Comment on: "Threading dislocation densities in semiconductor crystals: A geometric approach". Phys. Lett. A 376 (2012) 2838-2841

TL;DR

This paper critically examines a geometric model explaining shallow levels in dislocated semiconductors, revealing it cannot support bound states and clarifying the conditions for their existence, thus challenging previous claims.

Contribution

It provides a detailed analysis showing the model does not support bound states and corrects misconceptions about the conditions needed for such states to exist.

Findings

The model does not support bound states for any parameters.

Bound states exist only if the wave number k is non-zero.

The truncation condition limits solutions to a single energy, missing others.

Abstract

We analyze the solution of the Schr\"odinger equation arising in the treatment of a geometric model introduced to explain the origin of the observed shallow levels in semiconductors threaded by a dislocation density. We show (contrary to what the authors claimed) that the model does not support bound states for any chosen set of model parameters. Assuming a fictitious motion in the $x-y$ plane there are bound states provided that $k\neq 0$ and not only for $k>0$ as the authors believed. The truncation condition proposed by the authors yields only one particular energy for a given value of a chosen model parameter and misses all the others (conditionally solvable problem)