4

are close together or even overlapping, i.e. there are free charge carriers in the

conductionband and nobandgap.

The extent of the bandgap energy is temperature-dependent. Its greatest value is at T =

0K. If the temperature is increased, thermal vibrations occur within the solid object.

These vibrations also affect the energy bands. The higher the temperature, the greater

the thermal movement and the smaller the clearance between the energy bands,

including both the valence band and the conduction band. According to empirical work

byY.P. Varshni

this canbedescribed as follows:

( )

β−

⋅α

−

=

T

T )0(E TE

2

g

g

E

g

(0): Bandgap energy at T= 0K [eV]

α

,

β

: Empirically determined,material-dependent constants

hows this relationship for silicon. E

g

(0) thus has the value of 1.17eV,

α

=

K

eV 10 73.4

4

−

⋅

und

β

=636K.

Dependenceof the bandgapenergyE

g

on temperatureT for silicon

The statistical distribution of electrons F

n

(E) in the conduction band and the holes F

p

(E)

in the valence band can be described simplified as the function of the temperature T

using theMaxwell-Boltzmann statistic

:

Tk

EE

n

F C

e )E(F

⋅

−

−

=

Tk

EE

p

V F

e )E(F

⋅

−

−

=

F

n

(E): Statistical distributionof electrons in the conductionband [nounit]

F

p

(E): Statistical distributionof holes in the valenceband [nounit]

6

Named after Scottish physicist James Clerk Maxwell (1831 - 1879) and Austrian physicist Ludwig Boltzmann

(1844 - 1906).

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