Electron hopping‐randomwalk at localized band tail states with exponential density in amorphous hydrogenated silicon

Abstract

Monte Carlo simulation of hopping‐randomwalk at localized band tail states with the exponential density has been executed. The mean square hopping distance of electrons and the average density of electrons at the starting site after s steps are shown to be given by <r(s)2> ∼ sα and <N(r=0,s)> ∼ s–γ, respectively. The exponents α andγ increase with temperature and reach 1 and 3/2 at high temperatures, respectively. α is shown to be equal to the dispersion parameter, αi, at short time in the time‐of‐flight experiment. The temperature behaviour of α are shown to agree with that of αi in amorphous hydrogenated silicon (a‐Si:H) observed in the electric field lower than 1×104 V/cm. The average depth of electrons and holes in the exponential tail increases with steps and thermally balance at an energy, which is named the hopping‐edge. The temperature dependence of the hopping‐gap, which means the energy difference between electron and hole hopping‐edges, agrees with that obtained from the excitation energy dependence of the luminescence peak energy in a‐Si:H. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Hopping and radiative recombination at localized band tail states in hydro‐ genated amorphous silicon

“…The dispersion parameter α i at 1x10 4 V/cm increases slowly with increasing temperature until 220 K and then increases rapidly to attain to α i =1 of the Gaussian transport. The temperature dependence obtained from the Monte Carlo simulation of the hoppingrandomwalk in the exponential density of the localized band tail states with the tail parameter of E e =kT e =19 meV agrees with that of the slow dependence region lower than 220 K [15]. This shows that anomalous hopping is induced by the electric field at temperatures higher than 220 K. The threshold shifts to lower temperature with increasing electric field.…”

“…The temperature dependences of the dispersion parameter α i observed at different electric field 1x10 4 to 1x10 5 V/cm are shown in Fig. 5 [15]. The dispersion parameter α i at 1x10 4 V/cm increases slowly with increasing temperature until 220 K and then increases rapidly to attain to α i =1 of the Gaussian transport.…”

“…The temperature dependences of the dispersion parameter α i at different electric fields in a-Si:H [15]. The dashed and dotted curve show the temperature behaviours of α i obtained by the simulation of the hopping model and calculated from α i =T/T e (kT e =19 meV), respectively [15].…”

Temperature dependence of hopping‐edge in amorphous hydrogenated silicon

“…This shows that the luminescence center is in the localized band Figure 6 The temperature dependence of the hopping-gap in the A1 and D1 a-Si:H films obtained by the excitation energy dependence of the luminescence peak energy. Solid and dotted lines show those obtained by the hopping-randomwalk simulation [5].…”

Stretched exponential relaxation processes in hydrogenated amorphous and polymorphous silicon

“…(6) has been reported by Murayama et al [23,24] in the Monte Carlo simulation for electron transport in a-Si:H. They took 1000 electrons in 200×200×200 sites with different 50 simple cubic lattices [23] and further extended to 300×300×300 sites [24].…”