Understanding PN Junction Parameters and Temperature Effects

This explanation details how changes in temperature affect key parameters of a PN junction, specifically the depletion layer width, junction barrier voltage, and reverse leakage current.

How Temperature Impacts PN Junctions

Temperature significantly influences the behavior of semiconductor devices like PN junctions. Increased temperature affects the energy distribution and concentration of charge carriers (electrons and holes) within the semiconductor material.

Analysis of PN Junction Parameters with Rising Temperature

Let's examine each parameter mentioned:

Parameter A: Width of Depletion Layer

The depletion layer (or depletion region) is the area around the PN junction where mobile charge carriers are scarce. Its width is influenced by the built-in potential barrier.

• When the temperature of a PN junction rises, the thermal energy of the charge carriers increases.
• This increased thermal energy leads to a reduction in the junction barrier voltage (explained next).
• A lower barrier voltage means the electric field across the junction is less effective in preventing carrier diffusion or requires a smaller region to achieve equilibrium.
• Consequently, the width of the depletion layer decreases as temperature increases.

Parameter B: Junction Barrier Voltage

The junction barrier voltage, often called the built-in potential ($V_{bi}$), is the potential difference established across the junction due to the diffusion of carriers and the resulting uncovered charges.

• The built-in potential is directly related to the intrinsic carrier concentration ($n_i$) of the semiconductor material. The relationship is approximately given by: $$ V_{bi} \approx \frac{k T}{q} \ln\left(\frac{N_A N_D}{n_i^2}\right) $$ where $k$ is Boltzmann's constant, $T$ is the absolute temperature, $q$ is the elementary charge, $N_A$ is the acceptor concentration, and $N_D$ is the donor concentration.
• The intrinsic carrier concentration ($n_i$) increases exponentially with temperature.
• As $n_i$ increases, the term $\ln\left(\frac{N_A N_D}{n_i^2}\right)$ decreases.
• Therefore, the junction barrier voltage decreases as the temperature rises.

Parameter C: Reverse Leakage Current

The reverse leakage current (or reverse saturation current, $I_s$) is a small current that flows when the junction is reverse-biased. It is primarily caused by minority carriers.

• The magnitude of the reverse leakage current is proportional to the concentration of minority carriers.
• As temperature increases, the intrinsic carrier concentration ($n_i$) rises significantly. Since the concentration of minority carriers is proportional to $n_i^2$, it increases substantially with temperature.
• For example, in the n-side, the hole concentration ($p_n$) is given by $p_n = n_i^2 / N_D$. As $n_i$ increases, $p_n$ increases.
• A higher concentration of minority carriers leads to a larger reverse leakage current.
• Thus, the reverse leakage current increases as the temperature rises.

Conclusion on Parameter Changes

Based on the analysis:

• Width of depletion layer (A) decreases.
• Junction barrier voltage (B) decreases.
• Reverse leakage current (C) increases.

Therefore, the parameters that decrease when the temperature of the junction rises are the width of the depletion layer and the junction barrier voltage.