quantum{ region{ quantize…{ } } }

quantize_x{}

In 2D or 3D simulation, the Schrödinger equation is solved within the 1D slices parallel to the x direction. This results in the reduction of the calculation time. For example, if a 2D simulating has 100 grid points in x-direction and 50 grid points 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, nextnano++ solves the 1D Schrödinger equation along the x-direction at each grid point in y-direction. Therefore, 50 eigenvalue problems of 100x100 matrices are solved. Thus, the runtime of the eigenvalue solver can be roughly estimated (number of y-grids):math:^{-1}, but we should note that the runtime also depends on the number of eigenvalues to be calculated.

Only one quantization direction (x, y, z) can be specified at a time 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.

Currently, only one-band model (Gamma, X, Delta, LH, HH, etc.) without k-integration and without magnetic field is supported. Outputs based on wave functions (e.g., all outputs generated by run{ quantum_optics{ } }, any type of matrix elements, lifetimes, excitons) are not evaluated, since proper wave functions are not computed within this approximate method.

Note

Quantum decomposition regions cannot be used for CBR or run{ quantum_optics{ } } and shifted_neumann boundary conditions are not supported for the direction of the decomposition (here x-direction).

Warning

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

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.