Barrier-Layer Photocells

I. Kurchatov, Leningrad

In the last 3–4 years, a third has been added to the two long-known kinds of photoelectric effect (external and internal): the barrier-layer photoeffect.* The latter occurs at the boundary of contact between two bodies. Not at every contact, however, is a barrier-layer photoeffect possible—it arises only in the case when, between the contacting surfaces, there is a barrier layer that impedes electronic exchange between the two bodies entering into contact. Such a barrier layer may in some cases be formed by a very narrow gap, of thickness \(5 \cdot 10^{-8} \div 2 \cdot 10^{-7}\) cm. Electronic exchange through the gap is impeded; the probability of electrons passing through it is small and decreases very sharply as the thickness of the gap increases—at \(10^{-6}\) cm it is practically equal to zero (Frenkel\(^{1}\)). A barrier layer may also be formed by a layer of semiconductor; the mean free path of an electron in the semiconductor must then be less than the thickness of the layer. Through a barrier layer formed by an interlayer of such a semiconductor, obviously only those electrons will pass whose free path length is greater than the thickness of the layer. In the barrier-layer photoeffect, electrons are torn away in the bodies adjoining the barrier layer and, passing through the layer, charge one or the other (as will be clarified below, depending on the direction of the process) contact surface.

* In German terminology, Sperrschicht photoeffekte.

At the present time, sufficiently extensive work has already been carried out to make it possible to unite all the studies from a certain general point of view. The purpose of the present review was to record those conceptions which have crystallized in the course of the preceding work and which, insofar as the author can judge, are now being laid as the basis for the further development of the field under consideration.

1. General Characteristics

Although cases of the barrier photoeffect had been known for a long time (Ulyanin ²), the whole question underwent intensive development only after Lange’s ³ investigation of the so-called cuprous-oxide elements. These elements are described in Lange’s article, translated into Russian and published in No. 5 of Uspekhi fizicheskikh nauk for 1931.* There are also references there to the barrier photoeffect in sulfurous lead. In 1931 Bergmann ⁴ described selenium cells, and O. V. Losev ⁵—silicon-carbide barrier photoelements.

This list includes the most widespread types of devices of this kind; however, the barrier photoeffect is also reproduced on a number of other semiconductors—it is known, for example, for molybdenite and bismuthite.

All barrier photoelements are constructed from a semiconductor, onto the surface of which, by one method or another—most often by cathodic sputtering or evaporation—thin layers of metal are applied. The barrier layer is thereby formed, so to speak, by itself; only in recent times have investigators directed their efforts toward taking into account the conditions of formation of the layer and have made attempts to control experimentally its geometrical and physical structure.

In the case of Losev’s silicon-carbide elements, the barrier layer is formed by depositing on the surface of the crystal a special substance, the chemical nature of which is still unknown.

* We refer readers who would like to become acquainted with the constructive design of the device to this article.

The thickness of this layer varies from 10 to 1 μ; its presence on the crystal is absolutely necessary for the occurrence of the blocking photoeffect in the element.

When a blocking photocell is illuminated, an electromotive force arises in the circuit; according to its direction, elements with a front and with a back effect are distinguished. In elements of the first type, to which systems with selenium and carborundum belong, the upper electrode 1 (Fig. 1) is charged negatively with respect to the lower electrode 2. In elements with a back effect, electrode 2 is charged negatively with respect to electrode 1. Cuprous-oxide elements, depending on the method of manufacture, give one or the other effect. In some cases, however, for some regions of the spectrum these elements give a back effect, and for others a front effect.^6

Fig. 1.

At the present time it can be said with complete confidence that, at least in the blocking photocells listed above, the processes are purely electronic. In the elements, no traces of fatigue are observed even after very prolonged (300 hours) continuous illumination. The electrical conductivity of all the semiconductors listed above that form the blocking element is of a purely electronic character.

