Corso FS02: Materiali e Dispositivi per optoelettronica, spintronica e nanofotonica

Modulo 1: Crescita epitassiale di materiali semiconduttori (Giorgio Biasiol)

Corso FS02: Materiali e Dispositivi per optoelettronica, spintronica e nanofotonica

Modulo 1: Crescita epitassiale di materiali semiconduttori (Giorgio Biasiol)

Program:

1. General concepts in epitaxy

2. Epitaxial techniques: Molecular Beam Epitaxy (MBE)

3. Epitaxial techniques: Metal Organic Chemical Vapor Deposition (MOCVD)

4. Low-dimensional semiconductor nanostructures

PART I: GENERAL CONCEPTS IN EPITAXY

PART I: GENERAL CONCEPTS IN EPITAXY

Applications of compound semiconductors

Introduction to epitaxial techniques

Basic concepts in epitaxy

Crystallography of zinc-blende lattices

Applications of compound semiconductors

Applications of compound semiconductors

H. S. Bennett, "Technology Roadmaps for Compound Semiconductors”, http://nvl.nist.gov/pub/nistpubs/jres/105/3/j53ben.pdf

International Technology Roadmap for Compound Semiconductors (ITRCS) Bulletin Board, http://www.eeel.nist.gov/812/itrcs.html

Inorganic semiconductor materialsInorganic semiconductor materials

Inorganic semiconductors can be roughly divided into two categories:

Elemental semiconductors, belonging to the group IV of the periodic table (Si, Ge)

Compound semiconductors, synthetic materials not existing in nature, composed of elements from groups III (Al, Ga, In) and V (N, P, As, Sb), or from groups II and VI.

Crystal form of semiconductorsCrystal form of semiconductors

Most semiconductors crystallize in a form identical to diamond.

In compound semiconductors, group-III and group-V atoms alternate within the unit cell (zincblende).

AsGa

Unit cell of GaAs. The side is about 0.56nm

From silicon to compound semiconductorsFrom silicon to compound semiconductors

Traditional devices (electronics, computing): silicon-based.

New advanced devices: based on synthetic compound semiconductors.

New possibilities provided by compound semiconductors

New possibilities provided by compound semiconductors

These materials allow to overcome some limits intrinsic to Si technology:

In many cases, differing from Si, they have direct band gaps light emitters, both electronic and optoelectronics applications;

They generally have a larger electron mobility devices are faster and less power-consuming;

They allow a great flexibility in the fabrication of materials with the desired features, and in the combination of two or more materials in a device (heterostructures).

Semiconductor Heteroepitaxy “Road-map”Semiconductor Heteroepitaxy “Road-map”

Richness and variety of III-V’s high-performance "band-gap engineered" heterostructures and devices with optical and electronic

properties difficult to achieve in other materials.

Some applications of compound semiconductors

Some applications of compound semiconductors

Optoelectronic devices (LED, LASER) for the production and sensing of light, and for telecommunications

High-speed transistors (HEMT), used, e.g., in mobile telephony and satellite systems.

Compound semiconductors market shareCompound semiconductors market share

Material choices for device applications: Optoelectronics

Material choices for device applications: Optoelectronics

Application examples: optical communications, displays, sensors) wavelength ranges within which materials emit and absorb light efficiently:

major fiber-communications ’s: 1550nm - In0.58Ga0.42As0.9P0.1

1310nm - In0.73Ga0.27As0.58P0.42

GaN-related: 0.3-0.6 µm

GaP-related: 0.5-0.7 µm

GaAs-related: 0.8-1.0 µm InP-related: 1.3-1.7 µm

InSb-related : 2-10 µm

Material choices for device applications: Electronics

Material choices for device applications: Electronics

Applications examples: wireless communications based on high-frequency RF or microwave carriers, radars, and magnetic-field sensors)

trade-offs between performance and material robustness during device manufacture and operation. In practice, GaAs-related materials are the most common, but InP-related materials and InSb-related materials also have important applications.

Electron confinementElectron confinement

Many of these devices involve structures based on electron confinement. This effect limits electronic motion to two, one or zero dimensions.

