplification versus thelength of the SOA, to find the maximum amplification.Ideally we would like the peak of the gain spectrum at high currents (total popu-lation inversion) to be located at 1550nm because this would give us the highestamplification of the incident 1550nm signal. According to figure 3.9, the gainpeak at high currents of the 8QW SOA seems to be close to the 1550nm; for


Figure 3.12: Amplification of the SOA, or the responsivity of the SOA-PD,as function of the SOA current, and optical input power. The measurementsare performed on seven different 8QW SOA-PDs, with different lengths of theSOA. The two last SOA-PDs with the longest SOAs can lase, and the thresholdcurrent are indicated on those figures.

3.3. QW SOA 69



Caption: Same as previous page

a 250µm long 8QW SOA the gain peak is at ∼ 1520nm. We also saw that the8QW SOA had a broad gain peak, so that the decrease in gain from 1520nm to1550nm was small. From figure 3.8(a) we saw that a 800µm long 10QW SOAlased at ∼ 1560nm, so a shorter 10QW SOA that can not lase will probablyalso have a gain peak close to 1550nm.If the SOA-PD starts to lase, it was found that the lasing cavity is in the SOAsection with boundary r1 and r2, which also is why only the incident facet isAR coated.The 8QW SOA will start to lase when its length is somewhere between 620µmand 700µm, and the 10QW SOA will start to lase when its length is somewherebetween 530µm and 580µm.The maximum measured amplification is about 450 or 26.5dB for a 620µm long8QW SOA, and about 500 or 27dB for a 530µm long 10QW SOA.

3.4 SOA-Photodiode

In this section we will look at dynamical measurements, such as bandwidth andsensitivity, performed on the 8QW and 10QW SOA-PD devices. We have dis-carded the 3QW devices because it had very little amplification.For dynamical measurements the PD section are mounted just like the bulk PD,with a 50Ω load resistor in parallel, and an external bias tee, see figure 2.14.The SOA section is mounted with a separate lead, and do not need any externalcomponents.

3.4. SOA-PHOTODIODE 71

3.4.1 Bandwidth

From last chapter, we know that the bandwidth is defined as the modulationfrequency, of the incident signal, that decreases the AC responsivity 3dB.For these SOA-PD devices either the SOA or the PD will set the limit for thebandwidth. For the PD we know, from last chapter, that the key time parame-ters are the transit time τtr, and the RC time τRC . For the SOA there is anotherkey time parameter, namely the time it takes for the carriers to be injected intothe active region τin. In CW measurements τin could set a limitation; if wesend a high power CW beam into the SOA, so that the total recombinationrate becomes higher than the carrier injection rate (1/τin), we will deplete theactive region of carriers. This will cause the amplification of the SOA to drop,however such an effect has not been seen.In dynamical measurements τin could also set a limitation: When we send inan optical signal which is modulated between a high level and a low level, withan average power that do not deplete the active region of carriers, there will bea net decrease of carriers when the optical signal is high, and a net increase ofcarriers when the optical signal is low. This is simply because the high opticalsignal induces more recombinations, then the low optical signal. This effectmight degrade the signal, and therefore result in a lower bandwidth. But as wewill see in figure 3.13(a), such an effect is not seen either, which suggests thatthe carrier injection time τin is smaller than τtr + τRC . The bandwidth of theSOA-PD devices, is therefore probably limited by the PD.From last chapter we know that the bandwidth of the PD is given by equation2.24, from the transit time τtr, and the RC time τRC . Analog to last chapterwe can estimate the τtr, and τRC , and calculate the bandwidth, which is listedin table 3.4.

