Question

Q.5. (6 Marks ) a-Calculate the built-in potential barrier in a silicon pn junction at T =300 K with doping concentrations of Na=2 x10^17 cm3 and Nd =10x15 cm3. b- how would this potential change if we apply a forward bias = 0.6 Volts C-how would this potential change if we apply a reverse bias = 3 Volts d- Comment on the results

Answer 1

a) Built-in potential barrier is Vbi = 0.724 eV

b) New potential barrier is
`V_(new) = 0.124 eV\\`

c) New potential barrier is
`V_(new) = 3.724 eV\\`

d) These results demonstrate the characteristic behavior of a pn junction diode

How to calculate the built-in potential barrier in a silicon pn junction?

To calculate the built-in potential barrier in a silicon pn junction, we can use the equation:

`Vbi = (k * T / q) * ln(Na * Nd / ni^2)`

a) Calculating the built-in potential barrier:

Using the given values:

`Vbi = (8.617333262145 * 10^(-5) eV/K * 300 K / 1.602176634 * 10^(-19) C) * ln((2 * 10^(17 )cm^(-3)) * (10 * 10^(15) cm^(-3)) / (1.5 * 10^(10) cm^(-3))^2)`

Vbi = 0.724 eV

How to calculate a new potential barrier, when a forward bias of 0.6 Volts is applied?

b) When a forward bias of 0.6 Volts is applied to the pn junction, the potential barrier reduces. The new potential barrier can be calculated as:

`V_(new) = Vbi - V_(forward)\\V_(new )= 0.724 eV - 0.6 eV\\V_(new) = 0.124 eV\\`

How to calculate a new potential barrier, when a reverse bias of 3 Volts is applied?

c) When a reverse bias of 3 Volts is applied to the pn junction, the potential barrier increases. The new potential barrier can be calculated as:

`V_(new) = Vbi + V_(reverse)\\V_(new )= 0.724 eV + 3 eV\\V_(new) = 3.724 eV\\`

Write comment on the results.

d) Comment on the results:

• The built-in potential barrier of 0.724 eV is the potential difference that exists across the pn junction due to the difference in doping concentrations.
• When a forward bias of 0.6 Volts is applied, the potential barrier reduces to 0.124 eV. This reduction allows current to flow more easily across the junction.
• When a reverse bias of 3 Volts is applied, the potential barrier increases These results demonstrate the characteristic behavior of a pn junction diode, where forward bias allows current flow and reverse bias blocks current flow.