Analytical Model for 2DEG Density in Graded MgZnO/ZnO Heterostructures With Cap Layer

In this paper, we develop a generic analytical model for 2-D electron gas (2DEG) density (n(s)) and threshold voltage (V-OFF) of a fully strained graded ZnO-based heterostructure with a cap layer. The model is based on the continuity of electric field at the interfaces of different layers, dominant piezoelectric and spontaneous polarization components in different layers, Mg composition, and layer thickness. The generic model can be reduced to a simplified bilayer structure for calculating ns and VOFF. Results show that the graded heterostructure can result in higher values of 2DEG density and VOFF (absolute values) compared to the bilayer structure. A careful optimization of the structure is required to achieve a trade-off between ns and VOFF. An analytical expression of polarization charge density at buffer-barrier interface to better fit the experimental data available in the literature is also proposed. The model will be suitable for the design optimization of 2DEG density and VOFF for ZnO-based heterostructures.