SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

44 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

Vacuum energy

Conduction

band

Valence

band

Core level

Core level

Metal Semiconductor

Highest

occupied

band is

partially

filled

Highest occupied band

is completely filled

Work

function

e

Electron

affinity

e

φ

χ

Eg: Bandgap

Inert

bands

Figure 2.9: Electron occupation of the bands in a metal and semiconductor (or insulator). In a
metal, the highest occupied band at 0 K is partially filled with electrons. In a semiconductor at
0 K, the highest occupied band is completely filled with electrons and the next band is completely
empty. The separation between the two bands is the bandgapEg.

arise when we examine the electron occupation of allowed bands. As shown in figure 2.9 we
can have a situation where an allowed band is completely filled with electrons, while the next
allowed band is separated in energy by a gapEgand is completely empty at 0 K. In a second
case, the highest occupied band is only half full (or partially full).
When an allowed band is completely filled with electrons, the electrons in the band cannot
conduct any current. Since electrons are fermions they cannot carry any net current in a filled
band since an electron can only move into an empty state. Because of this effect, when we
have a material in which a band is completely filled, while the next allowed band is separated
in energy and empty, the material has, in principle, infinite resistivity and is aninsulator or a
semiconductor. The material in which a band is only half full with electrons has a very low
resistivity and is ametal.
Thebandthatisnormallyfilledwithelectronsat 0 Kinsemiconductorsiscalledthevalence
band,whiletheupperunfilledbandiscalledtheconductionband. The energy difference be-
tween the vacuum level and the highest occupied electronic state in a metal is called the metal
work function. The energy between the vacuum level and the bottom of the conduction band is
called the electron affinity.