Surface Recombination

The surface also play an important role in recombination. Typically the surfaces complicate the measurement of bulk lifetime. Recombination at the surfaces is typically described by a surface lifetime τs, which includes the fundamental decay mode but ignores higher decay modes. τs is function of the surface recombination velocities S1 and S2, the cell width W and the minority carrier diffusivity D. The precise solution is quite complicated but approximate solutions exist for special cases and are sufficiently accurate for most purposes [1].

The simplified formulas given below can be used for transient measurements when the effective lifetime is much greater than the transient surface lifetime (). The more exact expression [2] in transient measurements that works in all cases is:

For quasi-steady-state measurements the formulas are accurate if .


There is a list of approximate solutions for several important cases below:

Silicon wafer with a thickness of W

The surfaces are identical so S = S1 = S2.

One surface is perfectly passivated so S2 = 0.

Both surfaces are perfectly passivated so S1 = S2 = 0.

Both surface have high recombination so S1 and S2 are large.

One surface has a high recombination and the other has a low recombination so S1 = 0 and S2 = ∞


Effective Lifetime

The combination of the effects of surface and bulk recombination give the effective lifetime of carriers τeff within a sample.

For many measurements it is possible to reduce surface recombination of the surfaces to a low enough value so that τb ≫ τ eff. Alternatively if τb is sufficiently high the lifetime measurement is completely dominated by the surfaces and τs ≫ τeff. An accurate measurement of surface recombination is then possible.

Effective Lifetime Calculator


The second surface has:
The same surface recombination velocity as the first surface
Very low surface recombination velocity