FROM CURRENT LITERATURE.

Photoelectric Effect in Crystals.

V. Levshin.

1. Change in conductivity. The absorption of light by a crystal is in many cases accompanied by an internal photoelectric effect, as a result of which various properties of the crystal change, and above all its electrical conductivity.

The increase in the electrical conductivity of crystals under illumination has been established for a very large and varied body of material. However, closer examination revealed the complexity of the processes occurring in this case, which does not make it possible to put them into a general framework.

With respect to the photoelectric effect, crystals should be divided into two groups. The first includes: 1) crystals in which the photoelectric effect occurs in the main substance. Impurities, even insignificant ones, sharply reduce the effect observed in this case. Typical representatives of this subgroup are diamond and zinc sulfide; 2) crystals in which the photoelectric effect occurs both in the main material and in impurities. Representatives of this subgroup are many phosphors. The substances of the first group all have a high refractive index \((n > 2)\).

The second group consists of such crystals as cannot by themselves produce an effect; the phenomenon of increased conductivity under illumination is found in them only in the case of ultramicroscopic or submicroscopic disturbances of their crystal lattice or in the presence of colloidal impurities.

Crystals of the first group were investigated by Gudden (B. Gudden) and Pohl (R. Pohl), crystals of the second—by Röntgen, Ioffe, and Bingel (Bingel).

The phenomena occurring in the first group are simpler and therefore better studied. We shall dwell on them in somewhat greater detail.

The first investigations of the increase in conductivity under illumination were carried out by Gudden and Pohl on specimens of \(\mathrm{ZnS}\) containing admixtures of various metals.

Soon, however, it was found that, in order to investigate the mechanism of the phenomenon, it is necessary to separate the primary effect from the secondary one; for this purpose it is preferable to choose specimens as far as possible free of any impurities. Later investigations by Gudden and Pohl were conducted chiefly with pure diamond and zinc sulfide.

The current observed when a crystal is illuminated and high fields are applied to it consists of two parts: 1) a primary current, formed at the expense of charges liberated in the photoelectric effect, and 2) a secondary current, due to changes in the structure of the crystal that occur with time as the current passes through the crystal. It is known that the mere application of high fields

may reduce the specific resistance of the crystal. By gradually increasing the field strength in the dark, one may cause an increase of current that is not proportional to the increase of the field strength. With a prolonged current, further changes occur with time: conducting threads are formed along the field, and the current through them obeys Ohm’s law.

Curve \(b\) in Fig. 1 corresponds to such a current passing through the crystal after some interval of time has elapsed from the moment the current began. It can obviously be obtained by summing curve \(a\) and the straight line \(c\), of which the first corresponds to the initial current in the crystal, and the second to a current obeying Ohm’s law. Thus, when investigating the action of the photoelectric effect, it is first of all necessary to bear in mind the possibility that the imposition of high fields may influence the conductivity.

Fig. 1.

The primary current is due to the formation of charges under the influence of the photoelectric effect. We may assume that it will be proportional to the absorbed energy and does not depend on the field strength, if the latter is sufficiently high (i.e., with increasing voltage the current tends to a certain limiting value—the saturation current). If we add the assumption that the strength of the secondary current, due to changes in the structure of the crystal, may for small intervals of time be taken as proportional to the time during which the current has flowed, then for the quantity of electricity that has passed we obtain the expression \(J_p t + \dfrac{i_s t^2}{2}\), where \(J_p\) is the primary current, \(i_s t = J_s\), while \(J_s\) is the magnitude of the secondary current at the time \(t\). By varying the time of illumination, we should obtain a parabola, from which the values of \(J_p\) and \(i_s\) can be determined. In this way the total current is resolved into its component parts.

In order to satisfy the basic assumptions, illumination was carried out for short intervals of time, and the intensity of the light was taken to be small. The arrangement of the experiment is shown in Fig. 2.

