Tutorial 1. 2D lattice and Braggs Law
1.
a)
X-rays with wavelength 1.54 are reflected from the (1 1) planes of a square crystal with unit cell a = 6 .
What is the highest order Bragg angle?
n
1 n
For sin (
)to be real then
1
2d11
2d11
d11
a
2
h k
o
2
sol

ni2
J O = qDn
N BWB
VOC
b1 = 2
a2 a3
a1 a 2 a 3
b 2 = 2
SC
V = a1 a 2 a 3 = a 3
2
a1 a 2
a1 a 2 a 3
2
H ( x, t ) =
1
1 2 E(k )
meff 2 k 2
i
( x, t )
t
f = E/h
p = k
E =
p N Ve
p(E) = g(E) (1 f (E)
n = N d+ N a
if
N d+ N a > ni
n(E) = g(E) f (E)
1
(EE

The problems youll find in this file are meant to
be solved without the help of an equation sheet.
I recommend you dont attempt them until
youve memorised the equations. You can then
assess how well you know the

The problems in this file are meant to be solved with the aid of
the equation sheet provided for the midterm. The problems were
designed to be solved in 20 to 25 minutes maximum.
A Si wafer is simultaneously

Tut 9 Third Generation Solar Cell
1. Silicon nanocrystals
A silicon quantum dot (Si-QD) thin-film sample has been analysed using X rays with = 0.154 nm.
The XRD data shows three peaks at 2 = 28.43, 47.29 and 56.1. The l

Tut 8 PC1D as a
characterisation tool simulator
1.
Use PC1D to obtain the IV characteristics of an experimental 1mm2 solar cell fabricated on thin film silicon. The
SC is fabricated using a 1.8m thick p-type 1016cm-3 poly-Si film with a minority carrier l

Comments on Tutorial 7
By Craig J!
WARNING: This is not the final word on these rather
sophisticated issues. This is to help direct your thinking
about pn junction operation.
Q1
This question considers thermal equilibrium carrier dynamics and pn junction

Tut 6 PC1D input and output data
1.
Using PC1D simulate the amount of light absorbed by a 250m thick Si wafer when illuminated with a variable
light source with a wavelength range of 300nm to 1150nm in steps of 10nm and a constant 100mW/cm2 intensity at
e

Tut 5 Ques)on 1
In order to obtain resistivity, we need to first work out the doping and mobility of
material.
To find the doping density we cant assume all donor atoms are ionized as the
activation energy of Al is much higher than the thermal energy a

Tutorial 4 Band Structure
The E-k diagram for the conduction band in a square lattice can be described
by the following equation: E(k) = E "2 cos(k a) + cos(k a) $
o#
x
y
%
a. Working within the first Brillouin Zone, with a=5 and Eo=1eV:
Plot the equal

1
1
=
3
x N A+ N D
3
1
3
1
16 3
x =( N A + N D ) =( 6 10 ) =25.54 nm
k =
( 1 )=516 c m
1
=5.16 10 4 m1
E phonon =h f
k =2
( 1 )= 2 c f
f=
c
k
2
E phonon =h
c
k=c k
2
E phonon =c k=
6.626 1034 5.16 104 3 108
=0.0102 eV
2
1.602 1019
Etheshold =E g E p