How to Find Energy Gap in Semiconductors: A Comprehensive Guide

The energy gap, also known as the band gap, is a fundamental property of semiconductors that determines their electronic and optical characteristics. Accurately determining the energy gap is crucial for understanding and designing semiconductor-based devices, such as solar cells, light-emitting diodes (LEDs), and transistors. One of the most common methods to find the energy gap in semiconductors is through UV-Vis absorption spectroscopy. This comprehensive guide will walk you through the step-by-step process of using this technique to determine the energy gap in semiconductors.

Understanding the Energy Gap in Semiconductors

The energy gap in semiconductors is the energy difference between the top of the valence band and the bottom of the conduction band. This energy difference represents the minimum energy required for an electron to be excited from the valence band to the conduction band, enabling the flow of electric current. The size of the energy gap determines the semiconductor’s electrical and optical properties, such as its ability to absorb or emit light, its electrical conductivity, and its response to temperature changes.

Semiconductors can be classified into two main categories based on their energy gap:

1. Direct-gap semiconductors: In these materials, the minimum of the conduction band and the maximum of the valence band occur at the same point in the Brillouin zone, allowing for direct transitions between the bands.
2. Indirect-gap semiconductors: In these materials, the minimum of the conduction band and the maximum of the valence band occur at different points in the Brillouin zone, requiring the involvement of a phonon (lattice vibration) to facilitate the transition.

The energy gap in semiconductors can be determined using various techniques, including UV-Vis absorption spectroscopy, which is the focus of this guide.

Determining the Energy Gap Using UV-Vis Absorption Spectroscopy

UV-Vis absorption spectroscopy is a powerful technique that measures the absorption of light by a material as a function of wavelength or frequency. The absorption edge, which is the point at which the material begins to absorb light, can be used to determine the energy gap of the semiconductor.

Step 1: Prepare the Sample

1. Obtain a thin film or powder sample of the semiconductor material.
2. Ensure the sample is clean and free of any impurities or defects that could affect the absorption spectrum.
3. Mount the sample in a suitable holder or cuvette for the UV-Vis spectrophotometer.

Step 2: Measure the Absorption Spectrum

1. Set up the UV-Vis spectrophotometer and calibrate it according to the manufacturer’s instructions.
2. Place the sample in the spectrophotometer and measure the absorption spectrum over the desired wavelength range, typically from the ultraviolet (UV) to the visible (Vis) region.
3. Record the absorption coefficient (α) as a function of the photon energy (hν), where h is Planck’s constant and ν is the frequency of the incident photon.

Step 3: Analyze the Absorption Spectrum using the Tauc Equation

The energy gap of the semiconductor can be determined using the Tauc equation, which relates the absorption coefficient (α) to the photon energy (hν):

(αhν)^γ = A(hν – Eg)

Where:
– α is the absorption coefficient
– h is Planck’s constant
– ν is the frequency of the incident photon
– A is a proportionality constant
– Eg is the energy gap of the semiconductor
– γ is an exponent that depends on the nature of the electronic transition

The value of γ depends on the type of electronic transition:
– For direct allowed transitions, γ = 1/2
– For indirect allowed transitions, γ = 2

1. Plot the (αhν)^γ versus hν on a log-log scale.
2. Identify the linear portion of the curve, which corresponds to the absorption edge.
3. Extrapolate the linear portion of the curve to the x-axis intercept to determine the energy gap (Eg) of the semiconductor.

Step 4: Interpret the Results

1. Analyze the obtained energy gap value and compare it with the known values for the semiconductor material.
2. Consider the type of electronic transition (direct or indirect) based on the value of the exponent γ used in the Tauc equation.
3. Discuss the implications of the energy gap on the semiconductor’s electronic and optical properties, such as its ability to absorb or emit light, its electrical conductivity, and its response to temperature changes.

