SILICON SOLAR CELLS AS SOURCES OF ELECTRICAL POWER FOR ARTIFICIAL EARTH SATELLITES

V. S. Vavilov, V. M. Malovetskaya, G. N. Galkin,
A. P. Landsman

The electrical powering of the scientific apparatus and telemetry equipment of an artificial Earth satellite by means of storage batteries and galvanic batteries on board can take place only for a limited time. Prolonged operation of the apparatus is possible only if solar energy is used. Of the methods of converting solar energy into electrical energy known at the present time, the most promising is the use of photoelectric¹˒²˒³ semiconductor batteries*).

Solar batteries in combination with buffer storage batteries are rationally used on oriented artificial satellites, since in this case it will be possible to ensure maximum efficiency during the entire time the satellite is outside the Earth’s shadow.

1. PRINCIPLE OF OPERATION OF A SEMICONDUCTOR CONVERTER WITH A \(P—N\) JUNCTION

The initial process in the conversion of the energy of solar radiation into electrical energy is the absorption of a photon and the formation of an electron–“hole” pair. However, in the absence of a \(P—N\) junction²˒³˒⁴ near the region of light absorption, the result would be only an increase in the concentration of electrons and holes in the semiconductor (photoconductivity).

Fig. 1. Diagram of the energy bands near a \(P—N\) junction.

Let us consider the diagram of the energy states of electrons and holes in a semiconductor near an artificially created \(P—N\) junction, explaining the principle of operation of a photocell capable of serving as a generator of electrical energy. Figure 1 shows the conduction band and the valence band of a silicon crystal, separated by a forbidden band. It is evident from the figure that in the region of the \(P—N\) junction

*) The use of semiconductor thermobatteries, which have approximately the same efficiency, but in present-day designs possess considerably greater weight, will apparently become rational when the overall dimensions and weight of an artificial satellite reach a considerable magnitude.

there is a potential barrier, whose height \(V_k\) may be close to the width of the forbidden band \(E_g\), equal for silicon to \(1.1\ \mathrm{eV}\).

The electrons and holes produced upon absorption of light diffuse toward the \(P—N\) junction. One may assume that the potential barrier of the \(P—N\) junction “separates” them, since the electrons freely pass into the region of electronic (\(N\)) conduction of the crystal, charging it negatively, while the “holes,” passing into the region of hole conduction, charge it positively. As a result of the change in the carrier concentrations, the height of the potential barrier decreases. If the external circuit is open, a dynamic equilibrium is established between the primary diffusion current \(I_d\) of the excess carriers (for example, holes from the \(N\)-region of the crystal into the \(P\)-region), and the current opposite to it in direction and caused by the space charge of the excess holes in the \(P\)-region and electrons in the \(N\)-region. If the external circuit is short-circuited, the diffusion current will pass through it. In the intermediate case, corresponding to the real operating conditions of the converter as a current generator in a load, a branching of the currents takes place into the current in the external circuit and the current inside the crystal. The sum of these currents is still equal to the diffusion current, which in the general case can be expressed as

\[ I_d=\int_{\nu_{\min}=E_g/h}^{\nu_{\max}} N_{h\nu}(1-R(\nu))q\alpha(\nu)\,d\nu, \tag{1} \]

where \(N_{h\nu}\) is the number of photons incident on the semiconductor surface per second with energy \(h\nu>E_g\)*; \(R\) is the reflection coefficient, which is a function of frequency, \(q\) is the electron charge, and \(\alpha\) is a coefficient less than 1, which may be called the effective quantum yield or utilization coefficient\({}^{6,7}\). The emf developed by the semiconductor converter, and its efficiency, depend strongly on the magnitude of the saturation current \(I_s\) of the \(P—N\) junction, determined primarily by the width of the semiconductor forbidden band. In the case of not too large excess concentrations of carriers, the emf of the converter is equal to

\[ V=\frac{kT}{q}\ln\left(\frac{I_dR_0}{kT}+1\right), \]

where \(R_0\) is the resistance of the \(P—N\) junction at zero voltages, equal to

\[ \frac{kT}{qI_s}. \]

It has been shown that this formula agrees well with experiment for germanium photocells\({}^{6}\). Approximately this formula is also valid in the case of normal incidence of sunlight on a silicon photocell. In the work of Prince\({}^{8}\), who considered the question of the limiting efficiency of solar batteries, a curve is given for the dependence of the maximum efficiency \((\eta_{\max})\) on the forbidden-band width \(E_g\) (Fig. 2). Despite a number of arbitrary assumptions about the values of other quantities affecting the efficiency (such as, for example, the ratio of diffusion lengths and conductivities, assumed—