2. Theoretical scheme of the mechanism of the blocking photoeffect

It has been shown by numerous investigations (Schottky,^7 Juzé and Nasledov^8 et al.) that the presence of any appreciable blocking photoeffect in elements with a sufficiently transparent conductor (Cu₂O) is always connected with the unipolar electrical conductivity of the system. In addition, it is known (Kurchatov and Sinelnikov^9) that with such a change in the contact conditions, when the direction of rectification changes, the sign of the blocking pho-

photoeffect: the front effect changes into the back effect and conversely. Thus it must be admitted that the conditions for the occurrence of both rectification and the barrier photoeffect are the same. This connection enabled Schottky, and then Kurchatov, Sinelnikov, and Borisov^9, to develop a scheme for the mechanism of current in barrier photoelements, which amounts to the following. A necessary condition for the existence of the barrier photoeffect, according to this scheme, is the presence of a gap between the semiconductor \(B\) and the metallic electrodes \(1\) and \(2\) adjoining it (Fig. 1). When light falls (from above in Fig. 1), electrons are torn out in metal \(1\), in semiconductor \(B\), and in metal \(2\). (In selenium elements, where the semiconductor strongly absorbs in the visible region of the spectrum, the tearing out of electrons in metal \(2\) is, evidently, impossible.) In view of the fact that the incident light quanta interact in the metal with free electrons, and in the semiconductor with bound electrons, the number of liberated photoelectrons, calculated for one and the same absorbed energy, proves to be different in the two cases.

Recently theoretical considerations have appeared indicating that the absorption of light in a metal creates a smaller number of photoelectrons than in a semiconductor. Without dwelling on this in greater detail, we shall confine ourselves here to citing the works of Gudden and Pohl, which experimentally showed that every light quantum absorbed in a dielectric or semiconductor causes the appearance of one photoelectron. At the same time it is well known that light quanta lose their energy in a metal not only in the process of the photoeffect, and that the number of photoelectrons in them is smaller than the absorbed number of quanta.

Thus, when a barrier photoelement is illuminated, the electron flux from the semiconductor into the metal will be greater than the flux from the metal into the semiconductor, and the electrode adjoining the semiconductor will begin to be charged by the electrons that have slipped through the barrier layer; below the elements determining the electrical equilibrium of the system will be clarified.

In the case where the gaps \(a\) and \(b\) (Fig. 1) are completely identical and the semiconductor \(B\) is sufficiently transparent, the element, when illuminated, will give no current in the external circuit if electrodes \(1\)—\(2\) are closed. Upon illumination of such an element, only potential jumps of one and the same magnitude will arise in each of the gaps. If, however, the semiconductor is not transparent, only the upper electrode will be charged, and a current corresponding to the front effect will arise in the system. From the point of view developed here, it is evident that in elements with a sufficiently transparent semiconductor the presence of gaps does not yet ensure a current upon illumination: for a current to arise in the circuit, asymmetry of the gaps at the electrodes must be required. The asymmetry of the gaps at the semiconductor clamped between metallic electrodes leads to unipolar conductivity of the element, which accounts for the connection indicated above between rectification and the barrier photoeffect in cuprous-oxide elements.

Modern views on the mechanism of rectification in electron-conducting systems have been collected and developed in the work of Ioffe and Frenkel \(^{10}\). Using this work, it is easy to determine, without resorting to other methods, the presence of a gap at one or another electrode of an element from the direction of rectification of the system. Proceeding from the fact that the distribution of electrons over energies in a semiconductor obeys Boltzmann statistics, while in a metal it obeys Fermi statistics, Ioffe and Frenkel showed that the larger current through a gap will always pass in the case when electrons move from the metal into the semiconductor. Thus, in the case where (Fig. 1) the larger current passes at a negative potential of \(2\) with respect to \(1\), one may assert that the gap also lies at electrode \(2\); upon illumination this electrode will be charged negatively in the process of the barrier photoeffect—we shall obtain a barrier photoelement with a rear effect. In the other direction, the element will give a front effect, in connection with the fact that in this case the gap will prove to be at electrode \(1\). In this way, the fact established experimentally—and for a long time seeming mysterious—that in cuprous-oxide-

element, the electrode from which electrons easily depart during rectification itself becomes negatively charged in the process of the barrier-layer photoelectric effect. The considerations developed make it easy to explain the previously described inversion of the photoelectric effect when the element is illuminated with light of different wavelengths, if one takes into account the spectral distribution of light absorption by the semiconductor.

