Carrier Transport GATE PYQs

Q.1. An abrupt pn junction (located at x = 0) is uniformly doped on both p and n sides. The width of the depletion region is W and the electric field variation in the x-direction is E(x). Which of the following figures represents the electric field profile near the pn junction?
(a)
(b)
(c)
(d)

Correct Answer is Option (a)

• IF Left side is p-region and right side is n-region then electric field triangle will be down warded
• If Left side is n-region and right side is p-region, then electric field triangle will be upward.

Q.2. Consider a silicon sample at T = 300K, with a uniform donor density N_d = 5 x 10¹⁶ cm^-3 illuminated uniformly such that the optical generation rate is G_opt = 1.5 x 10²⁰ cm^-3 s^-1 throughout the sample. The incident radiation is turned off at t = 0. Assume low-level injection to be valid and ignore surface effects. The carrier lifetimes are т_po = 0.1 μs and T_no = 0.5  μS
(a) 1.5 x 10¹³ cm^-3 and 7.47 x 10¹¹ cm^-3
(b) 1.5 x 10¹³ cm^-3 and 8.23 x 10¹¹ cm^-3
(c) 1.5 x 10¹³ cm^-3 and 3.73 x 10¹¹ cm^-3
(d) 7.5 x 10¹³ cm^-3 and 4.12 x 10¹¹ cm^-3

Correct Answer is Option (a) 

Q.3. A piece of silicon is doped uniformly with phosphorous with a doping concentration 10¹⁶ /cm³. The expected value of mobility versus doping concentration for silicon assuming full dopant ionization is shown below. The charge of an electron is 1.6 x 10^-19 C.
The conductivity (in S cm^-1) of the silicon sample at 300 K is____
Hole and Electron Mobility in Silicon at 300 K

(a) 1.82
(b) 1.92
(c) 192
(d) 150.2

Correct Answer is Option (b)

Q.4. Consider a region of silicon device of electrons and holes, with an ionized donor density of N_d⁺ = 10¹⁷ cm^-3. The electric field at x = 0 is 0 V/cm and the electric field at x = L is 50 kV/cm in the positive x direction. Assume that the electric field is zero in the y and z directions at all points.

Given q = 1.6 x10^-19 coulomb,
∈₀ = 8.85 x 10^-14 F/cm,
∈_r = 11.7
for silicon, the value of L in nm is_____

Ans. 32.372 x 10^-9 m

Q.5. A dc voltage of 10 V is applied across an n-type silicon bar having a rectangular cross-section and a length of 1 cm as shown in figure. The donor doping concentration N_D and the mobility of electrons μ_n are 10¹⁶ cm^-3 and 1000 cm²V^-1s^-1, respectively. The average time (in μs) taken by the electrons to move from one end of the bar to other end is__________
(a) 100
(b) 200
(c) 300
(d) 400

Correct Answer is Option (a)

Given,

= 10⁴ cm/s

Q.6. Electric Field of 1 V/m is applied to a Boron doped Silicon semiconductor slab having doping density of 10¹⁶ atoms/cm³ at 300K temperature. Determine the approcimate resistivity of the slab. (Consider intrinsic carrier concentration of Silicon at 300 K = 1.5 x 10¹⁰ / cm³ Hole Mobility = 500 cm²/Vs at 300 K; Electron Mobilty = 1300 cm²/Vs at 300 K).
(a) 0.48 Ω-cm 
(b) 0.35 Ω-cm
(c) 0.16 Ω-cm
(d) 1.25 Ω-cm

Correct Answer is Option (d)
Conductivity of extrinsic semiconductor (σ)= nqμ_n + pqμ_p 
here , n and p are no. of electrons and protons respectively
q = 1.6 x 10^-9 C
μ_n = 1300 cm²/Vs
μ_p = 500 cm²/Vs
As it is Boron doped Silicon semiconductor so it is p-type.
Therefore p = N_A = 10¹⁶ atoms/cm³ 
Using mass action law , n = ni²/N_A
Then , σ = 1.6 x 10^-9 (nμ_n + pμ_p)
, 8 x 10^-1
Resistivity (ρ) = 1/σ
= 1.25 Ω-cm