1

Modeling of III-nitride Light-Emitting Diodes: Progress, Problems, and Perspectives

Sergey Yu. Karpov

SPIE Photonics West: GaN materials and devices VI, San Francisco, USA, 22-27 January, 2011

STR Group – Soft-Impact, Ltd (St.Petersburg, Russia)

2 Development of III-nitride LED technology and basic research

1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 20130

2

4

6

8

10

12

14

Rev

enuw

($b

il)

Year

High-brightness LED market

start of production

spontaneous polarization in III-N materials

correct bandgap of InN and InGaN alloys

Auger recombination

in InGaN

effect of InGaN composition fluctuations on IQE

ThinGaNtechnology

TFFC technology

Technological background:

• buffer layer inMOVPE for GaN

• p-doping of GaN

• InGaN growth,including QWs

LED modeling

Milestones of basic research:

we

are

here

EQE > 80% for blue LEDs

3Outline

Features of III-nitride LED modeling

Critical physical mechanisms

− carrier recombination in InGaN QW

− polarization doping

− current crowding in LED dice

− light conversion

Unsolved problems

Future developments

4 Multi-scale problem and simulation approach

Epi level

Chip level

Device level

Design and optimization of LED structures

Design and optimization of

LED chips

Design and optimization of DC & AC LED lams, arrays,

etc.

SimuLAMP

SiLENSe

SpeCLEDRATRO

http://www.str-soft.com/products/SimuLED

ToolsTargets Scales

~1-100 nm

~1-1000 µm

~0.01-1.0 cm

results transfer

results transfer

5 Interrelation of physical phenomena involved in LED operation

carrier transport in heterostructure, recombination and

light emission

heat transfer

current spreading in LED die and light extraction

light scattering and conversion in LED lamp/arrays

elasticity & electro-mechanical coupling dislocations & interaction with carriers electrostatics & spontaneous polarization band structure with strain effects carrier transport & recombination quantum mechanics

current flow in a complex structure ray tracing and scattering by surface

textures

electrodynamics & wave scattering light conversion, including multi-phosphor

interaction spectral ray tracing colorimetry

heat transfer

Multi-disciplinary physicsMechanisms involved in LED operation

Epi level

Chip level

Device level

6Outline

Features of III-nitride LED modeling

Critical physical mechanisms

− carrier recombination in InGaN QW

− polarization doping

− current crowding in LED dice

− light conversion

Unsolved problems

Future developments

7

Carrier recombination in InGaN QW active

region

8 Non-radiative recombination in III-nitride materials: effect of TDs

ωh

non-radiativechannel

TD

TD

TD

105 106 107 108 109 101010-2

10-1

100

101

102

103

104

105

heavy holes electrons

Life

tim

e (n

s)

Threading dislocation density (cm -2)

µµµµn = 350 cm2/ V•s

µµµµp = 10 cm2/ V•s

T = 300 K

100 200 300 4000

5

10

15

20

25

30µµµµ

n = 350 cm2/ V•s

µµµµp = 10 cm2/ V•s

TDD = 5x108 cm -2

heavy holes electrons

Life

tim

e (n

s)

Temperature (K)108 109 1010 1011

0

200

400

600

800

1000

1200

1400

, Ln

, Lp

Diff

usio

n le

ngth

(nm

)

Threading dislocation density (cm -2)

µµµµn = 350 cm2/ V•s

µµµµp = 100 cm2/ V•s

T = 300 K

−+

=

2321

ln4 2

thdddis Vaq

kT

NaπNπkT

qτ

µµ

S. Yu. Karpov and Yu. N. Makarov, Appl. Phys. Lett. 81 (2002) 4721

being non-radiative recombination centers, TDs affect appreciably the life times of electrons and holes :

GaNGaN

GaN

2/1)/( qkTL disD µτ=

9 Auger recombination in III-nitride semiconductors

0.0 0.6 1.2 1.8 2.4 3.0 3.610-33

10-31

10-29

10-27

10-25

10-23

direct bandgap indirect bandgap InGaN: experiment InGaN: theory

CdHgTe

4H-SiCGaP

SiGe

AlGaAsGaAs

InP

InGaAs

GaSb

InSb

Aug

er c

oeffi

cien

t (cm

6 s-1)

Bandgap (eV)

InAs

0 30 60 90 1200

5

10

15

20

25

30

35

Ext

erna

l qua

ntum

effi

cien

cy

Current density (A/cm 2)

materials quality improvementA. E.Chernyakov et al.,

Superlattices & Microstructures 45 (2009) 301

0 30 60 90 1200.0

0.2

0.4

0.6

0.8

Shockley-Read time 1 ns 3 ns 10 ns 100 ns

Inte

rnal

qua

ntum

effi

cien

cy

Current density (A/cm 2)

