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 (n_I = 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.

1. Calculate the built-in potential of this p-n junction.
2. Calculate the total width of the depletion region if the applied voltage V_a equals 0, 0.5 and -2.5 V.
3. Calculate maximum electric field in the depletion region at 0, 0.5 and -2.5 V.
4. 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 N_a = 10¹⁸ cm^-3 and N_d = 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 (N_a = 10¹⁶ cm^-3 and N_d = 4 x 10¹⁶ cm^-3) is biased with V_a = 0.6 V. Calculate the ideal diode current assuming that the n-type region is much smaller than the diffusion length with w_n^' = 1 mm and assuming a "long" p-type region. Use m_n = 1000 cm²/V-s and m_p = 300 cm²/V-s. The minority carrier lifetime is 10 ms and the diode area is 100 mm by 100 mm.

Example 4.5  

1. Calculate the diffusion capacitance of the diode described in Example 4.4 at zero bias. Use m_n= 1000 cm²/V-s, mp = 300 cm²/V-s, w_p^' = 1 mm and w_n^' = 1 mm. The minority carrier lifetime equals 0.1 ms.
2. 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.