A perfect semiconductor crystal with no impurities or lattice defects is called an intrinsic semiconductor. In such material there are no charge carriers at
0 K, since the valence band is filled with electrons and the conduction band is empty. At higher temperatures electron-hole pairs are generated as valence
band electrons are excited thermally across the band gap to the conduction band. These EHPs are the only charge carriers in intrinsic material.
- The generation of EHPs can be visualized in a qualitative way by considering the breaking of covalent bonds in the crystal lattice (Fig. given below).
- If one of the Si valence electrons is broken away from its position in the bonding structure such that it becomes free to move about in the lattice, a conduction electron is created and a broken bond (hole) is left behind.
- The energy required to break the bond is the band gap energy Eg.
- This model helps in visualizing the physical mechanism of EHP creation, but the energy band model is more productive for purposes of quantitative calculation.
- One important difficulty in the "broken bond" model is that the free electron and the hole seem deceptively localized in the lattice.
- Actually, the positions of the free electron and the hole are spread out over several lattice spacings and should be considered quantum mechanically by probability distributions.
Since the electrons and holes are created in pairs, the conduction band electron concentration n (electrons per cm3) is equal to the concentration of
holes in the valence band p (holes per cm3).
- Each of these intrinsic carrier concentrations is commonly referred to as ni.
- Thus for intrinsic material
- At a given temperature there is a certain concentration of electron - hole pairs ni.
- Obviously, if a steady state carrier concentration is maintained, there must be recombination of EHPs at the same rate at which they are generated.
- Recombination occurs when an electron in the conduction band makes a transition (direct or indirect) to an empty state (hole) in the valence band, thus annihilating the pair.
- If we denote the generation rate of EHPs as gi (EHP/cm3-s) and the recombination rate as ri, equilibrium requires that
Each of these rates is temperature dependent. For example, gi(T) increases when the temperature is raised, and a new carrier concentration ni, is
established such that the higher recombination rate ri(T) just balances generation.
- At any temperature, we can predict that the rate of recombination of electrons and holes ri is proportional to the equilibrium concentration of electrons n0 and the concentration of holes p0:
The factor αr is a constant of proportionality which depends on the particular mechanism by which recombination takes place.