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5), with the sign convention of taking currents in forward direction as positive. 3 A p–n Diode Under Irradiation with Light Irradiation with light will generate electron–hole pairs in a semiconductor. Pairs generated in the space-charge region of a p–n junction will be separated by the electric field. If the voltage across the junction is kept at the built-in potential by, for instance, shortening the external leads of the device, a photocurrent will be generated. 7). This voltage change appears as an output voltage at the external leads of the device.
It may be worthwhile to mention that this built-in voltage, which is also referred to as a diffusion voltage, will not appear on the same metal electrical connections attached to the device, since it will be compensated for by the built-in voltages in the metal– semiconductor contacts. This point will be taken up again after discussing the metal–semiconductor contact. Fig. 3. 1 Problem: Find the built-in voltage for a silicon p–n junction at room temperature with doping concentrations NA = 1016 cm−3 (acceptor) and ND = 1012 cm−3 (donor).
The origin of our one-dimensional coordinate system (x = 0) is put at the edge of the space-charge region on the p side, x pointing towards the neutral p region, and light is supposed to generate charge at x = x0 so that the generation rate of electrons by light is described by GL (x) = GL · δ(x − x0 ). 9) separately for the regions 0 < x < x0 and x0 < x < ∞ with boundary conditions at x = 0, x = x0 and x → ∞. 6), and thus qV n(x = 0) = np0 e kT . At x = x0 we require continuity of the electron density, and so n(x0 + ) = n(x0 − ) →0 and a discontinuity of the electron flux equaling the generation rate at x = x0 : F (x = x0 + ) − F (x = x0 − ) = GL .