Features of the acceptor band and properties of localized carriers from studies of the variable-range hopping conduction in single crystals of p-Cu2ZnSnS4

Disorder and variable-range hopping conductivity in Cu2ZnSnS4 thin films prepared by flash evaporation and post-thermal treatment

“…On the other hand, the VRH charge transfer is expectable when the Fermi level, , lies close to one of the edges of the impurity band (or the acceptor band (AB) in our case of the p-type semiconductor) [25]. This takes place for the cases of a weak (K << 1) or strong (1  K << 1) degree of the compensation, K, as it has been established in [26] and [30], respectively. Following the arguments in [26] and [30], we can assume one of the two cases, considering the proximity to the MIT given by the relatively small difference of |  E c |, where +E c and  E c are the mobility edges [20].…”

“…This takes place for the cases of a weak (K << 1) or strong (1  K << 1) degree of the compensation, K, as it has been established in [26] and [30], respectively. Following the arguments in [26] and [30], we can assume one of the two cases, considering the proximity to the MIT given by the relatively small difference of |  E c |, where +E c and  E c are the mobility edges [20]. Because the impurity states are extended within the ( E c , +E c ) interval around the center of an impurity band and are localized outside this interval, the position of  close to one of the AB edges or tails is consistent with the VRH conduction regime [20].…”

“…Such mechanism of the charge transfer has recently been established in CZTS single crystals [26] and films [27][28][29], as well as in Cu 2 ZnSiSe 4 single crystals [30], belonging to the same family of compounds. The upper border of the VRH conduction in the above materials, lying close to the room temperature, reflects the high lattice disorder [26][27][28][29][30]. Indeed, such disorder stimulates the localization of the conduction electrons, favoring the hopping conductivity [20].…”

“…4 within the broad intervals of the temperature given in Table 2 by the upper (T v ) and lower (T m ) borders, yielding the values of T 0 and A collected in Table 2. The semi-width of the AB evaluated with the expression W  0.5 (T v 3 T 0 ) 1/4 [26,30] is also displayed in Table 2, reflecting the enhanced disorder in the majority of the annealed films, where W exceeds the data of as-grown samples. In the approximation of the DOS with a rectangular shape, g ()  g av  N/(2W), is valid [26,30] in the next equation, yielding the values of the ratio N/N c collected in Table 2.…”

“…The semi-width of the AB evaluated with the expression W  0.5 (T v 3 T 0 ) 1/4 [26,30] is also displayed in Table 2, reflecting the enhanced disorder in the majority of the annealed films, where W exceeds the data of as-grown samples. In the approximation of the DOS with a rectangular shape, g ()  g av  N/(2W), is valid [26,30] in the next equation, yielding the values of the ratio N/N c collected in Table 2. The broadness of the AB for S1-1 and S2-1 (Table 2), connected to the high lattice disorder, correlates well with the above conclusion, taking into account that the high disorder stimulates considerably the localization of the charge carriers [20].…”