Download pdf - Novel Measurements and Models for Understanding the ...Novel Measurements and Models for Understanding the Efficacy Versus Luminance Trade-Off Daniel Feezell, Arman Rashidi, Morteza

Novel Measurements and Models for Understanding the Efficacy Versus Luminance Trade-Off

Daniel Feezell , Arman Rashidi, Morteza MonavarianCenter for High Technology Materials

Department of Electrical and Computer EngineeringUniversity of New Mexico, Albuquerque, NM – 87131

[email protected]

mailto:[email protected]

• Potential for high luminance• Stimulated emission mitigates droop• Linewidth smaller than LED, larger than laser• Spatially but not temporally coherent• Higher modulation rate than LEDs

2/11/2019 Daniel Feezell 2

Superluminescent Diodes (Poster No. 27)

0 5 10 15 20 25 30 350

5

10

15

20

Current Density (kA/cm2)

Volta

ge (V

)

SE

SE+ASE

0.5

1.0

1.5

2.0

Out

put L

ight

(mW

)

400 405 410 415 420 425 430 435 440Nor

mal

ized

Inte

nsity

(a.u

.)

Wavelength (nm)

SE SE+ASE

Laser

400 405 410 415 420 425 430 435 440103

104

105

106

Inte

nsity

(a.u

.)

Wavelength (nm)

12.0 kA/cm2

14.0 kA/cm2

16.0 kA/cm2

18.5 kA/cm2

21.0 kA/cm2

23.5 kA/cm2

26.0 kA/cm2

No cavity feedback

0 2000 4000 6000 8000 100000

2

4

6

8

10

Rel

ativ

e EQ

E (a

.u.)


• High luminance trades off with efficacy

• Fundamental challenges must be understood and solved

• Measure and analyze carrier dynamics under electrical injection and over wide range of injection levels

• Small-signal RF methods offer new insight!


Challenges for High-Luminance LEDsEfficiency droop

100 1000 10000

0.5

0.6

0.7

0.8

0.9

1.0

Differential Total


Inje

ctio

n Ef

ficie

ncy

(a)

1

10

Rela

tive

EQE

(a.u

.)

Injection efficiency

Green gap

10 100 1000 100000

20

40

60

80

100 25 °C 50 °C 75 °C 100 °C

Rel

ativ

e EQ

E

Current Density (A/cm2)

Thermal droop

M. Auf der Maur, et al., Phys. Rev. Lett. 116 (2016)


RF Measurement System

𝑆𝑆11= 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝐼𝐼𝐼𝐼𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅𝐼𝐼𝑅𝑅

𝑆𝑆21= 𝑇𝑇𝑇𝑇𝑇𝑇𝐼𝐼𝑇𝑇𝑇𝑇𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝐼𝐼𝐼𝐼𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅𝐼𝐼𝑅𝑅

Impedance = 𝑍𝑍 = 𝑍𝑍01+𝑆𝑆111−𝑆𝑆11

Frequency Response = 𝑆𝑆21


Modeling LED Carrier Dynamics

𝑨𝑨𝒊𝒊𝒆𝒆−𝒊𝒊𝝎𝝎𝒕𝒕

𝑨𝑨𝒓𝒓(𝝎𝝎)𝒆𝒆−𝒊𝒊(𝝎𝝎𝒕𝒕+𝝋𝝋𝒓𝒓)

𝑨𝑨𝒕𝒕(𝝎𝝎)𝒆𝒆−𝒊𝒊(𝝎𝝎𝒕𝒕+𝝋𝝋𝒕𝒕)