The crystal was placed between two electrodes, to which a high potential difference was applied (the field gradient reached \(20{,}000 \ \dfrac{V}{\mathrm{cm}}\)), measured with Braun’s electrometer. During illumination of the crystal, the current rushed into the condenser and caused a deflection of the needle of a sensitive ballistic galvanometer, \(7 \cdot 10^{-11}\ \mathrm{Coul}\). The discharge of the condenser through a huge resistance \((W = 10^{12}\ \Omega)\) proceeded very slowly, over tens of minutes.

Fig. 2.

The experiments fully confirmed the basic assumptions, and from analysis of the parabolas the form of the curves of the primary and secondary currents shown in Fig. 3 was found.

The mechanism of the process apparently consists in the following. At the moment of illumination, a photoelectric effect takes place inside the crystal. The electrons released, in the presence of a considerable external electric field, immediately rush ...

PHOTOELECTRIC EFFECT IN CRYSTALS

to the anode. This displacement of negative charge could also take place directly from pole to pole; however, it is more likely that the electrons make their way by gradually passing from molecule to molecule. The positive residue does not possess such considerable mobility, and in some cases the positive charge remains in place. Its presence may be demonstrated by a parallel measurement of the potential drop along the crystal with the aid of a special probe, in the dark and under illumination.

The movement of the positive charge toward the cathode can be considerably accelerated by illuminating the crystal with red light, which by itself does not produce a photoelectric effect. In all probability, the displacement of the positive charge proceeds by the tearing away of an electron from a neighboring molecule, so that it is the charge, but not the molecule itself, that is transferred toward the anode.

In the absence of red light the positive charge either remains in place or moves extremely slowly; therefore, if, after stopping the illumination with the exciting light, one begins to illuminate with red light, then one again obtains a current caused by the begun displacement of the positive charges that had previously remained in place. In the limiting case, the quantity of electricity that has passed will then be equal to the quantity of electricity that passed under the initial illumination with the exciting light. Under simultaneous illumination with the exciting and red light, the quantity of electricity that has passed is exactly equal to the sum of the quantities of electricity passing under the same conditions with separate illumination.

Charges that have moved toward the poles do not leave the crystal until their density at the electrodes exceeds a known limit \(\left(\sim 1.5 \cdot 10^{-10}\ \frac{\mathrm{coul.}}{\mathrm{mm}^2}\right)\). They form an opposing electric field, which impedes the subsequent flow of electrons. After illumination is stopped, in the dark, in the absence of an external field, this internal field may persist for many hours. By switching off the external field and illuminating, we obtain, under the influence of the internal field, a current in the direction opposite to the former one, which will gradually equalize the internal field. In this case the quantity of electricity that has passed during the destruction of the internal field proves equal to the quantity that passed during its formation; however, if the density of electricity at the electrodes turns out to exceed the above-mentioned value, then electricity begins to pass to the electrodes, and the process becomes irreversible.

Fig. 3.

With the mechanism described above, the law of additivity discovered by Gudden and Pohl becomes understandable; it consists in the fact that, when only one part of a crystal is illuminated, the specific resistance falls not in that part alone, but throughout the whole crystal, and the increase in conductivity is proportional to the size of the illuminated part.

Having studied in sufficient detail the mechanism of the decrease in resistance in crystals under illumination, Gudden and Pohl made use of this effect to verify quantum relations. According to Einstein, the energy of the electrons emitted in the photoeffect must be \(\le h\nu\), where \(\nu\) is the frequency of the exciting light; the number of emitted electrons \(N\) must equal \(\frac{Q}{h\nu}\), where \(Q\) is the absorbed energy. As is known, the first proposition is well confirmed by experiment. The second also should be justified if each absorbed quantum gives one and only one electron, i.e., if not a single quantum is lost and does not distribute its energy among several electrons. An experiment performed with the surface photoelectric effect gives

for \(N\) values considerably smaller than the required ones (thus, in the experiments of Pohl and Pringsheim the observed \(N\) amounted to only 3% of that expected theoretically). This circumstance may, however, be explained by the fact that only an insignificant part of the liberated electrons proves to be in a state to leave the surface. Therefore the internal photoelectric effect is of exceptional interest for testing the second quantum relation; in carrying out experiments, however, one must be extremely cautious in order to avoid secondary processes which, in turn, may influence the counting of electrons.

