Question

On the basis of energy band diagram in solids, explain the difference between conductor, semiconductor, and insulator. What is the need of doping in pure semiconductors? Write the value of current in the ideal diodes \( D_1 \) and \( D_2 \) in the given circuit.
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Hint:

In ideal diodes, current only flows in the forward bias condition. In reverse bias, no current flows. Doping in semiconductors is essential for controlling conductivity and creating useful electronic devices.

Answer 1

Difference between Conductor, Semiconductor, and Insulator:
In solids, the difference between conductors, semiconductors, and insulators can be explained based on their energy band diagrams. The energy band diagram represents the energy levels available for electrons in a solid.
1. Conductor:
- In a conductor, the conduction band and valence band overlap, allowing electrons to freely move through the material.
- There is no band gap between the conduction and valence bands.
- Examples: Metals like copper, aluminum, etc.
- Conductors have high electrical conductivity.
2. Semiconductor:
- A semiconductor has a small energy gap (band gap) between the valence band and the conduction band.
- At absolute zero, the conduction band is empty, and the valence band is full. At room temperature, some electrons gain enough energy to jump to the conduction band.
- Examples: Silicon, germanium.
- Semiconductors have moderate electrical conductivity, which increases with temperature.
3. Insulator:
- In insulators, the band gap between the conduction band and the valence band is large.
- The conduction band is empty, and the valence band is full, with no electrons able to move to the conduction band at room temperature.
- Examples: Rubber, wood, glass.
- Insulators have very low electrical conductivity.
Need of Doping in Pure Semiconductors:
Pure semiconductors, like silicon, have limited electrical conductivity. Doping introduces impurities into the semiconductor material to increase its conductivity. Doping creates either an excess of electrons (n-type doping) or a shortage of electrons (p-type doping), allowing current to flow more easily. Doping is crucial for creating practical semiconductors used in devices like diodes and transistors.
Current in Ideal Diodes \( D_1 \) and \( D_2 \):
In the given circuit, we have two diodes \( D_1 \) and \( D_2 \), with resistors \( 100 \, \Omega \) and \( 5 \, \Omega \), respectively, connected in series with a \( 2 \, \text{V} \) battery.
- For an ideal diode, the current flowing through the circuit is determined by Ohm's law. An ideal diode has zero resistance in the forward bias condition and infinite resistance in the reverse bias condition.
- For \( D_1 \), if it is forward biased, it will conduct current.
- For \( D_2 \), if it is reverse biased, it will not conduct any current.
Assuming both diodes are ideal: - Current through the circuit, \( I = \frac{V}{R_{\text{total}}} = \frac{2 \, \text{V}}{100 \, \Omega + 5 \, \Omega} = \frac{2}{105} \, \text{A} = 0.019 \, \text{A}.
Thus, the current through the circuit is \( 0.019 \, \text{A} \) if \( D_1 \) is forward biased and \( D_2 \) is reverse biased.