Such structures are composed of layers of a material where electrons are confined,sandwiched in layers acting asan energy barrier. They arecalled quantum wells, wiresor dots, depending ondimensionality.

Section of a LASER structure based on a GaAs QW embedded in AlGaAs barriers.

Typical sizes to observe quantum confinementTypical sizes to observe quantum confinement

Conduction electrons in semiconductors have wavelengths of the orderof 10nm.

To observe quantumconfinement effects, quantumwells (wires, dots) must havesizes around 10nm.

Next-generation devices (e.g.,quantum cascade lasers)may include layers<1nm thick.

Energy profile of a GaAs/AlGaAs quantum well and electronic wave functions of two confined

levels.

Si MOSFET: single bulk material, doping by diffusion or implantation

typical sizes ~ m

InGaAs/AlGaAs p-HEMT: abrupt heterostructures, planar (-)

doping

typical sizes < 10 nm

VCSEL (left: upper and lower DBRs and active region; right: blow-up of active region):

100s of layers of different materials withsub-ML precision

Bulk vs. Quantum-confined devicesBulk vs. Quantum-confined devices

Why Epitaxy?Why Epitaxy?

Sizes < 10nm

structure and composition control with accuracy better than the single atomic monolayer (~0.3nm)

Semiconductor growth techniques that allow this control are called epitaxial techniques.

Growth takes place on planar, single-crystal substrates, atomic layer – by – atomic layer.

Introduction to Epitaxial TechniquesIntroduction to Epitaxial Techniques

Crystallization and film growthCrystallization and film growth

Amorphous: no ordered structures

Polycrystalline: randomly oriented grains, oriented grains, highly oriented grains

Single crystal: bulk growth, epitaxyepitaxy: (upon) + (ordering)

Growth ProcessesGrowth Processes

Bulk techniques (massive semiconductors, wafers): Si, compounds semiconductors.

Epitaxy (higher cost of the growth process): high control of interfaces thin films, quantum confined systems.

Epitaxy : film growth phenomenon where a relation between the structure of the film and the substrate exists single crystalline layer grown on a single crystal surface. Film and substrate of the same material: homoepitaxy. Film and substrate are of different materials: heteroepitaxy

Epitaxial techniques:Epitaxial techniques:

LPE: near-equilibrium technique; fast, inexpensive, poor thickness/interface control (OK only for bulk growth)

MBE, MOCVD: slower, monolayer control on thickness and composition heterostructures, quantum confined systems, band-gap engineering

Interest for both studies of fundamental physics/materials science and for commercial applications of advanced devices

Comparison of MBE and MOCVDComparison of MBE and MOCVD

Feature MBE MOCVD

Source materials Elemental Gas-liquid compounds

Evaporation Thermal, e-beam Vapor pressure, Carrier gas

Flux control Cell temperature Mass flow controllers

Switching Mechanical shutters Valves

Environment UHV H2-N2 (10-1000mbar)

Molecular transport Ballistic (mol. beams)

Diffusive

Surface reactions Physi-chemisorbtion Chemical reactions

Advantages-disadvantages of MBE and MOCVDAdvantages-disadvantages of MBE and MOCVD

Feature MBE MOCVD

Thickness/composition control

+ -

Process simplicity + (ballistic transport, physisorption)

- (hydrodynamics, chemical reactions)

Abrupt junctions <1ML (Shutters) ~3ML (Valves)

In-situ characterization + (RHEED) Uncommon (RAS)

Purity + (UHV) - (C incorporation)

Health, safety + (solid sources) - (H2, Highly toxic gases)

Growth rates (GaAs) ~1m/h Up to ~4m/h

Wafer capacity 7X6”, 4X8” 10X8”, 5X10”

Environment UHV (sub)atmospheric pressure

Graded composition layers - (thermal evaporation) + (mass flow control)

Defect density - (oval defects) +

Downtime - +

Hybrid techniquesHybrid techniques

Gas source MBE, Metal Organic Molecular Beam Epitaxy (MOMBE), Chemical Beam Epitaxy (CBE).

Principle: using group V or/and group III gas sources in a UHV MBE environment.

