7.6. Current Expressions

The BJT has two junctions: the base-emitter junction (junction-1) and the base-collector junction (junction-2). The emitter is heavily doped n-region, the base is a p-region, and the collector is another n-region. In most cases, junction-1 is forward biased and junction-2 is reverse biased, with the base-emitter voltage represented as V_BE and the collector-base voltage as V_CB.

The Bipolar Junction Transistor (BJT) consists of three regions: the emitter, base, and collector. The emitter, typically an n-type material, is heavily doped to increase the conductivity of charge carriers. The base is p-type and relatively thin, which allows electrons from the emitter to flow into it. The collector, also n-type but often less heavily doped than the emitter, collects the carriers from the base. Under normal operation conditions, the base-emitter junction is forward biased, allowing current to flow easily between the emitter and base. In contrast, the base-collector junction is usually reverse biased, preventing current from flowing freely. Instead, it creates an electric field that helps in the movement of carriers from the base to the collector, allowing the transistor to amplify current.

Imagine the BJT as a local bus system. The emitter is like a bus station where people (electrons) from the outskirts of the town (n-type material) are picked up and sent toward a central town area (the base). After stopping at the base to let some passengers off, the bus continues towards another destination (the collector), but this destination is controlled by a one-way street (reverse bias), allowing only specific exits and controlling the flow of people. This system allows for an efficient transfer of people (current) while controlling how many reach the final destination.

When the base-emitter junction is forward biased, electrons move from the n-region to the p-region. The current flowing through this junction is related to the applied base-emitter voltage (V_BE) and has a dependence that can be modeled as I = I_s(e^(V_BE/V_T) - 1), where I_s is the saturation current and V_T is the thermal voltage.

In a forward-biased BJT, when a positive voltage is applied to the base relative to the emitter, electrons from the heavily doped emitter want to move into the less populated base region. This flow of electrons generates a current, which increases as the voltage V_BE increases due to the exponential relationship between voltage and current in a diode-like fashion. The saturation current (I_s) represents the minimal current that flows through the junction when a small voltage is applied. The thermal voltage (V_T) is a constant that relates to temperature and charge. This equation shows that even small increases in V_BE can lead to significantly larger currents, illustrating the amplification property of BJTs.

Think of a garden hose with a nozzle (the BJT). When you lightly squeeze the nozzle (apply a small forward voltage), water (current) starts trickling out. If you squeeze harder (increase the voltage), not only does more water flow out, but it sprays out farther and faster. The relationship between how much you press (V_BE) and how much water comes out (current) is similar to the exponential growth described by the current equation for the BJT.

When the base-collector junction is reverse biased, the current is dramatically reduced. The expression for reverse saturation current is another exponential function and is given as I = -I_s(e^(V_CB/V_T) - 1), where V_CB is the collector-base voltage.

In a reverse-biased condition, the collector-base junction does not allow free flow of charge carriers. The higher potential at the collector repels minority carriers in the base, thereby reducing the current flow compared to forward bias conditions. However, a small amount of reverse saturation current still flows, defined by a similar formula to the forward bias but negative due to the direction of the current flow being reversed. This saturation current is much lower than in the forward bias due to the barriers established by the reverse bias, which stops majority carriers from moving across the junction.

Imagine a one-way street (the reverse-biased collector-base junction). When a car (electron) tries to enter this street from the base, a roadblock (reverse bias) is put up preventing cars from flowing freely. Only an occasional car that is small enough to sneak through the barrier (reverse saturation current) can make it through to the collector side. Thus, most of the traffic is prevented from crossing, illustrating how the transistor effectively controls current flow.

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