Considered carrier processes:1. Carrier injection 2. Carrier diffusion and capture3. Recombination in QW4. Carrier leakage 5. Recombination in cladding

and overshoot

𝜏𝜏𝑇𝑇𝑅𝑅𝑅𝑅 = 𝑅𝑅𝑤𝑤𝐶𝐶𝑤𝑤

𝜏𝜏0 = 𝑅𝑅𝑅𝑅𝐶𝐶𝑅𝑅𝑡𝑡𝑅𝑅𝜏𝜏𝑅𝑅𝑇𝑇𝑅𝑅 = 𝑅𝑅𝑅𝑅𝐶𝐶𝑤𝑤

𝜏𝜏𝑅𝑅𝑅𝑅 =𝑅𝑅𝑇𝑇

𝑅𝑅𝑇𝑇 + 𝑅𝑅𝑅𝑅𝜏𝜏0

A. Rashidi, et al., J. of Appl. Phys. 122, 3 (2017)

𝑗𝑗𝑗𝑗𝑛𝑛𝑤𝑤 = − 1𝜏𝜏∆𝑟𝑟𝑟𝑟𝑟𝑟

+ 1𝜏𝜏∆𝑟𝑟𝑒𝑒𝑟𝑟

𝑛𝑛𝑤𝑤 + 𝐼𝐼𝑟𝑟𝜏𝜏∆𝑟𝑟

𝑗𝑗𝑗𝑗𝑛𝑛𝑅𝑅 = 𝐼𝐼𝑞𝑞− 𝑗𝑗𝑗𝑗𝑣𝑣𝑅𝑅

𝑅𝑅𝑒𝑒𝑟𝑟𝑞𝑞

+ 𝐼𝐼𝑤𝑤𝜏𝜏∆𝑟𝑟𝑒𝑒𝑟𝑟

− 𝐼𝐼𝑟𝑟𝜏𝜏∆𝑟𝑟

− 𝐼𝐼𝑟𝑟𝜏𝜏∆𝑟𝑟𝑟𝑟𝑟𝑟,𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐

Small-signal rate equations Small-signal equivalent circuit

Associated lifetimesA. Rashidi et al., Appl. Phys. Lett., 112, 031101 (2018)


Fitting Equivalent Circuit ModelSimultaneous fitting of full frequency response and impedance yields carrier lifetime and RC time constant

Fit to frequency response

𝑣𝑣𝑡𝑡𝑜𝑜𝑅𝑅𝑣𝑣𝐼𝐼𝐼𝐼

=𝑅𝑅𝑤𝑤

𝑅𝑅𝑇𝑇 1 + 𝑗𝑗𝑗𝑗𝜏𝜏𝑇𝑇𝑅𝑅𝑅𝑅 1 + 𝑗𝑗𝑗𝑗𝜏𝜏0 + 𝑅𝑅𝑇𝑇 𝑗𝑗𝑗𝑗𝑅𝑅𝑤𝑤𝐶𝐶𝑅𝑅𝑡𝑡𝑅𝑅 + 𝑅𝑅𝑅𝑅 1 + 𝑗𝑗𝑗𝑗𝜏𝜏𝑇𝑇𝑅𝑅𝑅𝑅 + 𝑅𝑅𝑤𝑤

𝑍𝑍𝐼𝐼𝐼𝐼 = 𝑅𝑅𝑇𝑇 +𝑅𝑅𝑅𝑅(1 + 𝑗𝑗𝑗𝑗𝑅𝑅𝑤𝑤𝐶𝐶𝑤𝑤) + 𝑅𝑅𝑤𝑤

1 + 𝑗𝑗𝑗𝑗𝑅𝑅𝑤𝑤𝐶𝐶𝑤𝑤)(1 + 𝑗𝑗𝑗𝑗𝑅𝑅𝑅𝑅𝐶𝐶𝑅𝑅𝑡𝑡𝑅𝑅) + 𝑗𝑗𝑗𝑗𝐶𝐶𝑅𝑅𝑡𝑡𝑅𝑅𝑅𝑅𝑤𝑤

Fit to input impedance

Input impedance:

Frequency response:

Extract carrier and RC lifetimes

3 dB attenuation

𝝉𝝉𝒓𝒓𝒆𝒆𝒓𝒓 = 𝑹𝑹𝒘𝒘𝑪𝑪𝒘𝒘

𝝉𝝉𝑹𝑹𝑪𝑪 =𝑹𝑹𝒔𝒔

𝑹𝑹𝒔𝒔 + 𝑹𝑹𝒓𝒓𝝉𝝉𝟎𝟎

A. Rashidi, et al., J. of Appl. Phys. 122, 3 (2017)

• Semipolar (2021) LEDs on free-standing GaN• SQW (1 x 12 nm) and MQW (3 x 4 nm)