Example: Determining the Energy Gap of TiO2-ZnFe2O4 Nanocomposites

In a study of TiO2-ZnFe2O4 nanocomposites, the energy gap was determined using the UV-Vis absorption spectroscopy and the Tauc equation.

1. The absorption coefficient (α) was plotted as a function of the photon energy (hν) for different molar concentrations of ZnFe2O4 in the TiO2 matrix.
2. The exponent γ was tested as both 1/2 and 2 to identify the correct transition type.
3. The linear portion of the (αhν)^γ versus hν curve was identified and extrapolated to the x-axis intercept to determine the energy gap (Eg) for each composition.
4. The results showed that the energy gap of the TiO2-ZnFe2O4 nanocomposites decreased with increasing ZnFe2O4 content, indicating that the addition of ZnFe2O4 can effectively tune the energy gap of the TiO2 semiconductor.

This example demonstrates the practical application of the UV-Vis absorption spectroscopy and the Tauc equation in determining the energy gap of semiconductor materials, which is crucial for understanding and optimizing their performance in various electronic and optoelectronic devices.

Advanced Techniques and Considerations

While the UV-Vis absorption spectroscopy and the Tauc equation provide a straightforward method for determining the energy gap in semiconductors, there are several advanced techniques and considerations that can further enhance the accuracy and reliability of the results:

1. Temperature-dependent measurements: Measuring the absorption spectrum at different temperatures can provide insights into the temperature dependence of the energy gap, which is important for understanding the semiconductor’s behavior in various operating conditions.

2. Ellipsometry: Ellipsometry is a non-destructive optical technique that can provide more detailed information about the dielectric properties of the semiconductor, including the energy gap.

3. Photoluminescence spectroscopy: This technique measures the light emitted by the semiconductor when it is excited by a light source, and can be used to determine the energy gap and other electronic properties.

4. Theoretical calculations: Computational methods, such as density functional theory (DFT), can be used to calculate the energy gap of semiconductors based on their atomic and electronic structure, providing a complementary approach to experimental measurements.

5. Defects and impurities: The presence of defects and impurities in the semiconductor can significantly affect the energy gap, and should be carefully considered when interpreting the experimental results.

6. Surface and interface effects: The energy gap of a semiconductor can be influenced by surface and interface effects, particularly in nanostructured materials, and should be taken into account when studying the semiconductor’s properties.

By understanding and applying these advanced techniques and considerations, researchers and engineers can obtain a more comprehensive and accurate understanding of the energy gap in semiconductors, enabling the development of more efficient and high-performance semiconductor-based devices.

Conclusion

Determining the energy gap in semiconductors is a crucial step in understanding and optimizing their electronic and optical properties. The UV-Vis absorption spectroscopy and the Tauc equation provide a straightforward and widely-used method for this purpose. By following the step-by-step guide outlined in this article, you can effectively determine the energy gap of semiconductor materials and gain valuable insights into their performance in various applications.

Remember to consider the advanced techniques and factors that can influence the energy gap, such as temperature, defects, and surface effects, to ensure the accuracy and reliability of your results. With a deep understanding of the energy gap in semiconductors, you can contribute to the development of cutting-edge electronic and optoelectronic devices that harness the unique properties of these materials.

References:

1. How to calculate band gap energy from UV-Vis absorption: https://youtu.be/LLESVSsZmlg
2. Simple Method of Measuring the Band Gap Energy Value: https://resources.perkinelmer.com/corporate/content/applicationnotes/app_uvvisnirmeasurebandgapenergyvalue.pdf
3. Energy Gap – an overview: https://www.sciencedirect.com/topics/engineering/energy-gap
4. Tauc, J. (1968). Optical properties and electronic structure of amorphous Ge and Si. Materials Research Bulletin, 3(1), 37-46.
5. Pankove, J. I. (1971). Optical processes in semiconductors. Courier Corporation.
6. Moss, T. S. (1959). Optical properties of semiconductors. Butterworth-Heinemann.