Boron is implanted into an n -type Si sample (Nd=10^16 cm^-3), forming an abrupt junction of sq

step 1 In this problem let us first calculate the value of D. So D is equal to D0 exponential minus Ea

Boron is implanted into an n -type Si sample (Nd=10^16...

Boron is implanted into an $\mathrm{n}$ -type Si sample $\left(N_{d}=10^{16} \mathrm{~cm}^{-3}\right)$, forming an abrupt junction of square cross section with area $=2 \times 10^{-3} \mathrm{~cm}^{2}$. Assume that the acceptor concentration in the p-type region is $N_{a}=4 \times 10^{18} \mathrm{~cm}^{-3}$. Calculate $V_{0}, x_{n 0}, x_{p 0}, Q_{+}$, and $E_{0}$ for this junction at equilibrium $(300 \mathrm{~K})$. Sketch $\mathscr{E}$ and the charge density to scale, as in Fig. $5-12$.

Key Concepts

PN Junction

A PN junction is formed by bringing together p-type and n-type semiconductors, leading to carrier diffusion and recombination at the interface. This process results in the creation of a built-in electric field and potential barrier that controls current flow and rectifying behavior in devices such as diodes.

Depletion Region

The depletion region, also known as the space charge region, is the area around the PN junction where mobile charge carriers (electrons and holes) have diffused away, leaving behind fixed ionized donor and acceptor atoms. This region is crucial because it establishes the electric field and voltage drop across the junction, and its width depends on the doping concentrations on either side.

Built-in Potential

The built-in potential is the voltage difference established across the PN junction at equilibrium, resulting from the diffusion of carriers and subsequent charge separation. It is a critical parameter as it determines the barrier height that carriers must overcome to contribute to conduction and is directly related to the doping levels and intrinsic properties of the semiconductor.

Charge Distribution

Charge distribution in a PN junction under the depletion approximation is characterized by uniformly distributed fixed positive charges in the n-region and fixed negative charges in the p-region. This step-like charge distribution establishes the internal electric field, enabling the calculation of quantities such as total charge, depletion widths, and capacitance.

Electric Field Distribution

The electric field in a PN junction, derived from Poisson's equation, has a linear profile within the depletion region and is zero outside it. Its maximum value, usually at the metallurgical junction, depends on the doping densities and built-in potential, and understanding its variation is essential for analyzing the junction’s response under different biasing conditions.

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