• Peak wavelength 435 nm to 440 nm

• MicroLEDs with 60 µm diameter mesa• IQE previously characterized


Example 1: Semipolar (𝟐𝟐𝟎𝟎𝟐𝟐𝟏𝟏) LED Carrier Dynamics

107 108 109-18

-15

-12

-9

-6

-3

0

5.0 kA/cm2

1.0 kA/cm2

MQW

SQW

MQW

MQW

SQW

Nor

mal

ized

Pow

er (d

B)

Frequency (Hz)

0.1 A/cm2

SQW

(a)0.1 1 10

0.1

1

(b)

SQW

Ban

dwid

th (G

Hz)


MQW

M. Monavarian, et al., Appl. Phys. Lett. 112, 191102 (2018)

• Recombination, RC, and net escape lifetimes extracted• MQW has smaller recombination lifetime• RC effects apparent around 3 kA/cm2

• Coulomb capture process prevents further leakage of carriers from the QW


Example 1: Semipolar (𝟐𝟐𝟎𝟎𝟐𝟐𝟏𝟏) LED Carrier Dynamics

10 100 100010-11

10-10

10-9

10-8

10-11

10-10

10-9

10-8

MQW

RC

Life

time

(s)

Rec

ombi

natio

n Li

fetim

e (s

)


SQW

SQW

MQW

(a)

10 100 100010-11

10-10

10-9

10-8

(b)

SQW

Net

Esc

ape

Tim

e (s

)


τleak

τcou

MQW

1𝜏𝜏𝑅𝑅𝑇𝑇𝑅𝑅

=1

𝜏𝜏𝑅𝑅𝑅𝑅𝑇𝑇𝑙𝑙−

1𝜏𝜏𝑅𝑅𝑡𝑡𝑜𝑜



Example 2: Injection Efficiency𝑑𝑑𝑑𝑑𝑑𝑑

(𝑑𝑑𝑁𝑁𝑤𝑤) =𝑑𝑑𝑁𝑁𝑅𝑅𝜏𝜏𝛥𝛥𝑅𝑅

−𝑑𝑑𝑁𝑁𝑤𝑤𝜏𝜏𝛥𝛥𝑇𝑇𝑅𝑅𝑅𝑅

−𝑑𝑑𝑁𝑁𝑤𝑤𝜏𝜏𝛥𝛥𝑅𝑅𝑇𝑇𝑅𝑅

𝑑𝑑𝑑𝑑𝑑𝑑 (𝑑𝑑𝑁𝑁𝑅𝑅) =

𝑑𝑑𝑑𝑑𝑞𝑞 −

C𝑇𝑇𝑅𝑅𝑞𝑞

𝑑𝑑𝑑𝑑𝑑𝑑 (𝑑𝑑𝑉𝑉𝑅𝑅)−

𝑑𝑑𝑁𝑁𝑅𝑅𝜏𝜏𝛥𝛥𝑅𝑅

+𝑑𝑑𝑁𝑁𝑤𝑤𝜏𝜏𝛥𝛥𝑅𝑅𝑇𝑇𝑅𝑅

−𝑑𝑑𝑁𝑁𝑅𝑅

𝜏𝜏𝛥𝛥𝑇𝑇𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅

• Rate equations under steady state yield injection efficiency

• Extracted lifetimes are used to calculate the injection efficiency

• Injection efficiency increases with current density

• Injection efficiency trend is not consistent with efficiency droop

100 1000 10000

0.5

0.6

0.7

0.8

0.9

1.0

Differential Total


Inje

ctio

n Ef

ficie

ncy

(a)

