SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

3.2. CHARGE TRANSPORT: AN OVERVIEW 93

FIXED CHARGES

• Ions and tightly bound
  electrons

Important in dielectric

response, polarization

effects

MOBILE CHARGES

• Electrons in the
  conduction band and holes
  in the valence band

Important for current flow

electronic and

optoelectronic devices

CHARGES IN SOLIDS

Figure 3.1: An overview of fixed and mobile charges in solids and their impact on physical
phenomena. Semiconductor devices are dependent upon mobile electrons and holes.

3.2 CHARGETRANSPORT:ANOVERVIEW

Before discussing issues in free carrier (or mobile carrier) transport we remind the reader of
the nature of electronic states in solids in figure 3.2. As noted in chapter 2, in the case of the
perfect crystal we see that in the conduction and valence bands the electronic states are “free,”.
There are no allowed energy levels in the bandgap (density of states is zero in the bandgap, as
shown). In the case of a crystal with defects we still have the free states in the conduction
and the valence bands, but we also have defect-related allowed states in the bandgap region, as
shown in figure 3.2b. In these states (trap states) electrons are not free to move.
We will first provide a simple overview of how electrons respond to applied electric fields. In
figure 3.3 we show a schematic of how electrons (holes) move through a sample when an electric
field is applied. In figure 3.3a we show the situation in a good-quality crystalline material. The
electron moves under the electric field force, but suffers a number of scattering processes. The
scattering occurs due to various imperfections, such as defects and vibrations of atoms (due to
thermal energy). The relation between the electron velocity or distance traveled and applied
field is complex. However at low fields the relation can be described by a simple relation. If
we examine the distance versus time trajectory of a typical electron we observe that the electron
shows a path as shown in figure 3.3. On average the electron trajectory is described by

d = vt

v = μE (3.2.1)

wheredis the distance traveled in timet. The velocityvis proportional to the electric field