1. DFT calculations identify hydrogenated gallium vacancies and oxygen-related defects as promising candidates to explain hot electron degradation in AlGaN/GaN HEMTs. 2. Monte Carlo simulations show a peak in electron concentration and energy near 1.5 eV below the conduction band minimum, matching the activation energy of hydrogenated defects. 3. A model combining DFT defect formation energies and densities with Monte Carlo transport simulations can reproduce experimentally observed shifts in pinch-off voltage over time under electrical stress.

1. Дефекты в полупроводниках
GaN и AlSb

2. Possible trap locations
AlGaN
Egap=4.2 eV
1 1. Thermally activated to AlGaN Ec
3 2. Tunneling to Gate
2 3. Tunneling to Channel
4. Thermally activated tunneling to
Channel
4
GaN Egap=3.4 eV
2’

3. Hydrogenated Antisite
NH3
Egain = 2.35 eV
Exothermic process
growth
NGaH3 : NEGATIVE FORMATION ENERGY

4. Defect Complex VGa-ON
E f Dq H x Etot Dq H x bulk
Etot ni i
q EF Ev V qocc Eshift ,
i
mGa + m N = mGaN
bulk
m N = m NH - 3 2 m H
gas gas
3 2
CBM(GaN)
mO = 1 2 m gas
O
2

5. ~ 0.5 eV

6. Results of calculations
“0” “-3”
C.-H. Lin et. al., Appl. Phys. Lett. (2009)
Y. S. Puzyrev, et al., Appl. Phys. Lett. 96, 053505 (2010).

7. Candidate defect: hydrogenated Ga vacancy
Coulomb Scatterer
Neutral defect Transconductance degradation
“0” “-3”
Remove H
Hydrogenated Ga vacancy
Yellow Luminescence

8. Electrical stress-induced degradation
(Process Splits; Critical Experiments)
MBE-grown devices (passivated)
Electrical stress :
VG = −4 V
VD = 20 V
T = 300 K
Positive shift in Ga-rich, N-rich Shift in Vpinch-off is permanent.
– acceptors created, or donors removed
Negative shift in NH3-rich T. Roy, et al., Appl. Phys. Lett.
– donors created or acceptors removed 96, 133503 (2010).

9. Source of degradation: hydrogenation of Ga-vacancies
• Hot electrons sequentially remove hydrogens from Ga-vacancies
• Different charge states “0”
Al0.3Ga0.7N
“-3”
“-2”
“-3”
“-1”
“0”
EF during stress
T. Roy, et al., Appl. Phys. Lett. 96, 133503 (2010).

10. Possible trap locations
AlGaN
1 1. Thermally activated to AlGaN Ec
3 2. Tunneling to Gate
2 3. Tunneling to Channel
4. Thermally activated tunneling to
Channel
4 GaN
2’

11. DFT calculation of Defect Candidates
Low formation energies
Vacancy complexes with impurities,- O and H
Oxygen complexes
• VGa-ON
• VGa-ON-O
Hydrogen Complexes
• VGa-VN-H
• VGa-VN-H2

12. Defect Candidates
Oxygen-Hydrogen Complexes
• VGa-ON-H
• VGa-ON-H2
For example: extended electron state for level ~0.7 eV below CBM of [VGa-ON-H]-2

13. Defect Complex VGa-VN-H
[VGa-VN-H]-1
CBM(GaN)
Localized state ~1.eV below AlGaN CBM

14. Thermodynamic Levels
ON
CBM(GaN)
LDA – (0/-1) trap level in conduction band?

15. Defect Complex VGa-ON
LDA state for [VGa-ON-H]-2 is delocalized
CBM(GaN)
LDA – (-1/-2) charge transition level in conduction band?

16. Defect Complex VGa-ON-H
Hybrid Functional calculation Egap = 4.7 V
LDA state for [VGa-ON-H]-2 is delocalized Localized state for [VGa-ON-H]-2 .
CBM(GaN) Level Ec - 0.7 eV
LDA

17. Defect Complex VGa-ON-H
Formation of the defect? Pre-existing either
[ON-H ]+1 or [VGa-ON]-2
Both have low formation energies
• H+ diffusion barrier ~2eV
• [VGa]-3 diffusion barrier ~1 eV

18. Degradation in AlSb/InAs HEMTs
Devices from Rockwell

19. Substitutional oxygen OSb
Ec AlSb InAs
1.7 eV
1.1 eV
Structure Charge
upon hole capture
EF
0.6 eV Ec
0.1 eV

Ev
S. Dasgupta, et al., IEEE Trans. Electron Dev. 58, 1499 (2011).

20. Bias Dependence of
Electron Concentration and Energy
(Michigan MC)
Large peak in
G-D region
Gate
Electric field

21. Electron Concentration and Energy
Two positions below the channel
Electron concentration with energy over 2 eV is significant
and exhibits a peak ~ 1.5 eV
Y. Puzyrev et. al “Gate bias dependence of hot-carrier degradation of GaN
Michigan Monte Carlo HEMTs”, submitted to IEEE Electron Device Letters

22. Defect density from Vpinch-off shifts
N d (t ) N d (t ) ( E ) n( E ) ( E )
t E>Ea
Experimentally observed
shifts in pinch-off voltage:
• Estimate defect density that contributes
to pinch-off voltage shifts
– Charge control model of HEMT
e N d (t ) 2
V pinch off (t ) d AlGAN

23. DFT: activation energy of defect
Activation energy of dehydrogenated N-anti-site
Eactivation ≈ 1.8 eV
N(E)
Electrons having energy greater than
activation energy of defect

24. DFT: activation energy of defect
Activation energy of dehydrogenated Ga-vacancies
Eactivation ≈ 0.5 eV
N(E)
Electrons having energy greater than
activation energy of defect
Accelerated testing performed at bias that gives maximum degradation rate
Simulations/Calculations allow extrapolation to device operating conditions

25. Scattering from bulk and defects
e
e

27. Modeling hierarchy
VGa-Hn
NGa-Hn
DFT
N d (t ) N d (t ) ( E ) n( E ) ( E )
t E Ea
DFT Monte-Carlo

28. Multiphonon Defect Reconfiguration
by Hot Electrons
Release of Hydrogen
E
Ec
E

29. Mutliphonon capture
Henry and Lang, 1977: Linear coupling to phonons 791
V(R,r)= V(R0,r)+q∙∂R V(R,r)
Ridley, 1978: Linear coupling is negligible for multiphonon processes
Must use non-adiabatic coupling, Kubo 1952 94

30. Multiphonon capture
Born-Oppenheimer Approximation
(ri , R ) X (R ) (ri , R ), Drop R (ri , R )
Non-adiabatic term Wave function 2nd derivative
2
X DFT implementation
H NA X  j X
j qj qj q2
j
is time-consuming
Wave function derivative

31. Multi-phonon electron scattering
Transition probability
2
P Xn f H NA i Xi
n i Ei E f
2
2
 j f i Xn Xi Xn Xi f i
j qj qj q2
j
n i Ei E f
N d (t ) N d (t ) ( E ) n( E ) ( E )
t E Ea
N d (t ) N d (t ) n( E )P ( E )
t E Ea

32. Overview & Approach
Materials and Process Splits
growth conditions Characterization
DFT
• Defect identification
 activation process
 multi-phonon
scattering rate
Simulation
We are here Degradation rate
• Electron distribution
 in space
 in energy
Accelerated
Operating conditions Reliability Test