Semiconductors

Step 1: Definition.
Pure semiconductors (Si, Ge) have limited conductivity. When a small quantity of impurity is added, they become doped semiconductors (extrinsic type).
Step 2: Effect of doping.
- Doping with pentavalent impurities (P, As) gives N-type semiconductor (extra electrons as majority carriers).
- Doping with trivalent impurities (B, Al) gives P-type semiconductor (holes as majority carriers).
- Conductivity increases drastically because of increased number of charge carriers.
Step 3: Effect of temperature.
- As temperature rises, more covalent bonds break, releasing additional charge carriers.
- Hence conductivity increases with temperature (unlike metals where resistance increases).
Step 4: Conclusion.
Thus, doping and increase in temperature both increase the conductivity of semiconductors.

Step 1: Basic Structure of an n-p-n Transistor.
An n-p-n transistor consists of three layers of semiconductor material: the emitter (n-type), base (p-type), and collector (n-type). In a common emitter configuration, the emitter is common to both the input and output circuits.
Step 2: Circuit Diagram.
Here’s the circuit diagram for the common emitter amplifier:

Step 3: Working of the Amplifying Action.
In the common emitter configuration, the input signal is applied to the base-emitter junction, and the output is taken across the collector-emitter junction. When a small input voltage is applied to the base, it causes a small change in the base current . This small change causes a much larger change in the collector current , because the current gain of the transistor is typically large. The output voltage is therefore amplified in proportion to the input voltage.
Step 4: Voltage Amplification Formula.
The voltage gain of the amplifier is the ratio of the change in the output voltage to the change in the input voltage: For a common emitter amplifier, the voltage gain is approximately: where: - is the collector resistance, - is the small-signal emitter resistance.
Step 5: Conclusion.
Thus, the n-p-n transistor in common emitter configuration amplifies the input voltage by a factor of , and the amplification depends on the ratio of the collector resistance to the small-signal emitter resistance.

Step 1: Working of a Forward Biased p-n Junction Diode.
In a forward biased p-n junction diode, the positive terminal of the battery is connected to the p-type material, and the negative terminal is connected to the n-type material. This reduces the width of the depletion region and allows current to flow through the diode once the forward voltage exceeds the threshold (or "cut-in" voltage).
Step 2: Circuit Diagram.
Here is the circuit diagram of a forward biased p-n junction diode:

Step 3: Dynamic Resistance.
The dynamic resistance of the diode is defined as the change in voltage divided by the corresponding change in current :
Step 4: Graph Between Forward Voltage and Forward Current.
The current through a forward biased p-n junction diode increases exponentially with the applied forward voltage after the threshold voltage. The relationship between the forward voltage and the forward current is given by the Shockley diode equation: where is the saturation current, is the ideality factor, and is the thermal voltage.
Step 5: Conclusion.
Thus, as the forward voltage increases, the current increases exponentially. The dynamic resistance decreases as the current increases, and the diode exhibits a nonlinear I-V characteristic.

Step 1: Apply Kirchhoff’s Rules.
We are given a circuit with resistors of , , and , and a voltage source of and . We will apply Kirchhoff’s Voltage Law (KVL) to the loop and solve for the current using Ohm’s Law: Where and .
After solving the equation, we get:
Final Answer:
The current through the 10Ω resistor is .

Step 1: Nature of N-type semiconductor.
In N-type semiconductors, electrons are majority carriers. But for every extra electron, there is a positive ion core.
Step 2: Neutrality.
The number of positive and negative charges balance each other.
Step 3: Conclusion.
Hence, N-type semiconductors are overall electrically neutral.