QUANTUM COMPUTING FOR VLSI : VERILOG IMPLEMENTATION OF REVERSIBLE LOGIC GATES
Undergraduate_Thesis_Presentation
1. 1
THEORETICAL CALCULATION OF ELECTRONTHEORETICAL CALCULATION OF ELECTRON
MOBILITY OF InN SEMICONDUCTOR BYMOBILITY OF InN SEMICONDUCTOR BY
MONTE CARLO SIMULATIONMONTE CARLO SIMULATION
SUPERVISED BY:SUPERVISED BY:
Dr. Ashraful Ghani BhuiyanDr. Ashraful Ghani Bhuiyan
Assistant Professor,Assistant Professor,
Department ofDepartment of
Electrical & Electronic EngineeringElectrical & Electronic Engineering
KUET, Bangladesh.KUET, Bangladesh.
PREPARED BY:PREPARED BY:
Z. M. Saifullah
Roll No: 0103020
Jayanta Kumar Debnath
Roll No: 0103027
6. 6
Monte Carlo methodMonte Carlo method
MonteCarlo simulation isastochastic technique.
Random selection processisrepeated many
times.
Use random number
Use Probability statistics
7. 7
Simple Monte Carlo exampleSimple Monte Carlo example
Randomly select alocation within therectangle
If it iswithin the blue area, record thisinstanceahit
Generateanew location and repeat 10,000 times
2
unit40
scenarios10,000
hitsblueofNumber
areaBlue ×=
8. 8
Definition of the
physical
System input of
physical
And simulation
parameters
Stochastic determination of
relaxation time for electron
Sum of the relaxation times
for scattering events
Scattering
event < 105
Stochastic
Determination of
Electron wave
vector just
After scattering
Evaluation
of mean
relaxation
time
Calculate
mobility from
mean
relaxation
time
Print
result
Sto
p
Flowchart of Monte Carlo program formobility calculation
Monte Carlo model for mobility calculationMonte Carlo model for mobility calculation
9. 9
Monte Carlo model for mobility calculationMonte Carlo model for mobility calculation
Determination of relaxationDetermination of relaxation
timetime
′−=+ ∑′k
kkSdttPdttP ),(1)()(The probability that
the electron is not
scattered
∑
′
′−=
k
kkSP
dt
dP
),(
′−= ∫ ∑
′
2
1
),(exp
t
t
k
kkSP
The total scattering
rate perunit time
probability of an electron being
scattered in the time interval
dt.
∑′
′
k
kkSdt ),(
10. 10
Monte Carlo model for mobility calculationMonte Carlo model for mobility calculation
totτ
1
∑
′
′
k
kkS ),(
......
)(
1
)(
1
)(
1
++=
kkk ph
tot
I
tot
all
tot τττ
−= ∫
2
1
)(
exp
t
t
t
dt
r all
tot
d
τ
−= ∫
3
2
)(
exp
t
t
t
dt
r all
tot
d
τ
1.
2.
3.
Determination of relaxationDetermination of relaxation
timetime
Evaluate
relaxation
time(t2) for1st
scattering
Evaluate relaxation
time(t3-t2) for2nd
scattering
Numerical scheme
to calculate the
mean relaxation
time for the
electrons
′−= ∫ ∑
′
2
1
),(exp
t
t
k
kkSP
11. 11
Monte Carlo model for mobility calculationMonte Carlo model for mobility calculation
Determination of the electronDetermination of the electron
wave vector after the scatteringwave vector after the scattering
The probability to select a
point P on an element ds
of the surface
φθθ ddds sin=
φθφθφθ
π
θ
π
ddPdd
ds
),(
4
sin
4
==
Thecomponents of the new wave vector in Cartesian coordinateare
.
K′
xk′ yk′ zk′and,
Density of probability
In spherical coordinates
12. 12
Monte Carlo model for mobility calculationMonte Carlo model for mobility calculation
The separate densities of
probability and forthe
two angels are
independent.
2
sin
),()(
2
0
θ
φφθθ
π
== ∫ dPP
∫ ==
π
π
θφθφ
0 2
1
),()( dPP
Values of and in any
particularscattering can be
determined by using two
random numbers (between 0
and 1) and as,
θ φ
π
φ
φφ
φ
φ
2
)(
0
== ∫ dPr
∫
−
==
θ
θ
θ
θθ
0 2
cos1
)( dPr
Determination of the electronDetermination of the electron
wave vector after the scatteringwave vector after the scattering
Random number
13. 13
Monte Carlo model for mobility calculationMonte Carlo model for mobility calculation
In Cartesian coordinates the intersections of the axes arefound by
φθ cossinra =
φθ sinsinrb =
θcosrc =
a
n
kx
π1
=′
b
n
ky
π2
=′
c
n
kz
π3
=′
222
zyx kkkk ′+′+′=′
Determination of the electronDetermination of the electron
wave vector after the scatteringwave vector after the scattering
components of
new wave vector
new wave vector
14. 14
ResultsResults
After calculating mean relaxation timeby MonteCarlo method
wehavefound mobility by
*
e
tot
m
e τ
µ =
At 77 Kand 1016
cm-3
concentration, mobility 25102 cm2
V-1
s- 1
At 77Kand 1019
cm-3
concentrations, mobility 2267 cm2
V-1
s-1
16. 16
ResultsResults
Mobility Vs Temperature curveMobility Vs Temperature curve
50 100 150 200 250 300
1675
1680
1685
1690
1695
1700
1705
1710
Mobility(cm
2
V
-1
s
-1
)
Temperature(K)
At 10
18
cm
-3
concentration
17. 17
ConclusionConclusion
The maximum mobility of our simulation at 77K and 1016
cm-3
is 25102cm2
V-1
s-1
.
From Variational Principle method it is 30000cm2
V-1
s-1
Our simulation shows high value of mobility of InN.
