Energy Bands and Generation Of Carriers Gate Questions - Electronic Devices

Q.1. At T = 300 K, the band gap and the intrinsic carrier concentration of GaAs are 1.42 eV and 10⁶ cm^-3 respectively. In order to generate electron hole pairs in GaAs, which one of the wavelength (λ_c) ranges of incident radiation, is most suitable? (Given that: Plank's constant is 6.62 x 10^-34 J-s velocity of light is 3 x 10¹⁰ cm/s and charge of electron is 1.6 x 10^-19 C)
(a) 0.42 μm < λ_c < 0.87 μm
(b) 0.87 μm < λ_c < 1.42 μm
(c) 1.42 μm < λ_c < 1.62 μm
(d) 1.62 μm < λ_c < 6.62 μm

Correct Answer is Option (a)
Energy of each photon in radiation is given by,

Now, since energy required is more than band gap and energy is inversely proportional to wavelength.
Therefore, λ < 0.87μm

Q.2. The donor and accepter impurities in an abrupt junction silicon diode are 1 x 10¹⁶ cm^-3 and 5 x 10¹⁸ cm^-3, respectively. Assume that the intrinsic carrier concentration in silicon n_i = 1.5 x 10¹⁰ cm^-3 at 300K, kT/q = 26 mV and the permittivity of silicon The built-in potential and the depletion width of the diode under thermal equilibrium conditions, respectively, are 
(a) 0.7 V and 1 x 10^-4 cm 
(b) 0.86 V and 1 x 10^-4 cm 
(c) 0.7 V and 3.3 x 10^-5 cm 
(d) 0.86 V and 3.3 x 10^-5 cm 

Correct Answer is Option (d)

Intrinsic carries concentration,

Build in potential of a p-n junction diode is given by

Depletion width of a p-n junction diode is given by

Q.3. A thin P-type silicon sample is uniformly illuminated with light which generates excess carriers. The recombination rate is directly proportional to
(a) The minority carrier mobility
(b) The minority carrier recombination lifetime
(c) The majority carrier concentration
(d) The excess minority carrier concentration

Correct Answer is Option (d)
Recombination rate,
= Electron and hole concentrations respectively under thermal equilibrium
n_n and p_n = Excess elements and hole concentrations respectively

Q.4. When a silicon diode having a doping concentration of N^A = 9 × 10¹⁶ cm^-3 on p-side and N_D = 1 × 10¹⁶ cm^-3 on n-side is reverse biased, the total depletion width is found to be 3μm. Given that the permittivity of silicon is 1.04 × 10^-12 F/cm, the depletion width on the p-side and the maximum electric field in the depletion region, respectively, are
(a) 2.7 μm and 2.3 × 10⁵ V/cm
(b) 0.3 μm and 4.15 × 10⁵ V/cm
(c) 0.3 μm and 0.42 × 10⁵ V/cm
(d) 2.1 μm and 0.42 × 10⁵ V/cm

Correct Answer is Option (b)
Given:
N_A = 9 × 10¹⁶/cm³
N_D = 10¹⁶/cm³


The maximum electric field occur at the junction.

Q.5. Consider an abrupt PN junction (at T = 300 K) shown in the figure. The depletion region width X_n on the N-side of the junction is 0.2 μm and the permittivity of silicon (ε_si) is 1.044 x 10^-12 F/cm At the junction, the approximate value of the peak electric field (in kV/cm) is _________.  

(a) 25.40
(b) 28.32
(c) 30.66
(d) 32.42

Correct Answer is Option (c)

Q.6. Assume electronic charge q = 1.6 × 10^-19 C, kT/q = 25 mV and electron mobility μ_n = 1000 cm²/V-s. If the concentration gradient of electrons injected into a P-type silicon sample is 1 × 10²¹/cm⁴, the magnitude of electron diffusion current density (in A/cm²) is _________.
(a) 2000 A/cm²
(b) 4000 A/cm²
(c) 6000 A/cm²
(d) 8000 A/cm²

Correct Answer is Option (a)

Q.7. The doping concentrations on the p-side and n-side of a silicon diode are 1 x 10¹⁶cm^-3 and 1 x 10¹⁷cm^-3, respectively. A forward bias of 0.3 V is applied to the diode. At T = 300K, the intrinsic carrier concentration of silicon n_i = 1.5 x 10¹⁰cm^-3 and kT/q = 26mV. The electron concentration at the edge of the depletion region on the p-side is 
(a) 2.3 x 10⁹cm^-3
(b) 1 x 10¹⁶cm^-3
(c) 1 x 10¹⁷cm^-3
(d) 2.25 x 10⁶cm^-3

