Final answer:
To calculate the built-in potential barrier of a pn junction with specific doping densities at room temperature, a formula involving the Boltzmann constant, temperature, charge of electron, and doping densities is used, and the resulting electric field at the junction is essential for the diode function.
Step-by-step explanation:
To find out the built-in potential barrier in a pn junction for a silicon semiconductor at T = 300 K with doping densities Na = 1 × 1016 cm−3 and Nd = 1 × 1015 cm−3, assuming that ni = 1.5 x 1010 cm−3, we use the contact potential formula:
Vbi = (kT/q)ln((Na · Nd)/(ni2))
Where:
- Vbi is the built-in potential
- k is the Boltzmann constant (8.617 x 10−5 eV/K)
- T is the temperature in Kelvin (300 K)
- q is the charge of an electron (1.602 x 10−19 coulombs)
- Na is the acceptor doping density
- Nd is the donor doping density
- ni is the intrinsic carrier concentration
Plugging in the values, we have:
Vbi = (8.617 x 10−5 eV/K · 300 K / 1.602 x 10−19 coulombs) · ln((1 × 1016 cm−3 · 1 × 1015 cm−3) / (1.5 x 1010 cm−3)2)
Calculating the built-in potential gives us the voltage that separates charges at the pn junction, forming the depletion region and establishing an electric field that prevents further migration of carriers thereby creating a balance.