3. Experimental substantiation of the scheme of operation of barrier-layer photocells

According to the scheme set forth, it is clear that the same electrons take part in the barrier-layer photoelectric effect as in the change of the resistance of a semiconductor under the action of light in the process of the internal photoelectric effect.

Fig. 2.

Fig. 3.

It must therefore be thought that only those semiconductors in which, in the given region of the spectrum, an internal photoelectric effect occurs are suitable for the construction of barrier-layer photocells. Moreover, one may expect a correspondence between the spectral distribution of the sensitivity of the barrier-layer photocell and the effect of the change in the resistance of the semiconductor-

...under the action of light, at least in regions of the spectrum remote from the sensitivity boundary.

Both conclusions are fully confirmed by experiment. The semiconductors of all existing barrier-layer photoelements possess an internal photoeffect; the spectral distributions of the sensitivity of both effects coincide with one another. Measurements of the sensitivity of barrier-layer photoelements with a Cu₂O semiconductor for the rear effect were carried out by Lange[^11], and for the frontal effect by the author and Sinel’nikov[^6], and are given, respectively, in Figs. 2 and 3.

In both cases, along the ordinate axis are plotted the current strengths in the photoelement closed through a galvanometer of low resistance (no extraneous electromotive force was included in the circuit). The current strengths in Figs. 2 and 3 are referred to the spectrum of constant energy. The effect of the change in the resistance of Cu₂O under the action of light of different wavelengths was measured at one time by Pfund[^12]. His data, likewise for a spectrum of constant energy, are presented in Fig. 4. Curve I refers to direct incidence of the light; curve II was taken from a source whose light passed through a layer of the same Cu₂O.

Fig. 4.

In Lange’s experiments with the rear effect it is necessary to compare the data of the curve with II; in those of the author and Sinel’nikov, with curve I. As is seen from a comparison of the data presented, between the spectral distribution of the intensity of the barrier-layer and of the internal photoeffect there is found the same parallelism that was postulated above. This parallelism, however, should be observed only in regions of the spectrum sufficiently remote from the boundary of action of the barrier-layer photoelements. Electrons torn away in the process of the internal effect, in passing through the barrier layer, must expend work; thus the spectral boundary of the barrier-layer photoeffect must be shifted toward shorter wavelengths in relation to the spectral boundary of the internal photoeffect. Such a shift

experimentally discovered by the author, Sinelnikov and Borisov[^9] for barrier photoelements with Cu\(_2\)O and selenium. For Cu\(_2\)O the limiting wavelength of light still producing the internal photoeffect, on the basis of Focht’s data[^13], was taken by the indicated researchers to be equal to 4000 mμ. The sensitivity boundary of the corresponding barrier photoelements lies at 1400 mμ. The work lost by an electron in passing through the barrier layer is thus equal to \(\sim 0.5\) V. For selenium, the limits of both effects were determined directly in experiment (Fig. 5). Curve 1 represents the effect of the change in resistance under the action of light; curve 2, the intensity of the barrier photoeffect in a selenium element with a semitransparent silver electrode; curve 3, with gold electrodes. The transition work here is likewise equal to \(\sim 0.5\) V. Depending on the method of preparing the plates, the boundary of the barrier photoeffect is shifted somewhat to one side or the other, and the transition work varies in the experiments from 0.6 to 0.4 V. No influence of the electrode material on the boundary was found in the experiments.

