quantum{ region{ quantize…{} } }

quantize_x{}

Warning

This keyword should be used only for structures in which quantization in x-direction is not expected to influence the results of interest. Otherwise, certain quantum properties of the simulated structure may get lost while using this group.

Note

Only Neumann and Dirichlet boundary conditions are supported for the direction of the decomposition (here x-direction).

In 2D or 3D simulation, the Schrödinger equation is solved within the slices perpendicular to x direction. This results in the reduction of the calculation time.

For example, if a 2D simulating has 100 grids in x-direction and 50 grids in y-direction, the normal calculation solves the eigenvalue problem of a (100x50) x (100x50) matrix. When quantize_x{} is specified, on the other hand, nn++ solves the 1D Schrödinger equations along y-direction at each grid point in x-direction so 100 eigenvalue problems of 50x50 matrices are solved. Thus, the runtime of the eigenvalue solver could be roughly estimated as (number of x-grids) \(^{-1}\) times, but we should note that the runtime also depends on the number of eigenvalues to be calculated.

Currently, only one-band (Gamma, X, Delta, LH, HH, etc.) without k-integration and without magnetic field is supported, and QM output is limited to local spectra and occupations. If strain is enabled, deformation potentials are ignored. Similarly, quantum boundary conditions are always Neumann or periodic, irrespective of what is specified in the input file. And quantum decomposition regions cannot be used for CBR or optics.

Only one quantization direction (x, y, z) can be simultaneously specified when quantum decomposition is used. Typically, the quantization direction is the growth direction.

Note that a similar number of states should be requested as for a corresponding 1D simulation (i.e. much less than normally needed in 2D or 3D), and that lateral (i.e. orthogonal to the quantization direction) grid spacing can be much larger than for “normal” quantum simulation, as the density from quantum decomposition is NOT affected by wide lateral grid spacing.

quantize_y{}

The same as quantize_x{}, but the slices are in y-direction.

quantize_z{}

The same as quantize_x{}, but the slices are in z-direction and only in 3D simulation.