The probability of electrons to be found in the conduction band of an intrinsic semiconductor at finite temperature is which of the following?

Which of the following statements is/are correct? 1) Conductor contains a large number of electrons in the conduction band at room temperature. No energy gaps exist and the valence and conduction bands overlap. 2) A semiconductor is a material in which the energy gap is so large that practically no electron can be given enough energy to jump this gap. 3) An insulator is a solid with an energy gap small enough for electrons to cross rather easily from the valence band to conduction band.

A

1 only

B

2 only

C

3 only

D

1, 2 and 3

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

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

B

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

C

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

D

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

In an intrinsic semiconductor relation between number of free electrons (ne) in conduction band and holes (nh) in valence band is given by:

A

n_e = 2n_h

B

n_e = n_h

C

n_e > n_h

D

n_e < n_h

An N-type semiconductor having uniform doping is biased as shown in the figure. If EC is the lowest energy level of the conduction band, EV is the highest energy level of the valance band and EF is the Fermi level, which one of the following represents the energy band diagram for the biased N-type semiconductor?

A

B

C

D

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 $$m_h^ * $$

Which of the following equations represent the correct expression for the band diagram of the p-n junction? (E1=difference between the fermi level of material and conduction band of n material and E2=difference between the conduction band of n material and fermi level of n material)

A

Ecn – E f = (1/2)*EG – E1

B

Ecn – E f = (1/2)*EG – E2

C

Ef – Ecp = (1/2)*EG – E1

D

Ecn – Ef = (1/2)*EG + E1

The effective density of states at the conduction band edge of Ge is 1.04 × 10¹⁹ cm^-3 at room temperature (300 K). Ge has an optical band gap of 0.66 eV. The intrinsic carrier concentration (in cm^-3) in Ge at room temperature (300 K) is approximately

A

3 × 10¹⁰

B

3 × 10¹³

C

3 × 10¹⁶

D

6 × 10¹⁶

Is the following statement true? Statement: On the basis of band theory of solids the semi-conductors have a completely filled valence band, a partially filled conduction band and a narrow forbidden band.

A

Statement is false

B

Statement is true

Which of the following components is used to create an N-type semiconductor? a. Trivalent impurity b. Pentavalent impurity c. Intrinsic semiconductor d. Extrinsic semiconductor

A

a and c

B

b and d

C

b and c

D

a and d

Diagram shows transient heat conduction in an infinite plane wall. Identify the correct boundary condition in transient heat conduction in solids with finite conduction

A

t = t i at T = 0

B

d t /d x = 1 at x = 0

C

d t /d x = infinity at x = 1

D

d t / d x = infinity at x = 0

The probability of electrons to be found in the conduction band of an intrinsic semiconductor at finite temperature is which of the following?

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