  Photoconductors based on semiconducting thin films, nanowires and
2-dimensional atomic layers have been extensively investigated. But there is no
explicit photogain equation that allows for fitting and designing
photoresponses of these devices. In this work, we managed to derive explicit
photogain equations for silicon nanowire photoconductors based on experimental
observations. The silicon nanowires were fabricated by patterning the device
layer of silicon-on-insulator wafers by standard lithography that were doped
with boron. It was found that the as-fabricated silicon nanowires have a
surface depletion region ~ 32 nm wide. This depletion region protects charge
carriers in the channel from surface scatterings, resulting in the independence
of charge carrier mobilities on nanowire size. It is consistent with our Hall
effect measurements but in contradiction with the accepted conclusion in the
past decades that charge carrier mobilities become smaller for smaller
nanowires due to surface scatterings. Under light illumination, the depletion
region logarithmically narrows down and the nanowire channel widens
accordingly. Photo Hall effect measurements show that the nanowire
photoconductance is not contributed by the increase of carrier concentrations
but the widening of the nanowire channel. As a result, a nanowire
photoconductor can be modeled as a resistor in connection with floating
Schottky junctions near the nanowire surfaces. Based on the photoresponses of a
Schottky junction, we derived explicit photogain equations for nanowire
photoconductors that are a function of light intensity and device physical
parameters. The gain equations fit well with the experimental data, from which
we extracted the minority carrier lifetimes that are consistent with the
minority carrier lifetime in nanowires reported in literature.