B = 2x10 -11 cm3/sC = 2x10-31 cm6/s d = 3 nm

ABC-model:

RSA

nCnBAnB

nCnBnAdqj

τ/1

)/(IQE

)(2

32

=++=

++=

experiment:

ab initiocalculations for InGaN:

C. Van de Walle, private communication

different trends in the Auger coefficient variation

with the bandgap for direct- and indirect-

bandgap materials; InGaN obeys the latter trend

300 K

300 K

10 Localized and delocalized states in InGaN quantum wells

InGaN InGaN QWQW

TD TD TD

-600 -400 -200 0 200 400 6000.0

0.2

0.4

0.6

0.8

1.0

Parameter Un :

5 meV 20 meV 50 meV 100 meV 200 meV

Nor

mal

ized

den

sity

of s

tate

s

Energy (meV)

106 107 108 109 10100.0

0.2

0.4

0.6

0.8

1.0

InGaNU

n= 30 meV

Up= 15 meV

Inte

rnal

qua

ntum

effi

cien

cyTDD (cm -2)

GaNU

n=U

p= 0

T = 300 K

CB

VB

-400 -200 0 200 4000.0

0.2

0.4

0.6

0.8

1.0 T = 300 K

U (meV) : 5 15 25 50

Fra

ctio

n of

del

ocal

ized

car

riers

Fn- E

0 (meV)

both QW thickness and composition fluctuations may produce DOS tails in the bandgap

n , p = 1017 cm -3

localized carriers: do not take part in recombination

at TDs

delocalized carriers:

participate in recombination

at TDs

localized states due to composition/QW thickness fluctuation in InGaN increase the material IQE

11 IQE of InGaN SQW LED structure vscurrent density and temperature

10-5 10-4 10-3 10-2 10-1 100 101 102 103 10410-4

10-3

10-2

10-1

100

, 100 K , 200 K , 250 K , 298 K , 353 K , 413 K , 453 K

Inte

rnal

qua

ntum

effi

cien

cy

Current density (A/cm 2)

non-thermal efficiency

droop caused by Auger

recombination practically

independent of temperature

IQE increase at low

temperatures and current densities due to carrier localization

Experiment: A. Laubsch et al., Phys, Stat. Solidi (c) 6 (2009) S9 13 (symbols)

Theory: S. Yu. Karpov, Phys. Stat. Solidi RRL 4 (2010) 320 ( lines)

ABC model predicts well the IQE variation

with the current density and

temperature in the range of ~200-450 K

)(

1

TconstC

TB

=∝ −

12

Distributed polarization doping in LED structures

13 Distributed polarization doping (DPD) in graded-composition materials

graded-

composition

AlGaN

GaN

polarization charge (PC)

D. Jena et al., Phys.Stat.Solidi (c) 0 (2003) 2339

zdPd

ρ z−=

Distributed polarization doping has been proposed, for the first time,

for HEMTs

0.3

0.5

0.1

XAlN

0.3

0.5

0.1

XAlN

0.3

0.5

0.1

XAlN

[0001]

[0001]

constant composition

descending composition

ascending composition

positive PC

negative PC

zero PCρ

z

[0001]

14 Using DPD for performance improvement in deep-UV LEDs

380 400 420 440 460 480-7

-6

-5

-4

-3

-2

-1

0

1

2

holeselectrons

Ene

rgy

(eV

)

Distance (nm)

1015

1016

1017

1018

1019

1020

1021

Car

rier

conc

entr

atio

n (c

m-3)

380 400 420 440 460 480

-7

-6

-5

-4

-3

-2

-1

0

1

2

holes

Ene

rgy

(eV

)

Distance (nm)

electrons

1015

1016

1017

1018

1019

1020

1021

Car

rier

conc

entr

atio

n (c

m-3)

constant composition

graded composition

λ = 280 nm

λ = 280 nm

85 A/cm 2

85 A/cm 2

LED with parabolic composition profiles in EBL and HBL produces

high electron and hole concentrations throughout the layers

Ga-polar structure withconstant-composition layers suffers from vanishing hole concentration in the contact

layerp-contact

layer

p-contact layer

15

Current crowding in LED dice

16 Current localization in LED die with ITO spreading layer

(a) (b) (c)

J , A/cm 2 J , A/cm 2 J , A/cm 2

nnspns dPLR /ρ≈

dITO= 20 nm d ITO= 50 nm d ITO= 100 nm

the principal origin of current crowding is nonlinear resistance of the p-n junction, depending on temperature

a more pronounced current crowding results in a lower LED series resistance:

Ρn and dn are the specific resistance and thickness of the n-contact layer, Lsp is the current spreading length and Pn is the outer perimeter of the n-electrode

n-pad

p-pad

ITO layer

sapphire substrate

I = 20 mAp-electrode

increasing series resistance

17 Current crowding effect on light extraction efficiency in a vertical LED die

n-pad

n-electrodesn-contact layer

textured surface

active region

p-contact layer

n-contact layer

highly reflective p-electrode

Γ-shaped

J (A/cm 2)