1

10

Rel

ativ

e EQ

E (a

.u.) Differential rate equations

𝜂𝜂Δ𝐼𝐼𝐼𝐼𝑖𝑖 =𝑑𝑑𝑑𝑑𝑤𝑤𝑑𝑑𝑑𝑑 =

𝑞𝑞 𝑑𝑑𝑁𝑁𝑤𝑤𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅𝑑𝑑𝑑𝑑 =

1

1 + 𝜏𝜏∆𝑅𝑅𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅

(1 + 𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅𝜏𝜏∆𝑅𝑅𝑇𝑇𝑅𝑅

)

Differential injection efficiency

𝜂𝜂𝐼𝐼𝐼𝐼𝑖𝑖 =𝑑𝑑𝑤𝑤𝑑𝑑 =

∫𝜂𝜂Δ𝐼𝐼𝐼𝐼𝑖𝑖𝑑𝑑𝑑𝑑𝑑𝑑

Total injection efficiency

A. Rashidi et al., Appl. Phys. Lett., 112, 031101 (2018)


Example 2: Injection Efficiency

• Carrier number and recombination current densities extracted

• At low current density, high carrier number in the QW leads to carrier leakage and injection efficiency < 1

• At high current density, recombination current density in the QW dominates

100 1000 10000104

105

106

107

108

(a) QW Cladding

Car

rier N

umbe

r (co

unt)

Current Density (A/cm2)100 1000 10000

101

102

103

104 QW Cladding

Rec

ombi

natio

n C

urre

nt D

ensi

ty (A

/cm

2 )Current Density (A/cm2)

(b)

𝑁𝑁𝑤𝑤 =1𝑞𝑞𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅𝜂𝜂Δ𝐼𝐼𝐼𝐼𝑖𝑖𝑑𝑑𝑑𝑑

𝑁𝑁𝑅𝑅 =1𝑞𝑞 𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅(1 − 𝜂𝜂Δ𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝑑𝑑

Carrier population

𝐽𝐽𝑤𝑤 = 𝑑𝑑𝐽𝐽𝑤𝑤 =𝑞𝑞𝑑𝑑𝑁𝑁𝑤𝑤𝐴𝐴𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅

=𝜂𝜂Δ𝐼𝐼𝐼𝐼𝑖𝑖𝑑𝑑𝐽𝐽

𝐽𝐽𝑅𝑅 = 𝑑𝑑𝐽𝐽𝑅𝑅 =𝑞𝑞𝑑𝑑𝑁𝑁𝑅𝑅

𝐴𝐴𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅= (1 − 𝜂𝜂Δ𝐼𝐼𝐼𝐼𝑖𝑖)𝑑𝑑𝐽𝐽

Recombination current density

A. Rashidi et al., Appl. Phys. Lett., 112, 031101 (2018)

• Pulsed RF measurement eliminates LED self-heating

• Pulse width 1 µs, duty cycle 10%

• Small AC signal added to pulses

• Central frequency harmonic picked by narrowband filter

• Temperature-controlled stage ensures controllable active region temperature

• Pulsed EQE and bandwidth measured


Example 3: Temperature Dependent Carrier Dynamics

A. Rashidi et al., submitted




• Temperature dependence of:(a) Differential carrier lifetime

(b) Injection efficiency

(c) Carrier density

(d) True radiative efficiency

• Efficiency more sensitive than lifetime to temperature

• Peak radiative efficiency occurs at lower current than peak EQE𝑛𝑛 =

1𝑞𝑞𝑑𝑑𝜂𝜂∆𝐼𝐼𝐼𝐼𝑖𝑖𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅𝑑𝑑𝐽𝐽

𝜂𝜂𝑇𝑇 =𝑅𝑅𝑇𝑇

𝑅𝑅𝑇𝑇 + 𝑅𝑅𝐼𝐼𝑇𝑇

𝜂𝜂𝐸𝐸𝐸𝐸𝐸𝐸 = 𝜂𝜂𝑅𝑅𝑒𝑒𝑅𝑅𝜂𝜂𝐼𝐼𝐼𝐼𝑖𝑖𝜂𝜂𝑇𝑇




• Temperature dependence of:(a) Radiative lifetime(b) Non-radiative lifetime(c) Radiative rate(d) Non-radiative rate

• Efficiency droop from increase of non-radiative rate and saturation of radiative rate with current

