This simulator walks through the birth of a PN junction. Holes and electrons diffuse across the boundary, leaving behind fixed ionized dopants that create an electric field opposing further diffusion. Change either doping level to see how the barrier and the depletion widths shift.
• A p-type reservoir and an n-type reservoir, uncovered fixed dopant charge, the internal electric field, a potential-profile curtain and diffusion and drift markers. • Controls for acceptor and donor concentration exponents (10¹⁵ to 10¹⁷ cm⁻³), a formation-progress slider from 0 to 1, and automatic advance. • Readouts for the equilibrium built-in voltage, the current illustrated barrier, total depletion width, p-side and n-side widths, and peak field magnitude. • Experiments for a symmetric junction (equal widths, built-in potential about 0.714 V) and a one-sided junction where the lightly doped p-side is 100 times wider than the n-side.
The built-in voltage is Vbi = VT ln(NA ND / ni²). In the depletion approximation W = √[(2εsi/q)(1/NA + 1/ND) Vbarrier], and charge balance NA xp = ND xn splits that width so the lightly doped side takes most of it: xp = W ND/(NA + ND), xn = W NA/(NA + ND). The peak field is Emax = 2 Vbarrier / W. At equilibrium the barrier equals Vbi, and the sequence shows the barrier rising as diffusion is opposed by drift.
The model is an abrupt homojunction at 300 K in the depletion approximation. Formation progress steps through charge-balanced electrostatic states; it is not a time-dependent drift-diffusion solution, and its seconds are not physical formation times.
It is the zone around the metallurgical junction where mobile carriers have diffused away, leaving fixed ionized donors and acceptors. That uncovered charge produces the internal electric field.
The built-in voltage depends on the doping levels of both sides: Vbi = VT ln(NA ND / ni²). Heavier doping on either side raises it logarithmically, to about 0.714 V for the symmetric example in the lab.
Charge balance requires NA xp = ND xn, so the side with fewer dopants per volume must extend farther to uncover the same amount of charge.
No. It interpolates through equilibrium-consistent states to teach the idea. The times shown are not physical formation times, which are far shorter.