SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

38 CHAPTER 2. ELECTRONIC LEVELS IN SEMICONDUCTORS

Free states

Bound st

ates

Isolated atoms

E 1

E 2

E 3

E 4

Evac

Free states

Evac

Crystal: Atomic spacing ~1-2 Å

}

}

}

}

}

}

Allowed

energy

bands

..

Bandgaps

Core bands

are like those

in isolated

atoms

Figure 2.5: A schematic description of allowed energy levels and energy bands in an atom and
in crystalline materials.

of allowed bands of energy separated by bandgaps is central to the understanding of crystalline
materials. Near the bandedges it is usually possible to define the electronE–krelation as

E=

^2 (k−ko)^2

2 m∗

wherekois thek-value at the bandedge andm∗is the effective mass. The concept of an effective
mass is extremely useful, since it represents the response of the electron–crystal system to the
outside world.

k-vector
According to the Bloch theorem, in the perfectly periodic background potential that the crystal
presents,theelectronpropagateswithoutscattering. The electronic state∼ exp (ik·r)is an
extended wave whichoccupiestheentirecrystal. To describe the response of the electron waves
to external forces one uses the wavepacket description. The equation of motion for electrons in