In a p-n junction, the n -side doping is five times the...

In a $\mathrm{p}-\mathrm{n}$ junction, the $\mathrm{n}$ -side doping is five times the p-side doping. The intrinsic carrier concentration $=10^{11} \mathrm{~cm}^{-3}$ and band gap is $2 \mathrm{eV}$ at $100^{\circ} \mathrm{C}$. If the builtin junction potential is $0.65 \mathrm{~V}$, what is the doping on the $\mathrm{p}$ side? If the relative dielectric constant of this semiconductor is 10, what is the depletion capacitance at $2 \mathrm{~V}$ reverse bias for a diode of cross-sectional area of $0.5 \mathrm{~cm}^{2} ?$ Draw a qualitatively correct sketch of the band diagram and label the depletion widths and voltage drops for this bias.

In a $\mathrm{p}-\mathrm{n}$ junction, the $\mathrm{n}$ -side doping is five times the p-side doping. The intrinsic carrier concentration $=10^{11} \mathrm{~cm}^{-3}$ and band gap is $2 \mathrm{eV}$ at $100^{\circ} \mathrm{C}$. If the builtin junction potential is $0.65 \mathrm{~V}$, what is the doping on the $\mathrm{p}$ side? If the relative
dielectric constant of this semiconductor is 10, what is the depletion capacitance at $2 \mathrm{~V}$ reverse bias for a diode of cross-sectional area of $0.5 \mathrm{~cm}^{2} ?$ Draw a qualitatively correct sketch of the band diagram and label the depletion widths and voltage drops for this bias.

Key Concepts

Energy Band Diagram

The energy band diagram of a p-n junction illustrates the alignment of the conduction band, valence band, and Fermi levels on both the p-type and n-type sides. It provides a visual representation of the built-in potential, the diffused depletion region, and the associated voltage drops across the junction. Under bias conditions, the diagram shifts to reflect changes in band bending and depletion width, helping to understand carrier transport mechanisms across the junction.

Depletion Capacitance and Reverse Bias

When a p-n junction is reverse-biased, the depletion region widens, reducing the junction capacitance. This depletion capacitance, which behaves similarly to a parallel-plate capacitor, depends on the semiconductor's dielectric constant, the cross-sectional area of the junction, and the width of the depletion region. The capacitance decreases with increasing reverse bias as the depletion width increases, affecting the junction's response to high-frequency signals.

Built-in Junction Potential

The built-in potential is the electric potential difference established across a p-n junction at thermal equilibrium due to the difference in dopant concentrations on each side of the junction. It is determined by the ratio of the dopant densities to the square of the intrinsic carrier concentration, as well as the temperature, and governs the initial barrier that must be overcome for current flow under forward bias conditions.

p-n Junction Doping

In semiconductor physics, controlled impurity doping is used to create the p-type and n-type regions in a semiconductor. The relative concentration of dopants determines many of the junction’s electrical properties. In an asymmetric p-n junction, where one side is doped more heavily than the other, the differences in charge carrier concentrations affect the built-in potential and the extent of the depletion region on either side of the junction.

Intrinsic Carrier Concentration

The intrinsic carrier concentration is a fundamental property of a semiconductor that represents the number of free charge carriers (electrons and holes) in a pure, undoped material at a given temperature. This quantity is crucial in determining the equilibrium carrier distribution and appears in the exponential relation for the built-in potential, linking the effects of doping and temperature on the junction properties.

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