7/28/2019 Notes I Basic concepts.pdf
1/20
NM6605 Design and modelling of
Dr. Fan Wei Jun
- -.
Phone: 6790 4359
. .
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
2/20
7/28/2019 Notes I Basic concepts.pdf
3/20
7/28/2019 Notes I Basic concepts.pdf
4/20
1. Semiconductor Fundamental
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
5/20
Elemental
IIIA IVA VA VIA5 6 7
semiconductors
(e.g. Si - Silicon)
B C N
13 14 15 16
Al Si P SIIB
30 31 32 33 34
Ga Ge AsZn Se48 49 50 51 52
In Sn SbCd Te
80
Hg ompoun sem con uc ors(e.g. III-V: GaAs, InP, GaN,
School of EEE, NTU
, , , .
7/28/2019 Notes I Basic concepts.pdf
6/20
Si is the diamond structure
sublattices, offset from one
.
a body diagonal.
Zinc blende structure: the two offset lattices are of different atoms.Each group III site is surrounded by 4 group V sites, and vice-versa.
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
7/20
The semiconductor is said to be indirect when the conduction band
m n mum an va ence an max mum o no co nc e e.g. e, , s,
AlP, AlSb, GaP). Example: Band diagram for Si - indirect (Eg=1.12 eV)Energy (E)
on uc on an
k[100]k[111]
bandgap
valence bandheavyholes
light holes
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
8/20
In a direct bandgap material, the conduction band minimum andrec an gap
valence band maximum coincide in k-space (e.g. GaAs, GaSb, InP,
InAs, InSb, GaN) Example: Band diagram for GaAs (Eg = 1.42 eV) k is specified in two different
crystallographic directions.
Energy (E)
conduction bandMinima referred to as , L and X
points
Two t es of holes exist with
XL
different effective masses -
heavy holes and light holes.
bandgapEgL Eg
EgX
ect ve mass s re ate to t e
E-k curvature.
Why GaN is transparent, GaAs not?valence band
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
9/20
r t ca po nts n t e rst r ou n zone o a z nc en e sem con uctor
(0, 0, 0)
L (0.5, 0.5, 0.5)
, ,U,K (0.25,0.25,1)
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
10/20
Band structure including spin-orbit interaction
One re evant con uct on an s
formed from S- like atomic orbitals
(wavefunction is approximately
spherically symmetric)
three u er valence bands formed
from (three) P- like orbitals
-
lowest, split-off hole (i. e., valence)
band remaining two hole bands have
zone center heavy hole (hh) band,
and the other is the light hole (lh)
School of EEE, NTU
an
7/28/2019 Notes I Basic concepts.pdf
11/20
Band diagram for GaAs
In a direct semiconductor, we
-
at the centre of the Brillouin zone.Energy (E)
*2 egC
m
kEE
*2 h
Vm
kE
If the interactions with the latticeare taken into account - so we
XL
introduce an effective mass
12
k[100]k[111]
2
2*
dk
me valence band
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
12/20
If the lattice constant of the e itaxial la er a is different from that
Lattice matching and strain
of the substrate (as), defects in the crystal structure can occur.
Misfit
isolated combined
School of EEE, NTU
att ces att ces
7/28/2019 Notes I Basic concepts.pdf
13/20
For perfect epitaxial growth af=as, there is no mismatch, so the
epi-layer is unstrained
However, a small mismatch can be accepted, causing an elasticallystrained layer, but the layer must be thin for defects not to occur.
Strained
z (growthdirection)
isolatedcombined
latticesx
y
School of EEE, NTU
lattices
7/28/2019 Notes I Basic concepts.pdf
14/20
Lattice matching and strain
-
=//= xx = yy = (as-af)/ af
s , -layer lattice constant without strain.
<
// >0 Tensile strain
r i l r in
= zz = - 2(C12/C11)//
h r 11 n 12 r l i iffn n n Formost of the III-V semiconductors, C12 0.5 C11.
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
15/20
Strain energy - will accumulate
and is linear with thickness. A
critical thickness occurs at whichstrain energy is higher than
dislocation energy - defects occur.
This happens at the criticalthickness: dc as / |2| . Accurate
calculation should use Matthews
equation.Substrate layer is many times thicker than the epitaxial layer. Defects are
School of EEE, NTU
.
7/28/2019 Notes I Basic concepts.pdf
16/20
ra n n uence on an structure
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
17/20
ue to y rostat c stra n, t e con uct on an e ge sshifted by
c = ac xx +yy +zz = ac - 12 11
and the valence band edge is shifted byP
= - av(xx +yy +zz ) = -2av(1-C12/C11)
So the bandgap after hydrostatic strain is
Egs = Eg + Ec + P= E + 2 a -a 1-C /C
Due to shear strain, the heavy hole is shifted by
= - - = - xx yy zz 12 11
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
18/20
Band lineup
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
19/20
Band offset calculation
EV = Evav + /3
EcEc=Ec(B)-Ec(A)
cEvEg=Ec-Ev
v
Evav/3
v=- V - V
A Bvav
School of EEE, NTU
7/28/2019 Notes I Basic concepts.pdf
20/20
uan um we n rare p o o e ec or QWIPs operate by photoexcitation of electrons between ground and
rst exc te state su an s o mu t -quantum we s s . n er
applied bias, the photo-excited carriers can escape from the potential
.
The lattice matched
x 1-x
system is commonly used tocreate a QWIP structure. Thelight detection can be at anywavelength range between 6-20
*
22
*
222
* 22)(
2
1),,(
m
k
m
k
W
n
mkknEE
yxyx
School of EEE, NTU