Developed in order to combine advantages (but also disadvantages!) of MBE and MOCVD.

Basic concepts in epitaxyBasic concepts in epitaxy

J. B. Hudson, “Surface Science – An Introduction”, Butterworth-Heinemann, Boston, 1992

I. V. Markov, “Crystal Growth for Beginners”, World Scientific, Singapore, 1995

A. Pimpinelli and J. Villain, “Physics of Crystal Growth”, Cambridge University Press, 1998

T. F. Gilbert, “Methods of Thin Film Deposition”, http://www.engr.sjsu.edu/cme/cmecourses/MatE270/

SupersaturationSupersaturation

Growth rate is thermodynamically limited by chemical potential difference between fluid phase and fluid-surface equilibrium:

= – eq ≡ supersaturation ≡ driving force for film growth

must be positive for growth to take place ( energy gain by adding atoms to the solid phase)

Real growth rates are limited by other factors (mass transport, reaction kinetics)

)gases (ideal

m)equilibriu(near 1exp

sat

sat

eq

eq

eqeq

P

PPkT

n

nnkT

kTn

kTnn

Molecular fluxMolecular flux

Molecular flux: # of molecules hitting a cross-sectional area in a time unit: J [molecules/(m2sec)]

Maxwell-Boltzmann distribution

0

xxdnvJ

sec)/()()/(

)(10513.3 222 cmmolecules

KTmolegM

torrPJ

Deposition rateDeposition rate

The flux of molecules of the surface leads to deposition, with the rate of film growth depending on J

Example: Silane (SiH4) in VPE:

P ~ 0.001 Torr (1 Torr = 133 Pa)

M: Si: 28 g/ mol and H: 1 g/ mol

film = 2.33 g/mol r ~ 50nm/sec

T ~ 400C = 673K

NA = 6.02X1023

AfilmNM

Jr

Mean free pathMean free path

d = molecular diameter ~ 0.5nm,

R = 8.31 J/(mol * K)

T ~ RT (300K)

1 Torr = 133 Pa

~10-5 Torr ~ 3m (e.g. As4 in MBE)

P

>10 Torr < 30m (MOCVD)

Pam2

Km 2 PNd

RT

A

Flow regimesFlow regimes

The magnitude of is very important in deposition. This determines how the gas molecules interact with each other and the deposition surface. It ultimately influences film deposition properties.

The flow of the gas is characterized by theKnudsen number: Kn= / L, where L is a characteristic dimension of the chamber (given).

Kn > 1: the process is in high vacuum (molecular flow regime).

Kn < 0.01 the process is in fluid flow regime.

In between there is a transition region where neither property is necessarily valid.

Steps for Deposition to OccurSteps for Deposition to Occur

Every film regardless of deposition technique (PVD, CVD, sputtering, thermally grown…) follows the same basic steps to incorporate molecules into the film.

1. Absorption/desorption of gas molecule into the filmPhysisorptionChemisorption

2. Surface diffusion

3. Nucleation of a critical seed for film growth

4. Development of film morphology over time

All processes must overcome characteristic activation energies Ei, with rates ri exp(Ei/kT), depending on atomic details of the process

Arrhenius-type exponential laws

Physi- and ChemisorptionPhysi- and Chemisorption

Physisorption: precursor state, often considered as having no chemical interaction involved (van der Waals).Ea ~ 100meV/atom

Chemisorption: dissociation of precursor molecule, strong chemical bond formed between the adsorbate atom or molecule and the substrate.Ea ~ a few eV/atom (>~ substrate sublimation energy)

chemisorption

chemisorbed statein

tera

ctio

n po

tent

ial

physisorbed precursorstate

distance to the substrate surface

tetramericmolecule

physisorption

Ea Edp

Edc

rc

rp

Chemisorption reaction rate:

R = k ns0 ; k = reaction rate constant = aexp(-Ea/kT), a = characteristic atomic vibration frequency, ns0 = ML surface concentration, = fractional surface coverage

Surface DiffusionSurface Diffusion

Overall surface energy can be minimized if the atom has enough energy & time to diffuse to a low energy add site (i.e., step or kink).

