Intrinsic Material

• It is a perfect semiconductor crystal with no impurities or lattice defects.
• No carriers at 0 K, as valence band are completely full and the conduction band is completely empty.
• For T > 0 K, electrons are thermally excited from valence band to the conduction band (EHP generation).
• EHP generation takes place because of breaking of covalent bonds required energy = E_g.
• Excited electron becomes free and leaves behind the empty state (hole).

• As these carriers are created in pairs, electron concentration ( n/cm³) is always equal to hole concentration ( p/cm³), and each of these is commonly referred to as intrinsic carrier concentration ( n_i).
• Hence, for intrinsic material n = p =  n_i.
• These carriers cannot be localized in lattice; instead they spread out over the several lattice spacings, and are given by the quantum mechanical probability distributions.
• Note that ni = f(T).
• To maintain the steady-state carrier concentration, the carriers should also recombine at same rate at which they are generated.
• Recombination takes place when an electron from conduction band makes a transition (direct or indirect) to an empty state in valence band, hence annihilating the pair.
• At the equilibrium, r_i= g_i, here  g_i and r_i are the generation and recombination rates respectively, and these are temperature dependent.
• g_i (T) increases with the temperature, and a new carrier concentration ni is established, so that the higher recombination rate   r_i (T) just balances the generation.
• At  any  temperature,  rate  of  the recombination  is  proportional  to  equilibrium concentration  of  the electrons  and  holes,  and  can  be  given  by   (2.5) here α_r is  a   constant   of  proportionality  ( which depends  on  mechanism  by  which recombination takes place). 

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