Unit 3: Solid State Physics (Lab: PHYDSC353P)

1. Laboratory Objectives
2. Energy Band Gap of a Semiconductor
3. Hall Effect in Semiconductors
4. Resistivity by Four-Probe Method
5. Magnetic Susceptibility (Quincke’s Method)
6. Lab Exam Focus Corner

1. Laboratory Objectives

The objective of this unit is to explore the electronic and magnetic properties of solids. You will perform measurements to identify carrier types, determine the energy required for electron excitation (band gap), and measure how materials respond to external magnetic fields.

2. Energy Band Gap of a Semiconductor

The Energy Band Gap (E_g) is the energy difference between the top of the valence band and the bottom of the conduction band. In this experiment, a P-N junction diode is used as a temperature sensor.

Working Principle:

In reverse bias, the saturation current (I_s) is primarily due to the thermally generated minority carriers. This current depends exponentially on the temperature (T).

log₁₀(I_s) = Constant - (5.036 · E_g · 10³) / (T)

Procedure: The diode is placed in an oil bath and heated. The reverse current is measured as the temperature decreases. A plot of log(I_s) vs. 10³/T yields a straight line, the slope of which gives E_g.

3. Hall Effect in Semiconductors

When a current-carrying conductor is placed in a transverse magnetic field, an electric field (Hall field) is generated in a direction perpendicular to both the current and the magnetic field.

Parameters Determined:

Hall Coefficient (R_H): R_H = (V_H · w) / (I · B) (where w is thickness).
Carrier Type: The sign of the Hall voltage indicates if the carriers are electrons (negative) or holes (positive).
Carrier Concentration (n): n = (1) / (R_H · e).

4. Resistivity by Four-Probe Method

The Four-Probe Method is an exceptionally accurate way to measure the resistivity of a semiconductor wafer. It uses four collinear probes; current is passed through the outer two, and voltage is measured across the inner two.

Advantages:

By separating the current and voltage leads, the method eliminates the error caused by contact resistance, which is significant in semiconductors.

ρ = (V) / (I) · 2π S

Where S is the spacing between the probes. For thin samples, a correction factor G(W/S) is applied.

5. Magnetic Susceptibility (Quincke’s Method)

This experiment measures the Magnetic Susceptibility (χ) of a paramagnetic liquid (like Manganese Sulfate or Ferric Chloride).

Mechanism: The liquid is placed in a U-tube with one limb between the pole pieces of a strong electromagnet. When the field is turned on, the liquid level rises (if paramagnetic) or falls (if diamagnetic).

χ = (2(h-h₀) ρ g) / (H²)

Where h is the rise in height, ρ is the density, and H is the magnetic field strength.

Lab Exam Focus Corner

Frequently Asked Questions

Why is Germanium (Ge) preferred over Silicon (Si) for band gap experiments in basic labs? Ge has a smaller band gap (~0.67 eV) compared to Si (~1.1 eV), making its thermal variations easier to measure at lower temperatures.
What is the unit of the Hall Coefficient? m³/C (Cubic meters per Coulomb).

Common Mistakes

Current Limits: In the Four-Probe method, do not pass high current as it causes Joule heating, which changes the resistivity you are trying to measure.
Magnet Calibration: Ensure the Hall probe used to measure the magnetic field (B) is calibrated and held perfectly perpendicular to the field lines.

Practical Tips

Tip: In the Band Gap experiment, always use Silicon oil in the bath rather than water to ensure electrical insulation and to reach temperatures above 100°C safely.