Parameter definitions for "bloch"
It's probably useful to look first at the special features page. You may also want to look at one of the general help files, Sliders, or
Graphs.
Inputs
- SLIDERS
- lattice const: defines the lattice constant, in angstroms, of the one-dimensional periodic potential. (Restricted to values greater than pot. width.)
- pot. depth: Defines the depths, in eV, of the various potentials. (Restricted to be zero or negative.)
- pot. width: defines the width, in angstroms, of the attractive well for the square well potential. (Restricted to be zero or positive but less than the lattice constant.)
- energy: the energy, in eV, for which the wave function is calculated.
- E min: the minimum, in eV, of the energy range for which the band structure is calculated. (Restricted to values less than Emax.)
- E max: the maximum, in eV, of the energy range for which the band structure is calculated. (Restricted to values greater than Emin.)
- mol. sep.: distance, in angstroms, between the centers of the two atoms of the molecule (Unrestricted, but useful only if its magnitude is less than the lattice constant.)
- MENUS
- show(graph type): allows the left-hand display to show one of---
- psi: a three dimensional plot of the wave function for the energy chosen by the energy slider. The real and imaginary components of the wave function, along the blue and green axes, respectively, are plotted as a function of distance z, the black axis, through one unit cell in the crystal. The plot can be rotated by dragging the cursor within the plot. The reference orientation, looking along the z-axis, can be recovered by clicking with the right mouse button (control-click with the Mac).
- psi squared: the square of the wave function (the electron density) as a function of z. The wave function is normalized to give an average density of unity. The potential, in arbitrary units, is also shown for comparison.
- phase of psi: the phase of the wave function, in units of pi, is plotted as a function of z. The phase is restricted to lie within the range -pi to pi (-1 to 1 in the plot): the discontinuous jumps of 2*pi are of no significance. The potential, in arbitrary units, is also shown for comparison.
- potential: several choices of potential are available, as described in more detail in Simulations for Solid State Physics, Appendix 8.B. They include:
- square well: square well, or Kronig-Penney, potential of variable depth, and well width.
- cosine:a cosinusoidal potential of variable peak-to-peak amplitude.
- atom: a cut-off 1/|z| potential of variable depth.
- molecule a pair of cut-off 1/|z| wells of variable depth and separation.
- TOGGLES
- band list: opens a new window giving, when you calculate bands, the energies of the edges of the bands, along with the band index, with 1 the lowest.
- BUTTONS
- calculate bands: calculates the band structure for the energy range Emin to Emax for the chosen potential. Key equivalent is the i-key.
- calculate psi: calculates the wave function for the chosen energy and potential. Key equivalent is the spacebar. A double click in the band-structure graph calculates psi for the energy corresponding to the position of the cursor.
- copy graph: (a button for each graph)see Graphs in the General help.
- presets:> Takes you to a tear-off menu with which you may select the presets. For more details, see the preset item in the miscellaneous help file.
- configure:
- resolution (dE/(Emax-Emin)): sets the resolution parameter for the energy band calculation: see Simulations for Solid State Physics, appendix 8.B, for details. (Restricted to positive values.)
- integration accuracy: sets the accuracy of the integration algorithms. You are welcome to trade speed of simulation for higher accuracy. The higher accuracy is useful for very narrow bands. (Restricted to positive values.)
- revert: updates the listed configure parameters to the current values (which may have been changed by a preset command).
- close: closes the configure window.
- help: Opens the help system which you have already found.
- quit: Terminates "bloch".
Outputs
- DISPLAYS
- left side: displays the wave function in one of three forms as described under the show menu item. To see a Ògap stateÓ be sure the axes are tilted from the reference orientation (line of sight parallel to the z-axis).
- right side: displays in red the calculated band structure for the chosen potential. The origin of the energy scale is at the maximum of the cosine and square well potentials, and at the z = infinity value of the 1/|z| potentials for the atom and molecule potentials. In blue is the free electron dispersion curve reduced to the first Brillouin zone appropriate to the chosen lattice constant. It is measured relative to the cell average of the potential.
- band list: a separate window, opened and closed by the band list toggle, displays the energies of the band edges along with the band indices. (CAUTION: the band indices are not always correct; and occasionally a single band will be artificially listed as two.)
- READOUTS
- band/gap index: in the upper left corner of the panel is the index of the band or gap state shown in the left-hand graph. Band index 1 is the lowest band; gap index 1 is below the first band. (Bug warning: the gap indices are occasionally off by 1.)