* Strictly speaking, expression (1) may be used only in the region where the quantum yield is equal to 1. In practice this is satisfied for silicon up to \(h\nu=3\ \mathrm{eV}\); in the more distant ultraviolet part of the spectrum, additional multiplication of carriers is possible due to impact ionization by photoelectrons or holes. However, the fraction of the energy of the solar spectrum falling in this region is small\({}^{5}\), and \(h\nu_{\max}=10\ \mathrm{eV}\) may be considered a good approximation. Usually the value of \(\alpha\) falls strongly owing to surface recombination for short wavelengths. It may be assumed that the total number of carriers generated in silicon by solar radiation corresponds, in the absence of reflection and at \(\alpha=\mathrm{const}=1\), to a current \(I_d=0.035\ \mathrm{A/cm^2}\) at sea level and increases to approximately 0.040 outside the atmosphere.

tion about the absence of reflection), the curve in Fig. 2 gives a clear idea of the possibilities of using solar batteries made from a number of semiconductors—both those that have already been studied and are available to experimenters, and those that can be obtained, for example, as a result of synthesis. Undoubtedly, at present the best semiconductor material for this purpose is silicon.

It is worth pointing out that in none of the known cases has the ideal efficiency of the order of 22% been achieved under real conditions. In recent years a number of reports have been published on tests of silicon, germanium, and other photocells as converters of

Fig. 2. Dependence of the efficiency of an ideal semiconductor converter with a \(P—N\) junction on the width of the forbidden band. Reflection of the light flux is not taken into account \(^{8,14,15}\).

solar energy \(^{1,2,4,6,9}\). The efficiencies achieved in experimental designs reach 6–7%; in one report, for individual silicon cells, an efficiency value of 11% is indicated \(^{1}\), which corresponds, at sea level under normal incidence of the solar rays, to about 100 W from \(1 \text{ m}^{2}\) of useful area.

The authors developed a method for obtaining \(P—N\) junctions in single crystals of \(P\)-type silicon by thermal diffusion of phosphorus from the gas phase. This method makes it possible to obtain junctions at a precisely specified depth from the crystal surface, which is important when using, for silicon photocells, a material with a short diffusion length of nonequilibrium carriers *).

To obtain sufficiently high utilization factors \(\alpha\), the depth of the \(P—N\) junction must be less than the diffusion length of holes in the layer of \(N\)-silicon doped with phosphorus. In the course of the work it was found that the lifetime of charge carriers in the silicon used decreases significantly during the heat treatment required for the diffusion of phosphorus. Fowler also pointed to this phenomenon \(^{10}\). In spite of this circumstance, measurements of the collection coefficient \(\alpha\) indicate that the excess carriers produced by absorbed photons with wavelengths from 1.1 to 0.4 \(\mu\) are utilized, for a sufficiently small depth of formation of the \(P—N\) junction, on average by 50% (Fig. 3). On the basis of preliminary data it may be asserted that the indicated—

*) More detailed data on the properties of the \(P—N\) junctions investigated will be published in the near future.

the value of \(a\) depends to a considerable extent on the rate of surface recombination. Further reduction of the thickness of the \(N\)-layer on the silicon surface by etching leads to a noticeable increase in the utilization factor. However, excessive thinning of the \(N\)-layer, for a considerable useful surface area of the photocell, causes a decrease in the efficiency due to the increase in the resistance of the layer, which is connected in series with the external load.

Fig. 3. Spectral dependence of the photon utilization factor \(a\). Curve 1: \(P\)—\(N\) junction at a depth of about 15 microns. Curve 2: \(P\)—\(N\) junction at a depth of about 9 microns.

Fig. 4. Design of an experimental silicon photocell (section): 1 — \(P\)-type silicon; 2 — silicon layer converted to \(N\)-type by thermal diffusion of phosphorus; 3 — ring electrode on \(N\)-type silicon; 4 — electrode on \(P\)-type silicon.

The question of the influence of series resistances \(R_{\text{ser}}\) was considered in work devoted to germanium photocells\(^6\), and also by Prince\(^8\). Reducing the value of \(R_{\text{ser}}\) to a minimum is of substantial importance. The resistance of the thin layer can be reduced by applying a semitransparent metallic electrode. However, this method is associated with a decrease in efficiency due to absorption of light in the metal, exceeding the gain in efficiency due to the reduction of the series resistance. Another possible method is the application of a metallic grid of high transparency. In addition, it is necessary to reduce the characteristic resistance of the silicon–metal transition contact to sufficiently small values.

The design of the experimental silicon photocell is shown in Fig. 4. As can be seen from the figure, the entire end surface of the silicon is useful. The area of an individual photocell is limited only by the dimensions of the initial single crystal and can at present, if necessary, be brought up to \(5\)—\(8\ \text{cm}^2\). The thickness of the wafer is usually \(0.7\)—\(1.0\ \text{mm}\).

2. VOLT-AMPERE AND LOAD CHARACTERISTICS

The volt-ampere characteristic of a photocell of area \(0.95\ \text{cm}^2\), illuminated by sunlight, is given in Fig. 5. The dark volt-ampere characteristic in the forward-current region is well described by the expression

\[ I = I_s \left( e^{\frac{q}{AKT}(U - IR_{\text{ser}})} - 1 \right), \]

where \(A = 1.4\). Comparing the theoretical volt-ampere characteristic of the \(P\)—\(N\) junction and the dark characteristic of the photocell, one can determine the total series resistance \(R_{\text{ser}}\) and determine the maximum efficiency \(\eta_n\) extrapolated to \(R_{\text{ser}} \to 0\).

