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1
Chapter 2-2. Carrier properties
Mass like charge is a very basic property of electrons and holes. The mass of electrons in a semiconductor may be different than its mass in vacuum.
Effective mass concept
t
v F q m d
d = − Ε = 0 t
v F q m* d
d = − Ε = n
- Electrons moving inside a semiconductor crystal will collide with semiconductor atoms, there by causing periodic deceleration of the carriers
- In addition to applied electric field, the electrons also experience complex field forces inside the crystals
- The effective mass can have different values along different directions
- The effective mass will be different depending on the property we are observing. So you can have conductivity effective mass, density of states effective mass, etc.
Effective mass
3
Carrier numbers in intrinsic materials
Intrinsic semiconductor or pure semiconductor has equal numbers of electrons and holes at a particular temperature.
Number of electrons/cm^3 [ n ] = number of holes/cm^3 [ p ] Why is n = p?
This is an intrinsic property of the semiconductor and is called intrinsic carrier concentration, n i
At T = 300 K, n i = 2 × 106 / cm^3 in GaAs 1 × 1010 / cm^3 in Si 2 × 1013 / cm^3 in Ge
How large is this compared to the number of Si atoms/cm^3? What happens to n i at higher temperature? At 0 K?
7
Visualization of (a) donors and (b) acceptors
Phosphorus (P) atom Boron (B) atom
Pseudo-hydrogen atom model for donors
0.05 eV
2
s 0
0 0
136 eV n 2 (4π )
*n q 2 s 0
4 d (^) ≈ −
ε
ε = − ε
= − m K
m . K
m E h
136 eV 2 ( 4 0 )^2
4 0 H_._
m q E = − πε
h
(see page 24 of text)
Instead of m 0 , we have to use m n*^. Instead of εo, we have to use K s εo.
K s is the relative dielectric constant of Si ( K s, Si = 11.8).
This is an approximate value. More accurate values are given next.
9
Binding energies for dopants
Questions: How much energy is required to break a Si-Si bond? How much energy is required to break the 5th electron from As in Si? How much energy is required to break a Si-Si bond when that bond is adjacent to a B atom? Does the freeing of an electron from a donor atom create an extra hole?
Energy-band model for donors
