半导体器件原理 1.1 From Atom to Band Diagram

About energy band, different materials, carrier motion, and the water analogy.

# Energy Bands

• When atoms are put together, orbits at the same energy level are combined and form a energy band across the entire crystal.
• Electrons can stay at a wider range of energies instead of just one particular level.
• Valence Band: the energy band where electrons are shared.
  • All spaces that can hold electrons are filled with electrons.
• Conduction Band: the first empty energy band above the valence band.
  • Almost empty.
• Band Gap: the energy difference between the conduction band and the valence band.
  • No electron states exist in this energy range.

# Metal, Insulator, Semiconductor

• Metal: valence band is only partially filled.
  • Electrons can move freely to conduct electricity.
• Insulator: full valence band and empty conduction band.
  • Cannot conduct electricity.
  • With energy supplied, electrons can be excited to the conduction band.
• Semiconductor: similar band diagram as insulator, but with a smaller band gap.
  • Room temperature is enough to excite a considerable amount of electrons to the conduction band.
• Material with a full valence band and an empty conduction band can be insulator or semiconductor, depending on the size of band gap and temperature of the working environment.

# Carrier Motion

• Diffusion: particles move from high concentration to low concentration.
• Drift: particles move under the influence of an electric field.
• They can co-exist: electrons carry charges, accumulation of negative charges raises energy of electrons, which leads to drift and diffusion at the same time.
• Motion of electrons and holes is needed for electrons to move in an energy band, and the motion of the smaller quantity is easier to observe.

• In metals, electrons move in the partially filled band, and either electrons or holes are counted.
• In semiconductors, conduction happens both in the conduction band and the valence band, and carriers cannot be mixed. Current is the sum of both electrons and holes.
• The total number of carriers in the semiconductor is still much smaller than that in metals.

# The Water Analogy

• Electrons when voltage is applied -> water molecules moving down the potential
  • Tend to stay at the lower part of energy band
• Holes when voltage is applied -> holes moving up the potential
  • Tend to stay near the top part of energy band
• Deficiency: water molecules and bubbles are electrically neutral, while electrons and holes are charged.

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