True Fractional Dimensional Nature of Semiconductor Nanostructures: Removing the Anomaly in the Estimation of Quantum Mechanical Properties

Here, we have investigated the fractional dimensional nature of the experimental semiconductor quantum mechanical systems to understand the effect on the accurate prediction of electronic and optoelectronic properties. The formalism presented in this paper, to estimate the actual dimensionality of the system, lifts the anomaly of using the conventional integer density of states (DOS), although the carrier confinement isn't infinite. The effective bound state widths estimated by considering the carrier wavefunction leakage is the basis of this formalism. We have experimentally verified the formalism in AlGaN/GaN high electron mobility transistors (HEMTs). The dimensionality varies over a wide range from 3 to 2.38, as the gate bias sweeps the channel from depletion to strong inversion. However, the manifestation of fractional dimension on Capacitance-Voltage characteristics is insignificant for planar HEMTs. The effect becomes noticeable with the increasing confining dimensions of the heterostructure, which is experimentally verified in AlGaN/GaN nanofins. The effect is manifested as a shift in the threshold voltage and the rate of conduction-band state filling. This efficient and accurate formalism can estimate the dimension of any quantum mechanical system, thereby enhancing the accuracy of the models.