The measurement was carried out in three stages. First, the distribution curve of the primary current, at equal incident energy, was determined as a function of the wavelengths of the exciting light for some definite (not too high) voltage of the external field; then the absorption curve of the crystal was measured. Knowing these two curves, it was possible to find the distribution curve of the primary current with respect to wavelengths, referred to equal absorbed energy for the given external field. Then special experiments established the form, identical for all waves, of the saturation curve of the primary current (i.e., the curve showing the change in the magnitude of the primary current, under the given illumination, as a function of the voltage of the external field). Knowledge of this curve made it possible to replace the values of the primary current at low voltage by the corresponding values of the saturation current.

Fig. 4.

The results for diamond are given in Fig. 4. We see that, for diamond, the electron yield referred to unit incident energy gives a sharp maximum at a wavelength of about \(260\ \mu\mu\), whereas when the electron yield is referred to unit absorbed energy there is no maximum. At the same time, in the region of weak absorption from 440 to \(270\ \mu\mu\), there is a rectilinear decrease in the number of emitted electrons with decreasing wavelength, just as follows from the 2-quantum relation of Einstein. The slope of the straight line makes it possible to calculate the value of Planck’s constant \(h\), for which in this case the very good value \(6.8 \cdot 10^{-27}\ \mathrm{erg}\times\mathrm{sec}\) is obtained. A few points in the region of long waves, which do not fall on the straight line by any means, are explained by experimental errors, since the measurements here are very difficult.

As for the region of strong absorption, here the quantum relation is not fulfilled at all, and the electron yield is many times smaller than the theory requires.

Entirely analogous results were obtained for zinc blende and cinnabar \((\mathrm{HgS})\), with the only difference that here the quantum relation could be verified only over a considerably smaller interval of wavelengths. In the region of considerable absorption the quantum relation is not satisfied for them either.

The second group of crystals, whose conductivity under illumination depends on the presence of disturbances of the crystal lattice and on various impurities, was investigated by Röntgen, Joffe, and Bingel. The last carried out his investigations with colored specimens of rock salt. The quantities of electricity liberated by light were measured electrometrically. In order to obtain comparable results it was necessary to resort to the same procedures as Gudden and Pohl; moreover, in order to avoid

…to avoid structural changes, low light intensities and short illumination intervals were used. In order to remove the small accumulated changes after the end of each series of experiments, the external field was switched off, the crystal was short-circuited, and it was strongly illuminated. Under these conditions the experiments could be reproduced over whole weeks.

In this way it was established that, at an illumination of \(5 \cdot 10^{-3}\ \dfrac{\text{cal}}{\text{sec}\cdot\text{cm}^{2}}\), it is possible to vary the field strength from 5 to 50 thousand volts per cm without obtaining a saturation current. The magnitude of the current obeys Ohm’s law. It was further shown that the current strength is proportional to the incident energy, and that the law of additivity established by Gudden and Pohl for crystals of the first group (see above) is well justified when separate parts of the crystal are illuminated; but in the case where the entire crystal is illuminated at once, a disproportionate increase of the current immediately occurs. To decide whether in crystals of this group we are dealing with a true electric current or only with polarization of molecules, Bingle takes as a basis the quantum law

\[ N = \frac{Q}{h\nu} \]

and calculates what displacements of charges would have to be in order to explain the observed current. The calculation showed that in any case the displacements of the charges very greatly exceed the dimensions of the molecules; however, a complete transfer of charges from electrode to electrode does not occur.

