The 2D Debye length: An analytical study of weak charge screening in 2D semiconductors

Simple perturbations (such as a line charge or a sheet charge) in 2D semiconducting materials create difficult solutions to the Poisson equation due to the non-uniform out-of-plane electric fields that result from the perturbative charge. Here, for the first time, we determine simple and general analytical expressions for the potential profile, its Fourier representation, the corresponding 2D Debye screening length, and the charge screening behavior in 2D semiconductors due to a line charge perturbation. In contrast to conventional 3D semiconductors, we find that the 2D Debye length goes as 1/ND,2D, where ND,2D is the 2D semiconductor doping density, and this leads to markedly different Debye lengths as compared to those determined by the conventional (3D) Debye length expression. We show that the potential profile due to a charge perturbation in a 2D semiconductor does not decay exponentially with distance from the perturbation (as is the case for 3D semiconductors) but instead decays logarithmically in the immediate vicinity of the perturbation and as 1/x2 when the distance is approximately equal to or greater than the 2D Debye length. Overall, this work establishes an analytical approach for determining a fundamental electrostatic parameter for 2D semiconductors.