semiconductor physics and Devices

Week 1: Semiconductors - Introduction and Intrinsic Properties

Lecture Topics:

1. Introduction to Semiconductors

   • Overview of semiconductors and their importance in modern technology (e.g., electronics, solar cells, LEDs).

   • Comparison with metals and insulators in terms of electrical conductivity and band structure.

   • Types of semiconductors:

     • Intrinsic Semiconductors: Pure materials with no impurities.

     • Extrinsic Semiconductors: Doped semiconductors with controlled impurities to alter conductivity.

   • Common semiconductor materials: Silicon (Si), Germanium (Ge), Gallium Arsenide (GaAs).

2. Band Structure of Semiconductors

   • Recap of the energy band structure: Valence band, conduction band, and band gap.

   • Difference between direct and indirect band gaps:

     • Direct band gap: Electrons can transition from the valence to conduction band without changing momentum (e.g., GaAs).

     • Indirect band gap: Transitions require a change in momentum, often involving a phonon (e.g., Si).

   • Explanation of why semiconductors have a small energy gap compared to insulators, allowing for thermal excitation of electrons into the conduction band.

3. Intrinsic Carrier Concentration

   • In intrinsic semiconductors, the number of electrons in the conduction band equals the number of holes in the valence band.

   • Thermal excitation of electrons across the band gap leads to electron-hole pair generation.

   • Expression for the intrinsic carrier concentration

where NC and Nv are the effective density of states in the conduction and valence bands, Eg​ is the energy band gap, kB​ is Boltzmann’s constant, and T is the temperature.

1. Temperature dependence of carrier concentration and the importance of band gap size in determining the material’s behavior at different temperatures.

Fermi Level in Intrinsic Semiconductors

• Introduction to the Fermi level: The energy level at which the probability of an electron occupying a state is 50%.

• For intrinsic semiconductors, the Fermi level lies near the middle of the band gap.

• Temperature dependence of the Fermi level position in intrinsic semiconductors.

Electrical Conductivity of Intrinsic Semiconductors

• Calculation of the electrical conductivity σ for an intrinsic semiconductor

1. where ni​ is the intrinsic carrier concentration, μe is the electron mobility, and μh​ is the hole mobility.

2. Discuss how temperature influences conductivity in intrinsic semiconductors, with conductivity increasing as more electron-hole pairs are thermally excited.

Examples:

• Calculate the intrinsic carrier concentration for silicon at room temperature, given the band gap and effective density of states.

• Estimate the electrical conductivity of an intrinsic semiconductor at a given temperature.

• Graph the temperature dependence of the carrier concentration and explain its behavior at different temperature ranges.

Homework/Exercises:

1. Calculate the intrinsic carrier concentration for germanium at 300 K, given the band gap and effective density of states.

2. Explain the difference between direct and indirect band gap semiconductors and give examples of materials for each type.

3. Derive the expression for intrinsic carrier concentration nin_ini​ and explain its temperature dependence.

Suggested Reading:

• Charles Kittel, Introduction to Solid State Physics, Chapter 8: Semiconductors.

Key Takeaways:

• Intrinsic semiconductors are pure materials where the number of electrons and holes are equal, and their electrical properties are highly temperature-dependent.

• The energy band gap is crucial in determining a material’s conductivity and carrier concentration, with smaller gaps leading to higher conductivity at room temperature.

• Understanding the Fermi level, intrinsic carrier concentration, and temperature dependence is essential for analyzing semiconductor behavior.

This week introduces the fundamental concepts of intrinsic semiconductors, setting the foundation for more advanced topics like doping, extrinsic semiconductors, and semiconductor devices in subsequent weeks.