1. Relation between phosphorescence and the increase in conductivity under illumination. It is also interesting to note the relation that exists between the increase of conductivity under illumination and phosphorescence. According to Lenard’s views, phosphorescence occurs at the moment when electrons ejected from the molecule by the photoeffect return to their original position. Lenard, however, considers that the increase in the electrical conductivity of phosphors under illumination is not directly connected either with excitation or with the glow of the phosphors.

The experiments of Gudden and Pohl are in contradiction with these views. The named investigators showed first of all that the maxima of conductivity upon excitation by light of different wavelengths coincide very well with the \(d\)-maxima of excitation of Lenard’s phosphors. These conductivity maxima in phosphors under illumination with light of certain wavelengths depend on the appearance of a secondary current, since for detecting them it is necessary to apply high fields and since the addition of red light, which prevents the formation of structural changes, considerably diminishes the current.

The existence of the primary current upon excitation of phosphorescence is also not difficult to detect, although, owing to the fact that phosphors can be obtained only in the form of small crystals, the path of the charges from pole to pole proves to be interrupted; and therefore the observed primary current always proves to be smaller than that required by the quantum relation. The process proceeds as in pure crystals: the negative part of the current appears at once, the motion of positive charges proceeds slowly, and illumination with red light increases their mobility.

When the electrons of an excited molecule return to their original position, a process often (but not necessarily) accompanied by phosphorescence, an increase in conductivity must also occur. Experiments confirm this. However, to detect the effect it is necessary to produce an enhanced transition of electrons, which can be achieved either by applying red light, as was done by Gudden and Pohl, or by heating, as Rupp did. Under both these conditions a flash of phosphorescence is simultaneously observed.

It should also be mentioned that in one of their works Gudden and Pohl describe a new method of exciting sharp flashes of phosphorescence. Their method consists in applying high fields to phosphors, causing the rapid return of the electrons ejected during excitation to their normal position.

3. Change of the dielectric constant. In some crystals, illumination can be found to produce an increase in the dielectric constant. This property is possessed by one of Sidot’s phosphors, ZnS with a slight admixture of Cu as the active metal. The measurement was carried out by comparing the capacitances of two capacitors, one of which had phosphor powder as its dielectric; the capacitance of the other was constant. The observed effect reached a considerable magnitude; thus, in the case of thin transparent layers, the dielectric constant doubled.

The increase of the dielectric constant with time at a constant specified intensity of the exciting light, as well as its decrease after illumination is stopped, proceed over the course of several seconds (in the experiments of Gudden and Pohl this time was 20–40 sec.).

As the intensity of the exciting light increases, the observed effect increases, but more slowly than in proportion to the intensity of the light, and tends toward a certain limiting value. This circumstance cannot be explained by the excitation of all the active centers, since the layers used were sufficiently thick and opaque; therefore one must assume that, in addition to the direct action increasing the dielectric constant, light also produces an opposite action, so that two opposing processes take place in the crystal, mutually balancing each other when the dielectric constant reaches its limiting value. Investigation of the action of light of different wavelengths at the same intensity of the incident light established the existence of a sharply expressed maximum of sensitivity to light of a definite wavelength (about \(400\,m\mu\)), evidently due to greater absorption in this region. However, the effect can be produced even by red light, which does not excite phosphorescence. Sidot phosphors with admixtures other than Cu gave almost no effect. The curves for the increase of the dielectric constant and for the increase of conductivity for different wavelengths of the exciting light have the same general course. However, the first effect is observed only in ZnS with an admixture of Cu. This, as well as certain other circumstances, compels one to regard the two phenomena as merely parallel, but not identical.

LITERATURE

Gudden u. Pohl. Zeitschr. f. Phys. 1, 365. 1920; 2, 181. 1920; 2, 361. 1920; 3, 98. 1920; 3, 123. 1920; 4, 206. 1921; 5, 176. 1921; 6, 248. 1921; 7, 65. 1921; 16, 170. 1923; 17, 331. 1923; 18, 199. 1923; 2, 192. 1920; 3, 1. 1923; 21, 229. 1924.

Bingel. Zeitschr. für Phys. 1924.