intrinsic material a perfect semiconductor

Question

Intrinsic Material

1. A perfect semiconductor crystal with no impurities or lattice defects.
2. No carriers at 0 K, since the valence band is completely full and the conduction band is completely empty.
3. For T > 0 K, electrons are thermally excited from the valence band to the conduction band (EHP generation).
4. EHP generation takes place due to breaking of covalent bonds => required energy = Eg.
5. The excited electron becomes free and leaves behind an empty state (hole).
6. Since these carriers are created in pairs, the electron concentration (n/cm³) is always equal to the hole concentration (p/cm³), and each of these is commonly referred to as the intrinsic carrier concentration (n_i).
7. Thus, for intrinsic material n = p = n_i.
8. These carriers are not localized in the lattice; instead they spread out over several lattice spacings, and are given by quantum mechanical probability distributions.
9. Note: n_i = f (T).
10. To maintain a steady-state carrier concentration, the carriers must also recombine at the same rate at which they are generated.
11. Recombination occurs when an electron from the conduction band makes a transition (direct or indirect) to an empty state in the valence band, thus annihilating the pair.
12. At equilibrium, r_i =g_i, where g_i and r_i are the generation and recombination rates respectively, and both of these are temperature dependent.
13. g_i(T) increases with temperature, and a new carrier concentration ni is established, such that the higher recombination rate r_i(T) just balances generation.
14. At any temperature, the rate of recombination is proportional to the equilibrium concentration of electrons and holes, and can be given by r_i= α_rn₀p₀ = α_rn_i²=gi(5) where α_ris a constant of proportionality (depends on the mechanism by which recombination takes place).