• Thermal droop from increase of SRH rate and reduction of radiative rate with temperature

𝜏𝜏∆𝐼𝐼𝑇𝑇−1 = 𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅−1 (1− 𝜂𝜂𝑇𝑇)− 𝑅𝑅𝑑𝑑𝜂𝜂𝑇𝑇𝑑𝑑𝑛𝑛𝜏𝜏∆𝑇𝑇−1 = 𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅−1 𝜂𝜂𝑇𝑇 + 𝑅𝑅

𝑑𝑑𝜂𝜂𝑇𝑇𝑑𝑑𝑛𝑛

𝑅𝑅𝐼𝐼𝑇𝑇 = 𝜏𝜏∆𝐼𝐼𝑇𝑇−1 𝑑𝑑𝑛𝑛𝑅𝑅𝑇𝑇 = 𝜏𝜏∆𝑇𝑇−1 𝑑𝑑𝑛𝑛


Small-Signal RF Methods Summary

Differential rate equations

Equivalent circuit

Carrier lifetimes Derive injection efficiency

Injection efficiency

Small-signal

Steady-state

Measurement

Droop & green gap

Device properties

Device design optimization

Active region design optimization


Thank You!

• Small area reduces RC parasitics• 50 – 100 µm diameter• Can be driven at high current density• Arrays to increase light intensity


Micro-Scale GaN-Based LEDs

https://www.lifi.eng.ed.ac.uk/lifi-news/2015-11-28-1320/how-fast-can-lifi-be


High-Speed Micro-LED Fabrication

Fitting

parameter

Lower confidence

boundary

Estimated

parameter

Higher confidence

boundary

𝑹𝑹𝒓𝒓 (𝛀𝛀) 15.730 15.951 16.172

𝑹𝑹𝒘𝒘(𝛀𝛀) 9.088 9.464 9.840

𝝉𝝉𝒓𝒓𝒆𝒆𝒓𝒓 (𝒔𝒔) 7.425×10-10 7.611×10-10 7.797×10-10

𝝉𝝉∆𝟎𝟎 (𝒔𝒔) 2.187×10-10 2.249×10-10 2.310×10-10


Fitting and Confidence Intervals


RF method to probe carrier processes

𝑨𝑨𝒊𝒊𝒆𝒆−𝒊𝒊𝝎𝝎𝒕𝒕

𝑨𝑨𝒓𝒓(𝝎𝝎)𝒆𝒆−𝒊𝒊(𝝎𝝎𝒕𝒕+𝝋𝝋𝒓𝒓)

𝑨𝑨𝒕𝒕(𝝎𝝎)𝒆𝒆−𝒊𝒊(𝝎𝝎𝒕𝒕+𝝋𝝋𝒕𝒕)

Derive electrical circuit representing carrier dynamics

Considered carrier processes:1. Carrier injection 2. Carrier diffusion and capture3. Recombination in QW4. Carrier leakage 5. Recombination in cladding