Fig. 5.

We conclude this paragraph with the presentation of the material given, although the experimental data supporting our theoretical scheme are by no means exhausted by it; on the contrary, the content of the following paragraphs reduces to the same experimental description of further aspects of the scheme. It seems to us, however, that without the experiments cited, with the spectral distribution of the intensity of both effects, all the remaining, rather extensive experimental material would still not make it possible to create a clear conception of the mechanism of the barrier effect.

4. ELECTRICAL EQUILIBRIUM IN BARRIER-LAYER PHOTOCELLS

The equivalent circuit of a photocell may be given in the form shown in Fig. 6. A barrier-layer photocell is a current source (solid arrows), which is then distributed in the circuit, closing through \(R_1\) and \(R_2\)—the resistance of the semiconductor and of the external circuit—and through \(R_3\)—a resistance not obeying Ohm’s law and characterizing the outflow of electrons (dashed arrows) from the metallic electrode back into the bulk of the semiconductor. The nature of this outflow cannot yet be regarded as definitively established. Generally speaking, one may think that the outflow consists of an electron current through the barrier layer and of “eddy short circuits” through those points of contact between the metal and the semiconductor where complete contact is effected (Fig. 7). Using the circuit, let us first consider the dependence of the voltage of an open-circuit photocell on the intensity and wavelength of the incident light. In the case of a vacuum photocell, in an equilibrium electrical system the electromotive force of an open-circuit photocell does not depend on the light intensity and is determined from the equation

\[ V=\frac{h\nu-P}{e}. \tag{1} \]

In a barrier-layer photocell, because of the outflow of electrons from electrode 1 (Fig. 6), the electromotive force will not attain the values required by the quantum law (1), and will depend on the intensity of the incident light. Auwers and Kerschbaum\(^{14}\) were the first to work out this question in detail.

From measurements of the passage of current in a dark barrier-layer photocell, which, as we know, at the same time,

is also a rectifier, it is known that the dependence of the current through it on the voltage, with a negative charge on electrode 1 (Fig. 6), can be represented by the curve in Fig. 8.

Fig. 8.

The current through the dark rectifier will evidently be the outflow of electrons in a photoelement operating in the light. Thus, as the intensity of the incident light increases, with the current from 2 to plate 1 increasing linearly with it, the outflow from plate 1 into the semiconductor will grow faster than according to a linear law, and the electromotive force of the open-circuit element, as a function of the intensity of the incident light, will give a curve having the character of saturation. This kind of dependence has been studied many times by various investigators. Fig. 9, taken from the work of Krakau-Lepeshinskaya[^15], well illustrates the theoretical relations. The data refer to a valve photoelement with \(\mathrm{Cu_2O}\) and were taken for the back effect (the curve \(E_\phi\)). From the circuit of Fig. 6 it is evident that the current in a short-circuited element must increase linearly with the light intensity, since the potential difference between 1 and 2 will then still be so insignificant that the outflow from 1 to 2 will still increase linearly with the voltage. This dependence was carefully traced by Auzr and Kerschbaum[^14], as well as by Krakau-Lepeshinskaya (the curve \(I_\phi\) in Fig. 9). The equivalent-

Fig. 9.

... scheme makes it possible simply to analyze the rather complex picture of the temperature dependence of a number of characteristics of barrier-layer photocells[^16],[^17]. Without going here into a detailed exposition of all the material collected, we consider it useful to examine the question of the dependence of the current strength in a barrier-layer photocell on temperature at constant intensity of the incident light and at various external resistances of the circuit. This dependence for the front effect in elements with Cu₂O is presented in Fig. 10[^6]. When the temperature is lowered, an increase of the current is first observed, followed by its decrease. In analyzing this course of the current one should bear in mind that the electronic photocurrent, at least in a first approximation, does not depend on temperature.

