Electronic Devices: Band Model

Summary

This video explains the band model of a semiconductor, focusing on silicon. Starting from the electron configuration of an isolated silicon atom, it explores how energy levels evolve as atoms come together to form a crystal. The concept of energy level splitting due to atomic interactions is introduced, leading to the formation of energy bands. The video distinguishes between the valence band, fully occupied by electrons, and the conduction band, initially empty, separated by the energy band gap (E_G). It also highlights the temperature dependence of the band gap, using silicon and germanium as examples, illustrating how crystal structures can be represented using the band model.

Takeaways

• 💡 Silicon has an atomic number of 14, and its electron configuration includes a partially filled valence shell with 4 out of 8 electrons in the outermost shell.
• 🏗️ In a silicon crystal, atoms are arranged at an interatomic distance R, forming an interacting system that affects energy levels.
• 🔬 Isolated silicon atoms have discrete energy levels (1s, 2s, 2p, 3s, 3p) that are identical across all atoms when the interatomic distance is very large.
• ⚛️ As silicon atoms come closer, energy levels start splitting due to electron interactions governed by the Pauli exclusion principle.
• 📈 Inner shell electrons (1s, 2s, 2p) are less affected by interatomic interactions, while outer shell electrons (3s, 3p) show significant splitting.
• 🏞️ When energy levels split and merge in a crystal, they form continuous bands, known as the valence band and the conduction band.
• ⛔ The energy range between the valence and conduction bands with no available energy levels is called the forbidden energy gap or band gap (Eg).
• 📊 The valence band is fully filled with electrons, while the conduction band is initially empty, allowing electrons to move when energy is applied.
• 🌡️ The energy band gap is temperature-dependent: increasing temperature causes lattice expansion and decreases the band gap.
• ⚡ Example values: Silicon has Eg of 1.21 eV at 0 K and 1.1 eV at 300 K; Germanium has Eg of 0.74 eV at 0 K and 0.66 eV at 300 K.
• 🧩 The bottom edge of the conduction band is denoted as Ec and the top edge of the valence band as Ev, with Eg = Ec - Ev, an important parameter in semiconductor physics.

Q & A

What is the electron configuration of an isolated silicon atom?

The electron configuration of an isolated silicon atom (atomic number 14) is 1s² 2s² 2p⁶ 3s² 3p², where the inner shells are completely filled and the outer valence shell has 4 out of 8 electrons filled.

Why does the energy level splitting occur in a silicon crystal?

Energy level splitting occurs because when silicon atoms are close enough to interact, the Pauli exclusion principle prevents electrons from sharing the same quantum state, causing levels like 3s and 3p to split and form energy bands.

Which energy levels are least affected by interatomic interactions in silicon?

The inner energy levels (1s, 2s, 2p) are least affected because they are very close to the nucleus and do not significantly interact with neighboring atoms.

What are the valence band and conduction band in a semiconductor?

The valence band is the energy range fully occupied by electrons, while the conduction band is the higher energy range that is completely empty. The gap between them is the forbidden energy gap or band gap.

How is the energy band gap (EG) defined?

The energy band gap, EG, is the energy difference between the bottom of the conduction band (EC) and the top of the valence band (EV), expressed as EG = EC - EV.

Why does the energy band gap of a semiconductor change with temperature?

As temperature increases, the interatomic distance increases due to thermal expansion, which reduces the interaction between atoms and thus decreases the energy band gap.

What is the energy band gap of silicon at 0 K and 300 K?

For silicon, the energy band gap is 1.21 eV at 0 K and 1.1 eV at 300 K.

How many electrons fill the valence band in a silicon crystal at 0 K?

At 0 K, the valence band in silicon is completely filled with 4N electrons, where N is the number of silicon atoms in the crystal.

What happens to the 3p energy levels as silicon atoms come closer together?

As silicon atoms come closer, the 3p energy levels split and eventually merge to form a band structure due to atomic interactions.

Why is the band between the valence and conduction bands called the forbidden gap?

It is called the forbidden gap because there are no allowed energy states in this range, meaning electrons cannot occupy this energy region.

How does the concept of isolated atoms help in understanding the band model?

Starting with isolated atoms helps visualize how individual discrete energy levels of atoms gradually broaden and split into bands as the atoms interact in a crystal lattice.

What is the significance of the conduction band in semiconductors?

The conduction band is significant because electrons in this band are free to move under an electric field, enabling electrical conduction in semiconductors.