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Дефекты в полупроводниках
GaN и AlSb
1
4
32
2’
1. Thermally activated to AlGaN Ec
2. Tunneling to Gate3. Tunneling to Channel4. Thermally activated tunneling to
Channel
AlGaN
GaN
Possible trap locations
Egap=3.4 eV
Egap=4.2 eV
Hydrogenated Antisite
Egain = 2.35 eVExothermic process
NH3
growth
NGaH3 : NEGATIVE FORMATION ENERGY
CBM(GaN)
, (1)i
f q q bulk
x tot x tot i F vi
occ shiftE H E D H E n q E E V q ED
Defect Complex VGa-ON
~ 0.5 eV
“-3”“0”
C.-H. Lin et. al., Appl. Phys. Lett. (2009)
Y. S. Puzyrev, et al., Appl. Phys. Lett. 96, 053505 (2010).
Results of calculations
Coulomb ScattererTransconductance degradationNeutral defect
Remove H
Yellow Luminescence
“-3”“0”
Hydrogenated Ga vacancy
Candidate defect: hydrogenated Ga vacancy
MBE-grown devices (passivated)
Positive shift in Ga-rich, N-rich – acceptors created, or donors removed
Negative shift in NH3-rich – donors created or acceptors removed
Electrical stress-induced degradation(Process Splits; Critical Experiments)
Shift in Vpinch-off is permanent.
T. Roy, et al., Appl. Phys. Lett. 96, 133503 (2010).
Electrical stress :
VG = −4 V
VD = 20 V
T = 300 K
Source of degradation: hydrogenation of Ga-vacancies
“0”
• Hot electrons sequentially remove hydrogens from Ga-vacancies
• Different charge states
EF during stress
Al0.3Ga0.7N
“0”
“-1”
“-2”
“-3”
“-3”
T. Roy, et al., Appl. Phys. Lett. 96, 133503 (2010).
1
4
32
2’
1. Thermally activated to AlGaN Ec
2. Tunneling to Gate3. Tunneling to Channel4. Thermally activated tunneling to
Channel
AlGaN
GaN
Possible trap locations
Oxygen complexes
• VGa-ON
• VGa-ON-O
DFT calculation of Defect Candidates
Low formation energies Vacancy complexes with impurities,- O and H
Hydrogen Complexes
• VGa-VN-H
• VGa-VN-H2
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
Defect Complex VGa-VN-H
CBM(GaN)
~1.eV below AlGaN CBMLocalized state
[VGa-VN-H]-1
ON
CBM(GaN)
LDA – (0/-1) trap level in conduction band?
Thermodynamic Levels
CBM(GaN)
LDA – (-1/-2) charge transition level in conduction band?
Defect Complex VGa-ON
LDA state for [VGa-ON-H]-2 is delocalized
Defect Complex VGa-ON-H
Hybrid Functional calculation Egap = 4.7 V
Localized state for [VGa-ON-H]-2 .
CBM(GaN)
LDA
Level Ec - 0.7 eV
LDA state for [VGa-ON-H]-2 is delocalized
• H+ diffusion barrier ~2eV
• [VGa]-3 diffusion barrier ~1 eV
Defect Complex VGa-ON-H
Pre-existing either [ON-H ]+1 or [VGa-ON]-2
Both have low formation energies
Formation of the defect?
Devices from Rockwell
Degradation in AlSb/InAs HEMTs
EF 0.6 eV
0.1 eV
Ev
Ec
1.7 eV
1.1 eV
AlSb InAs
Ec
Structure Charge upon hole capture
S. Dasgupta, et al., IEEE Trans. Electron Dev. 58, 1499 (2011).
Substitutional oxygen OSb
Bias Dependence ofElectron Concentration and Energy
(Michigan MC)
Large peak in G-D region
Gate
Electric field
Electron concentration with energy over 2 eV is significant and exhibits a peak ~ 1.5 eV
Electron Concentration and Energy
Two positions below the channel
Y. Puzyrev et. al “Gate bias dependence of hot-carrier degradation of GaN HEMTs”, submitted to IEEE Electron Device LettersMichigan Monte Carlo
Defect density from Vpinch-off shifts
• Estimate defect density that contributes to pinch-off voltage shifts
– Charge control model of HEMT
2)()( AlGAN
doffpinch d
tNetV
Experimentally observed shifts in pinch-off voltage:
( ) ( ) ( ) ( ) ( )d dN t N t E n E Et
aE>E
DFT: activation energy of defect
Electrons having energy greater than activation energy of defect
N(E
)
Eactivation ≈ 1.8 eV
Activation energy of dehydrogenated N-anti-site
DFT: activation energy of defect
Activation energy of dehydrogenated Ga-vacancies
Electrons having energy greater than activation energy of defect
N(E
)
Eactivation ≈ 0.5 eV
Accelerated testing performed at bias that gives maximum degradation rateSimulations/Calculations allow extrapolation to device operating conditions
Scattering from bulk and defects
Bulk Polar Optical Phonon scattering
Defect Optical Phonon scattering
Single phonon emission
Hydrogen release or defect reconfigurationMultiphonon emission ΔE
Coulomb scattering
e
e
For a phonon scattering test calculation we can provide
• total scattering rate as shown on the Figure above• scattering rate dependence on point• energy loss as a function of
Modeling hierarchy
VGa-Hn
NGa-Hn
( ) ( ) ( ) ( ) ( )a
d dE E
N t N t E n EEt
Monte-Carlo DFT
DFT
Multiphonon Defect Reconfiguration by Hot Electrons
Ec
E
Release of Hydrogen
E
V(R,r)= V(R0,r)+q ∂∙ R V(R,r)Linear coupling to phonons
Mutliphonon capture
Henry and Lang, 1977:
Ridley, 1978: Linear coupling is negligible for multiphonon processes Must use non-adiabatic coupling, Kubo 1952
791
94
Multiphonon capture
2
2NA jj j j j
XH X X
q q q
Non-adiabatic term
Born-Oppenheimer Approximation
Wave function derivative
Wave function 2nd derivative
DFT implementationis time-consuming
( , ) ( ) ( , ),i iX r R R r R Drop ( , )i R r R
2
22
2
n i i f
n i i f
n f NA i iE E
j f i n i n i f ij j j j
E E
P X H X
X X X Xq q q
Transition probability
Multi-phonon electron scattering
( ) ( ) ( ) ( ) ( )a
d dE E
N t N t E n EEt
( ) ( ) ( ) ( )a
d dE E
N t N t n E Pt
E
Operating conditions
Overview & Approach Materials and
growth conditions
DFT
• Defect identification
activation process multi-phonon
scattering rate
Simulation
• Electron distribution
in space in energy
Degradation rate
Accelerated Reliability Test
We are here
Process SplitsCharacterization