# 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) = ℏvF|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)𝑒𝑖𝑘𝑎, 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?

a)𝜓(𝑥 + 𝑎) = 𝑢(𝑥)𝑒^𝑖𝑘𝑥

b)𝜓(𝑥 + 𝑎) = 𝑢(𝑥 + 𝑎)𝑒^𝑖𝑘𝑎

c)𝜓(𝑥) = 𝑢(𝑥)𝑒^𝑖𝑘(𝑥+𝑎)

d) 𝜓(𝑥) = 𝑢(𝑥)𝑒^𝑖𝑘𝑥

10. Molybdenum (Mo) crystalizes in a body-centered cubic structure with a lattice constant of 𝑎 = 3.147 Å. If the radius of a Mo atom is one-half of the center-tocenter spacing of the nearest neighbours, compute the percent of the cubic volume, 𝑎3, that is occupied by Mo atoms.

a)50 %

b)32 %

c) 68 %

d)78 %