Correct Answer is Option (a)
Given the doping concentration on p-side
NA = 1 x 10¹⁶ cm^-3
Forward bias voltage, V = 0.3 V
Intrinsic carrier concentration,
n_i = 1.5 x 10¹⁰cm^-3
Thermal voltage,

So, the equilibrium electron concentration on the p-side is

Q.8. An n-type silicon sample is uniformly illuminated with light which generates 10²⁰ electron hole pairs per cm³ second. The minority carrier lifetime in the sample is 1 μs. In the steady state, the hole concentration in the sample is approximately 10^x, where x is an integer. The value of x is_______.
(a) 4
(b) 14
(c) 2
(d) 12

Correct Answer is Option (b)

• Rate of generation =10²⁰ electron-hole pairs per cm³ per second. 
• At steady state (at the end of lifetime) t = 1μsec, concentration of hole-electron pair in 1 μsec is

= 10²⁰ × 10^-6 = 10¹⁴ 
So, x = 14

Q.9. The I-V characteristics of three types of diodes at room temperature made of semiconductors X, Y, and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in all respects except their materials. If E_gX, E_gY, and E_gZ are the band gaps of X, Y, and Z, respectively, then 

(a) E_gX > E_gY > E_gZ
(b) E_gX = E_gY = E_gZ
(c) E_gX < E_gY < E_gZ
(d) no relationship among these band gaps exists

Correct Answer is Option (c)
The current through a diode is given by:

Va = Applied forward voltage

I_s = Saturation current given by the expression:

p_n0 and n_p0 are the minority carrier concentration of holes and electrons respectively given by: 

Also, the intrinsic carrier concentration n_i is related to the Energy bandgap as: 

Thus for greater E_g (bandgap), I₀ will be less at a given bias.

∴ E_gX < E_gY < E_gZ

Q.10. A silicon sample is uniformly doped with donor type impurities with a concentration of 10¹⁶/cm³. The electron and hole mobilities in the sample are 1200 cm²/V-s and 400 cm²/V-s respectively. Assume complete ionization of impurities. The charge of an electron is 1.6 × 10^-19C. The resistivity of the sample (in Ω-cm) is _______

Ans. 0.52
Given,

Resistivity of a semi conductor is given by

= 0.52 Ω-cm

Q.11. A MOS capacitor is fabricated on p-type Si (Silicon) where the metal work function is 4.1 eV and electron affinity of Si is 4.0 eV. E_C - E_F = 0.9 eV, where E_C and E_F are the conduction band minimum and the Fermi energy levels of Si, respectively. Oxide ϵ_r = 3.9, ϵ_o = 8.85 × 10^-14 F/cm, oxide thickness t_ox = 0.1 μm and electronic charge q = 1.6 × 10^-19 C. If the measured flat band voltage of this capacitor is -1 V, then the magnitude of the fixed charge at the oxide-semiconductor interface, in nC/cm², is ________.

Ans. 6.85 - 6.95

Q.12. Red (R), Green (G) and Blue (B) Light Emitting Diodes (LEDs) were fabricated using p-n junctions of three different inorganic semiconductors having different band-gaps. The built-in voltages of red, green and blue diodes are V_R, V_G and V_B, respectively. Assume donor and acceptor doping to be the same (N_A and N_D, respectively) in the p and n sides of all the three diodes.
Which one of the following relationships about the built-in voltages is TRUE?
(a) V_R > V_G > V_B
(b) V_R < V_G < V_B
(c) V_R = V_G = V_B
(d) V_R > V_G < V_B

Correct Answer is Option (b)

• For LED and emitting lights if Red, Blue and Green colours, doping concentration on both sides are equal. 
• We know that energy band gap and built in potential of a p-n junction is inversely proportional to wavelength, i.e.

Energy gap,
Hence, as λ increases, the bandgap, and the build-in potential decreases, i.e.

For λ_R > λ_G > λ_B, the bandgap of the respective diodes will be:

⇒ V_R < V_G < V_B

Q.13. The quantum efficiency (η) and responsivity (R) at wavelength λ (in μm) in a p-i-n photodetector are related by
(a)
(b)
(c)
(d)

Correct Answer is Option (b)

Q.14. Which one of the following options describes correctly the equilibrium band diagram at T = 300 K of a Silicon pnn⁺p⁺⁺ configuration shown in the figure?
(a)
(b)
(c)
(d)

Correct Answer is Option (b)
Fermi level for n & p type semiconductor are given by

E_F = Fermi level
E_c - Conduction band energy
E_v - Valence band energy
N_c - Density of conduction states
N_v - Density of valence states
n - electron density
p - Hole density
from (i) As n increass E_f(n) moves closer to E_c and from (ii), as p increase E_f(p) moves closer to E_v. So fermi level must get closer to E_v for p type and to E_c for n type.