# Basic Principles

Photoconductivity effects in solids were discovered by Smith  at the end of the nineteenth century. In the 1920s, Gudden  developed the photoconductivity theory demonstrating the dependence of photoconductivity, light absorption and luminescence on the light wavelength and assessing that the interaction occurs between one photon and one electron.

The dark conductivity a of a semiconductor is given by:

a = e (n pn + p pp) (5.6)

with and pp the electrons and holes mobility, respectively, and n and p their con­centrations, respectively.

Photoconductivity  Aa is defined as the increase of conductivity occurring in a semiconductor under optical excitation.

When light of near-bandgap energy hits a homogeneous semiconductor, the conduc­tivity increases by an amount Aa due, in most cases, to the increase of the free-carrier densities Ap and An:

Aa = e(An + Ap pp) (5.7)

We recall here that only the majority carrier transport, electrons for n-type and holes for p-type semiconductors, is usually considered since low injection conditions are used. Moreover, the charge neutrality is assumed to be maintained during illumination, i. e., Ap = An. Photogenerated excess carriers in semiconductors are typically orders of magnitude lower than their density in the dark (Ap ^ p and An ^ n); conversely in semi-insulators the excess carriers are much higher than the dark density. Photo-carrier densities An = f Tn; Ap = f Tp depend on the number f of electron-hole pairs gener­ated per second per unit volume. The parameter f is, in turn, related to the excitation intensity Ф(Х) and to the absorption coefficient a(X). The spectral response is therefore a function of X.

By accounting for the Beer’s law

A = a(X)xNt (5.8)

where A is the absorbance, a(X) is the absorption coefficient, x is the penetration depth and Nt is the absorbing species concentration, f can be expressed by:

f = ва(Х)Ф(Х) (5.9)

where в is the number of carrier-pairs generated by each photon (typically в < 1) .

The photoconductivity Aa can be finally expressed, taking into account reflection coefficient R and penetration depth x, as:

Aa = e ваФ(1 – R)(1 – e-a x )(pnrn + pprp) (5.10)

A strict correlation thus exists between a (hv) and Aa (hv), as depicted in Figure 5.6 . Figure 5.6 Light wavelength dependence of the absorption coefficient a and of the photo­conductivity a in the regions above (I), near (II) and below (III) bandgap.

For photon energies h v> EG, corresponding to the high absorption region I in Figure 5.6 the light is mainly absorbed close to the surface, hence the photoconductivity Aa is controlled by the surface carrier lifetime. In the intermediate region h v & EG, (region II) the photoconductivity is controlled by the bulk lifetime, with a maximum occurring for a & 1 /d, d being the sample thickness.

For h v ^ Eg (region III) the bulk lifetime still controls the photoconductivity, which decreases by orders of magnitude as absorption coefficient does. In this region, however, the impinging light induces transitions involving deep levels (DL) in the bandgap. Here, the absorption coefficient a is proportional to the density of deep levels centers NDL by the relation:

a = SNdl (5.11)

with so the optical capture cross section of the centers .

At photon energy exciting extrinsic transitions, the photoconductivity spectra show peaks, the heights of which is related to the density NDL of the deep levels involved in the process.

Usually, photoconductivity measurements are carried out in an ohmic planar configuration, (Figure 5.7(a)). The use of a rectifying Schottky contact configuration (Figure 5.7(b)) sensibly increases the signal intensity. The high collection efficiency, due to the electric field acting across the depletion region, allows well-resolved spectra to be obtained from which many details can be inferred.

The Schottky contact configuration, however, limits the exploration to the depletion region w also when w is much lower than the light-penetration depth.

Light absorption can induce processes other than the intrinsic and extrinsic transi­tions , as for instance intraband transitions, i. e., transitions between internal levels. Intraband transitions cannot be, however, detected by photoconductivity measurements since they do not involve carrier transfer to the conduction or valence band, hence do not affect the free-carrier concentration.