Fig. 10.

The increase of the current when the temperature is lowered is caused by an increase in the resistance \(R_3\) for the outflow of electrons from 1 to 2; from experiments on rectification in a dark element it is known that the current through the barrier decreases when the temperature is lowered. Thus, when the temperature is lowered, a larger part of the primary photocurrent branches off into the external circuit. The smaller the resistance of the external circuit, the smaller the role played by the currents branching off into the resistance \(R_3\), and the flatter the dependence on temperature becomes, as is clearly visible in Fig. 10.

Fig. 11.

The decrease of the current upon further lowering of the temperature is connected with the growth of the internal resistance \(R_1\) of the semiconductor; the current in the circuit almost ceases to depend on the external resistance \(R_2\).

Concluding the consideration of the equivalent circuit, it is necessary to point out an interesting attempt by Körös and Zeleny[^18] to construct a physical model of a barrier-layer photocell. This model includes a vacuum photocell, a detector, and a number of resistances. The model circuit, shown in Fig. 11, requires no special explanation.

Comparative measurements of a number of characteristics were carried out on the model and on a selenium barrier-layer photocell. In Fig. 12 the relation is given between the intensity of light (axis of abscissae) and the open-circuit voltage of the selenium photocell for different regions of the spectrum; in Fig. 13 the same relation is given for the model. In both cases, along the abscissa axis there is plotted not the light intensity directly, but the current in a short-circuited circuit, proportional to it. As can be seen, not only the character but also the numerical values of the voltages in both cases are the same—the constants of the circuit were chosen so successfully. The model was used to determine the work that can be obtained from the element at different intensities of the incident light, depending on the external resistance. The work at a given light intensity depends on the magnitude of the external resistance, giving maximum values for certain definite values of it. At higher illumination intensities this optimum resistance is smaller than at weaker ones, which is connected with the presence of the detector in the model, and in the barri—

tail photocell—the currents of “eddy short circuits” and electronic diffusion from the metal into the semiconductor. The experimentally measured energy in the external circuit as a function of the external resistance and the intensity of illumination is presented in logarithmic coordinates in Fig. 14.

5. Characteristics of barrier-layer photocells with an additional electromotive force in the circuit

The study of the electrical characteristics of an illuminated barrier-layer photocell in the presence of an additional electromotive force in the circuit has been carried out by many investigators. But it must be said that only O. V. Losev\(^5\) obtained results allowing a simple physical interpretation. The results of other authors retain value at present only as a phenomenological characterization of barrier devices of one type or another. Among such studies, the most thorough should be considered the work of V. N. Krakau-Lepeshinskaya\(^ {15}\) on the back effect in cuprous-oxide elements manufactured by the Central Radio Laboratory. Here we consider it useful to set forth in sufficient detail the methods and results of the work of V. N. Krakau-Lepeshinskaya, with the aim of giving an idea of the order of magnitude of the voltages and currents in an illuminated element. The production of the indicated elements was standardized in the laboratory of the CRL headed by B. A. Ostroumov, and the data given below thus characterize devices whose properties are firmly ensured by taking account of the experimental conditions of their manufacture. It must be said that the cuprous-oxide barrier-layer photocells of the CRL by no means give the maximum values of current and voltage of devices of this kind, which by one or another

Fig. 14.

were recorded experimentally by researchers, and in a number of cases give values tens of times greater than the values for TsRL photocells. Interest in TsRL cells, however, still remains very great, since other researchers have not been able to determine the conditions ensuring large values of the corresponding characteristics of the cell that are stable from one instrument to another.

Kuproxide valve photocells of the TsRL are constructed in the form of rods 50 mm long and 2 mm in diameter. To eliminate possible subsequent changes, the rods are placed in evacuated glass tubes. In the experiments described below, illumination was produced by white light from a pointolite lamp, the light of which, after passing through a heat filter, was focused on the surface of the photocell.