The setup for measuring the bandwidth is the same as for the bulk PD fromlast chapter (figure 2.16), where we just exchange the bulk PD with a polariza-tion controller and the SOA-PD device. The bandwidth is measured for both8QW and 10QW SOA-PD devices, with different lengths of the SOA. In figure3.13 measurements of the responsivity as function of the modulation frequencyfor five 10QW SOA-PD devices with different lengths of the SOA, is shown.For each device we change one parameter; in figure 3.13(a) we change the aver-age input power, in (b) and (d) we apply different bias voltages to the PD, andin (c) and (e) we apply different current to the SOA.We can see that the bandwidth depend very little on the optical input power,current to the SOA, and length of the SOA. By applying from 2volt to 5voltto the PD the bandwidth do not change either, and the decrease in bandwidthwhen we apply less then 2volt to the PD is probably due to an increased transittime in the PD. This all agrees with the bandwidth being limited by the PD,and not the SOA.Similar measurements are performed on 8QW devices, and averages of the mea-sured bandwidths are listed in table 3.4, for comparison with the calculatedbandwidths.


Figure 3.13: Measured responsivity in dB units as function of modulation fre-quency, for five 10QW SOA-PD devices with different length of the SOA. In (a)the measurement is performed with different average optical input powers, in(b) and (d) with different applied voltages to the PD, and in (c) and (e) withdifferent applied current to the SOA.


8QW 10QW UnitEmax 216 180 KV/cmDepletion region 274 324 nmDiode capacitance 4.7 4.0 fFBond capacitance 30 32 fFRC time τRC

∗ 1.75 1.81 psTransit time τtr 2.74 3.24 psBandwidth of PDCalculated∗∗ 35.45 31.52 GHzMeasured 30 30 GHz

Table 3.4: Measured and calculated bandwidths, and corresponding estimateddynamical parameters. Calculations are made at -5 volt bias. ∗Bond capac-itance and diode capacitance in parallel multiplied by the 50Ω load resistor.∗∗Calculated bandwidth according to equation 2.24.

Averages of the measured bandwidths are ∆f = 30GHz for both the 8QW and10QW SOA-PDs, which matches quite well with the calculated bandwidths.

3.4.2 Sensitivity

The sensitivity is, as discussed in the last chapter, the optical input powerwhere the BER reaches some level, and in this project this level is defined to beBER = 10−9.The sensitivity will increase when the eye opening increases and/or when thenoise of the bit1’s, and bit0’s decreases. Noise in the PD is due to thermal noise,and shot noise, as discussed in section 2.5.2. But in these SOA-PD devices, theSOA section is also contributing to the noise, where the noise originates fromASE.So the SOA amplifies the incident signal, which opens the eye, but it also gen-erates ASE, which induces more noise and smears the eye. We therefore wantthe SOA to have a high amplification to ASE ratio, which will depend on thelength of the SOA, and the applied SOA current.An electrical eye diagram of a 10QW SOA-PD device is shown on the front pageof this thesis, where a short PRBS of 107− 1 is used. Every measurement pointin such an eye diagram is from a different bit, it therefore contains bits withmany different histories, and by looking at the front page we can actually seethat the eye diagram is composed of bits with different histories. Especially thebit0 region of the eye diagram is composed of several lines, which each stemsfrom a different bit-history.

The measurement setup to measure the sensitivity is very similar to the oneused for the bulk PD in figure 2.18, the only difference is that we have exchanged


the PD with a polarization controller and the SOA-PD device. For all the sen-sitivity measurements, we again use B = 10Gbit/s, a PRBS of 1031 − 1, andNRZ format.In figure 3.14 measured BER versus average optical input power for five 10QWSOA-PD devices with different length of the SOA, is shown. Similar measure-ments for five 8QW devices has been performed, and the sensitivity versus thelength of the SOA section is shown in figure 3.15(a). The sensitivity will dependon the current to the SOA, and in figure 3.15(b) the SOA-current that gives thehighest sensitivity is plotted versus the length of the SOA.