and overshoot

Small-signal RF wave is added to electrical DC bias of an LED as a probe

Time-consuming carrier processes in the LED cause phase delay and

amplitude change to the reflected and output RF signals


Rate equation analysis and circuit derivation

𝑅𝑅𝑁𝑁𝑤𝑤𝑅𝑅𝑅𝑅

= −( 1𝜏𝜏𝑟𝑟𝑟𝑟𝑟𝑟

+ 1𝜏𝜏𝑟𝑟𝑒𝑒𝑟𝑟

)𝑁𝑁𝑤𝑤 + 𝑁𝑁𝑟𝑟𝜏𝜏𝑟𝑟

𝜏𝜏𝑅𝑅 = 𝜏𝜏𝑅𝑅𝑇𝑇𝑐𝑐 + 𝜏𝜏𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅

𝑅𝑅𝑁𝑁𝑟𝑟𝑅𝑅𝑅𝑅

= 𝐼𝐼𝑞𝑞− 𝑅𝑅𝑒𝑒𝑟𝑟

𝑞𝑞𝑅𝑅𝑉𝑉𝑟𝑟𝑅𝑅𝑅𝑅

+ 𝑁𝑁𝑤𝑤𝜏𝜏𝑟𝑟𝑒𝑒𝑟𝑟

− 𝑁𝑁𝑟𝑟𝜏𝜏𝑟𝑟− 𝑁𝑁𝑟𝑟

𝜏𝜏𝑟𝑟𝑟𝑟𝑟𝑟,𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐

Rate equations

𝑗𝑗𝑗𝑗𝑛𝑛𝑤𝑤 = − 1𝜏𝜏∆𝑟𝑟𝑟𝑟𝑟𝑟

+ 1𝜏𝜏∆𝑟𝑟𝑒𝑒𝑟𝑟

𝑛𝑛𝑤𝑤 + 𝐼𝐼𝑟𝑟𝜏𝜏∆𝑟𝑟

𝑗𝑗𝑗𝑗𝑛𝑛𝑅𝑅 = 𝐼𝐼𝑞𝑞− 𝑗𝑗𝑗𝑗𝑣𝑣𝑅𝑅

𝑅𝑅𝑒𝑒𝑟𝑟𝑞𝑞

+ 𝐼𝐼𝑤𝑤𝜏𝜏∆𝑟𝑟𝑒𝑒𝑟𝑟

− 𝐼𝐼𝑟𝑟𝜏𝜏∆𝑟𝑟

− 𝐼𝐼𝑟𝑟𝜏𝜏∆𝑟𝑟𝑟𝑟𝑟𝑟,𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐

Small-signal rate equations

Boltzmann statistics

𝑁𝑁𝑅𝑅 ∝ 𝑒𝑒 𝑉𝑉𝑟𝑟𝑚𝑚𝑉𝑉𝑇𝑇

𝑛𝑛𝑅𝑅 = )𝑅𝑅𝑟𝑟𝑣𝑣𝑟𝑟(𝜔𝜔𝑞𝑞

(Well)

(Cladding)𝑗𝑗𝑗𝑗𝐶𝐶𝑤𝑤 + 1

𝑅𝑅𝑤𝑤+ 1

𝑅𝑅𝑟𝑟− 1

𝑅𝑅𝑟𝑟

− 1𝑅𝑅𝑟𝑟

𝑗𝑗𝑗𝑗 𝐶𝐶𝑅𝑅 + 𝐶𝐶𝑇𝑇𝑅𝑅 + 1𝑅𝑅𝑟𝑟

+ 1𝑅𝑅𝑟𝑟𝑟𝑟𝑟𝑟,𝑟𝑟𝑐𝑐𝑐𝑐𝑐𝑐

𝑣𝑣𝑤𝑤𝑣𝑣𝑅𝑅 = 0

𝑖𝑖

Rashidi et al., Journal of Applied Physics, 122, 3, 035706 (2017)

𝑛𝑛𝑤𝑤 = )𝑅𝑅𝑤𝑤𝑣𝑣𝑤𝑤(𝜔𝜔𝑞𝑞

𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅 = 𝑅𝑅𝑤𝑤𝐶𝐶𝑤𝑤𝜏𝜏∆𝑅𝑅 = 𝑅𝑅𝑅𝑅𝐶𝐶𝑅𝑅 𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅 = 𝑅𝑅𝑇𝑇𝑅𝑅𝑅𝑅,𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅𝐶𝐶𝑅𝑅

𝜏𝜏∆𝑅𝑅𝑇𝑇𝑅𝑅 = 𝑅𝑅𝑅𝑅𝐶𝐶𝑤𝑤

0 1 2 3

0

50

100

150

200

250

300 50 um 60 um 70 um 80 um

Rc(Ω

)

Current Density (kA/cm2)0.01 0.1 1

10-10

10-9

10-8

τesc

τRC

50 µm60 µm70 µm80 µm

Diff

eren

tial L

ifetim

e (s

)


