In a semiconductor, the concentration of free
electrons is 7 x 1015/cm and that of holes is 3 x
1021/cm?. The semiconductor is
Answers
1. Carrier Concentration
a) Intrinsic Semiconductors
- Pure single-crystal material
For an intrinsic semiconductor, the concentration of electrons in the conduction band is
equal to the concentration of holes in the valence band.
We may denote,
ni : intrinsic electron concentration
pi : intrinsic hole concentration
However,
ni = pi
Simply,
ni :intrinsic carrier concentration, which refers to either the intrinsic electron or hole
concentration
Commonly accepted values of ni at T = 300°K
Silicon 1.5 x 1010 cm-3
Gallium arsenide 1.8 x 106 cm-3
Germanium 2.4 x 1013 cm-3
b) Extrinsic Semiconductors
- Doped material
The doping process can greatly alter the electrical characteristics of the semiconductor.
This doped semiconductor is called an extrinsic material.
n-Type Semiconductors (negatively charged electron by adding donor)
p-Type Semiconductors (positively charged hole by adding acceptor)
c) Mass-Action Law
n0 : thermal-equilibrium concentration of electrons
p0 : thermal-equilibrium concentration of holes
n0p0 = ni
2 = f(T) (function of temperature)
The product of n0 and po is always a constant for a given semiconductor material at a
given temperature.
d) Equilibrium Electron and Hole Concentrations
Let,
n0 : thermal-equilibrium concentration of electrons
p0 : thermal-equilibrium concentration of holes
nd : concentration of electrons in the donor energy state
pa : concentration of holes in the acceptor energy state
Nd : concentration of donor atoms
Na : concentration of acceptor atoms
Nd
+ : concentration of positively charged donors (ionized donors)
Na
-
: concentration of negatively charged acceptors (ionized acceptors)
By definition,
Nd
+ =Nd - nd
Na- = Na – pa
by the charge neutrality condition,
n0 + Na- = p0 + Nd
+
or
n0 + (Na - pa) = p0 + (Nd – nd)
assume complete ionization,
pa = nd = 0
then, eq # becomes,
n0 + Na = p0 + Nd
by eq # and the Mass-Action law (n0p0 = ni
2
)