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Published online by Cambridge University Press: 01 February 2011
We theoretically model the transport of holes across graded wurtzite Indium Gallium Nitride layers with large barriers to metals of the order of 2 electron volts. The effect of continuous strain grading and the resulting piezoelectric grading is explicitly taken into account. As data about critical thicknesses for dislocation creation are scarce for these materials, the grading widths considered for the calculations are deliberately kept small to ensure that the layers are below theoretically predicted critical thickness limits. The spatial variation of spontaneous and piezoelectric polarization creates bulk bound polarization charges that have a strong effect on the electrostatics of the layers, and creates the optimum conditions for efficient tunneling of holes. We also explicitly model the effect of the different hole masses for the valence band. Three orders of magnitude increase of tunneling intensity is seen for split-off holes with effective masses of 0.15 for the case of moderate grading from 30 % Indium to 0% Indium over 30 angstroms, compared to the case without grading. The case of very aggressive grading of the same change in composition over 10 angstroms does not lead to any extra benefits and leads to a decrease in tunneling intensity. The electric field for more aggressive grading dominates the electric field for the moderate grading both near the top and the bottom of the barrier. However, the effective barrier width at the valence band edge becomes higher for the case of aggressive grading, and most of the carriers see a damped tunneling amplitude.