CMPE 103 Electronic Materials
Mid Term Solution
Q 1(a) [5 marks]
Epitaxy is one of the methods of growing crystal lattices using a seed on a material
called substrate. There are two types: a) seed and crystal to be grown are of same type.
b) seed and crystal are different but have the same lattice constant.
Some of the methods of epitaxy are
(i) liquid phase epitaxy (LPE)
(ii) vapour phase epitaxy (VPE)
(iii) molecular beam epitaxy (MBE)
(b) [5 marks]
Kd = 0.3
CS = 1015 cm-3
Kd = CS / CL
CL = CS / Kd = 1015 = 3.33 x 1015 cm-3
Weight of Si = 1 kg = 1000 g
Volume of initial solution = mass / density = 1000 / 2.33 = 429.18 cm3
No. of Arsenic atoms required in the initial mixture = 429.18 x 3.33 x 1015
= 1.43 x 1018 atoms
23
6.02 x 10 atoms of Arsenic = 74.9 grams
1.43 x 1018 atoms of Arsenic = (74.9 / 6.02 x 1023) x 1.43 x 1018
= 1.779 x 10-4 grams
Q 2(a)(i) [3 marks]
λ = 522 x 10-9 m
f = c / λ = 3 x 108 / 522 x 10-9 = 5.74 x 1014 Hz
Em = 0
Em = hf – qФ
0 = (6.63 x 10-34 x 5.47 x 1014) – qФ
Work function = qФ = 3.81 x 10-19 J
(ii) [3 marks]
λ = 250 x 10-9 m
f = c / λ = 3 x 108 / 250 x 10-9 = 1.2 x 1015 Hz
Em = 0
Em = hf – qФ
Em = (6.63 x 10-34 x 1.2 x 1015) – (3.81 x 10-19)
Em = 4.145 x 10-19 J
(b) [4 marks]
Si = 1s2 2s2 2p6 3s2 3p2
Ge = 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p2
Na+ = 1s2 2s2 2p6
Cl- = 1s2 2s2 2p6 3s2 3p6
CMPE 103 Electronic Materials
Q 3(a) [5 marks]
Type
Since VAB is negative, there are more electrons in the semiconductor. Therefore, it is an
n-type semiconductor material.
Concentration
B = 10 x 10-5 Wb.cm-2 = 10-4 Wb.cm-2 = 1 Wb.m-2
no = Ix Bz / q t VAB
no = (1 x 10-3 x 1) / (1.6 x 10-19 x 10 x 10-6 x 2 x 10-3)
no = 3.125 x 1023 m-3 = 3.125 x 1019 cm-3
Mobility
R = L / Wtσ ------- (1)
R = VCD / I -------- (2)
Equating equation (1) and (2)
L / Wtσ = VCD / I
σ = L I / WtVCD
σ = (5 x 10-3 x 1 x 10-3) / (0.1 x 10-3 x 10 x 10-6 x 100 x 10-3)
σ = 50000 (Ωm)-1
Ignoring po as this is an n-type semiconductor, σ = µn q no
µn = σ / q no = 50000 / (1.6 x 10-19 x 3.125 x 1023) = 1.0 m2 V-1 s-1 = 1.0 x 10-4 cm2 V-1 s-1
(b) [5 marks]
At very low temperatures, the electrons do not have sufficient energy to jump from the
valence band to the conduction band, so they remain in the valence band whereas the
conduction band remains empty. Therefore conductivity happens mainly due to
ionization of the semiconductor.
At around room temperature, Electron Hole Pairs (EHP) begin to form as electrons gain
energy to cross the band gap and jump to the conduction band. Since holes are being
caused by displacement of electrons, the number of holes is equal to the number of
electrons. Electrons and holes both cause current to flow but in opposite directions so
the net effect is no current. Therefore to make the semiconductor conduct electricity
during this temperature range, doping has to be done i.e. some impurity has to added
that results in either more electrons or more holes for a net current to flow. So the
extrinsic semiconductor character is dominant during this temperature range.
As temperature increases to very high temperatures, intrinsic character starts
dominating because lattice scattering dominates impurity scattering.