The matched (optimal) load resistance \(R_{\text{l}}\) can be determined from the load characteristic, and also by calculation\(^7\).

In the photoelements investigated, with an area of \(0.95\ \mathrm{cm}^2\), under illumination by normally incident sunlight, \(R_{\mathrm{n}}\) was equal to \(39\ \Omega\).*)

Without carrying out more detailed calculations, we indicate four principal ways of further increasing the efficiency of conversion:

Simultaneously bringing \(\alpha\) to a value close to 1, reducing reflection to a minimum, and making \(R_{\mathrm{series}}\) negligible leads to an efficiency of about 15%; a significant gain by improving the form of the load characteristic is unlikely, since the construction of the characteristic corresponding to \(R_{\mathrm{series}} = 0\) (Fig. 5) shows that the area of the rectangle inscribed in it cannot be substantially increased.

3. TEMPERATURE REGIME OF THE SOLAR BATTERY

According to the theory\(^{11}\), the emf developed by a silicon photoelement should increase with decreasing temperature. A preliminary investigation of the change of \(V\) with temperature gave a dependence of the form

\[ \frac{dV}{dT} = -0.00252\ \mathrm{V}/^\circ\mathrm{C}^{**}). \]

Figure 6 shows the dependence of \(V\) on temperature in the range from \(-70\) to \(+90^\circ\mathrm{C}\).

Fig. 5. Load current-voltage characteristic of an experimental silicon photoelement with an area of \(0.95\ \mathrm{cm}^2\), illuminated by normally incident solar radiation with a power of \(100\ \mathrm{mW}/\mathrm{cm}^2\). The dashed curve corresponds to the load characteristic of the same element with \(R_{\mathrm{series}} = 0\).

*) When the photoelement was illuminated by a \(500\ \mathrm{W}\) lamp through a \(4\ \mathrm{cm}\)-thick layer of water, the short-circuit current reached \(125\ \mathrm{mA}/\mathrm{cm}^2\), the emf exceeded \(0.65\ \mathrm{V}\), and the maximum electric power was \(50\ \mathrm{mW}\) per \(1\ \mathrm{cm}^2\). This fact makes it possible to assert that, with a rational heat-removal system, the necessary area of the solar battery can be substantially reduced by concentrating sunlight.

**) Prince\(^{8}\) gives a dependence of the form

\[ \frac{dV}{dT} = 0.0288\ \mathrm{V}/^\circ\mathrm{C}. \]

Obviously, the condition for obtaining maximum power from the solar battery in flight is a sufficiently low equilibrium temperature of the solar battery. An approximate calculation of the thermal regime for a silicon plate is quite simple. The reflection coefficient of Si in the region of the solar spectrum, which in the present case plays the principal role, has been well studied. It may be taken, on average, as 0.35. In the region of the principal radiation at comparatively low temperatures (near \(300^\circ\) abs.), silicon is a nonselective “gray” body with an emission coefficient \(\xi = 0.7\). Taking the solar constant to be

Fig. 6. Temperature dependence of the e.m.f. of silicon photocells. The solid curve corresponds to a photocell made of silicon with initial \(\rho \cong 20\ \Omega\cdot\text{cm}\), the dashed curve—to a photocell made of silicon with initial \(\rho \cong 0.6\ \Omega\cdot\text{cm}\) (the assumed curve was drawn through one experimental point).

\(0.135\ \text{W}/\text{cm}^2\), from the equation of thermal balance and Stefan’s law one can determine, with an error not exceeding 5%, the absolute temperature of a thin silicon plate on which sunlight falls normally. This temperature turns out to be \(324^\circ\) abs. (the transparency of silicon at \(\lambda > 1.1\) microns has not been taken into account). This temperature is acceptable; however, the efficiency can be increased considerably by making the reverse (rear) surface of the solar battery “black” in the region of 2–15 microns and by increasing the area of the scattering surface. An approximate calculation shows that in this case an equilibrium temperature not higher than \(260\text{–}270^\circ\) abs. may well be attained. Further lowering of the operating temperature and simultaneous improvement in the utilization of the active part of the solar-radiation spectrum can be achieved by applying an interference layer for antireflection of the surface in the region \(0.5\text{–}0.9\,\mu\), with a simultaneous increase of the reflection coefficient immediately outside this region[^12]. Of course, practical use of the indicated method must be preceded by experimental work under terrestrial conditions.

Experience in the application of solar batteries under terrestrial conditions[^13] has given quite unambiguous positive results. Under conditions of prolonged flight of an artificial satellite, this possibility of obtaining electrical energy is as yet the only one, which justifies the most laborious and complex means of its realization.

Obtaining data on the actual temperature regime, efficiency, energy flux of solar radiation, and the very fact of verifying the operation of a solar battery under real conditions will make it possible to begin work on the creation of solar batteries of considerable area, intended for prolonged use on a satellite.

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