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(elec221)[2010](f)midterm~867^_10304.pdf
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a) Briefly define the three types of solids : crystalline, amorphous and polycrystalline. (9) b) Use Miller index notation to label the following plane and direction. (6)
z
4
z
2
1
0
.2
y
0
y
1
1
x x
Solution
a)
Crystalline : atoms arranged in a perfect periodic fashion (3)
Amorphous : no periodic arrangement (3)
Polycrystalline : many small regions of single crystals (3)
b)
),,(x y z = (1, 2, 4). 1,4 . . . . ,2 1 4 1 . . . . (421) (3)
),( ,x y z = (1, 1, 2) . [112] (3)
a) A light source contains a 10W mercury-vapor lamp. Assuming that 0.2 % of the electric energy is converted to
the ultraviolet emission line of 253.7nm, calculate the number of emitted photons per second at this wavelength. (9) b) Which of the following case(s) satisfies Pauli exclusion principle ? Briefly explain your answer. (7)
E
E
E
E
electron ___ energy state
Solution a)
Energy provided per second = 0.2 10 .2 (10) = 0.02 J (3)
. 34 8
c (6.6310 )(310 ) . 19
Energy required to emit one photon =hv = h == 7.84 10 J (3)
. 9
(253.7 10 ) No. of photons = 0.02 = 2.56 1016 (3)
7.84 10 . 19 b) Case 3 and case 4 since there is no two electrons to occupy the same energy state. (3)
(2) (2)
Given the energy band diagram corresponding to a Si sample doped with 1014 cm C 3 of phosphorus at room temperature. Sketch the new Fermi level in the given energy band diagram for each of the following changes. Specify the material type (p-type or n-type, intrinsic or extrinsic) for each case after the change.
a) 1017 cm C 3 of boron added to the sample (4) b) 1018 cm C 3 of phosphorus added to the sample (4)
Ec Ec
EF EF
Ei Ei
Ev Ev
c) Temperature is changed to 1000K (4) d) 1016 cm C 3 of boron and 1016 cm C 3 of phosphorus are added to the sample (4)
Ec Ec
EF
EF Ei
Ei
Ev Ev
Solution
a) p-type (2) b) n-type (2)
EF Ec Ei EF Ec Ei EF (new) (2)
Ev EF (new) (2) Ev
c) intrinsic (2) d) n-type (2)
EF Ei Ec EF (new) (2) EF Ec Ei EF (new) (2)
Ev Ev
An unknown semiconductor has Eg = 1 eV and the intrinsic level is in the middle of the bandgap. It is doped with 1015 cm. 3 donors where the donor level is 0.24 eV below Ec . Given that EF is 0.3 eV below Ec and the semiconductor is at room temperature.
a) Calculate the percentage of ionization. (6) b) Calculate the electron concentration. (6) c) Calculate the intrinsic carrier concentration. (6)
Solution 11
(a) f (Ed ) == = 0.09 = 9 % (3)
E . E 0.3 . 0.24
dF
kT 0.026
1 + e 1+ e
Ionization = 100 C 9 = 91 % (3)
15 14 . 3
(b) no = 10 (91 %) = 9.110 cm (6)
E .E 0.5 . 0.3
Fi
14 11 . 3kT 0.026
(c) n = ne . 9.110 = ne . n = 4.1510 cm (6)
oi ii
A Si bar is doped with 81015 cm . 3 boron atoms and unknown number of donor atoms such that the Fermi level is
0.4 eV above Ei at room temperature.
a) What is the donor concentration