⚡ Experiment: Electrical Conduction in Semiconductors

Objective

To study how the electrical conductivity of a semiconductor changes with temperature and to determine the energy gap (E_g).

Required Equipment (Basic Setup)

• Semiconductor sample (e.g., pure silicon or germanium)
• Heater or temperature-controlled setup
• Thermometer or thermocouple
• AC power supply (for safety)
• Ammeter (to measure current)
• Voltmeter (to measure voltage across the sample)
• Connecting wires and sample holders

Theory

The electrical conductivity (σ) of an intrinsic semiconductor increases with temperature. The theoretical relationship is:

σ ∝ exp(-E_g / 2 k_B T)

Where:

E_g = energy gap of the semiconductor

k_B = Boltzmann constant

T = absolute temperature (Kelvin)

Taking the natural logarithm gives:

ln(σ) ∝ -E_g / (2 k_B T)

This produces a straight line when ln(σ) is plotted versus 1/T.

Procedure

1. Connect the semiconductor sample in the circuit with the voltmeter and ammeter.
2. Gradually heat the sample while monitoring its temperature.
3. Measure and record the voltage across and the current through the sample at various temperatures.
4. Calculate the conductivity for each measurement using: σ = (I × L) / (V × A) where L = length of the sample, A = cross-sectional area.
5. Plot ln(σ) against 1/T to obtain a straight line.
6. Determine the energy gap from the slope of the line: E_g = -2 × k_B × slope

Observations

Conductivity increases with temperature due to the generation of electron-hole pairs. The ln(σ) vs 1/T graph can be used to calculate the semiconductor's energy gap accurately.