8.4.2. Electrons and Holes Contribution

BJT particularly say n-p-n transistor it is having three regions namely n, then p-region and n-region. In between it is having junction, junction-1 and also junction-2. They may be having different cross sectional area A and A. For active region of operation, particularly one of these junctions to be forward biased by this voltage; base to emitter voltage and this junction on the other hand; it will be reverse biased. The polarity of the V_CE is such that the n-region is at higher potential than the p-region.

In a BJT (Bipolar Junction Transistor), particularly the n-p-n type, there are three main regions: two n-type materials and one p-type material. The junctions formed between these regions are labeled junction-1 (between the first n-type region and the p-type region) and junction-2 (between the p-type region and the second n-type region). For the transistor to operate in the active region, one junction, typically the base-emitter junction (junction-1), must be forward biased which means applying a voltage that allows current to flow through. The other junction (junction-2) is reverse biased, meaning it stops current from flowing. This differential behavior allows the transistor to function as an amplifier or switch, utilizing the positive voltage at the n-region compared to the p-region.

You can think of the BJT like a water tap: when you push the handle (which represents applying forward bias voltage), water (the current) flows out. The tap is designed so that water can flow easily in one direction (forward bias) while blocking it in the other direction (reverse bias). This control of water flow is akin to how BJTs control electric current.

Whenever we talk about these two junctions and if we say that these two are wide apart and they are not influencing each other; then whatever the minority carrier concentration we have seen in particularly in the p-region; it is having an exponential change.

At the junctions of the n-p-n transistor, minority carriers (electrons in the p-region and holes in the n-regions) exist in lower concentrations compared to majority carriers. In the case of a forward-biased junction, the minority carrier concentration in the base-region (p-type) increases exponentially due to the injection of electrons from the emitter. This exponential change in minority carrier concentration is crucial, as it affects how easily carriers can recombine and thus determines the transistor's performance.

Imagine a garden where sunlight (current) is critical for plants (carriers) to grow. During the day (forward bias), the light helps more seeds (minority carriers) germinate exponentially compared to nighttime (reverse bias), when very few seeds sprout. The better the light conditions, the faster the growth, paralleling how increased carrier concentrations lead to better conductivity in a transistor.

Junction current I is having two components namely the current carried by electrons I_n1 and then current carried by holes I_p1. So likewise I_2 is also having two current components namely we do have I_n2 and then we do have I_p2.

In a BJT, the total current flowing through each junction can be split into components based on the type of charge carrier. For example, in junction-1 (forward-biased), there are two components: one due to the flow of electrons (I_n1) and another due to the flow of holes (I_p1). Similarly, in junction-2 (reverse-biased), the current components are I_n2 and I_p2. These components work together to explain the behavior of the BJT in an active region, where one is designed to allow maximal current flow, while the other limits it.

Think of a highway where there are both cars (electrons) and trucks (holes) traveling. Each type of vehicle has its lane (current components), but together, they form the total traffic (total current). If there’s a toll booth that restricts one type of vehicle (as in junction-2, which is reverse-biased), it affects overall traffic flow, similar to how junctions affect charge carrier movement in a BJT.

If I take these two junctions close to each other; let us see what are the things are happening. We have taken these two junctions in the near vicinity. And, due to that the interesting change of the minority carrier concentration; particularly in the p-region the base region.

When the distance between the two junctions in a transistor is reduced, as they come closer, the behavior of minority carrier concentrations is affected. The minority carriers from one junction can influence the other junction due to a change in electric fields. As carriers from the forward-biased end are injected into the base, they might experience forces that draw them towards the collector terminal, which can enhance the efficiency of the transistor. This interaction can increase the rate of charge injection into the collector.

Consider a crowded room where two different groups of people (carriers) are trying to interact (transfer charge). If the groups are close together, they can share ideas quickly and easily, just like how reduced separation between junctions allows carriers in a transistor to interact more effectively and contribute to current flow in the collector.

The current carried by electrons is actually it is having two components; one is it is getting recombined with the holes coming from this base region namely it is contribute in the base terminal current. On the other hand, the other component it is basically electrons are moving here which is contributing additional current of the collector terminal.

When electrons move into the base region of the transistor, they can either recombine with holes (which contributes to the base current) or continue moving to the collector terminal (contributing to the collector current). This dual pathway emphasizes the transistor's role in amplifying current: a small change at the base can lead to a larger current at the collector due to the proportionality of injected and recombined electrons.

Imagine a factory where raw materials (electrons) either get used in production (recombination at the base) or get packaged directly for shipment (current at the collector). Efficient usage of raw materials can balance out production and shipping, illustrating how the behaviors of carriers in a BJT help control overall current flow.

So, by considering different junction current component; we may be able to easily get the terminal current namely this current I_E, it is a summation of these two currents. So, likewise I_C, it is summation of these two currents.

The terminal currents, such as the emitter current (I_E) and collector current (I_C), can be derived by summing the contributions from both the electron and hole currents flowing through the junctions. This summation approach allows us to simplify the calculation and understand the overall current flow through the BJT, which is key for analyzing its performance.

Think of gathering donations from different sources (currents) for a charity event (terminal current). You gather money from patrons (electron contributions) and company sponsors (hole contributions). The total amount of donations is the sum of all contributions, akin to how the total terminal current is calculated in a BJT.

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