Energy Bandgap

Aim

To determine the energy band gap of a given semiconductor material by measuring its electrical resistance as a function of temperature.

Apparatus

Semiconductor sample (e.g., Ge or Si)
Thermometer
Microammeter
Connecting wires
Regulated DC power supply
In built heater

Pre-Lab Questions

What is the energy band gap in a semiconductor?
The energy band gap (E_g) is the energy difference between top of the valence band and bottom of the conduction band, which determines the ease of electron excitation in a semiconductor.
Why does the resistance of a semiconductor decrease with temperature?
As temperature increases, more electrons gain energy to jump from the valence band to the conduction band, increasing charge carriers and reducing resistance.
How do you differentiate between a conductor, insulator and semiconductor based on energy gap?
Conductors have no energy gap (Eg ≈ 0 eV), allowing high conductivity; insulators have a large gap (>5 eV), blocking conduction. Semiconductors have a moderate gap (0.1–2 eV), enabling tunable conductivity.
What is the significance of the band gap in semiconductors?
The band gap determines the semiconductor’s electrical and optical properties, affecting its use in devices like diodes and transistors.
How is the band gap related to temperature in this experiment?
As the temperature increases, the thermal energy excites more electrons from the valence band to the conduction band, increasing the reverse saturation current \(I_S\). The band gap \(𝐸_𝑔\) decreases slightly with increasing temperature due to the expansion of the crystal lattice and increased electron-phonon interactions.
Why does a semiconductor behave as an insulator at very low temperature?
At very low temperatures, a semiconductor behaves as an insulator because there’s insufficient thermal energy to excite electrons across the moderate energy gap (Eg ≈ 0.1–2 eV) from the valence band to the conduction band. Without these charge carriers, conductivity drops to near zero, hence it is acts an insulator.
What is the typical band gap value for silicon and germanium?
Silicon has a band gap of ~1.12 eV, and germanium has ~0.67 eV at room temperature.

Theory

In semiconductors, the energy band gap (E_g) separates the valence band (filled with electrons) from the conduction band (empty at absolute zero). As temperature increases, thermal energy excites electrons across the band gap, increasing the number of charge carriers (electrons and holes). The electrical conductivity (σ) of a semiconductor is given by σ = σ₀ e^-E_g/(2kT), where resistance (R) is inversely proportional to conductivity. By measuring resistance at different temperatures and plotting ln(R) vs. 1/T, the band gap can be determined from the slope of the resulting straight line.

Diagram

Working Formula

\[ E_g = \frac{2\times2.303\times slope \times k_B}{1.6\times 10^{-19}} eV\] Where :

-Slope obtained from the graph of \( log_{10}𝐼_𝑆 \text{ versus } 1/T. \)

-\(k_B\)- Boltzman Constant \(1.38\times 10^{-23} J/K \)

Calculations

\[ E_g = \frac{2\times2.303\times slope \times k_B}{1.6\times 10^{-19}} eV\]

Example:

Slope = 3000 \[ E_g = \frac{2\times2.303\times 3000 \times 1.38\times 10^{-23}}{1.6\times 10^{-19}} eV\] \[ E_g = \frac{19068.84}{1.6\times 10^{-19}} eV\] \[ E_g = 11918 \times 10^{-4} eV\] \[ E_g = 1.1918 \text{ eV} \]

Procedure

Connect the circuit as shown in Diagram section.
Carefully insert the thermometer through the hole on the top surface of the wooden box, ensuring that the thermometer is fully immersed in the oil.
Turn on the main power supply and switch on the heater. This will gradually increase the oil temperature. Once the temperature reaches 65°C, switch off the heater.
As a result of the heating effect, the temperature will continue to rise up to 80°C. Record the corresponding current reading from the micrometer for every 5°C drop in temperature until it returns to room temperature.
Record all the measured values in the observation table. Plot a graph of log₁₀ Iₛ versus 1/T.
Determine the slope from the graph. Substitute the calculated slope and other values into the working formula to compute the energy gap value.

Observation Table

T (°C)	T(K) = T°(C) + 273	\( \frac{1}{T}\) \( (K^{-1}) \)	\( I_s ( \mu A) \)	\( I_s ( A) \)	\( log_{10} ( I_s) \)
80
75
70
65
60
55
50
45
40
35
30

Model Graph

Precautions

Ensure uniform heating of the sample to avoid temperature gradients.
Allow sufficient time for the sample to stabilize at each temperature.
Use a calibrated thermometer and multimeter for accurate readings.
Avoid exceeding the melting point or damage threshold of the semiconductor.
Record current only after the reading stabilizes to minimize errors.

Applications

Designing semiconductor devices (e.g., diodes, transistors) based on band gap properties.
Developing solar cells, where band gap affects efficiency.
Temperature sensors utilizing resistance variation.
Optoelectronic devices like LEDs and photodetectors.
Research in material science for characterizing semiconductors.

Post-Lab Questions

Why does the resistance decrease with increasing temperature?
More electrons are thermally excited across the band gap, increasing charge carriers and conductivity.
How junction diode can be used as rectifier?
A junction diode acts as a rectifier by allowing current to flow in one direction (forward bias) while blocking it in the opposite direction (reverse bias). This property converts alternating current (AC) to direct current (DC) by filtering out the negative or positive portion of the AC signal, depending on the diode's orientation.
Why is the band gap important for electronic devices?
It determines the voltage required to excite electrons and the wavelengths of light a material can emit or absorb.
What would happen if the temperature were too high?
The semiconductor could melt or become extrinsic, altering its properties and invalidating the experiment.
What do you understand by reverse saturation current of a diode?
The reverse saturation current of a diode is the small, constant current that flows in the reverse bias direction due to thermally generated minority charge carriers (electrons in the p-region and holes in the n-region) moving across the junction.

Outcomes

Determined the energy band gap of the semiconductor.
Verified the exponential relationship between current and temperature.
Gained insight into the thermal behavior of semiconductors and its relation to the band gap.
Developed skills in experimental data analysis and plotting.

List of Experiments