Measurement of the minority carrier diffusion length (L) can be performed by measurement of the rate of decay of excess minority carriers with the distance (x) of an electron beam excitation source from a p-n junction or Schottky barrier junction perpendicular to the surface in an SEM. In an ideal case, the decay is exponential according to the equation, I = Ioexp(−x/L), where I is the current measured at x and Io is the maximum current measured at x=0. L can be obtained from the slope of the straight line when plotted on a semi-logarithmic scale. In reality, carriers recombine not only in the bulk but at the surface as well. The result is a non-exponential decay or a sublinear semi-logarithmic plot. The effective diffusion length (Leff) measured is shorter than the actual value. Some improvement in accuracy can be obtained by increasing the beam-energy, thereby increasing the penetration depth and reducing the percentage of carriers reaching the surface. For materials known to have a high surface recombination velocity s (cm/sec) such as GaAs and its alloys, increasing the beam energy is insufficient. Furthermore, one may find an upper limit on beam energy as the diameter of the signal generation volume approaches the device dimensions.
Dielectric screening in perovskite photovoltaics