Fundamental concepts of semiconductors
 
 
 
 
2.3 Degenerate and non-degenerate semiconductors
    So far we made the following assumptions:

  • Band structures are not disturbed by the doping

  • Band structures are still represented as ( so called) parabolic

  • Dopants are independent from each other

  • Dopants levels are low


It is also to be noted that the donors (or acceptors) energy levels are assumed as atom like. Such assumptions are limited up to to a certain level of dopant concentration and such extrinsic semiconductors are called non-degenerate semiconductors.

What happens if we add dopants at much higher concentrations? Dopant atoms come much closer to each other and it is no longer valid to assume the donor levels as atom like. If the inter-atomic distance is closer (typically < 10nm) then the atomic levels turn into bands. This leads to significant changes in the crystal structure as well as the physical properties. Another very important effect is, highly doped semiconductors come to freeze-out at much lower temperatures, meaning the freeze-out region is almost eliminated!. Such highly doped semiconductors are called Degenerate semiconductors.



 

Fig.2.32.Effect if band gap (both electrical (ΔEel) and as well as optical (ΔEopt) ) change in heavily doped Silicon.


 
Another important effect of heavy doping is narrowing of the band gap. This can seriously affect the device performance. For example, in silicon we can approximate the effect of donor densities (Nd) on change in the band gap (ΔE) as ΔEg(eV) ~ 3.5x10-8•Nd1⁄3 which is shown in the figure2.32. If you look at the doping effect on the Fermi level (Fig 2.31), as the dopant concentration increases, at a particular concentration, the Fermi level enters into the conduction band, which changes from non-degenerate to degenerate case . For example, in the case of silicon, the effect is plotted in figure 2.33. Just to mention, heavily doped silicon is often used as a replacement for metals where the resistance is much lower than 0.01Ω/cm.


 
Fig. 2.33. Effect of dopant ( donor) concentration on Fermi level position, with respect to conduction band in silicon.