Obtainment of the density of states in the band tails of hydrogenated amorphous silicon

In this work, we present two new pairs of formulas to obtain a spectroscopy of the density of states (DOS) in each band tail of hydrogenated amorphous silicon (a-Si:H) from photoconductivity-based measurements. The formulas are based on the knowledge of the small-signal recombination lifetime τ′, the characteristic decay time of the concentration of trapped carriers generated in excess by the illumination, and that can be measured by methods like the Oscillating Photocarrier Grating (OPG) or Moving Grating Technique (MGT). First, we deduce the formulas and test their accuracy by numerical simulations using typical a-Si:H parameters. Next, we characterize an a-Si:H sample using well-known methods, like Fourier transform photocurrent spectroscopy to evaluate the valence band tail and modulated photoconductivity to measure the conduction band tail. We also performed measurements of steady-state photoconductivity, steady-state photocurrent grating and MGT, for a range of generation rates. From these measurements—and taking typical values for the capture coefficients, the extended states mobilities and the DOS at the band edges—we apply the new formulas to get the band tails. We find that the results obtained from the application of our formulas are in good agreement with those found with the traditional methods for both band tails. Moreover, we show that MGT/OPG measurement to get τ′ can be avoided if one of the band tails is measured by one of the traditional methods, since the known band tail can be used to evaluate τ′ with one pair of equations, and then the other pair can be applied to get the other band tail.