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