Semiconductors

We use the mass action law:
Given:
So,

In a semiconductor material, the electrical conductivity is significantly lower than that of conductors but higher than that of insulators at room temperature.
The conductivity depends on the concentration of charge carriers, which are free electrons and holes.
At temperatures above absolute zero, thermal energy can excite electrons from the valence band to the conduction band, creating free electrons in the conduction band and leaving behind holes in the valence band.
This process is called thermal generation of electron-hole pairs.
When the temperature of a semiconductor increases: - More thermal energy is available to break covalent bonds in the semiconductor lattice.
- This increased energy causes more electrons to be excited from the valence band to the conduction band.
- As a result, the number of free electrons in the conduction band increases.
- Simultaneously, for every electron that moves to the conduction band, a hole is created in the valence band.
- Therefore, the number of holes in the valence band also increases.
The increase in both the number of free electrons and the number of holes leads to an increase in the conductivity of the semiconductor with increasing temperature.
Options (A) and (B) are incorrect because the generation of free electrons and holes occurs in pairs due to thermal excitation.
Option (D) is incorrect because increasing temperature provides more energy for carrier generation, thus increasing their numbers.

Step 1: Apply Carrier Concentration Formula For intrinsic semiconductors: Step 2: Compute Electron Concentration Thus, the correct answer is m . \bigskip

A PN junction diode is primarily used as a rectifier. It is a semiconductor device that allows current to flow in only one direction, making it ideal for converting alternating current (AC) to direct current (DC). This process of conversion is known as rectification. In the context of the options provided, the correct and commonly accepted use of a PN junction diode is as a rectifier.

Let’s break this down step by step to determine the behavior of an intrinsic semiconductor at absolute zero and why option (3) is the correct answer.
Step 1: Understand the behavior of an intrinsic semiconductor
An intrinsic semiconductor is a pure semiconductor without impurities. Its conductivity depends on the excitation of electrons from the valence band to the conduction band, which requires thermal energy to overcome the band gap.
Step 2: Analyze the behavior at absolute zero
At absolute zero temperature ( ), there is no thermal energy available to excite electrons across the band gap. As a result:

• No electrons are in the conduction band.
• The valence band is completely filled.
• No charge carriers (electrons or holes) are available for conduction.

Therefore, the intrinsic semiconductor behaves as an insulator, as it cannot conduct electricity.
Step 3: Confirm the correct answer
Since an intrinsic semiconductor has no free charge carriers at absolute zero, it behaves as an insulator, matching option (3).
Thus, the correct answer is (3) insulator.

- For a transistor to work as an amplifier, it must operate in the active region.
- In this region, the emitter-base junction is forward biased to allow current injection of charge carriers from emitter to base.
- The base-collector junction is reverse biased so that the charge carriers injected into the base are swept into the collector, resulting in current amplification.
- Other biasing configurations result in cutoff or saturation, not amplification.

A diode is forward biased when the anode is at a higher potential than the cathode. In this case, the correct forward bias configuration is +2V → -2V.

In a transistor, the collector (Z) is the largest in size, followed by the emitter (X), and the base (Y) is the smallest. This size difference is crucial for the transistor's operation.

Step 1: Voltage Gain Formula The voltage gain for a transistor in common emitter configuration is: where: - (current gain), - (collector resistance), - . Step 2: Solving for Conclusion Thus, the correct answer is:

Given: , , V, k , k .
Base current A.
Collector current: Since , the collector voltage is the same as the emitter (ground), so A.
Current amplification factor .

Step 1: Voltage Gain Formula The voltage gain for a transistor in common emitter configuration is: where: - (current gain), - (collector resistance), - . Step 2: Solving for Conclusion Thus, the correct answer is:

Let's analyze the output of each gate.
NAND gate 1: Inputs are A and A.
Output .
(A NAND gate with inputs tied together acts as a NOT gate).
NAND gate 2: Inputs are B and B.
Output .
(Acts as a NOT gate).
NAND gate 3: Inputs are X and Y.
Output .
Substitute X and Y: Using De Morgan's theorem : Since : The expression represents the OR logic operation.
Therefore, the equivalent logic gate is OR.
This matches option (3).

Step 1: Circuit analysis
Supply voltage , Zener voltage .
Voltage across resistor: Step 2: Calculate current through resistor
Step 3: Current division
Current divides through resistor and Zener diode.
Current through : Step 4: Current through Zener diode
Step 5: Conclusion
The current through Zener diode is 6 mA.