Fig. 15.

The measurement of the photo-electromotive forces and photocurrent when the cell was connected in a circuit with an external source of e.m.f. was carried out in the compensation circuit shown in Fig. 15. By the photocurrent and photo-electromotive force of a cell connected in a circuit with an external e.m.f., we shall in what follows understand the differences of the e.m.f.’s and current intensities determined in the compensation circuit for the illuminated and dark photocell. In addition, let us agree to call the direction of the external e.m.f. positive when it is directed opposite to the e.m.f. of the valve photocell. Figures 16, 17, 18, 19, and 20 present the results of the measurements. In Fig. 16 the dependence of the photocurrent and photo-electromotive force on the externally applied voltage is given for a luminous flux of 38 lumens. First of all it should be noted that both the photocurrent and the photo-electromotive force, at a certain external positive

voltage changes its sign. As was found, the magnitude of this voltage does not depend on the intensity of the light and remains unchanged, within \(0.095 \div 0.1\ \mathrm{V}\), for all specimens.

Fig. 16.

This remarkable result has not yet been explained at the present time. In Fig. 17 the dependence is given

Fig. 17.

photocurrent on the magnitude of the external negative voltage for the value of the flux indicated on each of the curves. In Fig. 18 the same dependence is given for an external positive voltage. Finally, in Figs. 19 and 20 the

Fig. 18.

Fig. 19.

dependence of the photoelectromotive force on the external negative (respectively positive) voltage is given for different fluxes of light incident on the photocell.

The difficulty of a physical interpretation of the data obtained comes down to the fact that the change in the barrier photoeffect in the electric field formed in the barrier layer by the additional e.m.f. is superimposed by currents through the semiconductor. It does not seem possible to eliminate this influence by measuring the currents through the element in the dark, since

Fig. 20.

when the element is illuminated, owing to the internal photoeffect the electrical conductivity of the semiconductor changes.

In carborundum barrier photoelements, in all probability because of the strong absorption of light, this distorting influence of the internal photoeffect has little effect on the purity of the resulting picture, at least if one judges this from the clarity of the theoretical conclusions that can be drawn from the experiment.

In Fig. 21 is given the dependence of the current strength in the circuit on the electromotive force for the illuminated \(L\) and non-illuminated \(A\) contact of a steel point on carborundum with an active layer (Losev). Noteworthy in these curves are: 1) the presence of saturation current for voltages drawing electrons out of the crystal—the curve \(L\) in the left-hand part of the figure runs paral-

...the curve \(A\); 2) the equality of the current in the dark and illuminated photocell for a voltage of the other sign, which signals the complete absence, in the experiment, of any distorting influence of the internal photoeffect; 3) the occurrence of an e.m.f. in the barrier-layer photocell of the order of whole volts; as is seen from Fig. 21, the current is reduced to zero at an opposing e.m.f. of \(3.4\ \mathrm{V}\). In these experiments the contact was illuminated by a 2-ampere voltaic arc through a glass light filter that did not appreciably transmit rays with wavelengths shorter than \(3300\ \text{Å}\). Quanta of this wavelength carry an energy of \(3.73\ \mathrm{V}\); the \(3.4\ \mathrm{V}\) found in the experiment thus indicate the possibility of converting, in the barrier-layer photoeffect, \(90\%\) of the light energy of a quantum into electrical energy. The thickness of the active layer of silicon carbide was determined by O. V. Losev for this crystal and proved to be equal to \(1\mu\).

Fig. 21.

It is necessary, from these experiments, and also from certain other investigations by the same author, to accept that within a semiconductor an electron can travel, without any special loss of energy, distances of the order of \(10^{-4} \div 10^{-5}\ \mathrm{cm}\). Below we shall see that almost the same conclusions, on quite different and, it must be said, not so convincing grounds, are reached by Schottky and Gudden.

