Deck 41: Conduction of Electricity in Solids

Question 1

The Fermi-Dirac probability function P(E) varies between:

A) 0 and 1
B) 0 and infinity
C) 1 and infinity
D) -1 and 1
E) 0 and E_F

Answer 1

0 and 1

Question 2

At T = 0 K the probability that a state 0.50 eV below the Fermi level is occupied is:

A) 0
B) 5.0* 10^-9
C) 5.0* 10^-6
D) 5.0 *10^-3
E) 1

Answer 2

1

Question 3

If E₀ and E_T are the average energies of the "free" electrons in a metal at 0 K and room temperature respectively, then the ratio E_T/E₀ is approximately:

A) 0
B) 1
C) 100
D) 10⁶
E) infinity

Answer 3

1

Question 4

We classify solids electrically according to three basic properties. What are they?

A) Conductivity, resistivity, and crystal structure
B) Resistivity, temperature coefficient of resistivity, and crystal structure
C) Resistivity, crystal structure, and number density of conduction electrons
D) Resistivity, temperature coefficient of resistivity, and number density of conduction electrons
E) Conductivity, temperature coefficient of resistivity, and crystal structure

Question 5

Possible units for the density of states function N(E) are:

A) J/m³
B) 1/J
C) m^-3
D) J^-1 . m^-3
E) kg/m³

Question 6

A certain material has a resistivity of 7.8 *10³ $\Omega$ .m at room temperature, and its resistivity decreases as the temperature is raised by 100 $\degree$ C. The material is most likely:

A) a metal
B) a pure semiconductor
C) a heavily doped semiconductor
D) an insulator
E) none of the above

Question 7

In a metal at 0 K, the Fermi energy is:

A) the highest energy of any electron
B) the lowest energy of any electron
C) the mean thermal energy of the electrons
D) the energy of the top of the valence band
E) the energy at the bottom of the conduction band

Question 8

The number density n of conduction electrons, the resistivity $\rho$ , and the temperature coefficient of resistivity α are given below for five materials. Which is a semiconductor?

A) n = 10²⁹ m^-3, $\rho$ = 10^-8 $\Omega$ . m, α = +10^-3 K^-1
B) n = 10²⁸ m^-3, $\rho$ = 10^-9 $\Omega$ .m, α = -10^-3 K^-1
C) n = 10²⁸ m^-3, $\rho$ = 10^-9 $\Omega$ . m, α = +10^-3 K^-1
D) n = 10¹⁵ m^-3, $\rho$ = 10³ $\Omega$ . m, α = -10^-2 K^-1
E) n = 10²² m^-3, $\rho$ = 10^-7 $\Omega$ . m, α = +10^-3 K^-1

Question 9

A certain material has a resistivity of 7.8 *10³ $\Omega$ .m at room temperature, and its resistivity increases as the temperature is raised by 100 $\degree$ C. The material is most likely:

A) a metal
B) a pure semiconductor
C) a heavily doped semiconductor
D) an insulator
E) none of the above

Question 10

For a metal at absolute temperature T, with Fermi energy E_F, the occupancy probability is given by:

A)
B)
C)
D)
E)

Question 11

The energy level diagram shown applies to:

A) a conductor
B) an insulator
C) a semiconductor
D) an isolated molecule
E) an isolated atom

Question 12

The Fermi energy of a metal depends primarily on:

A) the temperature
B) the volume of the sample
C) the mass density of the metal
D) the size of the sample
E) the number density of conduction electrons

Question 13

The speed of an electron with energy equal to the Fermi energy for copper is on the order of:

A) 10^-6 m/s
B) 10^-1 m/s
C) 10 m/s
D) 10⁶ m/s
E) 10⁹ m/s

Question 14

A certain material has a resistivity of 7.8 *10^-8 $\Omega$ .m at room temperature, and its resistivity increases as the temperature is raised by 100 $\degree$ C. The material is most likely:

A) a metal
B) a pure semiconductor
C) a heavily doped semiconductor
D) an insulator
E) none of the above

Question 15

If ρ_m is the mass density of a conducting material, V its volume, M its molar mass, and N_A Avogadro's number, the number density n of conduction electrons in the material is given by:

A)
B)
C)
D)
E)

Question 16

The energy level diagram shown applies to:

A) a conductor
B) an insulator
C) a semiconductor
D) an isolated atom
E) a free electron gas

Question 17

The density of states for a metal depends primarily on:

A) the temperature
B) the energy associated with the state
C) the density of the metal
D) the volume of the sample
E) none of these

Question 18

Electrons in a full band do not contribute to the current when an electric field exists in a solid because:

A) the field cannot exert a force on them
B) the individual contributions cancel each other
C) they are not moving
D) they make transitions to other bands
E) they leave the solid

Question 19

The energy gap between the valence and conduction bands of an insulator is of the order:

A) 10^-19 eV
B) 0.001 eV
C) 0.1 eV
D) 10 eV
E) 1000 eV

Question 20

Which one of the following statements concerning electron energy bands in solids is true?

A) the bands occur as a direct consequence of the Fermi-Dirac distribution function
B) electrical conduction arises from the motion of electrons in completely filled bands
C) within a given band, all electron energy levels are equal to each other
D) an insulator has a large energy separation between the highest filled band and the lowest empty band
E) only insulators have energy bands

Question 21

Compared to an insulator, the energy gap of a semiconductor is:

A) much smaller
B) about the same
C) much larger
D) full of holes
E) full of charge carriers

Question 22

The occupancy probability for a state with energy equal to the Fermi energy is:

A) 0
B) 0.5
C) 1
D) 1.5
E) 2

Question 23

Magnesium has 8.6 x 10²⁸ conduction electrons per cubic meter. What is the Fermi energy for magnesium?

A) 1.8 eV
B) 7.1 eV
C) 9.1 eV
D) 22 eV
E) 28 eV

Question 24

An acceptor replacement atom in silicon might have ______ electrons in its outer shell.

A) 3
B) 4
C) 5
D) 6
E) 7

Question 25

A given doped semiconductor can be identified as p or n type by:

A) measuring its electrical conductivity
B) measuring its magnetic susceptibility
C) measuring its coefficient of resistivity
D) measuring its heat capacity
E) performing a Hall effect experiment

Question 26

A pure semiconductor at room temperature has:

A) more electrons/m³ in its conduction band than holes/m³ in its valence band
B) more electrons/m³ in its conduction band than a typical metal
C) more electrons/m³ in its valence band than at T = 0 K
D) more holes/m³ in its valence band than electrons/m³ in its valence band
E) none of the above

Question 27

A hole refers to:

A) a proton
B) a positively charged electron
C) an electron which has somehow lost its charge
D) a microscopic defect in a solid
E) the absence of an electron in an otherwise filled band

Question 28

Compared to the number of conduction electrons in pure silicon, the number of conduction electrons in doped silicon is:

A) lower by about a factor of 10
B) about the same
C) higher by about a factor of 10
D) higher by about a factor of 1000
E) higher by about a factor or 1,000,000

Question 29

For a pure semiconductor at room temperature the temperature coefficient of resistivity is determined primarily by:

A) the number of electrons in the conduction band
B) the number of replacement atoms
C) the binding energy of outer shell electrons
D) collisions between conduction electrons and atoms
E) none of the above

Question 30

Acceptor atoms introduced into a pure semiconductor at room temperature:

A) increase the number of electrons in the conduction band
B) increase the number of holes in the valence band
C) lower the Fermi level
D) increase the electrical resistivity
E) none of the above

Question 31

A donor replacement atom in silicon might have ______ electrons in its outer shell.

A) 1
B) 2
C) 3
D) 4
E) 5

Question 32

At room temperature, kT is about 0.0259 eV. The probability that a state 0.50 eV above the Fermi level is occupied at room temperature is:

A) 1
B) 0.05
C) 0.026
D) 5.0 *10^-6
E) 4.1 * 10^-9

Question 33

The energy level diagram shown applies to:

A) a conductor
B) an insulator
C) a semiconductor
D) an isolated molecule
E) an isolated atom

Question 34

At room temperature, kT is about 0.0259 eV. The probability that a state 0.50 eV below the Fermi level is unoccupied at room temperature is:

A) 1
B) 0.05
C) 0.026
D) 5.0 * 10^-6
E) 4.1 * 10^-9

Question 35

The contact electric field in the depletion region of a p-n junction is produced by:

A) electrons in the conduction band alone
B) holes in the valence band alone
C) electrons and holes together
D) charged replacement atoms
E) an applied bias potential difference

Question 36

If the density of states is N(E) and the occupancy probability is P(E), then the density of unoccupied states is:

A) N(E) + P(E)
B) N(E)/P(E)
C) N(E) - P(E)
D) N(E)P(E)
E) N(E)(1 − P(E))

Question 37

For a pure semiconductor the Fermi level is:

A) in the conduction band
B) well above the conduction band
C) in the valence band
D) well below the valence band
E) near the center of the gap between the valence and conduction bands

Question 38

For a metal at room temperature the temperature coefficient of resistivity is determined primarily by:

A) the number of electrons in the conduction band
B) the number of impurity atoms
C) the binding energy of outer shell electrons
D) collisions between conduction electrons and atoms
E) none of the above

Question 39

Donor atoms introduced into a pure semiconductor at room temperature:

A) increase the number of electrons in the conduction band
B) increase the number of holes in the valence band
C) lower the Fermi level
D) increase the electrical resistivity
E) none of the above

Question 40

At T = 0 K the probability that a state 0.50 eV above the Fermi level is occupied is:

A) 0
B) 5.0 * 10^-9
C) 5.0* 10^-6
D) 5.0 *10^-3
E) 1

Question 41

A light emitting diode emits light when:

A) electrons are excited from the valence to the conduction band
B) electrons from the conduction band recombine with holes from the valence band
C) electrons collide with atoms
D) electrons are accelerated by the electric field in the depletion region
E) the junction gets hot

Question 42

The gap between the valence and conduction bands of a certain semiconductor is 0.85eV. When this semiconductor is used to form a light emitting diode, the wavelength of the light emitted:

A) is in a range above 1.5 * 10^-6 m
B) is in a range below 1.5 * 10^-6 m
C) is always 1.5 * 10^-6 m
D) is in a range centered on 1.5 *10^-6 m
E) has nothing to do with the gap

Question 43

Application of a forward bias to a p-n junction:

A) increases the drift current in the depletion zone
B) increases the diffusion current in the depletion zone
C) decreases the drift current on the p side outside the depletion zone
D) decreases the drift current on the n side outside the depletion zone
E) does not change the current anywhere

Question 44

When a forward bias is applied to a p-n junction the concentration of electrons on the p side:

A) increases slightly
B) increases dramatically
C) decreases slightly
D) decreases dramatically
E) does not change

Question 45

Application of a forward bias to a p-n junction:

A) narrows the depletion zone
B) increases the electric field in the depletion zone
C) increases the potential difference across the depletion zone
D) increases the number of donors on the n side
E) decreases the number of donors on the n side

Question 46

A sinusoidal potential difference V_in = V_msin( $\omega$ t) is applied to the p-n junction as shown. Which graph correctly shows V_out as a function of time?

A) I
B) II
C) III
D) IV
E) V

Question 47

In an unbiased p-n junction:

A) the electric potential vanishes everywhere
B) the electric field vanishes everywhere
C) the drift current vanishes everywhere
D) the diffusion current vanishes everywhere
E) the diffusion and drift currents cancel each other

Question 48

Which of the following is NOT true when a back bias is applied to a p-n junction?

A) Electrons flow from the p to the n side
B) Holes flow from the p to the n side
C) The electric field in the depletion zone increases
D) The potential difference across the depletion zone increases
E) The depletion zone narrows

Question 49

"LED" stands for:

A) Less Energy Donated
B) Light Emitting Degrader
C) Luminescent Energy Diode
D) Laser Emitting Device
E) none of the above

Question 50

Switch S is closed to apply a potential difference V across a p-n junction as shown. Relative to the energy levels of the n-type material, with the switch open, the electron levels of the p-type material are:

A) unchanged
B) lowered by the amount e^-Ve/kT
C) lowered by the amount Ve
D) raised by the amount e^-Ve/kT
E) raised by the amount Ve

Question 51

For an unbiased p-n junction, the energy at the bottom of the conduction band on the n side is:

A) higher than the energy at the bottom of the conduction band on the p side
B) lower than the energy at the bottom of the conduction band on the p side
C) lower than energy at the top of the valence band on the n side
D) lower than energy at the top of the valence band on the p side
E) the same as the energy at the bottom of the conduction band on the p side