The reaction rate (in molecules/cm2s) for surface diffusion is given as:

kT

EkknR d

ddds exp,

withns = surface concentration of reactant,d = characteristic diffusion frequency ~ 1014s-1

Ed = migration barrier energy

In unit time the adatom makes d attempts to pass the barrier, with a probability of exp (-Ed/kT) of surmounting it on each try.

Ed << Ea surface diffusion is far more likely than desorption.

Diffusion coefficient, diffusion lengthDiffusion coefficient, diffusion length

Diffusion coefficient (mean square displacement of the random walker per unit time):

kT

EaD d

d exp2

with a = lattice constant

Adatom lifetime before desorption:

kT

Eaaa exp1

Diffusion length (characteristic length within which the adatom can move):

kT

EEaD da

a

da 2

exp

Measurable quantity!

NucleationNucleation

Homogeneous nucleation: takes place in the gas phase (only in MOCVD), parasitic reactions

Heterogeneous nucleation: takes place on the film surface

Competing processes in nucleationCompeting processes in nucleation

Gain in bulk free energy Gv with respect to individual atoms

Loss of surface free energy with respect to individual atoms

For a stable film, a critical size nuclei is needed.

With embryos smaller than that, the surface energy is to large and the overall reaction is thermodynamically unfavorable (the overall G is positive).

With larger nuclei, the free energy from converting a volume of atoms to solid overcomes the added surface energy (the overall G is negative).

Energetics of homogeneous nucleationsEnergetics of homogeneous nucleations

vapor

nucleus

r

Bulk contribution:Gv = -vf;

= v-f = kT ln(p/p0) = supersaturation,vf = V / NA = molecular volume

Surface contribution: = surface energy per unit area

Total energy change on cluster formation:G = (4/3) r3 Gv + 4 r2

<0 >0

Critical nucleusCritical nucleus

Critical radius for stable nucleation (only for positive

supersaturation):

d(G)/dr = 0

>0<0

0

G

r

r*

G

*

3

1

43

1

3

16

2

2*2

23*

*

rv

G

vr

f

f(a few atoms) – Thomson-Gibbs equation

universal results (liquid and crystal phases)

unstable equilibrium!

Heterogeneous nucleationHeterogeneous nucleation

vf

sv fs

Young’s equation: sv = fs + vf cos , = wetting angle

1. sv fs + vf (highly reactive substrate surfaces) cos 1; = 0 or undefined wetting

2. sv < fs + vf (poorly reactive substrate surfaces) cos < 1; 0<< no wetting

3. sv ≈ fs + vf (metastable situation)

Typical case 3: lattice-mismatched, strained heteroepitaxy

Strain energy (needed to adjust to substrate lattice) depends on fs and increases linearly with film thickness

If at 0 thickness sv fs + vf , at some critical thicknesssv < fs + vf will be realized 2D wetting layer + 3D islands

vapornucleus

substrate

Energetics of heterogeneous nucleationsEnergetics of heterogeneous nucleations

vapornucleus

substrate

r

vf

Volume of nucleus:

Surface area of nucleus:

cos2cos1

4

1,

3

4 23 ffr

fr 24

00

43

4 23

vfV frGfrG

0

0.2

0.4

0.6

0.8

1

0 /2

f (

)

Energetics of heterogeneous nucleationsEnergetics of heterogeneous nucleations

vapornucleus

substrate

r

vf

fGfv

G

vr

fvf

fvf

*hom2

23

*

*

3

16

2

same as hom. nucl., no dependence on

0

0.2

0.4

0.6

0.8

1

0 /2

f (

)

= 0 G* = 0; 3D droplets thermodynamically unfavored wetting of continuous 2D film

= G* = Ghom*; no influence of substrate

Growth modesGrowth modes

< 1 ML

> 2 ML

1 ML< < 2 ML

layer by layergrowth

layer plus island

growth

islandgrowthFM: Frank-van der

Merwe (2D) modeVW: Volmer-

Weber (3D) mode

SK: Stranski-Krastanov

(2D+3D) mode

FM growth: The interatomic interactions between substrate and film materials are stronger and more attractive than those between the different

atomic species within the film material. VW growth: opposite situation.SK growth occurs for interaction strengths somewhere in the middle.