With an increase in the thickness of the active layer, the e.m.f. of the barrier-layer silicon-carbide photocell decreases; at \(11\mu\) it is only \(0.03\ \mathrm{V}\), at \(3\mu\)—about \(0.7\ \mathrm{V}\) for the same illumination intensity as in the data of Fig. 21. Unfortunately, the quantum yield of the photoeffect was not determined in the investigation, and thus it is impossible to form a judgment about the energetic properties of silicon-carbide cells with an active layer.

6. The Barrier Photoeffect in Polarized Light

Measurements with polarized light were carried out by Lange, Nasledov, Ruse, the author, Sinelnikov, and others, but only Bergman[^19] obtained positive results, having set up the experiments under clean conditions with the surface of the semiconductor, which could be regarded as plane. His measurements were made with a selenium barrier photocell. The strength of the photocurrent as a function of the angle of incidence is represented by the solid lines in Fig. 22 for light polarized parallel and perpendicular to the plane of incidence.

Fig. 22.

Bergman explained the resulting difference by using Drude’s formulas for the amplitude of the refracted ray at different angles of incidence and different states of polarization of the ray. The result of the calculation, under the assumption of proportionality to the amount of light energy entering the body, is also shown by the dashed lines in Fig. 22 according to Drude’s formulas. The values of the refractive index and absorption coefficient of selenium for the wavelength \(6150\,\text{\AA}\) (at which the measurements were made), respectively equal to 3.2 and 0.25, were substituted into the formulas. The values of the refractive index were taken from tabular data; the values of the absorption coefficient, however, were chosen so as to satisfy the experiments in the best possible way, and do not agree with the data of other authors, who find for this modification of selenium a value of 0.58. One may think that this discrepancy, as well as some un-

agreement between calculated and measured data is connected, first of all, with the difficulties of isolating, in the process of fabrication, selenium elements of a definite modification of this semiconductor.

7. Quantum Yield in Barrier-Layer Photoelements

One of the very important questions connected with the processes in barrier-layer photoelements is the question of the quantum yield, i.e., of the number of electrons reaching the electrode calculated per one quantum of incident light.

Fig. 23.

Fig. 24.

The magnitude of this yield naturally depends on the wavelength of the incident light; the distribution of the quantum yield \(\eta\) over the spectrum was determined by Waibel* for the case of the front effect in cuprous-oxide elements; it is shown in Fig. 23. Along the ordinate axis \(\eta\) is given in percent of the number of electrons per one incident light quantum. According to these data, the maximum yield reaches 25%, but in individual cases larger values were also observed—up to 50%, giving up to 1 coul. for each cal. The course of the curve \(\eta\) can be explained by the course of the absorption coefficient of \(\mathrm{Cu_2O}\). In Fig. 24

* The data cited were reported by Schottky\({}^{30}\) in his review lecture at the meeting in Bad Elster; Waibel’s original work has not yet been printed.

the dependence of the absorption coefficient \(\chi\ \mathrm{cm}\) on wavelength. In the region \(6500 \div 5500\,\text{\AA}\), the increase of the absorption coefficient is accompanied by an increase of the quantum yield. The greater the absorption, the greater the fraction of electrons torn off by the light that is in the immediate vicinity of the barrier layer, and the greater the number of them that succeed in reaching the electrode. The values of \(\eta\) and \(\chi\) make it possible to calculate the thickness of the layer through which the electrons torn off by light can pass inside the body. These calculations show that such large quantum yields at relatively small absorptions can be explained only on the assumption that electrons torn off by light at a distance of \(10^{-4}\ \mathrm{cm}\) from the surface can still emerge from the semiconductor into the barrier layer.

This fact, in Schottky’s opinion, is one of the most essential points in the region of the photoelectric effect under consideration. Until now it has been customary to think that the mean free path of an electron, both in a conductor and in a semiconductor, is of the order of \(10^{-6}\ \mathrm{cm}\). But under these assumptions the quantum yield in barrier-layer photocells could not exceed \(1\%\). Thus it is necessary to accept that photoelectrons in a semiconductor, even after a very large number of collisions, do not lose their energy entirely and are still capable of penetrating into the barrier layer.