τrec


Differential Lifetimes and Circuit Parameters

𝐶𝐶𝑅𝑅 =𝑞𝑞𝑁𝑁𝑅𝑅0𝑚𝑚𝑉𝑉𝑇𝑇

𝑅𝑅𝑅𝑅 =𝑚𝑚𝑉𝑉𝑇𝑇𝑑𝑑0

1

1 + 𝜏𝜏∆𝑇𝑇𝑅𝑅𝑅𝑅𝜏𝜏∆𝑅𝑅𝑇𝑇𝑅𝑅

𝜏𝜏𝑅𝑅𝑅𝑅 =𝑅𝑅𝑇𝑇

𝑅𝑅𝑇𝑇 + 𝑅𝑅𝑅𝑅𝜏𝜏0

• Lifetimes and circuit parameters are direct results of the fittings

• Validity of the fittings is checked by consistency of parameters with LED diameter and current density

• Although the expressions are derived independent of the fittings, they describe the trends of

measurements

0 1 2 35

10

15

20

25

30

35

40

Cc+

Csc

(pf)


50 um 60 um 70 um 80 um

Rashidi et al., Journal of Applied Physics, 122, 3, 035706 (2017)

• High bandwidth at low current density to mitigate droop effects (peak IQE @ 100 A/cm2)• SQW structure achieves the highest IQE

• MQW structure achieves the highest BW


Semipolar (𝟐𝟐𝟎𝟎𝟐𝟐𝟏𝟏) LEDs: IQE vs. BW

BW x IQE product highest for MQW structure, especially at low current density



Polarization in III-Nitrides

• Piezoelectric polarization (PPZ) – due to strain (e.g. –InGaN/GaN or AlGaN/GaN)

• Spontaneous polarization (PSP) – present in unstrained lattices and is due to charge asymmetry

• PPE becomes larger for higher indium contents (i.e. – green and yellow emitters)

Polarizations induce large internal electric fields (~MV/cm) which distort the band diagrams

We can use nonpolar and semipolar orientations to eliminate the effects of polarizationD. Feezell, J. Disp. Technol. 9, 190-198 (2013)


Energy Band Diagrams for SQW Blue LEDs

𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒 (𝟐𝟐𝟎𝟎𝟐𝟐𝟏𝟏)𝐏𝐏𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒 (𝟎𝟎𝟎𝟎𝟎𝟎𝟏𝟏) 𝐍𝐍𝐒𝐒𝐍𝐍𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒 (𝟏𝟏𝟎𝟎𝟏𝟏𝟎𝟎)

D. Feezell, J. Disp. Technol. 9, 190-198 (2013)

Goal: Investigate the effects of orientation on modulation bandwidth

Carrier recombination lifetime (rate) influenced by orientation (𝑓𝑓3𝑅𝑅𝑑𝑑 ∝ ⁄1 𝜏𝜏):

• Goal for Li-Fi networks is >10 Gb/s

• Commercial LEDs can only modulate at about 20 MHz

• Equivalent data rate of ~40 Mb/s

• Faster LEDs speeds will enable higher data rates

• Several problems exist with COTS LEDs


Why are Commercial-Off-The-Shelf LEDs Slow?Problem 1 - Large-Area:

Problem 2 - Phosphor Converted: Problem 3 - Polar c-Plane Orientation:

Ce:YAG phosphor decay time is on the order of 70 ns (~2 MHz)

Large-area chips (>1 mm2) increase RC parasitics

Internal electric fields increase electron/hole recombination time

𝑓𝑓3𝑅𝑅𝑑𝑑 ≈1

2𝜋𝜋𝜏𝜏𝑇𝑇𝑅𝑅𝑅𝑅


Nonpolar LED with 1.5 GHz Modulation Bandwidth

0 200 400 600 800 1000

4

5

6

7

8

9


Volta

ge (V

)

0.0

0.3

0.6

0.9

1.2

1.5

1.8

Lig

ht (m

W)

0 200 400 600 800 1000

454

456

458

460

462

464

466

468

Peak

Wav

eleng

th (n

m)


0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

-30-27-24-21-18-15-12

-9-6-3036

PD cut off

20 A/cm2

50 A/cm2

100 A/cm2

250 A/cm2

500 A/cm2

1000 A/cm2

PD Response

Norm

alize

d Po

wer (

dB)

