Extrinsic Material

• In addition to thermally generated carriers, it is possible to create carriers in the semiconductor by purposely introducing impurities into the crystal => doping.
• Most common technique for varying the conductivity of semiconductors.
• By doping, the crystal can be made to have predominantly electrons (n-type) or holes (p- type).
• When a crystal is doped such that the equilibrium concentrations of electrons (n0) and holes (p0) are different from the intrinsic carrier concentration (ni), the material is said to be extrinsic.
• Doping creates additional levels within the band gap.
• In Si, column V elements of the periodic table (e.g., P, As, Sb) introduce energy levels very near (commonly 0.03-0.06 eV) the conduction band.
• At 0 K, these levels are filled with electrons, and very little thermal energy (50 K to 100 K) is required for these electrons to get excited to the conduction band.
• Since these levels donate electrons to the conduction band, they are referred to as the donor levels.
• Thus, Si doped with donor impurities can have a significant number of electrons in the conduction band even when the temperature is not sufficiently high enough for the intrinsic carriers to dominate, i.e., n₀>> n_i, p₀ => n-type material, with electrons as majority carriers and holes as minority carriers.
• In Si, column III elements of the periodic table (for example, B, Al, Ga, In) introduce energy levels very near (commonly 0.03-0.06 eV) the valence band.
• At 0 K, these levels are empty, and very little thermal energy (50 K to 100 K) is required for electrons in the valence band to get excited to these levels, and leave behind holes in the valence band.
• Since these levels accept electrons from the valence band, they are referred to as the acceptor levels.
• Thus, Si doped with acceptor impurities can have a significant number of holes in the valence band even at a very low temperature, i.e., p₀>> n_i, n₀ =>, p-type material, along with holes as majority carriers and electrons as minority carriers.
• The extra electron for column V elements is loosely bound and it can be liberated very Easily => ionization; thus, it is free to participate in current conduction.
• Similarly, column III elements create holes in the valence band, and they can also participate in current conduction.
• Rough calculation of the ionization energy can be made based on the Bohr's model for H₂ atoms, considering the loosely bound electron orbiting around the tightly bound core electrons. Thus,

  

Where ε_r is the relative permittivity of Si.