Extraction probability

(%)

0 200 400 600 8000.0

0.2

0.4

0.6

0.8

1.0

1.2

700 mA

130 mA

Nor

mal

ized

cur

rent

den

sity

Distance ( µµµµm)

10 mA

n-electroden-electrode

A

B

A-B cross-section

probability of light extraction falls down under and next to the n-electrodes

die micrograph by MuAnalysis, Inc., 2008

current density non-uniformity depends on the total operating current

4%

87%

57%

18 Reduction of the crowding effect on LEE via LED chip design

n-electrodes in etched holes

p-GaN contact layer

textured back

surface

n-GaN contact

layer

highly reflective p-electrode

0 300 600 90040

50

60

70

80

90

vertical improved

vertical

Ligh

t ext

ract

ion

effic

ienc

y (%

)

Current (mA)

planar

because of smaller total n-electrode

perimeter, the current crowding

is more pronounced

improvements in vertical die design

TFFC planar die

comparison of the die designs

M. V. Bogdanovet al.,

Phys.Stat.Solidi(c) 7 (2010) 2124

19

Light conversion in LED lamps

20 Modeling of light conversion in white-LED lamps

200 300 400 500 6000.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Qua

ntum

effi

cien

cy

Temperature ( oC)

YAG:Ce3+

LED die

conversion medium

LED die

conversion medium

420 440 460 480 500 5200.0

0.2

0.4

0.6

0.8

1.0

1.2

250 K 460 K

Nor

mal

ized

em

issi

on in

tens

ity

Wavelength (nm)

many phosphors and/or conversionmedia →→→→ spectral ray-tracingtemperature-dependent phosphorQE and LED characteristics →→→→coupled optical/thermal analysis

Mie theory is now widely usedfor modeling light scattering andabsorption by phosphor particles

1.5 2.0 2.5 3.0 3.5 4.00

200

400

600

800

1000 250 K 298 K 340 K 380 K 420 K 460 K

Cur

rent

(m

A)

Forward bias (V)

temperature-dependent LED characteristics

(K)

21 Effect of white LED operation conditions on the white light quality

heatsink

domeinternal

lens

LED die

phosphor

300 K

450 K

0 200 400 600 800 1000

60

62

64

66

68

70

72

74

250 300 350 400 450 500

@ Ia = 700 mA

Col

or r

ende

ring

inde

x

Current (mA)

@ Ta = 300 K

Ambient temperature (K)

conversion medium is primarily heated

by LED

current dimming moves the chromatic coordinates away

from the black-body radiation locus

chromatic coordinates variation with temperature

color angular non-uniformity in the far-field zone

O. V. Khokhlev et al., Proc. 3 rd Int. Conf. on White LEDs & Solid State Lighting (2010) 29

30 60 900 θ30 60 900 θ

30 60 900 θ30 60 900 θ

22Outline

Features of III-nitride LED modeling

Critical physical mechanisms

− carrier recombination in InGaN QW

− polarization doping

− current crowding in LED dice

− light conversion

Unsolved problems

Future developments

23 Overestimated operation voltage in III-nitride LEDs

250 300 350 400 450

-6

-5

-4

-3

-2

-1

0

1λλλλ = 515 nm T = 300 K

Fp

Ene

rgy

(eV

)

Distance (nm)

Fn

250 300 350 400 450

-6

-5

-4

-3

-2

-1

0

1

λλλλ = 515 nm T = 300 K

Fp

Fn

Ene

rgy

(eV

)

Distance (nm)0 1 2 3 4 5 6 7

0

15

30

45

60

75

90

(c)

Cur

rent

(m

A)

Voltage (V)

A = 10-3 cm2

RS= 3 ΩΩΩΩ

nom

inal

with

incr

ease

d m

obili

ty

35 A/cm 2 35 A/cm 2300 K

with nominal mobilities in the structure

with artificially increased mobilities

high ballistic electron leakage is expected

no electron leakage at flat band diagram

direct or defect-assisted tunneling in MQW barriersdislocation-mediated conductivityballistic transport in the barriers & incomplete carrier capture in the QWsreduction of the barrier heights due to composition fluctuations in InGaN

Possible channels of additional conductivity:

24 Using of quantum potential for solution of transport equations

380 400 420 440 460 480-5

-4

-3

-2

-1

0

1

standard

Ene

rgy

(eV

)

Distance (nm)

electron quantum levels

380 400 420 440 460 480

-5

-4

-3

-2

-1

0

1 standard

holes

Ene

rgy

(eV

)

