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
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.
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.
(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
c) remains constant
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
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.
c) 68 %
1 – D, 2 – B, 3 – D, 4 – C, 5 – D, 6 – A, 7 – A, 8 – B, 9 – D, 10 – C
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