Semiconducter Devices And Circuit :-Semiconducter Assignment 2 Answers

WEEK 2 – Excursion in Solid State Physics

In this blog we are providing semiconducter assignment 2 answers of NPTEL/SWAYAM. We will provide answers of every week of nptel courses.

1.Number of lattice points per unit cell in a body centered cubic lattice is 

 a) 4 

b) 3 

c) 1 

d) 2

2. Gallium Arsenide (GaAs) has a zinc-blend crystal structure (which is equivalent to face-centered cubic lattice with two atoms per lattice point). Assume a lattice spacing of a = 5.65 Å. How many numbers of atoms per cc are there in GaAs? 

 a) 2.22 × 10^22  

b) 4.44 × 10^22 

c) 1.42 × 10^8  

d) 2.51 × 10^15 

3. X-rays of wavelength 0.5 angstrom undergo a second order reflection at a glancing angle of 10 degrees from a crystal. Find the spacing (in angstrom unit) of the atomic planes in the crystal. 

a) 164.1 

b) 1.44 

c) 0.96 

d) 2.88

4. Consider a semiconductor whose energy dispersion relation [E(k)] for the conduction band is defined by 𝐸 = 𝐴 + 𝐵((𝑘 − 𝐶))^2 where, A, B and C are constants. Assume the mobility of the electron is µ0. Find the mean free time of electrons in the conduction band. 

(a)µ0/2Bqℏ²

(b)Bqℏ²/µ0

(c)µ0ℏ²/2Bq

(d) None of These

5. Assume that the electrons in an n-doped crystalline silicon suffer scattering only due to i) the lattice vibration and ii) the interaction with impurity ions. At an extremely low temperature region, mobility _________ with increase in temperature. (Fill in the gap) 

 a) becomes zero  

b) decreases  

c) remains constant  

d) increases 

6. Consider a 1D crystal with lattice constant ′a′ and crystal length ′L′. Where do you observe the energy band gaps on the energy dispersion graph (E-k diagram)? 

a) At k=nπ/a, where n is an integer

b) At k=nπ/L, where n is an integer.

c) At k=nπ/a, where n is any real number.

d) At k=nπ/L, where n is any real number.

7. What is a Brillouin zone? 

 a) A region of k-space that contains all the unique solutions of the wave-equation.  

b)A region of position-space where the electrons can reside within.  

c)Another name for the unit cell of the crystal.  

d)A region of energy-space that contains all the allowed energy levels. 

8. Consider the 1D band structure E(kx) = ℏv_F|kx|. where, vF is a velocity. What is the effective mass (m∗)?

 a) 𝑚∗ = ℏ𝑣𝐹  

b)Not defined  

c)𝑚∗ = 0  

d) 𝑚∗ = ∞ 

9. Bloch’s theorem for a periodic potential is given by, 𝜓(𝑥 + 𝑎) = 𝜓(𝑥)𝑒^𝑖𝑘𝑎, where ‘a’ is the lattice constant. Assume that 𝑢(𝑥) is the periodic lattice potential given by 𝑢(𝑥 + 𝑎) = 𝑢(𝑥). Which of the following represents an equivalent mathematical form of Bloch’s theorem?