These very interesting considerations now receive, after the work of Gudden and Pohl, and especially of Techt,* some experimental basis. Techt’s experiments were carried out on AgCl crystals which, after X-raying, possess an internal photoelectric effect. A well-insulating crystal, under voltage in the dark, was illuminated for a short and quite definite time by a narrow light beam at different distances from the anode. The quantities of electricity flowing in the circuit during illumination were measured with an electrometer. Fig. 25 presents the results of the measurements, with the distance of the beam from the

* The work has not yet been published; the data are taken from Gudden’s report \(^{21}\) at the congress in Bad Elster.

of the anode; along the ordinate axis—the measured quantity of electricity; the parameter chosen is the field strength in the crystal. Suppose that electrons are produced in the crystal at the point where the beam strikes (Fig. 26). Under the action of the applied electric field they will move toward the anode, and the charge that is recorded on the electrode will be equal to \(en\frac{a}{d}\), where \(e\) is the charge of the electron, \(n\) is the number of electrons, \(a\) is the path that the electrons traverse in the body without sticking, and \(d\) is the distance between the electrodes. If \(a\) were a quantity greater than any \(x\), then, moving the beam away from the anode, we would observe a linear dependence between the quantity of electricity measured by the electrometer and the distance of the beam from the anode. The electrons would, at any position of the light beam, traverse the path \(x\). If, on the contrary, \(a\) were much smaller than \(x\), the charge of the electrometer would not depend on the distance of the beam from the anode. The experiment gave, as is seen from Fig. 25, a picture not coinciding with the limiting cases considered.

Fig. 25.

Fig. 26.

At small distances of the beam from the anode the charge of the electrometer increases linearly with distance; the electrons traverse the whole path from the place of their formation to the electrode. At larger distances the charge does not depend on the distance; the electrons stick to the lattice elements while moving from the point of ejection to the anode and pass through some path \(l\), indicated by the dotted line in Fig. 25 and dependent on the field strength in the crystal. From consideration of Fig. 25 it is seen that the length of the path which the electron traverses in the crystal without sticking depends on the field strength in it and, even in small fields with a gradient of \(300\ \mathrm{V/cm}\), reaches a magnitude of the order of millimeters.

These works of Pohl’s school, in connection with Schottky’s considerations, acquire very great interest, significantly

changing the usual notions about the behavior of electrons in heteropolar crystals and semiconductors.

The data on the quantum yield obtained by Bäybel make it possible to estimate approximately the efficiency of existing barrier-layer photocells as devices transforming light energy into electrical energy. As an upper limiting value of this coefficient one may indicate a value of 20%, proceeding from the maximum yield observed by Bäybel, and from the large electromotive forces discovered by Losev. This figure, however, may turn out to be greatly exaggerated, since some of the measurements refer to an element with Cu₂O, while others refer to a carborundum element. A much more probable efficiency should be considered to be 2%. On barrier-layer cuprous-oxide elements manufactured in certain laboratories of the Union, according to the author’s information, for the frontal effect e.m.f.’s of 1 V were observed under illumination by light with quantum energies up to 3 V; this value of the e.m.f. at a yield of 25% gives the efficiency indicated above. Both values cited refer to exceptional elements; in common models of this type of device the efficiency does not exceed (0.005–0.01%).

The author considered it unnecessary in the present review to dwell on those applications which barrier-layer photocells have already found—so far, mainly in laboratory technique—since this question has already received sufficient coverage in the pages of the Journal of Technical Physics³², ³³.

LITERATURE

1. Frenkel, Phys. Rev. 36, 1604, 1930.
2. Uljanin, Wied. Ann. 36, 241, 1888.
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