Highly anisotropic electronic transport properties of monolayer and bilayer phosphorene from first principles

Abstract

The intrinsic carrier transport dynamics in phosphorene is theoretically examined.Utilizing a density functional theory treatment, the low-field mobility and the saturation velocity are characterized for both electrons and holes in the monolayer and bilayer structures. The analysis clearly elucidates the crystal orientation dependence manifested through the anisotropic band structure and the carrier-phonon scattering rates. In the monolayer, the hole mobility in the armchair direction is estimated to be approximately five times larger than in the zigzag direction at room temperature (460 cm 2 /Vs vs. 90 cm 2 /Vs). The bilayer transport, on the other hand, exhibits a more modest anisotropy with substantially higher mobilities (1610 cm 2 /Vs and 760 cm 2 /Vs, respectively). The calculations on the conduction-band electrons indicate a comparable dependence while the characteristic values are generally smaller by about a factor of two. The variation in the saturation velocity is found to be less pronounced.With the anticipated superior performance and the diminished anisotropy, few-layer phosphorene offers a promising opportunity particularly in p-type applications.

First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials

“…In contrast to the measurements by Cao [274] and the ab initio calculations by Jin et al [282], the bilayer mobilities obtained by Gaddemane et al [283] were almost identical or even smaller than in the monolayer.…”

“…Jin et al [282] later calculated the intrinsic electron and hole mobilities of both monolayer and bilayer phosphorene, using a full-band Monte Carlo method for the solution of the BTE [23]. Their study confirmed earlier findings that the anisotropic crystal structure of phosphorene imparts anisotropic transport properties via the anisotropic band structure and scattering rates.…”

“…This effect was ascribed to the presence of low-energy interlayer optical phonons. Despite the similar methodology adopted by Jin et al [282] and Gaddemane et al [283], the origin of the large mobility difference between the two studies remains unclear at the time of writing.…”

Mobility of two-dimensional materials from first principles in an accurate and automated framework

“…In the general case, including semiconductors, the major challenge is that the integrodifferential BTE does not have a closedform solution. Most approaches use then some form of relaxation-time approximation 24,[39][40][41][42][43][44][45][46][47][48][49] to obtain a closedform result.…”

“…Graphene has been studied extensively 24,40,41,43,44,60,[63][64][65][66][67][68][69][70][71][72][73][74][75] , showing excellent agreement 44 with experiments 1 and a detailed understanding of the main processes limiting mobility 41 , including the effects of dimensionality and charging by field effect 29,75 . MoS 2 , another prototypical 2D material, has also been studied in several works 24,42,43,[52][53][54] , as well as phosphorene [45][46][47][48]76,77 , arsenene [78][79][80] , silicene 24 , and other TMDs 42 . On the other hand, the effects of periodic images and dimensionality are explicitly treated only in some of the first-principles efforts 24,52,53 .…”