  Low dimensional material systems provide a unique set of properties useful
for solid-state devices. The building block of these devices is the PN
junction. In this work, we present a dramatic difference in the electrostatics
of PN junctions in lower dimensional systems, as against the well understood
three dimensional systems. Reducing the dimensionality increases the depletion
width significantly. We propose a novel method to derive analytic equations in
2D and 1D that considers the impact of neutral regions. The analytical results
show an excellent match with both the experimental measurements and numerical
simulations. The square root dependence of the depletion width on the ratio of
dielectric constant and doping in 3D changes to a linear and exponential
dependence for 2D and 1D respectively. This higher sensitivity of 1D PN
junctions to its control parameters can be used towards new sensors.
