7.2.3. Current Equation of Normal or Standard p-n Junction

So, if you see the BJT as you may be aware from semiconductor device, what it is having it is the basic structure it is having two junctions, say for example, n-p junction and then p-n junction. And in this n-region, we do have electrical connection; we may be aware of this called say emitter. So, likewise in the other side of the device the other n-region, it is having a terminal called collector terminal, then the middle portion in between which is p-type. And in this p-region, it is also having one terminal through which you can apply voltage and you can observe the current and this terminal it is referred as base.

The BJT (Bipolar Junction Transistor) has a unique structure that consists of two types of semiconductor materials: n-type and p-type. The n-type regions serve as the emitter and collector, while the p-type region is the base. The emitter is heavily doped with electrons, and the base is doped in such a way that it can control the transistor's behavior. Understanding this structure is crucial for analyzing how the device operates in terms of current flow.

Think of the p-n junction as a water faucet. The water (current) flows through the faucet (the transistor) when it is turned on (the base is energized). If there are two separate pipes (n-type and p-type regions), the proper opening of the faucet will allow water to flow smoothly, just like how the current can flow when the transistor is properly biased.

In normal circumstances, particularly for analog operation unless otherwise it is stated, base emitter junction the junction-1 it is forward biased which means that the p-region it is having a +ve voltage with respect to the emitter n-region. So, this junction-J1 it will be forward biased by a voltage called base to emitter voltage. So, on the other hand, base to collector junction again for normal operation, so this junction-J2, it is reverse bias which means that this n-region it is having higher potential than the p-region.

In typical use of BJTs for analog applications, the base-emitter junction (J1) must be forward biased, meaning that there is a positive voltage applied to the base relative to the emitter. This allows charge carriers (electrons) to flow from the emitter into the base. Conversely, the base-collector junction (J2) is reverse biased, meaning the collector is at a higher potential than the base. This configuration sets up the conditions necessary for the transistor to operate effectively.

Imagine pushing water through two valves. The first valve (base-emitter) is opened (forward-biased) to allow water to flow in. The second valve (base-collector) is shut (reverse-biased), ensuring water flows in one direction. This setup facilitates a controlled environment, just like a BJT controlling current flow.

Now, we know that through a p-n junction if this junction is say a forward bias, and if this second junction if it is far away from this junction, then we know that this current it will be having exponential dependency of this forward bias on the forward bias voltage. So, if I ignore the second junction and if I concentrate only junction-1, and if it is getting forward biased by VBE, the current it will be flowing through this base terminal into the device, the same current it will depart, the emitter terminal.

When the base-emitter junction is forward biased, an exponential relationship describes how the current flows through this junction. This current depends on the base-emitter voltage (VBE). As the forward bias voltage increases, the current flowing through the junction increases exponentially. This is important because it shows how sensitive the junction is to changes in voltage, highlighting the key principle of diode behavior in electronics.

Think of a garden hose with a nozzle at the end. The more you open the nozzle (increase the voltage), the greater the flow of water (current) out of the hose. Just like how a small increase in voltage leads to a large increase in current in a forward-biased p-n junction.

So, if at any point, if you take the gradient of this n at any distance at x, then it will be giving us the current the rate at which the electrons are now getting into the, I should say moving from left to right.

The current flowing through the junction can also be analyzed by understanding how minority charge carriers (electrons in a p-type region and holes in an n-type region) contribute to current flow. When these carriers move across the junction, they can create a current that is also dependent on their concentration gradient. As the concentration of minority carriers increases within the base region, so does the current.

Imagine a crowded event where a certain number of people (minority carriers) are trying to exit through a door (the junction). The more people pressing towards the door (the concentration), the more quickly they can exit, increasing the overall flow rate of people (current). The greater the difference in density of people (the gradient), the faster they will move toward the exit.

Under reverse bias condition, I1 is well approximated by qADn· and this part at x = 0, p this becomes 1, so becomes 1. So, we do have only this part. So, under reverse bias condition, I1, well approximated by qADn.

In the reverse bias condition, the currents for both the electron and hole movements (I1 and I2) are much smaller compared to in forward bias condition. However, the fundamental equations that govern these currents remain similar. The total current flow under reverse bias conditions is negligible, reaffirming the diode's characteristics in terms of current behavior in both bias scenarios.

Consider a closed valve that prevents water from flowing. Even if there is pressure behind the valve, very little (if any) water (current) can pass through. This reflects how reverse bias in a diode restricts current flow, thus protecting the circuit.

--