Frequency (GHz)

PD artifact

10 100 1000

600

900

1200

1500

1800

3dB

Band

widt

h (M

Hz)


PD 3dB Bandwidth

10 100 100010-11

10-10

10-9

10-8 τrec

τRC

Life

time (

s)


Record high modulation bandwidth for GaN-based LEDs!A. Rashidi, et al., Elect. Dev. Lett. 39, 520 (2018)

• Compared 450 nm LEDs on polar, semipolar (2021), and nonpolar orientations• Bandwidth trends follow wavefunction overlap trends• 𝑓𝑓3𝑅𝑅𝑑𝑑−𝐼𝐼𝑡𝑡𝐼𝐼𝑐𝑐𝑡𝑡𝑅𝑅𝑇𝑇𝑇𝑇 > 𝑓𝑓3𝑅𝑅𝑑𝑑−𝑇𝑇𝑅𝑅𝑇𝑇𝐼𝐼𝑐𝑐𝑡𝑡𝑅𝑅𝑇𝑇𝑇𝑇 > 𝑓𝑓3𝑅𝑅𝑑𝑑−𝑐𝑐𝑡𝑡𝑅𝑅𝑇𝑇𝑇𝑇


Example: Orientation Dependence of Bandwidth

107 108 109-18

-12

-6

0

Nor

mal

ized

Pow

er (d

B)

Frequency (Hz)

Nonpolar Semipolar Polar

1.0 kA/cm2

a1

a2

a3

[0001]

a1

a2

a3

[0001](𝟐𝟐𝟎𝟎𝟐𝟐𝟏𝟏)

a1

a2

a3

[0001]

Polar Semipolar Nonpolar

(𝟏𝟏𝟎𝟎𝟏𝟏𝟎𝟎)(𝟎𝟎𝟎𝟎𝟎𝟎𝟏𝟏)


• Nonpolar and semipolar bandwidth is significantly higher at low current densities• Polar LED experiences screening of the internal electric fields above 500 A/cm2

• Large bandwidth at low current density important to avoid efficiency droop


Example: Orientation Dependence of Bandwidth

10 100 1000

0.1

1Slope = 0.08

Slope = 0.4

3dB

Ban

dwid

th (G

Hz)


Nonpolar

Semipolar

PolarSlop

e = 0.

84

(a)


10 100 10000.1

1

DLT

(ns)


Nonpolar

Semipolar

Polar

• Differential carrier lifetime (DLT) follows inverse trend to bandwidth• Carrier density for a given current density always lower on nonpolar and semipolar


Differential Carrier Lifetime and Carrier Density

1.0 1.5 2.0 2.5 3.0 3.516.0

16.5

17.0

17.5

18.0

18.5

19.0

19.5

log(

n) (c

m-3

)

log(J) (A/cm2)

Nonpolar

Semipolar

Polar

𝑛𝑛 =1𝑞𝑞𝑑𝑑

0

𝐽𝐽𝜏𝜏Δ𝐼𝐼 𝐽𝐽′ 𝑑𝑑𝐽𝐽𝑑


0 500 1000 1500 20000.00.20.40.60.81.01.21.41.6


Out

put P

ower

(mW

)

Nonpolar

Polar

Semipolar

(b)

c-plane bandwidth is fundamentally lower due to internal electric fields (QCSE)


Comparison of Bandwidth for Various Orientations


1 10 100 1000 1000010

100

1000Semipolar (11-22)

UNM Polar c-plane/Sapphire

UNM Nonpolar (EDL)UNM Nonpolar (APL)UNM SemipolarUNM Polar UNM NanowireMcKendry et al.24 Liao et al.25

Quan et al.26

Ferreira et al.12

Shi et al.27

Corbett et al.22

Dinh et al.23

Dinh et al.23

Polar c-plane/PSS

Polar c-plane/Sapphire


UNM Nonpolar m-plane


3dB

ban

dwid

th (M

Hz)


Flip chip

Flip chip

UNM Semipolar (20-2-1)

Semipolar (11-22) UNM Nanowire