# Chapter 4: p-n Junctions

## Examples

 Example 4.1 An abrupt silicon p-n junction consists of a p-type region containing 2 x 1016 cm-3 acceptors and an n-type region containing also 1016 cm-3 acceptors in addition to 1017 cm-3 donors. Example 4.2 An abrupt silicon (nI = 1010 cm-3) p-n junction consists of a p-type region containing 1016 cm-3 acceptors and an n-type region containing 5 x 1016 cm-3 donors. Calculate the built-in potential of this p-n junction.Calculate the total width of the depletion region if the applied voltage Va equals 0, 0.5 and -2.5 V.Calculate maximum electric field in the depletion region at 0, 0.5 and -2.5 V.Calculate the potential across the depletion region in the n-type semiconductor at 0, 0.5 and -2.5 V. Example 4.3 Consider an abrupt p-n diode with Na = 1018 cm-3 and Nd = 1016 cm-3. Calculate the junction capacitance at zero bias. The diode area equals 10-4 cm2. Repeat the problem while treating the diode as a one-sided diode and calculate the relative error. Example 4.4 An abrupt silicon p-n junction (Na = 1016 cm-3 and Nd = 4 x 1016 cm-3) is biased with Va = 0.6 V. Calculate the ideal diode current assuming that the n-type region is much smaller than the diffusion length with wn' = 1 mm and assuming a "long" p-type region. Use mn = 1000 cm2/V-s and mp = 300 cm2/V-s. The minority carrier lifetime is 10 ms and the diode area is 100 mm by 100 mm. Example 4.5 Calculate the diffusion capacitance of the diode described in Example 4.4 at zero bias. Use mn= 1000 cm2/V-s, mp = 300 cm2/V-s, wp' = 1 mm and wn' = 1 mm. The minority carrier lifetime equals 0.1 ms.For the same diode, find the voltage for which the junction capacitance equals the diffusion capacitance. Example 4.6 A 1 cm2 silicon solar cell has a saturation current of 10-12 A and is illuminated with sunlight yielding a short-circuit photocurrent of 25 mA. Calculate the solar cell efficiency and fill factor.