A Compact Model for Polar Multiple-Channel Field Effect Transistors: A Case Study in III-V Nitride Semiconductors

TL;DR

This work addresses the challenge of efficiently predicting mobile carrier densities in polar multi-channel nitride heterostructures by deriving closed-form, analytically tractable expressions that couple electrostatics with quantum confinement. It extends a single-channel model to a multi-channel stack via periodic boundary conditions and augments it with intentional doping schemes (delta-doping and modulation-doping) to control 2DEG/2DHG populations, yielding total densities $n_s^{tot}$ and $p_s^{tot}$ and channel-threshold voltages $V_T^{pc}$ and $V_T^{tc}$. Validation against Schrödinger–Poisson simulations for various III-N configurations (AlGaN/GaN, AlInN/GaN, AlScN/GaN) shows good agreement and demonstrates how doping can reduce epitaxial thickness while maintaining carrier densities. The framework offers a fast, physically transparent design tool for next-generation nitride MC-FETs and establishes a foundation for incorporating source/drain/gate effects in future work.

Abstract

A compact analytical model is developed for the mobile charge density of polar multiple channel field effect transistors. Two dimensional electron and hole gases can be potentially induced by spontaneous and piezoelectric polarization in polar heterostructures. Focusing on the active region of devices that employ a multiple quantum-well layout, the total electron and hole populations are estimated from fundamental electrostatic and quantum mechanical principles. Hole gas depletion techniques, revolving around intentional donor doping, are modeled and evaluated, culminating in a generalized closed-form equation for the mobile carrier density across the doping schemes examined. The utility of this model is illustrated for the III-Nitride material system, exploring AlGaN/GaN, AlInN/GaN and AlScN/GaN heterostructures. The compact framework provided herein considerably elucidates and enhances the efficiency of multi-layered transistor design.

Figures (8)

• Figure 1: (a) Charge, (b) electric field, and (c) energy band diagrams of an indicative single channel FET. In (a) and (b), the energy band diagram is overlaid (dashed line) as a guide to the eye. All values shown are extracted from the analytical model. The inset plot is a schematic of the epitaxial structure modeled. Notations are explained in the text.
• Figure 2: Calculated sheet density versus barrier thickness for single channel Al(Ga,In,Sc)N/ GaN heterostructures. A 2 nm GaN cap layer is considered, with a surface barrier height of 0.8 eV. No interlayers are considered. Solid lines correspond to results extracted from Eq. \ref{['ns_SC']}, while points are acquired from self-consistent numerical calculations using nextnanonextnano.
• Figure 3: (a) Energy band diagram of an indicative five channel field effect transistor. The active region is divided into three regions of interest: the top channel, periodic channels, and the bottom channel. (b), (c), (d) Magnified charge, electric field, and energy band diagrams of the top, periodic and bottom channels, respectively. The energy band diagram is overlaid (dashed line) in the charge and field diagrams as a guide to the eye. All values shown are extracted from the analytical model. Notations are explained in the text.
• Figure 4: Total sheet density versus (a) the number of channels for Al(Ga,In,Sc)N/(GaN/AlN IL)/GaN heterostructures, and (b) channel thickness for a 5-channel AlGaN/2 nm AlN/GaN structure. A 2 nm GaN cap layer is considered, with a surface barrier height of 0.8 eV. Solid lines correspond to results obtained from Eqs. \ref{['ns_SC']} for $N=1$ and \ref{['final result']} for $N\geq 2$, while points are acquired from self-consistent numerical calculations using nextnanonextnano. The shaded areas in (a) correspond to ranges of $\alpha$ values as indicated.
• Figure 5: Contour plots of total two-dimensional electron gas (2DEG) density as a function of channel and barrier thickness for 5-channel (a) AlInN/2 nm GaN/ 3 nm AlN/GaN and (b) AlScN/1 nm GaN/2 nm AlN/GaN heterostructures, respectively. A 2 nm GaN cap layer is considered, with a surface barrier height of 0.8 eV. A constant $\alpha$ value of 0.90 is used. The non-monotonic relation between 2DEG density and channel thickness stems from the 2DEG reduction in the bottom channel with channel thickness, which -prior to 2DEG formation within the periodic channels- constitutes the majority of mobile charge for this configuration. The dashed gray lines correspond to constant period thickness ($t_{\rm ch} + t_{\rm b}$) lines and indicate the thinnest period configuration necessary for the given total sheet carrier density. Results are obtained from Eq. \ref{['final result']}.