In figure 3.15(a), we see that the SOA-PD devices has an optimum lengthof the SOA; for the 10QW SOA-PD it is at LSOA ∼ 475µm, and for the 8QWdevices it is at LSOA ∼ 565µm. This optimum length of the SOA can be ex-plained as the point where the amplification to ASE ratio is highest. Becauseby making the SOA longer, the ASE would then increase more than amplifica-tion, and by making the SOA shorter the amplification would begin to decreaserapidly, which both corresponds to a more closed eye diagram, and in turn aworse sensitivity.We know from section 3.3.3 that lasing can start when the length of the SOAis at 620µm to 700µm for the 8QW SOA-PDs, and at 530µm to 580µm forthe 10QW SOA-PDs. So, this suggests that the optimum sensitivity is reachedsomewhat before threshold. This could be because ASE begins to increase morerapidly as we approach threshold, and that the highest amplification to ASEratio therefore is reached somewhat before threshold.The best 8QW SOA-PD device has a sensitivity of ∼ −24dBm, and a SOAlength of LSOA ∼ 565µm. According to 3.15(b) the best sensitivity is reached atISOA ∼ 130mA, and according to figure 3.12 it has a max amplification of ∼ 300(24.8dB), and at the maximum sensitivity (Pin = −24dBm, ISOA = 130mA) ithas an amplification of ∼ 250 (24.0dB).The best 10QW SOA-PD device has a sensitivity of ∼ −20dBm, and a SOAlength of LSOA ∼ 475µm. The best sensitivity is reached at ISOA ∼ 125mA,and it has a max amplification of ∼ 350 (25.4dB), and at the maximum sensitiv-ity (Pin = −20dBm, ISOA = 125mA) it has an amplification of ∼ 300 (24.8dB).

The threshold gain can be calculated by equation 3.3; the 565µm long 8QWSOA has a modal threshold gain of about 〈g〉SOA

th ∼ 120cm−1, and the 475µmlong 10QW SOA has 〈g〉SOA

th ∼ 140cm−1. We know that both of them cannot lase which means that they can not reach a gain this high. The maxi-mum modal gain can be calculated by 〈g〉max = ln(Gmax)/L, where Gmax isthe maximum measured amplification. The 565µm long 8QW SOA has a maxmodal gain of about 〈g〉max ∼ 100cm−1, and the 475µm long 10QW SOA has〈g〉max ∼ 125cm−1.

Figure 3.7 shows that at total population inversion we have a material gainof about 10000cm−1, and with a confinement factor of 17% it gives a modalgain of 1700cm−1, which is more that 10 times larger than the maximum modal


Figure 3.14: Measurements of BER versus average optical input power at aPRBS of 1031−1, and in the NRZ format, for five 10QW SOA-PD devices withdifferent length of the SOA.

3.5. SUMMARY AND DISCUSSION 77

Figure 3.15: Measurements on five 10QW SOA-PD and five 8QW SOA-PDdevices. In (a) sensitivity versus length of SOA, and in (b) current to the SOAthat gives the best sensitivity versus length of SOA.

gains that we have just calculated. This indicates that the SOAs are far fromtotal population inversion.

3.5 Summary and discussion

To summarize this chapter, the most important parameters for the 8QW and10QW SOA-PD devices, are listed i table 3.5. The 3QW SOA-PD device hasbeen discarded because of the low amplification.The 8QW and 10QW SOA-PD devices are very similar, which would be ex-pected because the only difference is the number, depth, and width of the QWs(see table 3.1). We saw in figure 3.3 that the 10QW PD had some leakagecurrent. Besides that, the largest difference between the two is the sensitivity,where the 8QW SOA-PD is 4dB better. Another difference is the amplification,where the 10QW SOA-PD has about ∼ 20% more amplification.The amplification of the SOA is intended to give the SOA-PD a large dynamicrange of optical input powers, so that it is capable of working in many differ-ent environments with different optical powers. If the optical power of somebit stream in an environment is low, say −15dBm, we just apply a high SOA-current, and if the optical power i relative high, say 0dBm, we just apply a lowSOA-current. The sensitivity is therefore a more important parameter than theamplification, and the 8QW SOA-PD device is therefore best.

