Abstracts

MECHANISM OF ELECTRONIC CONDUCTIVITY IN DIELECTRICS AND SEMICONDUCTORS *

In the field of the internal photoelectric effect, Gudden is responsible for numerous and very thorough works. Systematic investigations in this field—if one does not count certain individual works that appeared earlier—have been conducted since about 1920. In this short time, however, a rich and very clear experimental body of material has accumulated, awaiting theoretical formulation.

The question may be posed more broadly: what is involved is the mechanism of electronic conductivity of nonmetallic origin.

For metals we now have a comparatively well-developed picture of conductivity, based on the concept of an electron gas. The physical model—a metallic lattice floating in an electron gas—was proposed by Drude quite a long time ago and, in its main features, has survived to the present day. The impact of wave mechanics, whose appearance was marked by such a rapid flowering of metal physics, affected not so much the physical model as the methods of its mathematical description.

On the other hand, the twenty-five years of work by A. F. Ioffe’s school have, in broad outline, revealed to us the mechanism of ionic conductivity in monocrystalline dielectrics. Here we have a lattice with a certain density of “empty” sites and a certain number of free ions torn from the lattice and wandering through the crystal (Zwischengitter-

* Abstract of the article by B. Gudden, “Über Leitungs-und Photoelektronen in Isolatoren und Halbleitern,” Physik. Zeitschrift 21, 1931.

raum Frenkel), or, according to another picture (Hevesy, Braunbek), as a moving ion chain, whose motion is expressed by the spontaneous jumping of an ion from one lattice site directly to the neighboring “empty” site. A series of Hochberg’s works established, in the region of crystals, the validity of Ohm’s law (with allowance for polarization), and thereby the concept of specific electrical conductivity in this region retained its usual meaning.

Between these two rather vivid pictures (electronic conductivity in a metal and ionic conductivity in a monocrystalline dielectric) there lies a much more obscure region: electronic conductivity in a dielectric, caused by the action of light.

In the review article under consideration, Gudden examines two questions: 1) what is the mechanism of photoconductivity in a dielectric (in a semiconductor)? 2) in what way and in precisely which places of the crystal does the influence of light lead to the liberation of electrons?

In a dielectric, electronic conductivity apparently has a completely special character, having nothing in common with the picture of electronic conductivity constructed by us for metals. In connection with this, the criteria by which we are accustomed to distinguish electronic conductivity from ionic conductivity (for example, the sign of the temperature coefficient of electrical conductivity) require reconsideration here and may lead to errors. The only criteria that remain worthy of confidence are the Hall effect for electronic conductivity and the transport of matter for ionic conductivity.

First of all, in order to give at least an approximate answer to the first question posed by Gudden, let us recall the known results of his previous works. Let us imagine a crystal clamped between two flat parallel electrodes. The arrangement of the apparatus is very simple: the cathode is connected to a battery, the anode to ground through a galvanometer. When the crystal was illuminated for a time \(t\), the galvanometer gave a deflection \(I\), which, according to Gudden and Pohl (1921), could be represented in the form

\[ I = I_p t + I_s t^2 \]

\(I_p\) was called the “primary” current, \(I_s\) the “secondary.” The primary current, in turn, is divided into the “negative” primary current and the “positive” primary current, or, in the new terminology, Einsatzstrom and Ersatzstrom.

Electrons liberated by light and going to the anode form the “negative” current. They leave behind positive ions, which impart to the crystal an overall positive potential and weaken the external field. This leads to a weakening of the photocurrent (the “negative” current) and may lead to its complete destruction. To avoid this distorting influence of positive space charges, one may heat the crystal or illuminate it with long rays. In this case the positive ions are given the possibility of being enriched with electrons, torn from the cathode in one way or another. The displacement of these foreign electrons from the cathode—from ion to ion—into the interior of the crystal constitutes the content of what is called the “positive” current. Finally, the secondary current, which grows rapidly with the field strength, is considered by Gudden in the article under review as an electron avalanche—something similar to a discharge in a gas. Each electron, colliding with an ion of the lattice, liberates a new electron. Thus the electron flux rapidly increases as it approaches the anode.

Fig. 1.

Let us dwell in more detail on the “negative” primary current. The dependence on field voltage is shown in Fig. 1 (the case of complete illumination of the entire crystal). The initial part of the curve justifies Ohm’s law. The onset of saturation at a given light intensity is determined by the length of the crystal. As is known, it was precisely from the saturation current, recalculated for the number of absorbed quanta, that it proved possible to establish the elementary character of the process: each quantum leads to the formation of one electron (Pohl and Gudden, 1923).

