Strain-tunable charge carrier mobility of atomically thin phosphorus allotropes

Abstract

We explore the impact of strain on charge carrier mobility of monolayer $\ensuremath{\alpha}$-, $\ensuremath{\beta}$-, $\ensuremath{\gamma}$-, and $\ensuremath{\delta}$-P, the four well-known atomically thin allotropes of phosphorus, using density functional theory. Owing to the highly anisotropic band dispersion, the charge carrier mobility of the pristine allotropes is significantly higher (more than 5 times in some cases) in one of the principal directions (zigzag or armchair) compared to the other. Uniaxial strain (up to 6% compressive/tensile) leads to band gap alteration in each of the allotropes, especially a direct to indirect band gap semiconductor transition in $\ensuremath{\gamma}$-P and a complete closure of the band gap in $\ensuremath{\gamma}$- and $\ensuremath{\delta}$-P. We find that the charge carrier mobility is enhanced typically by a factor of \ensuremath{\sim}5--10 in all the allotropes due to uniaxial strain; notably, among them an \ensuremath{\sim}250 (30) times increase of the hole (electron) mobility along the armchair (zigzag) direction is observed in $\ensuremath{\beta}$-P ($\ensuremath{\gamma}$-P) under a compressive strain, acting in the armchair direction. Interestingly, the preferred electronic conduction direction can also be changed in the case of $\ensuremath{\alpha}$- and $\ensuremath{\gamma}$-P by applying strain.