Transcript Strain Induced Band Structure Change on Wurzite GaN

Biaxial Strain-modified Acceptor
Activation Energy of Wurtzite GaN
Analyzed by k∙p Method
Presented by:
Instructor:
12/13/2004
Ning Su
John Simon
Lili Ji
Dr. Debdeep Jena
EE698D Advanced semiconductor physics
Outline

Introduction



Band structure calculation



Conduction and valence band Hamiltonian
Band structure modification by biaxial strain
Acceptor activation energy and conductivity



Background
Motivation
Density of States (DOS) calculation
Effective mass calculation
Conclusion
12/13/2004
EE698D: Advanced Semiconductor Physics
Introduction

Role of strain on electronic and optical properties of
semiconductors has been carefully studied for several decades
device applications: HBTs
Lasers

To better understand the effect of strain on semiconductor
properties, fundamental studies of band structure is of great
importance
e.g. 1) tight-binding method
2) K∙P method--- used in this work
12/13/2004
EE698D: Advanced Semiconductor Physics
Introduction-cont’d

Biaxial strain in Wurtzite Gallium Nitride (GaN)
 Large biaxial strain in bulk wurtzite GaN
large lattice
mismatch between GaN & substrate, post-cooling
 Less well understood compared to zinc-blend GaN

Acceptor activation energy in GaN
 Large Ea of Mg-doped GaN (120~260meV)
limits room
temperature p-GaN conductivity
 Strained modified Ea, a potential way to improve electrical
property
Motivation of this work !!
12/13/2004
EE698D: Advanced Semiconductor Physics
Simulation Model
k∙P method
Hamiltonian derivation
Band Structure under strain
m* tensor
DOS
Hole distribution
mobility
Fermi-Direc
conductance
life time
Critical thickness
12/13/2004
EE698D: Advanced Semiconductor Physics
Band Structure under Strain

Conduction and valence bands Hamiltonian
Conduction band
( parabolic band model)


Valence band (ref. a)
where

F
H 3U3 (k )   K t
iH t
Kt
G
  iH t
 2 kt2 k z2
H (kt , k z )  ( )( t  z )  Ec
2 me me
c
H 66
 iH t 
  iH t 
 
v
 H 3U3 (k )
0 
(k )  

H 3L3 (k )
 0
and H 3L3 (k )  conj ( H 3U3 (k )
Band structure can be obtained by finding eigenvalues of
the Hamiltonians defined above
ref. a: S. L. Chuang and C. S. Chang, Phys. Rev. B, 54, 2491 (1996)
12/13/2004
EE698D: Advanced Semiconductor Physics
Band structure-cont’d

Energy values for band edge
as a function of strain ( -2%~2%)

At the tensile strain of 0.107%,
the LH band rises above the HH
band edge

Band gap
12/13/2004
for compressive strain
for tensile
EE698D: Advanced Semiconductor Physics
Band structure-cont’d

Valence band dispersions
1% compressive
unstrained

kx and kz are transverse
and longitudinal axes along
[0001] direction
1% tensile
12/13/2004
EE698D: Advanced Semiconductor Physics
Acceptor Activation Energy

Assumption:
Acceptor energy level is
fixed with respect to
vacuum level

Typical value of EA =160 meV
is chosen for Mg-doped
GaN

EA decreases faster with
tensile strain
12/13/2004
EE698D: Advanced Semiconductor Physics
Effective Mass
effective mass as a function of strain derived from band structure
12/13/2004
EE698D: Advanced Semiconductor Physics
DOS and Hole Distribution
DOS
Hole distribution
Fermi-Dirac
function
12/13/2004
EE698D: Advanced Semiconductor Physics
Hole Concentration
NA=1018cm-3
Hole concentration as a function a strain
12/13/2004
EE698D: Advanced Semiconductor Physics
Mobility and Conductivity
Mobility and conductivity along transverse and longitudinal
directions under strain (Assume life time  =0.1ns )
12/13/2004
EE698D: Advanced Semiconductor Physics
Conductance
Critical thickness is used for the layer thickness
12/13/2004
EE698D: Advanced Semiconductor Physics
Conclusion

Strain modified Band structure was calculated using
k∙p method

Acceptor activation energy was found to decrease with
strain

Hole concentration increases rapidly with tensile strain

µ & σ was enhanced in the [0001] direction
12/13/2004
EE698D: Advanced Semiconductor Physics
Acknowledgement
We acknowledge Prof. Debdeep Jena for his directions
and helpful discussions.
12/13/2004
EE698D: Advanced Semiconductor Physics