Synopsys: QM1D(nx,Neig,grid, [optional] interface, [optional] charge_T)
QM1D is the NanoTCAD ViDES class, for the solution of the 1D Schroedinger equation in the discretized one-dimensional domain specified in the vector grid. As inputs, it requires the number of atoms grid points nx, the number of eigenvalues to be computed Neig, the one-dimensional interface p and the one-dimensional grid.
For a complete understanding of such quantities, please refer to Tutorial 15.
The attributes of the classes are the following:
  • nx (int) the number of points of the grid.
  • Neig (int) the number of eigenvalues to be computed.
  • x: (numpy array of length nx) x coordinates of the points where the 1D-Schroedinger equation is solved.
  • Phi: (numpy array of length nx) electrostatic potential in correspondence of each grid points.
  • Ei (numpy array of length nx) the intrinsic Fermi level in correspondence of each grid points.
  • Temp (double) the temperature of the nanoribbon
  • charge(numpy array of length nx) free charge computed in correspondence of each grid point.
  • Psi(numpy matrix [nx,Neig]) Eigenfunction computed for each grid point and for each eigenvalue.
  • eig : (numpy matrix  [1,Neig]) Computed eigenvalues. E.g. the i-th eigenvalue is stored in the matrix eig[1,i].
  • mel (double) longitudinal effective mass.
  • met (double) transversal effective mass.
  • mhole (double) hole effective mass.
  • ecs : (numpy array of length nx) conduction band computed in correspondence of each grid point. In particular, ecs=Ei+Egap*0.5
  • Ef (double) Fermi Level used for computing the free charge.
  • charge_T : (function) function for the calculation of the free charge. By default the electron density is computed considering quantum confinement of the electron for an anisotropic material, while the hole density is computed within the semiclassical approximation.

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