Extrinsic Material

• Additionally  to the  thermally  generated  carriers,  it  is  possible  to  create  carriers  in  semiconductor by purposely introducing impurities into crystal    doping.
• The most common technique for varying conductivity of the semiconductors.
• By doping, the crystal can be made to have the predominantly electrons (n-type) or holes (p-type).
• When a crystal is doped such that equilibrium concentrations of the electrons (n0) and holes (p0) are different from intrinsic carrier concentration (ni), the material is said to be extrinsic in nature.
• Doping creates the additional levels within band gap.
• In Si, column V elements of periodic table (such as P, As, Sb) introduce energy levels quite near (typically 0.03-0.06 eV) the conduction band.
• At 0 K, these levels are filled with the electrons, and very small thermal energy (50 K to 100 K) is required for the electrons to get excited to the conduction band.
• As these levels donate electrons to conduction band, they are referred as the donor levels.
• Therefore the Si doped with donor impurities can have a major number of electrons in conduction  band  even when the temperature  is  not  adequately  high enough  for  intrinsic carriers to  dominate,  that is   n₀>> n_i, p_o    n-type material,  with the electrons  as majority carriers and holes as the minority carriers.

• In the Si, column III elements of periodic table (such as B, Al, Ga, In) introduce energy levels very near (around 0.03-0.06 eV) the valence band.
• At 0 K, these levels are empty, and very less thermal energy (50 K to 100 K) is needed for electrons in valence band to get excited to these levels, and leave behind holes in valence band.
• As these levels accept electrons from valence band, they are referred to as acceptor levels.
• Hence, Si doped with the acceptor impurities can have a significant number of the holes in the valence band even at very low temperature that is p_o >> n_i , n_o p-type material, with holes as the majority carriers and electrons as minority carriers.
• The extra electron for column V elements is quite loosely bound and it can be liberated easily    ionization; thus, it is free to take part in current conduction.

• Likewise, column III elements create holes in valence band, and they can also take part in the current conduction.
• Rough calculation of ionization energy can be made based on Bohr's model for H₂ atoms, considering loosely bound electron orbiting around tightly bound core electrons. Thus,
    (2.6) where is the relative permittivity of Si.

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