I will here suggest a few improvements: The first and most obvious improve-ment, is to make device polarization independent. E.g. just by using a bulkactive layer, instead of QWs, because bulk material will absorb TE and TMpolarization equally.Another improvement is to make an even better AR coat, which would increase


Device characteristicsSOA-PD 8QW 10QW Unit

Bandwidth 30 30 GHzSensitivity -24 -20 dBm

@ current to SOA 130 125 mAMax Responsivity 300 350 A/WResponsivity @ max sensitivity 250 300 A/W

SOALength of SOA 565 475 µmMax amplification 300 350Amplification @ max sensitivity 250 300Max modal gain 100 125 cm−1

Threshold modal gain ∼ 120 ∼ 140 cm−1

gain peak 1520 - nmContact resistance ∼ 3 ∼ 3 Ω

PDLength of PD 50–100 50–100 µmBias voltage 2–5 2–5 voltResponsivity 0.95 0.95 A/WBreakdown voltage 7 7 voltDark current (< 1) - nAContact resistance ∼ 20 ∼ 20 ΩCapacitance 35 36 fFAbsorption coefficient 1 1 µm−1

Mode characteristics8QW 10QW Unit

Mode overlap with Gauss 79% 78%1/e lateral 1.55 1.56 µm1/e transverse 0.50 0.49 µmConfinement factor 16.8% 17.1%Effective refractive index 3.20 3.21

Table 3.5: Data sheet for the 8QW and 10QW SOA-PD devices. The table issectioned in device characteristics of the SOA-PD, SOA, and PD device, andcharacteristics of the mode in the waveguide.

3.5. SUMMARY AND DISCUSSION 79

the threshold amplification. This could be used to make the SOA amplify more,and in turn also give a better sensitivity.We know that the bulk PD, from last chapter, had mode overlaps up to 95%,therefore a ∼ 10% improvement of the mode overlap for these SOA-PDs couldprobably also be obtained.The bandwidth can not be improved much since the transit time, and the RCtime, are relative close (see table 3.4).We have seen that the peak in the gain spectrum for a 8QW SOA with LSOA =250µm is located at about ∼ 1520nm. By decreasing the effective bandgap abit, the gain peak could be shifted to 1550nm, which would increase the ampli-fication. Since the noise originating from ASE, not would be affected much bysuch a change, the sensitivity would probably also be better.

I will here suggest a few changes that might improve the SOA-PDs:(1) An EDFA could be used as an external optical preamplifier, instead of theSOA. Such a setup could probably give even better sensitivities, because it takesadvantages of the large gain of the EDFA (typically > 30dB). The disadvantageof such a setup is that it is much more expensive, and complicated, than theintegrated SOA.(2) We saw that the SOA is far from total population inversion. If the SOAcould work at total population inversion we would have a much higher modalgain, and could therefore make the the SOA much shorter and still have thesame amplification. The advantage is that a short SOA with high gain mighthave less ASE then a long SOA with low gain (when they both are operatedclose to threshold, and have the same AR coating).(3) To insert a small bandwidth optical filter between the SOA, and the PD,that only transmits wavelengths close to 1550nm. This would reduce the noise,because only ASE from from 1550nm would be detected. The disadvantagewith such a filter is that the reflection between the SOA, and PD (r2), willbe close to one, and the threshold amplification therefore will drop to aboutGth = (r1)−0.5. So such a filter might give a better sensitivity, but a smalleramplification.

Chapter 4

Conclusion

We have in this thesis characterized and optimized two different types of PDsfor use in an optical fiber communication system. The first type was a PINWGPD with a bulk absorbing layer of InGaAs, it was designed by GiGA-Inteland a total of 22 different designs were made (eleven different heterostructuresall with two different ridges).The second PD was a PIN WGPD with a SOA that was integrated along onecontinues waveguide, with an active layer of InGaAsP QWs. Three differentheterostructures was characterized, each with a number of different lengths ofthe SOA, for the optimization part.