sv fs + vf sv fs + vf sv < fs + vf

Examples: Frank-van der Merwe growthExamples: Frank-van der Merwe growth

TEM micrograph of the active region of a lattice-matched AlInAs/GaInAs QCL grown

by MBECho et al., J. Cryst. Growth 227-228, 1 (2001)

Layer-by-layer growth (Frank - van der Merwe) is the most used epitaxial process in semiconductor device production. It is most often realized for lattice matched combinations of semiconductor materials with high interfacial bond energies (i.e., AlxGa1-

xAs/GaAs).

Examples: Stranski-Krastanov growthExamples: Stranski-Krastanov growth

AFM image of uncapped InAs/GaAs quantum dots formed just afted the critical thickness on a wetting layer showing monolayer-high 2D islands. The sample is MBE-grown at

TASC.

Stranski-Krastanov - grown islands can be overgrown by the same barrier material as the substrate, to form buried quantum dots, completely surrounded by a larger band gap barrier material.

These dots are optically active due to their damage-free interfaces and are very well suited for studies of quantum phenomena. They are very promising systems for laser production, once high enough uniformity is achieved

Crystallography of zinc-blende latticesCrystallography of zinc-blende lattices

0.56 nm

(011

)

(100)

AsGa

1

2

11

{n11

}A s

idew

all

Technologically important surfacesTechnologically important surfaces

(100)

Alternating equidistant Ga-As planes

2 dangling bonds/atom

Monoatomic steps Similar As-Ga concentrations (depending on reconstruction)

The most important orientation for epitaxy

{111}

Alternating Ga + As planes with alternating 3 + 1 dangling bonds and 1/3 + 2/3 interplane distances

Surfaces can be formed only by breaking the weakly bond planes

Intrinsically polar surfaces on opposite sides of wafer:{111}A (Ga-terminated), {111}B (As-terminated)

(011)

Planes with 50% Ga + 50% As

Nonpolar surfaces

Strong intra- and weak inter-plane bonding

natural cleavage planes

stable surfaces, growth difficult

(01-1) cross section

{n11}

Alternating k X (100) + h X {111} with k/h = (n-1)/2

Real surfaces: surface relaxation, reconstruction, faceting

Examples:

(100): reconstruction linked to As/Ga ratio on surface, depends on supersaturation

{n11}: needed to satisfy electron counting criterion (electrons from dangling bonds must be on states below EF), charge neutrality. E.g., {311}A breaks into {-233} facets

Equilibrium shape of crystalsJ. Y. Tsao, Material Fundamentals of Molecular Beam Epitaxy (Academic Press, Boston, 1993)

Equilibrium shape of crystalsJ. Y. Tsao, Material Fundamentals of Molecular Beam Epitaxy (Academic Press, Boston, 1993)

(n)equilibrium surface

n(n)

0

Wulff theorem: equilibrium crystal shape minimizes total surface free energy:

= (anisotropic) specific surface free energy

n = local surface orientation

Construction: given (n) set of planes n(n) from origin, passing through (n). Equilibrium shape: inner envelope of these planes.

dS n

Low-energy planes are favored and more extended ( closer to origin)

(n) has cusps for lowest-energy orientations (generally high-simmetry, low-Miller index planes) flat facets

As T increases (n) gets less cusped disappearence of facets as T>Tr (roughening T for each facet), until spheric shape for isotropic (n)

a) b) c) d)

Equilibrium shape of GaAsN. Moll et al., Phys. Rev. B 54, 8844 (1996)

Equilibrium shape of GaAsN. Moll et al., Phys. Rev. B 54, 8844 (1996)

{100}, {011}, {111}A and {111}B considered (lowest-energy from experience)

Calculation of absolute surface energies as a function of chemical potentials and related surface reconstructions

As-rich environments (usual for MBE, MOCVD): all four orientation coexist in equilibrium, with small (~10%) differences in surface energy

Applicable to InAs and other III-Vs with similar surface reconstructions