Lesson_4a.pdf

Lesson 4

Following to B.G. Streetman

4 . EXCESS CARRIERS IN SEMICONDUCTORS

Most semiconductor devices operate by the creation of charge carriers in excess of the thermal

equilibrium values. These excess carriers can be created by optical excitation or electron

bombardment, or as we shall see in Chapter 5, they can be injected across a forward-biased p-n

junction. However the excess carriers arise, they can dominate the conduction processes in the

semiconductor material. In this chapter we shall investigate the creation of excess carriers by optical

absorption and the resulting properties of photoluminescence and photoconductivity. We shall study

more closely the mechanism of electron-hole pair recombination and the effects of carrier trapping.

Finally, we shall discuss the diffusion of excess carriers due to a carrier gradient, which serves as a

basic mechanism of current conduction along with the mechanism of drift in an electric field.

4.1 OPTICAL ABSORPTION

An important technique for measuring the band gap energy of a semiconductor is the absorption of

incident photons by the material. In this experiment photons of selected wavelength are directed at the

sample, and the relative transmission of the various photons is observed. Since photons with energies

greater than the band gap energy are absorbed while photons with energies less than the band gap are

transmitted, this experiment gives an accurate measure of the band gap energy.

It is apparent that a photon with energy hv ≥ E g can be absorbed in a semiconductor (Fig. 4-1).

Since the valence band contains many electrons and the conduction band has many empty states into

which the electrons may be excited, the probability of photon absorption is high. As Fig. 4-1 indicates,

an electron excited to the conduction band by optical absorption may initially have more energy than

is common for conduction band electrons (almost all electrons are near E c unless the sample is very

heavily doped). Thus the excited electron loses energy to the lattice in scattering events until its velocity

reaches the thermal equilibrium velocity of other conduction band electrons. The electron and hole

created by this absorption process are excess carriers; since they are out of balance with their

environment, they must eventually recombine. While the excess carriers exist in their respective

bands, however, they are free to contribute to the conductivity of the material.

A photon with energy less than E g is unable to excite an electron from the valence band to the

conduction band. Thus in a pure semiconductor, there is negligible absorption of photons with hv < E g .

This explains why some materials are transparent in certain wavelength ranges. We are able to "see

through" certain insulators, such as a good NaCl crystal, because a large energy gap containing no

electron states exists in the material. If the band gap is about 2 eV wide, only long wavelengths

(infrared) and the red part of the visible spectrum are transmitted; on the other hand, a band gap of

about 3 eV allows infrared and the entire visible spectrum to be transmitted.

If a beam of photons with hv > E g falls on a semiconductor, there will be some predictable amount

of absorption, determined by the properties of the material. We would expect the ratio of transmitted to

incident light intensity to depend on the photon wavelength and the thickness of the sample. To

calculate this dependence, let us assume that a photon beam of intensity I 0 (photons/ cm 2 -s) is directed

at a sample of thickness l (Fig. 4-2). The beam contains only photons of wavelength λ, selected by a

monochromator. As the beam passes through the sample, its intensity at a distance x from the surface

can be calculated

by considering the probability of absorption within any increment dx . Since a photon, which has

survived to x without absorption, has no memory of how far it has traveled, its probability of absorption

in any dx is constant. Thus the degradation of the intensity - d I( x )/ dx is proportional to the intensity re-

maining at x :

−

(

)

(

)

(4-1)

The solution to this equation is

(

)

= (4-2)

−

and the intensity of light transmitted through the sample thickness l is

I t

= e

−

(4-3)

The coefficient α is called the absorption coefficient and has units of cm -1 . This coefficient will of

course vary with the photon wavelength and with the material. In a typical plot of α vs. wavelength

(Fig. 4-3), there is negligible absorption at long wavelengths (hv small) and considerable absorption of

photons with energies larger than E g . According to Eq. (2-2), the relation between photon energy and

wavelength is E = hc/λ. If E is given in electron volts and X in micrometers, this becomes E —

1.24/ λ.

Figure 4-4 indicates the band gap energies of some of the common semiconductors, relative to the

visible, infrared, and ultraviolet portions of the spectrum. We observe that GaAs, Si, Ge, and InSb lie

outside the visible region, in the infrared. Other semiconductors, such as GaP and CdS, have band

gaps wide enough to pass photons in the visible range. It is important to note here that a

semiconductor absorbs photons with energies equal to the band gap, or larger. Thus Si absorbs not only

band gap light (≈ 1 μm) but also shorter wavelengths, including those in the visible part of the

spectrum.

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