Question

Explain the energy bands in solids.

Hint:

Discrete atomic levels split and merge into valence and conduction bands separated by a forbidden gap Eg; the size of Eg (0, about 1 eV, or large) classifies metals, semiconductors and insulators.

Answer 1

Step 1: Origin of energy bands.
In an isolated atom the electrons occupy sharp, discrete energy levels. In a solid a very large number of atoms are packed close together, so the electrons of neighbouring atoms interact. Because of the Pauli exclusion principle no two electrons can have exactly the same energy, so each sharp atomic level splits into a very large number of closely spaced levels. These closely spaced levels are so near to one another that they form a continuous range of allowed energies called an energy band.

Step 2: Valence band.
The band formed by the energy levels of the valence (outermost) electrons is called the valence band. At absolute zero it is completely filled with electrons.

Step 3: Conduction band.
The band just above the valence band, in which electrons are free to move and take part in electrical conduction, is called the conduction band. In it electrons can drift under an applied field and carry current.

Step 4: Forbidden energy gap.
Between the top of the valence band and the bottom of the conduction band there may be a range of energies that no electron can possess. This is called the forbidden energy gap \( E_g \).

Step 5: Classification of solids.
• Conductors (metals): the valence and conduction bands overlap (\( E_g = 0 \)), so electrons conduct freely.
• Insulators: a large forbidden gap (\( E_g \gt 3\ \text{eV} \), e.g. about 6 eV for diamond) prevents electrons from reaching the conduction band, so no conduction.
• Semiconductors: a small gap (\( E_g \approx 1\ \text{eV} \), e.g. 1.1 eV for Si, 0.7 eV for Ge); at room temperature a few electrons cross into the conduction band, giving small conductivity.
\[\boxed{\text{Metal: } E_g=0,\quad \text{Semiconductor: } E_g\approx1\text{ eV},\quad \text{Insulator: } E_g\gt3\text{ eV}}\]