Lecture 4

Question 1

The donor binding energy is often ____. These donor states are called _______ ______.

Answer 1

Small
Shallow donors

Question 2

What are hydrogenic donors?

Answer 2

Donor states that have a similar electron state to that of an electron in a hydrogen atom.

Question 3

Give the equation for the ground state wavefunction of an electron in a hydrogen atom

Answer 3

Question 4

Why is the Bohr radius of an electron bound to a positively charged donor atom much bigger than that of an electron bound to a hydrogen atom?

Answer 4

• The free electron mass is much smaller than the conduction band effective mass for a semiconductor (m_e* ~ 0.1 m_e).
• ε0 is replaced by ε0 εr where εr is the dielectric constant of a semiconductor.

Question 5

Give the equation for the typical Bohr radius of a semiconductor

Answer 5

Question 6

Give the equation for the typical binding energy of an electron to a donor atom

Answer 6

Question 7

Why is the binding energy of an electron to a donor atom much smaller than for an electron to a hydrogen atom?

Answer 7

The reduced effective mass and increased dielectric constant reduce the overall binding energy.

Question 8

Give the equation for the donor energy of an n-type semiconductor with N_D donors per metre cubed

Answer 8

∆E_D = donor binding energy

Question 9

What happens to the energy states of an extrinsic semiconductor at T=0?

Answer 9

All the valence band and donor impurity states will be full so there will be no electrons in the conduction band. The semiconductor will be an insulator.

Question 10

What happens to the energy states of an extrinsic semiconductor at kT < ∆E_D?

Answer 10

The probability of an electron being excited across the semiconductor bandgap is almost 0. But some electrons can be excited from the donor level to the conduction band. The number in the conduction band can be calculated by determining the number density of conduction band electrons.

Question 11

What happens to the energy states of an extrinsic semiconductor at kT ~ ∆E_D?

Answer 11

Almost all the electrons from the donors are excited into the conduction band and n ~ N_D. This is because the thermal energy is comparable to the ionisation energy and the number of available states in the conduction band is usually much larger than the number of donors.

Question 12

What happens to the energy states of an extrinsic semiconductor when kT&raquo_space; ∆E_D?

Answer 12

The number of electrons excited across the bandgap becomes significant and eventually larger than the number of donors. It behaves like an intrinsic semiconductor.

Question 13

Describe the graph of the change in the number density of an n-type semiconductor with 1/T

Answer 13

Question 14

Give the equation for Ohms Law

Answer 14

V = IR

Question 15

Give the equation for resistivity

Answer 15

ρ = AR/L

ρ = resistivity
R = resistance

Question 16

Give the equation for conductivity

Answer 16

σ = 1/ρ = neµ

ρ = resistivity
σ = conductivity
n = number of charged particles
e = charge
µ = mobility

Question 17

Give the equation for current density

Answer 17

j = σE = nev

j = current density
σ = conductivity
E = electric field
n = number of charged particles
e = charge
v = velocity

Question 18

Give the equation for the conductivity in terms of the number of electrons and holes

Answer 18

σ = conductivity
neµ_e = electron conductivity
neµ_h = hole conductivity

Question 19

Give the equation for the Hall coefficient for n-type semiconductors

Answer 19

Question 20

Give the equation for the Hall coefficient for p-type semiconductors

Answer 20

Question 21

Give the equation for the Hall coefficient in semiconductors

Answer 21