Electronic Bands and Semiconductors - Solid State Physics - Physics Previous Year Questions

1

2007 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2007

Variation of electrical resistivity \( \rho \) with temperature \( T \) of three solids is sketched (on different scales) in the figure, as curves P, Q and R.
Which one of the following statements describes the variations most appropriately?

A

P is for a superconductor, and R for a semiconductor.

B

Q is for a superconductor, and P for a conductor.

C

Q is for a superconductor, and R for a conductor.

D

R is for a superconductor, and P for a conductor.

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2

2007 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2007

An extrinsic semiconductor sample of cross-section \( A \) and length \( L \) is doped in such a way that the doping concentration varies as \( N_d(x) = N_0 \exp\left(-\frac{x}{L}\right) \), where \( N_0 \) is a constant. Assume that the mobility \( \mu \) of the majority carriers remains constant. The resistance \( R \) of the sample is given by

A

\(R = \frac{L}{A\mu e N_0}[\exp(1.0) - 1] \)

B

\(R = \frac{L}{\mu e N_0}[\exp(1.0) - 1] \)

C

\(R = \frac{L}{A\mu e N_0}[\exp(-1.0) - 1] \)

D

\(R = \frac{L}{A\mu e N_0} \)

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3

2007 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2007

An extrinsic semiconductor sample of cross-section \(A\) and length \(L\) is doped in such a way that the doping concentration varies as \(N_d(x) = N_0 \exp\left(-\frac{x}{L}\right)\), where \(N_0\) is a constant. Assume that the mobility \(\mu\) of the majority carriers remains constant. The resistance \(R\) of the sample is given by

A

\(R = \frac{L}{A \mu e N_0} [\exp(1.0) - 1]\)

B

\(R = \frac{L}{\mu e N_0} [\exp(1.0) - 1]\)

C

\(R = \frac{L}{A \mu e N_0} [\exp(-1.0) - 1]\)

D

\(R = \frac{L}{A \mu e N_0}\)

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4

2007 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2007

The drift mobility (in \(m^2 V^{-1} s^{-1}\)) of the conduction electrons is

A

\(6.67 \times 10^{-3}\)

B

\(6.67 \times 10^{-6}\)

C

\(7.63 \times 10^{-3}\)

D

\(7.63 \times 10^{-6}\)

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5

2007 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2007

The relaxation time (mean free time), in seconds, of the conduction electrons is

A

\(3.98 \times 10^{-15}\)

B

\(3.79 \times 10^{-14}\)

C

\(2.84 \times 10^{-12}\)

D

\(2.64 \times 10^{-11}\)

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6

2008 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2008

The kinetic energy of a free electron at a corner of the first Brillouin zone of a two dimensional square lattice is larger than that of an electron at the mid-point of a side of the zone by a factor b. The value of b is

A

\(b = \sqrt{2}\)

B

b = 2

C

b = 4

D

b = 8

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7

2008 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2008

An intrinsic semiconductor with mass of a hole \(m_h\) and mass of an electron \(m_e\) is at a finite temperature T. If the top of the valence band energy is \(E_v\) and the bottom of the conduction band energy is \(E_c\), the Fermi energy of the semiconductor is

A

\(E_F = \left(\frac{E_c + E_v}{2}\right) - \frac{3}{4}k_B T \ln\left(\frac{m_h}{m_e}\right)\)

B

\(E_F = \left(\frac{k_B T}{2}\right) + \frac{3}{4}(E_v + E_c)\ln\left(\frac{m_e}{m_h}\right)\)

C

\(E_F = \left(\frac{E_c + E_v}{2}\right) + \frac{3}{4}k_B T \ln\left(\frac{m_h}{m_e}\right)\)

D

\(E_F = \left(\frac{k_B T}{2}\right) - \frac{3}{4}(E_v + E_c)\ln\left(\frac{m_e}{m_h}\right)\)

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8

2008 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2008

Consider a two dimensional electron gas of \(N\) electrons of mass \(m\) each in a system of size \(L \times L\). The density of states between energy \(\epsilon\) and \(\epsilon + d\epsilon\) is

A

\(\frac{4\pi L^2 m}{h^2} d\epsilon\)

B

\(\frac{4\pi L^2 m}{h^2} \frac{1}{\sqrt{\epsilon}} d\epsilon\)

C

\(\frac{4\pi L^2 m}{h^2} \sqrt{\epsilon} d\epsilon\)

D

\(\frac{4\pi L^2 m}{h^2} \epsilon d\epsilon\)

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9

2008 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2008

The ground state energy \(E_0\) of the system in terms of the Fermi energy \(E_F\) and the number of electrons \(N\) is given by

A

\(\frac{1}{3} NE_F\)

B

\(\frac{1}{2} NE_F\)

C

\(\frac{2}{3} NE_F\)

D

\(\frac{3}{5} NE_F\)

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10

2009 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2009

An electron of wavevector \( \vec{k}_e \), velocity \( \vec{v}_e \) and effective mass \( m_e \) is removed from a filled energy band. The resulting hole has wavevector \( \vec{k}_h \), velocity \( \vec{v}_h \), and effective mass \( m_h \). Which one of the following statements is correct?