The optimization part for bulk PD was to optimize its responsivity from dif-ferent optical fibers. About ten different optical fibers, from GiGA and COM,were used for this optimization, where three of them were shown in figure 2.13.From measurements of the farfield of the optical fibers, and numerical calcula-tions of the transverse mode profile in the waveguide, a maximum mode overlapof about ∼ 95%, was achieved for the optical fiber A4-2, and PIN5. Further-more, a transmission through this optical fiber of 92% was measured. Thesecoefficients seemed to match well with the measured responsivities of just above1A/W (including AR coating).The characterization of the bulk PDs involved measuring the responsivity, band-width, dark current, bias voltage range, breakdown voltage, contact resistance,and sensitivity (with an external electrical amplifier), which all were collectedin the data sheet in table 2.7. This table is for the devices with a 2µm ridge,because we saw that the devices with a 2µm ridge generally had a higher re-sponsivity than the corresponding devices with a 1.5µm ridge. From table 2.7,it was concluded the best device was PIN5 (with a 2µm ridge).We can see from table 2.7 that all the requirements GiGA-Intel made on theirPD (see section 1.2), were actually met by PIN5. Especially the bandwidth,which is about three times larger then the requirement.The bulk PD was, as discussed in the introduction, designed for a receiver unitby GiGA-Intel. The best receiver unit that GiGA-Intel has made uses PIN5,

81

82 CHAPTER 4. CONCLUSION

and measurements performed by GiGA shows that this receiver has a maximumsensitivity of about −19dBm.

The optimization part of the SOA-PDs was to optimize the length of theSOAs, so that the SOA-PDs would give the maximum sensitivity. This wasperformed for the 8QW and 10QW SOA-PDs, and the optimized length of theSOAs were found to be LSOA = 565µm, and LSOA = 475µm respectively.With these optimized lengths of the SOAs, the 8QW and 10QW SOA-PD gavesensitivities of ∼ −20dBm, and ∼ −24dBm respectively.The characterization part was performed on these two devices, and it involvedmeasuring quantities like sensitivity, bandwidth, responsivity, amplification, andgain peak, which all were listed in the data sheet in table 3.5.From table 3.5 we concluded, that the best device was the 8QW SOA-PD (withLSOA = 565µm).The biggest advantage of this SOA-PD is its high sensitivity of about −24dBm(4µW ), which gives it a large dynamical range of optical input powers. ThisSOA-PD actually has about 5dB better sensitivity than the PIN5-based receiverthat GiGA-Intel has designed.

Abbreviations

AC Alternating currentAPD Avalanche photodiodeAR Anti reflectionASE Amplified spontaneous emissionBCB Benzocyclobutene polymerBER Bit error rateCW Continuous waveDC Direct currentEA Electro absorberEAM Electro absorptions modulatorEDFA Erbium doped optical fiber amplifierEHP Electron hole pairFWHM Full width half maximumhh heavy holehh-c heavy hole-conduction band (transition)I-V Current versus voltagelh light holelh-c light hole-conduction band (transition)NRZ Non return to zeroOTDM Optical time division multiplexingPD PhotodiodePRBS pseudo random bit sequenceQW Quantum wellrf Radio frequencyRZ Return to zeroSCH Separate confinement heterostructureSOA Semiconductor optical amplifierSOA-PD Photodiode with integrated semiconductor optical amplifierTE Transverse ElectricTM Transverse magneticUV Ultra violetWDM Wavelength division multiplexingWGPD Waveguide photodiode

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84 ABBREVIATIONS

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waveguide photodiodes - kuhij/public/master thesis.pdfwaveguide photodiodes { with high mode overlap...

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