Semiconductors/Diodes from an Engineering Perspective

A P-N junction is useful in electrical engineering as a Diode. Diodes have various purposes, including: - Preventing current from flowing in one direction but not the other - Regulating voltage (when used in reverse bias) - Voltage-dependent capacitors (when used in reverse bias)

Diode construction and properties
As noted in the previous chapter, diodes are constructed at the physical interface of a P-doped semiconductor and an N-doped semiconductor. When these two regions meet, holes and electrons diffuse across the junction due to the differing concentration at the junction:

This diffusion does not continue indefinitely. Instead, as the electrons diffuse to the P-side and the holes diffuse in the N-side, a charge imbalance arises, creating a voltage which eventually prevents any further diffusion from occuring. The voltage is an inherent property of the diode and depends on the amount that the P-side is doped relative to the N-side. From this arises what is known as the Built-in potential, $V_{bi}$.

Biasing diodes
- When a diode is subject to an external electric field, it is said to be biased. - If the field is in the opposite direction to the built-in voltage, it will counteract the diffusion, making the depletion region thinner. This is known as forward biasing. - In addition to counteracting diffusion, forward biasing also injects charge carriers (holes and electrons) into the P and N regions of the diode. This encourages further diffusion from P to N, leading to current flow. - However, if the field is in the same direction as the built-in voltage, it will encourage the diffusion, making the depletion region thicker. This is known as reverse biasing. - In this mode, charge carriers are injected into the opposite regions of the diode (holes in N and electrons in P), where they instantly recombine. This prevents any current flowing, up to a certain point.

Circuit models of diodes
When analysing diodes, a number of models can be used, including:

Ideal diode model
In the ideal diode model, there are two states: on and off. In the on-state, the diode acts as a short circuit, allowing any amount of current to flow through and forcing the potential between its ends to be 0. In the off-state, the diode acts as an open circuit, so that no current can flow through the diode.

Voltage drop model
In the voltage drop model, there are similarly two states: on and off. The off state is the same as above; the circuit prevents any current from flowing. In the on-state however, the diode acts as a voltage source that maintains a constant voltage between its two terminals equal to its built-in voltage.

Empirical model
In the empirical model, we treat the diode as a circuit component governed by $I = I_s (e^{\frac{V_f}{V_T}}-1)$, giving us an exponential curve. This model typically requires numerical iteration to evaluate.

VRC model
In the VRC model, we model the diode as a voltage source, capacitor and resistor. This is typically used when the diode is being used in reverse-bias.

Voltage regulator
Todo

Voltage dependent capacitors
Todo