A

\(\vec{k}_h = -\vec{k}_e; \vec{v}_h = -\vec{v}_e; m_h = -m_e \)

B

\(\vec{k}_h = \vec{k}_e; \vec{v}_h = \vec{v}_e; m_h = m_e \)

C

\(\vec{k}_h = \vec{k}_e; \vec{v}_h = -\vec{v}_e; m_h = -m_e \)

D

\(\vec{k}_h = -\vec{k}_e; \vec{v}_h = \vec{v}_e; m_h = -m_e \)

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11

2009 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2009

For a Fermi gas of \( N \) particles in three dimensions at \( T = 0 \) K, the Fermi energy, \( E_F \) is proportional to

A

\(N^{2/3} \)

B

\(N^{3/2} \)

C

\(N^3 \)

D

\(N^2 \)

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12

2010 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2010

The valence electrons do not directly determine the following property of a metal.

A

Electrical conductivity

B

Thermal conductivity

C

Shear modulus

D

Metallic lustre

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13

2010 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2010

The Hall coefficient, \( R_H \), of sodium depends on

A

The effective charge carrier mass and carrier density

B

The charge carrier density and relaxation time

C

The charge carrier density only

D

The effective charge carrier mass

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14

2010 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2010

For a two-dimensional free electron gas, the electronic density \( n \), and the Fermi energy \( E_F \), are related by

A

\(n = \frac{(2mE_F)^{3/2}}{3\pi^2 \hbar^3} \)

B

\(n = \frac{mE_F}{\pi \hbar^2} \)

C

\(n = \frac{mE_F}{2\pi \hbar^2} \)

D

\(n = \frac{2^{3/2} (mE_F)^{3/2}}{\pi \hbar^3} \)

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15

2011 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2011

For an intrinsic semiconductor, \(m_e^*\) and \(m_h^*\) are respectively the effective masses of electrons and holes near the corresponding band edges. At a finite temperature, the position of the Fermi level

A

depends on \(m_e^*\) but not on \(m_h^*\)

B

depends on \(m_h^*\) but not on \(m_e^*\)

C

depends on both \(m_e^*\) and \(m_h^*\)

D

depends neither on \(m_e^*\) nor on \(m_h^*\)

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16

2011 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2011

The density of states of electrons (including spin degeneracy) in the band is given by

A

\(\frac{L}{\pi \gamma a \sin(ka)} \)

B

\(\frac{L}{2\pi \gamma a \sin(ka)} \)

C

\(\frac{L}{2\pi \gamma a \cos(ka)} \)

D

\(\frac{L}{\pi \gamma a \cos(ka)} \)

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17

2011 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2011

The effective mass of electrons in the band is given by

A

\(\frac{\hbar^2}{\gamma a^2 \cos(ka)} \)

B

\(\frac{\hbar^2}{2\gamma a^2 \cos(ka)} \)

C

\(\frac{\hbar^2}{\gamma a^2 \sin(ka)} \)

D

\(\frac{\hbar^2}{2\gamma a^2 \sin(ka)} \)

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18

2012 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2012

For an ideal Fermi gas in three dimensions, the electron velocity $v_F$ at the Fermi surface is related to electron concentration $n$ as,

A

v_F \propto n^{2/3}

B

v_F \propto n

C

v_F \propto n^{1/2}

D

v_F \propto n^{1/3}

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19

2012 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2012

A Ge semiconductor is doped with acceptor impurity concentration of $10^{15}$ atoms/cm$^3$. For the given hole mobility of 1800 cm$^2$/V-s, the resistivity of this material is

A

0.288 $\Omega$ cm

B

0.694 $\Omega$ cm

C

3.472 $\Omega$ cm

D

6.944 $\Omega$ cm

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20

2012 · Physics · Solid State Physics · Electronic Bands and Semiconductors

Physics (PH) 2012

Identify the CORRECT energy band diagram for Silicon doped with Arsenic. Here CB, VB, E_D and E_F are conduction band, valence band, impurity level and Fermi level, respectively.

A

Diagram A

B

Diagram B

C

Diagram C

D

Diagram D

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