Minority carrier lifetimes in silicon

As semiconductor designers we grew up with the concept of lifetimes of minority carriers in silicon. Our task was to take the process parameters and design rules from the foundry and fashion a chip. However, once we venture beyond this safe boundry and pit our skills against device design from scratch, a number of issues come up with which we are not too familiar with. One such came up for me this weekend. I was trying to calculate minority carrier lifetimes for specific conditions. I found out that this is a very difficult thing to do. Minority carrier lifetimes vary quite broadly and are dependent on a number of factors. Among these are Auger recombination, band to band recombination and Shockley-Read-Hall (SRH)recombination.

The lifetime is a strong function of the doping concentration of the silicon. It is easier to use analytical formulas for lifetime calculation when the concentration is high ( > 1E17).

High resistivity material is harder to handle analytically. The lifetimes in these materials can be a function of the construction of the crystal(CZ versus FZ). In addition various processing steps can have an impact on the lifetime.

Nevertheless analytical formulas do exist for estimation of lifetimes. The one that I am now using is: lifetime = 5E-7/(1.0 + 2.0E-17)N, where N is the doping concentration in cm**3.

Roulston has published a curve that also shows the approximate variation of lifetime with concentration. Both of these techniques are just approximations. I compared calculations of the lifetime for various concentrations using the analytical formula with Roulston's curve. The fit became very close as the concentrations increased, but was poor at low concentrations (highly resistive silicon).

My conclusions are that if the need is simply to estimate the lifetime to a rough order of magnitude then by all means one can use the analytical formula given above or Roulston's curve. However, if precise numbers are required then measurements must be made on samples of doped silicon under the conditions of operation. There is no shortcut here for that kind of accuracy!