Electronic- Intrinsic Semiconductors

Question 1

Families of semiconductors

Answer 1

Group 4 Si and Ge.
Group 3 Al to In bonded to group 5 N to Sb.
Group 6 S to Te bonded to last TM group Zn to Hg

Question 2

Describe the bonding in silicon

Answer 2

Bands correspond to sp3 hybridised molecular orbitals. These have a tetrahedral symmetry appropriate to crystal structure. Has diamond lattice structure. There are 4 levels per atom in the first band

Question 3

What other crystal structure can semiconductors have?

Answer 3

Zinc blend. Group 3 and 5 bonded semiconductors

Question 4

How to work out critical wavelength for semiconductor

Answer 4

This is where a photon is absorbed to excite and electron from the valence to conduction band. Know the band gap.
λc=hc/Eg
This is maximum wavelength (min energy) of photon

Question 5

How to tune the band gap of a semiconductor

Answer 5

Can vary the ternary composition. Can make not whole number ratio between elements in compound. Changes the lattice constant a. Generally decreasing a increases the band gap

Question 6

What happens when a semiconductor is at 0K

Answer 6

The valence band of the semiconductor is full. It is an insulator because there are no empty levels in the VB, no overlapping bands, no thermal energy to excite any electrons across band gap into empty levels in conduction band

Question 7

What happens to semiconductors above 0K?

Answer 7

Some electrons can be promoted to conduction band due to thermal energy. When in CB, behave like free electrons in a metal (easily accelerated by electric field as there are many empty levels).

Question 8

Other ways of making semiconductors conduct

Answer 8

Light of appropriate wavelength can excite electrons leading to temporary conduction (photoconductivity). Electrons with high potential can be injected into CB from another material

Question 9

What does an excited electron from the VB leave behind?

Answer 9

A positively charged hole in the VB

Question 10

E-k curves for valence and conduction bands

Answer 10

Not straight lines. VB starts low then curves up a bit before levelling off at π/a. Conduction band starts at π/a and above end of VB. similar shape but stretched vertically. Solutions for particular bands are periodic with every 2π/a change with k. Means the band gap is not constant it depends on k (will be vertical distance between VB and CB at any k).

Question 11

What is a direct band gap material?

Answer 11

Where the minimum CB energy aligns (same k) with the maximum energy in the VB

Question 12

Effective masses of electrons and holes in semiconductors

Answer 12

Symbol m* with subscript e or h. The effective mass of an electron is not the same as the mass of a free electron and not equal to the mass of its corresponding hole. Because of interaction of the electron with the crystal lattice

Question 13

Energy of CB formula

Answer 13

ECB=hbar^2k^2/2me*

hbar is h/2π

Question 14

Energy of valence band formula

Answer 14

EVB=hbar^2k^2/2mh*

Question 15

Band diagram for T>0K

Answer 15

Energy vs F(E) fractional occupancy. Small amount of conduction electrons above band gap at low fraction. Equal area omitted in VB at high fraction for holes. No electrons in band gap. Ef half way up Eg

Question 16

How to determine population of electrons in CB

Answer 16

Probability of occupation of the state times number of available energy states

Question 17

Formula for Fermi function

Answer 17

F(E)=1/(exp(E-Ef/kBT)+1)
Approximately
exp(-(E-Ef)/kBT)

Question 18

Formula for density of conduction electron states

Answer 18

ρ(E)=((8rt(2π)m^3/2)/h^3)rt(E-Eg)

To find Ncb integrate from Eg to infinity

Question 19

Formula for number of electrons in CB per unit volume, ne (=Ncb)

Answer 19

ne=2((me*kBT/2πhbar^2)^3/2)(exp(-Eg/2kBT)

Same formula for holes (np) but with mh*

Question 20

Formula for intrinsic carrier density

Answer 20

ni=rt(nenp)

Number of e times number of holes

Question 21

How does intrinsic carrier concentration vary with temperature?

Answer 21

It increases steeply at first and then starts to level off (constant curve)

Question 22

What is the band gap for Si?

Answer 22

1.12eV

Question 23

How does conductivity work in Si?

Answer 23

An electron in the CB behaves like a free electron in a metal. The hole it leaves behind moves by VB electrons filling it and leaving a different hole

Question 24

Why does increasing temperature not decrease conductivity like in metals?

Answer 24

The effect of scattering (reduction in mean free path) is much smaller than the effect of the number of charge carriers rapidly increasing with temperature