A theory of an n‐p‐p+ junction is developed, entirely based on Shockley’s depletion layer approximation. Under the further assumption of uniform doping the electrical characteristics of solar cells as a function of all relevant parameters (cell thickness, diffusion lengths, etc.) can quickly be ascertained with a minimum of computer time. Two effects contribute to the superior performance of a BSF cell (n‐p‐p+ junction) as compared to an ordinary solar cell (n‐p junction). The sharing of the applied voltage among the two junctions (the n‐p and the p‐p+ junction) decreases the dark current and the reflection of minority carriers by the builtin electric field of the p‐p+ junction increases the short‐circuit current. The theory predicts an increase in the open‐circuit voltage (VOC) with a decrease in cell thickness. Although the short‐circuit current decreases at the same time, the efficiency of the cell is virtually unaltered in going from a thickness of 200 μm to a thickness of 50 μm. The importance of this fact for space missions where large power‐to‐weight ratios are required is obvious.

Topics
Electric currents, Short circuit, Electrical properties and parameters, Solar cells, Surface physics
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H. J. Hovel, Solar Cells, Vol. II of Semiconductors and Semimetals (Academic, New York, 1975) contains an excellent bibliography.
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We neglect the recombination current generated in the depletion layer since it is small compared to the photon‐generated current.
8.
See the list of symbols at the end of this paper.
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H. J. Hovel, in Ref. 6, p. 20, Eq. (20).
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See for instance: A. S. Grove, Physics and Technology of Semiconductor Devices (Wiley, New York, 1967), pp. 157ff.
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Actually, the external load resistance R determines the applied voltage V through jRA = V where A is the area of the solar cell. The dark current corresponds then to the forward‐bias mode of junction operation.
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H. J. Hovel, in Ref. 6, p. 187.
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For long wavelengths (λ ≈ 1 μm) absorption is fairly small but so is production of free carriers.
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16.
J. Scott‐Monck (private communication).
17.
G. B. Turner (private communication).
18.
B. Anspaugh and T. Miyahira provided preliminary results of bulk diffusion lengths measurements (unpublished).
19.
The depletion layer width increase by a factor of 3 in going from NA = 1016 cm−3 to NA = 1015 cm−3.
20.
All one‐dimensional theories possess this defect. It is conjectured that the current‐collecting “fingers” on the sun exposed surface of the cell make an at least two‐dimensional analysis mandatory, the reason being that the collecting conductors “pinch” the current, narrowing it down to their own geometrical size. In a one‐dimensional analysis the equivalent surface recombination velocity S should be smaller than the adopted value of 104 cm/sec. An analysis of this situation is beyond the scope of this paper.
21.
For cells less than 10 μm thick the depletion layer approximation breaks down and the concept of a surface recombination velocity breaks down. Structures this thin are really Schottky barriers becasue the Ohmic contacts become an integral part of the device.
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© 1978 American Institute of Physics.
1978
American Institute of Physics
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