The motion of electrons here does not have the character of a chaoti-

of the motion of gas particles, as in metals. On the contrary, each torn-off electron is carried in the direction of the field over some segment \(W\) (Wegstrecke, or Schubweg, in Gudden), after which it again gets stuck in the lattice. There exists a certain probability of “getting stuck” (Wiederanlagerungwahrscheinlichkeit), depending on the field strength, on the temperature, and on the structure of the lattice, but not depending on the wavelength of the illuminating light. Thus the successive layers of the crystal in the direction toward the anode absorb the electrons liberated by light in the preceding layers. In this case the absorption coefficient is

\[ \alpha=\frac{1}{W}, \]

where \(W\)—the mean “displacement” of the electron (mittlerer “Schubweg”)—is a quantity that here replaces the concept of the mean free path. The mean “displacement” has nothing in common with the mean free path. Indeed, the mean free path, i.e. the mean distance after traversing which the electron gives up to the lattice the energy it has accumulated in the electric field, should not depend on the field strength, whereas the mean “displacement,” for not very strong fields and not very small crystals, is proportional to the field (the rectilinear portion of the curve in Fig. 1). Saturation occurs when the mean “displacement” becomes equal to the length of the crystal; in this case all (or almost all) of the torn-off electrons reach the anode.

This point of view explains well those dependences which are obtained when the crystal is illuminated not as a whole, but only by a narrow strip of light (a “light probe”), which can be moved along the length of the crystal. Gudden gives curves of the dependence of the current on the position of the light probe on the crystal. The magnitude of the saturation current, according to our mechanism, should increase as the strip of illumination is moved away from the anode. This is indeed observed in reality.

The mechanism of conductivity is most closely connected with the mechanism of electron formation. At exactly what place in the crystal, in what manner, and under what conditions does the interaction of the light quantum with the lattice lead to the liberation of an electron?

It goes without saying that photoconductivity is always determined by the absorption of light; however, not every absorption is accompanied by a photocurrent. As is known, photocurrent maxima are caused by those regions that are best absorbed by the given dielectric. But the reverse is not true: some absorption bands are not reflected in any way on the photocurrent curve.

The reasons for the absence of photoconductivity in these cases may be of twofold origin: 1) purely electrical—when, quite simply, the average magnitude of the “displacement” (Schubweg) is too small, or 2) optical, when the energy of the absorbed quantum is spent, for example, on destroying a molecule (a photochemical effect) or is converted into the thermal energy of the lattice—processes not accompanied by the release of a free electron.

Usually all photoconducting dielectrics are divided into two groups: a) dielectrics possessing direct photoconductivity, i.e. those in which illumination is directly accompanied by the appearance of a photocurrent, and b) those which, before reacting to illumination by an increase in their electrical conductivity, require an increase in sensitivity. The sensitivity to particular wavelengths can again be increased by preliminary illumination of the dielectric with light of another characteristic wavelength. (Thus, for example, NaCl, as is known, becomes sensitive to visible light only after preliminary illumination with X-rays.)

These two groups of dielectrics, however, do not differ in any fundamental way from one another, as might be thought at first glance. The mechanism of electron formation, according to Gudden, is the same in both cases. Here, however, it is necessary to distinguish strictly two successive moments in the process of electron liberation:

1. First of all, under the influence of light, a photochemical process occurs (when NaCl is illuminated with X-rays—the liberation of metallic Na). It has its own characteristic frequency region (the lattice’s own absorption). As a result, in the dielectric there are formed—

there arises something like a “latent image” (latentes Bild).

1. The “latent image” consists of those centers in which the liberation of free electrons can already take place. The absorption of light by these centers—and for them a new frequency interval is already characteristic—leads directly to the internal photoelectric effect.

Depending on how far the region of the lattice’s intrinsic absorption coincides with the absorption region of the “latent image,” we shall have, as two limiting cases, dielectrics of the first or of the second group. The first is when the two regions coincide; the second is when, on the contrary, they lie in different parts of the spectrum.

Such, in its essentials, is the scheme into which we wish to fit the phenomena of photoconductivity. It cannot yet be regarded as either complete or exhaustive. It is not so much a theory of the phenomenon as a direction in which the theory is to be developed.