Analytical solution of phototransport problem under the presence of a small-signal photocurrent based on method of weighted residuals - R.I. Badran (Results in Physics, 2020)
The nonlinear phototransport differential equations are analytically solved for a small-signal steady-state photocarrier grating in the presence of external electric field using the method of weighted residuals. Two-term ansatz sinusoidal solution is initially considered as approximate and is then corrected to get the optimum derived expressions for density grating of photoelectrons and photoholes. Both the approximate and corrected expressions of the derived grating amplitudes of the two photocarriers are employed to find corresponding expressions of the coefficient β. The expressions of β are examined by re-producing the field-dependent experimental data of β obtained at room temperature from steady-state photocarrier grating (SSPG) technique for a hydrogenated nanocrystalline silicon sample. The fittings to experimental data are obtained using physical transport quantities as adjustable parameters. We believe that the average value of ambipolar diffusion length of 212 nm with an uncertainty of ~ 6%, obtained from this analysis, which is close to the experimental error of the SSPG measurements, is acceptable. The excess photoelectron and photohole densities in addition to electric field grating are demonstrated. The current analysis reveals that the spatial electric field grating exhibits an increase with increasing applied field and until a certain point where it starts slowly falling off at high values of applied field. This fall off becomes shallower with increasing grating periods.