Upload
others
View
9
Download
0
Embed Size (px)
Citation preview
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
• 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.)
Current Density (kA/cm2)
• 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!
2/11/2019 Daniel Feezell 3
Challenges for High-Luminance LEDsEfficiency droop
100 1000 10000
0.5
0.6
0.7
0.8
0.9
1.0
Differential Total
Current Density (kA/cm2)
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)
2/11/2019 Daniel Feezell 4
RF Measurement System
𝑆𝑆11= 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝐼𝐼𝐼𝐼𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅𝐼𝐼𝑅𝑅
𝑆𝑆21= 𝑇𝑇𝑇𝑇𝑇𝑇𝐼𝐼𝑇𝑇𝑇𝑇𝐼𝐼𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝐼𝐼𝐼𝐼𝑅𝑅𝐼𝐼𝑅𝑅𝑅𝑅𝐼𝐼𝑅𝑅
Impedance = 𝑍𝑍 = 𝑍𝑍01+𝑆𝑆111−𝑆𝑆11
Frequency Response = 𝑆𝑆21
2/11/2019 Daniel Feezell 5
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)
2/11/2019 Daniel Feezell 6
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
2/11/2019 Daniel Feezell 7
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)
Current Density (kA/cm2)
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
2/11/2019 Daniel Feezell 8
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
)
Current Density (A/cm2)
SQW
SQW
MQW
(a)
10 100 100010-11
10-10
10-9
10-8
(b)
SQW
Net
Esc
ape
Tim
e (s
)
Current Density (A/cm2)
τleak
τcou
MQW
1𝜏𝜏𝑅𝑅𝑇𝑇𝑅𝑅
=1
𝜏𝜏𝑅𝑅𝑅𝑅𝑇𝑇𝑙𝑙−
1𝜏𝜏𝑅𝑅𝑡𝑡𝑜𝑜
M. Monavarian, et al., Appl. Phys. Lett. 112, 191102 (2018)
2/11/2019 Daniel Feezell 9
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
Current Density (kA/cm2)
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)
2/11/2019 Daniel Feezell 10
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
2/11/2019 Daniel Feezell 11
Example 3: Temperature Dependent Carrier Dynamics
A. Rashidi et al., submitted
2/11/2019 Daniel Feezell 12
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
2/11/2019 Daniel Feezell 13
Example 3: Temperature Dependent Carrier Dynamics
A. Rashidi et al., submitted
• 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
2/11/2019 Daniel Feezell 14
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
2/11/2019 Daniel Feezell 15
Thank You!
• Small area reduces RC parasitics• 50 – 100 µm diameter• Can be driven at high current density• Arrays to increase light intensity
2/11/2019 Daniel Feezell 16
Micro-Scale GaN-Based LEDs
https://www.lifi.eng.ed.ac.uk/lifi-news/2015-11-28-1320/how-fast-can-lifi-be
2/11/2019 Daniel Feezell 17
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
2/11/2019 Daniel Feezell 18
Fitting and Confidence Intervals
2/11/2019 Daniel Feezell 19
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
2/11/2019 Daniel Feezell 20
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
)
Current Density (kA/cm2)
τrec
2/11/2019 Daniel Feezell 21
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)
Current Density (kA/cm2)
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
2/11/2019 Daniel Feezell 22
Semipolar (𝟐𝟐𝟎𝟎𝟐𝟐𝟏𝟏) LEDs: IQE vs. BW
BW x IQE product highest for MQW structure, especially at low current density
M. Monavarian, et al., Appl. Phys. Lett. 112, 191102 (2018)
2/11/2019 Daniel Feezell 23
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)
2/11/2019 Daniel Feezell 24
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
2/11/2019 Daniel Feezell 25
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
2/11/2019 Daniel Feezell 26
Nonpolar LED with 1.5 GHz Modulation Bandwidth
0 200 400 600 800 1000
4
5
6
7
8
9
Current Density (A/cm2)
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)
Current Density (A/cm2)
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)
Current Density (A/cm2)
PD 3dB Bandwidth
10 100 100010-11
10-10
10-9
10-8 τrec
τRC
Life
time (
s)
Current Density (A/cm2)
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
2/11/2019 Daniel Feezell 27
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)
M. Monavarian, et al., Appl. Phys. Lett. 112, 041104 (2018)
• 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
2/11/2019 Daniel Feezell 28
Example: Orientation Dependence of Bandwidth
10 100 1000
0.1
1Slope = 0.08
Slope = 0.4
3dB
Ban
dwid
th (G
Hz)
Current Density (A/cm2)
Nonpolar
Semipolar
PolarSlop
e = 0.
84
(a)
M. Monavarian, et al., Appl. Phys. Lett. 112, 041104 (2018)
10 100 10000.1
1
DLT
(ns)
Current Density (A/cm2)
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
2/11/2019 Daniel Feezell 29
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
M. Monavarian, et al., Appl. Phys. Lett. 112, 041104 (2018)
0 500 1000 1500 20000.00.20.40.60.81.01.21.41.6
Current Density (A/cm2)
Out
put P
ower
(mW
)
Nonpolar
Polar
Semipolar
(b)
c-plane bandwidth is fundamentally lower due to internal electric fields (QCSE)
2/11/2019 Daniel Feezell 30
Comparison of Bandwidth for Various Orientations
M. Monavarian, et al., Appl. Phys. Lett. 112, 041104 (2018)
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
Polar c-plane/Sapphire
UNM Nonpolar m-plane
Polar c-plane/Sapphire
3dB
ban
dwid
th (M
Hz)
Current Density (A/cm2)
Flip chip
Flip chip
UNM Semipolar (20-2-1)
Semipolar (11-22) UNM Nanowire