Analysis of electronic structures of quantum dots using meshless Fourier transform k.p method

We develop a complete Fourier transform k.p method and present its application for a theoretical investigation on electronic structures of quantum dots with consideration of the built-in strain effects. The Fourier transform technique is applied to the periodic position-dependent Hamiltonian, and a simple and neat expression of the Hamiltonian matrix in the Fourier domain is formulated due to the orthogonality of exponential functions. Spurious solutions can be avoided due to the truncation of high Fourier frequencies. A kinetic Hamiltonian matrix in momentum domain is formulated by entering the analytical Fourier transform of the quantum-dot shape function into the neat Hamiltonian matrix easily, which allows meshless numerical implementation. The formulation of strain Hamiltonian matrix is done by convolution of Fourier series of strain components and Fourier series of the quantum-dot shape functions. Therefore, an original Fourier transform-based k.p approach is developed by combining the kinetic Hamiltonian matrix and the strain Hamiltonian. This approach is adopted to study the dimension effect and strain effect on the ground states of electrons and holes of pyramidal quantum dots that are truncated to different heights. The ground-state energy variation shows that the electron state is the most sensitive to these effects and the strain effect on E1, LH1, and HH1 is more prominent for sharperquantum dots. This investigation shows that band mixing between the conduction band and valence band, and band mixing between heavy-hole and light-hole bands are reduced due to the strain effect, whereas this effect is more prominent for nontruncated pyramidal quantum dots due to the stress concentration. Among the three ground states, light-hole states are more weakly confined in the nonpyramidal quantum dot and shift to the tip of the pyramid due to the strain. VC 2011 American Institute of Physics. [doi:10.1063/1.3549686]