This module gives a set of problems on Band Theory of Solids.
Tutorial on Chapter 2: Insulator, Semi-conductor and Metal.
Q.1. Fermi-level in Metal :
Determine the Fermi-level of Sodium and Copper where n = 2.5×10
22 electrons/cc and n = 8.5×10
22 electrons/cc.
Metals
E
F (eV)
n(#/cc)
W
F (eV)
Light absorbed and re-emitted
Li
4.72
Na
3.12
2.5×10
22
2.3
K
2.14
-
2.2
Rb
1.82
-
Cs
1.53
1.8
Cu
7.04
8.5×10
22
2
Orange
Ag
5.51
4
Appears White because reflects the visible spectrum
Au
11.7
2.3
Yellow
Ca
3.2
Ba
2.5
Pt
5.3
Ta
4.2
W
4.5
StBaCuO
1
Most suitable as Cathode material in Thermoionic Tubes.
Q.2.Density of States [N(E)] is defined as number of permissible states per unit volume per unit energy level:
Show that mean energy of electron in conduction band is (3/5)E
F .
Q.3. Determine P(E
F + kT) in Fermi-Dirac Statistics. Determine Temperature T at which P(E
F + 0.5eV) = 1%.[Answers: 0.27, 1262Kel]
Q.4. Determine the density of occupied states at (E
F + kT) at T=300K. Find the energy E below (E
F ) which will yield the same density of occupied states. [Answer 0.92eV]
Q.5.Determine the Fermi Velocity of conduction electron in Metal Copper and Thermal Velocity of conduction electron or hole in Semi-conductor.
[Hint:
]
{Answer : Fermi Velocity in Metal Copper is 2.7256×10
6 m/s and in semi-conductor Thermal Velocity is 1.17×10
5 m/s]
Q.6.In Copper, ρ(resisitivity)=1.67×10
-8 Ω-m and σ(conductivity)= 6×10
7 S/m = qμn. Where n=8.5×10
28 electrons/m
3 . Determine conduction electron mobility. [ 40cm
2 /(V-s)]
Q.7. 3 m long Copper wire of R= 0.03Ω and the current I through the wire is 15A.
Determine Voltage Drop across the Wire.[0.45V]
Determine the Electric Field within the Wire.[0.15V/m]
Determine the drift velocity of electron within the wire.[0.6×10
-3 m/s]
Determine the Fermi Velocity.[2.7256×10
6 m/s]
Determine the Mean Free Time or Relaxation Time.[2.27×10
-14 s]
Determine the Mean Free Path and compare with the lattice parameter of Copper.[618A°]
Q.8. Typical Resistivity of N-Type Silicon is 1 Ω-cm and typical current density is 100A/cm
2 . Calculate the applied Electric Field in Silicon Sample and calculate the drift velocity. Assume mobility of electron to be 1400cm
2 /(V-s) [Answer:100V/cm and 140×10
3 cm/s]
Q.9. Calculate the intrinsic resistivity of Ge, Si and GaAs. [107Ω-cm; 3.4×10
5 Ω-cm; 7×10
8 Ω-cm].
Q.10. In all the calculations above we have assumed that the effective mass of electron or hole within the solid is the same whereas it is not true. The effective mass in Metals are generally higher than the free space mass and in semiconductors it is lighter as seen from the Table below.
Material
Si
Ge
GaAs
InAs
AlAs
m
*e /m
e
0.26
0.12
0.068
0.023
0.88
m
*hole /m
e
0.39
0.3
0.5
0.3
0.3
E
g (eV)
1.12
0.67
1.42
0.35
2.2
Electrons and holes in a crystal interact with the periodic potential field in the crystal. They surf over the periodic potential variation of the crystal developing roller coaster effect which leads to drastic reduction in effective mass. If effective mass is considered the thermal velocity comes to be much higher.
For electron with effective mass of 0.26m
e the thermal velocity is 2.3×10
5 m/s.
For hole with effective mass of 0.39m
e the thermal velocity is 2.2×10
5 m/s.
Q.11.Find the drift velocity, mean free time and mean free path in a P-Type Sample with hole mobility = 470cm
2 /(V-s) and applied Electric Field E= 10
3 V/cm. All calculations will have to be carried out in Rationalized MKS units that is mobility will be taken as 0.047m
2 /(V-s). Thermal Velocity at Room Temperature is approximately 10
5 m/s.[ 4.7×10
5 cm/s, τ =0.1ps, MFP = 100A°]
Questions & Answers
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