Distance (nm)

electrons

1014

1015

1016

1017

1018

1019

1020

1021

Con

cent

ratio

n (c

m-3)

380 400 420 440 460 480

-5

-4

-3

-2

-1

0

1 standard EP

holes

Ene

rgy

(eV

)

Distance (nm)

electrons

1014

1015

1016

1017

1018

1019

1020

1021

Con

cent

ratio

n (c

m-3)

actual band diagram effective band diagram

2.0 2.5 3.0 3.5 4.0 4.50

50

100

150

200

250

drift-diffusion with quantum

effects

Cur

rent

den

sity

(A

/cm

2 )

Bias (V)

use of quantum potential improves operation

voltage predictability and modifies properly the

electron and hole density distributions

quantum potential accounts approximately tunneling and confinement effects

380 400 420 440 460 480-5

-4

-3

-2

-1

0

1

electron quantum levels

standard - EP

Ene

rgy

(eV

)

Distance (nm)

drift-diffusion model

drift-diffusion model

with quantum effects

with quantum effects

λ = 450 nmT = 300 K

25 Prediction of emission spectra and their blue shift with current

-600 -400 -200 0 200 400 600

5x1012 cm -2

1x1013 cm -2

3x1013 cm -2

3x1011 cm -2

Em

issi

on in

tens

ity (

a.u.

)

Photon energy (meV)

Un+ U

p= 50 meV

3x109 cm -2

-600 -400 -200 0 200 400

77 K

450 K

Em

issi

on in

tens

ity (

a.u.

)

Photon energy (meV)

Un+ U

p= 50 meV

5x1012 cm -2

300 K

109 1010 1011 1012 1013

-300

-200

-100

0

100

T = 300K U

n+ U

p :

10 meV 20 meV 50 meV

Em

issi

on e

nerg

y sh

ift (

meV

)

Sheet concentration (cm -3)

with account of localized states formed by composition/thickness fluctuations in InGaN QW

2.5 2.6 2.7 2.8 2.9 3.0

uniformbroadening

Inte

nsity

(a.

u.)

Photon energy (eV)

300 KΓΓΓΓ = 20 meV

carriertemperature theoretical

spectra shapes do not fit the experimental

ones

low-energy spectrum wing is determined by DOS tail due to fluctuations of thickness or composition of InGaN QW

the model of localized

states predicts enhanced emission

spectrum blue shift caused by filling the DOS tails

Model: M. A. Jacobson et al., Semiconductors 39 (2005) 1410

26Outline

Features of III-nitride LED modeling

Critical physical mechanisms

− carrier recombination in InGaN QW

− polarization doping

− current crowding in LED dice

− light conversion

Unsolved problems

Future developments

27 Technological factor: effect of In surface segregation on InGaN QW profile

Experiment:C. Kisielowski et al., Jpn. J. Appl. Phys.

36 (1997) 6932

0 2 4 6 8 100.0

0.2

0.4

0.6

0.8

Nominal Experiment Theory

GaN/InGaN/AlGaN SQW

InN

mol

e fr

actio

n

Well thickness (nm)

growth of AlInGaN

Theory:R. A. Talalaev et al., Phys. Stat. Solidi (c)

0 (2002) 311

Indium surface segregation results in:

delayed indium incorporation at thebottom QW interface

indium tail in the AlGaN or GaN cap layer

Now it has become possible to make coupled simulation of LED structure growth by MOVPE and operation of the

grown device

Other transient effects:

indium deposition priorInGaN QW growth

growth interruption temperature ramping, etc.

28 Technological factor: redistribution of impurities during LED structure growth

@ 1000°C @ optimal T

(optimal T)

back diffusion of Mg removes the acceptors from the active region toward the AlGaN EBL and p-contact layer

K. Köhler et al., J. Appl. Phys. 97 (2005) 104914 ;

Phys. Stat. Solidi (a) 203 (2006) 1802

optimum doping for high LED efficiency

29Conclusions

to account for and utilize in practice unique properties of III-nitride materials, a number of critical mechanisms should be considered: multi-channel recombination in LED active region, distributed polarization doping, 3D coupled current spreading & heat transfer in LED dice, multi-phosphor light conversion, etc.

a number of issues, like enhanced electrical conductivity in LED structures, impact of carrier localization on the emission spectra, cavity effects, microscopic nature of Auger recombination, etc. should be studied experimentally and theoretically in future to generate respective physical models

strong influence of technological factors on III-nitride LED properties requires a coupled simulations of the heterostructure epitaxial growth and device operation

30Acknowledgment

I am grateful to my colleaguesK. A. BulashevichO. V. KhokhlevI. Yu. EvstratovV. F. MymrinM. S. Ramm

M. V. BogdanovA. I. Zhmakin

contributed much to development, numerical implementation, and validation of models for

III-nitride LED simulation