21
Review of Basic Device Physics
The bandgap energy, E g , for silicon at room temperature (300 K) is ~1.12 eV.
As  the temperature increases, the value of E g for most semiconductors
decreases due the increase in the crystal lattice spacing by thermal expansions. For silicon, the temperature coefficient of E g at 300 K temperature is:
dE dT
g
≅ −
×
−
2 73 10
4
.
e V/K [16]. The temperature dependence of E g for silicon can be modeled by using polynomial equations valid for different range
of temperatures [16,17]. However, in circuit CAD tool SPICE (Simulation
Program with Integrated Circuit Emphasis) [18], the temperature dependence of E g is modeled by [19]
E T
T
g ( )
.
.
=
−
×
+
−
1 160
7 02 10
4 2
1108 T
(2.2)
where:
T is the temperature in Kelvin (K)
E g (T) is in eV
2.2.2 Carrier Statistics
The electrical properties of a semiconductor are determined by the number of carriers available for conduction. This number is determined from the
density of states and the probability that these states are occupied by carriers. The probability that an available state with energy E is occupied by an
Conduction band
Electron energy
Kinetic energy
of electron = E − E c
Kinetic energy
of hole = E v − E
Valence band
E
E g
E
Hole energy
E v
E c
FIGURE 2.1
Energy band diagram of a semiconductor like silicon: E c is the bottom edge of the CB and E v is
the top edge of the VB; the CB and VB are separated by an energy gap E g  = E c –E v .