Visual Quantum Mechanics
Energy Band Creator
STEP 1: Discrete Energies in an Individual Atom
Begin by determining the energies of single atom represented by a rectangular potential energy diagram. The opening screen of the program shows a default potential energy well (Depth = 100eV, Width = 0.1nm).
- Changing the Depth of a Single Potential Well: Change the depth of the single potential well using the "Depth" (eV) slider in the "Regular Solid" tab below the potential energy graph. The depth can be varied from 0eV to 400eV.
- Changing the Width of a Single Potential Well: Change the width of the single potential well using the "Width" (nm) slider in the "Regular Solid" tab below the potential energy graph. The width can be varied from 0.05nm to 0.2nm.
- Determining the Allowed Energies: After altering the parameters of the potential well representing a single atom, click the "Find Energies" button. The allowed energy levels for the atom whose potential energy diagrams are displayed, will appear on the diagram as horizontal red lines.
STEP 2: Energy Bands in Solids -- Multiple Atoms
Having observed the energy levels of a single atom, investigate changes in these energy levels when several atoms are brought close together.
- Changing the Number of Atoms: Increase the number of atoms in the "Regular Solid" by moving the "Number of Atoms" slider from its default value of 1 to any number up to 50. The single potential well that was created in Step 1 duplicates appropriate number of times to indicate multiple atoms. If the array of identical atoms extends off the screen a message (graph extends off screen) appears near the bottom right of the top pane.
- Changing the Separation between Atoms: Change the "Separation" (nm) between adjacent atoms that you created above using the appropriate slider in the "Regular Solid" tab below. The range for the separation extends from 0.05 to 1.0nm. However, if you choose a "Separation" (nm) less than the "Width" (nm) that you specified in Step 1, the program will prompt you for a new value.
- Determining the Allowed Energies -- an Energy Band: After altering all the parameters representing the "Regular Solid", click the "Find Energies" button. The allowed energy levels for the atom whose potential energy diagram is displayed, will appear on the diagram as horizontal red lines. If you have chosen several, closely spaced atoms, the energy levels will appear as a continuum of states -- an energy band.
- Observing the Energy Levels more closely: Click on the "Zoom" button (magnifying glass tool), and then click within the potential energy diagram, to enlarge the energy diagram so that individual energies in a closely spaced energy band become visible. Clicking in the energy graph repeatedly, zooms further into the graph. Clicking the "Zoom" button, restores the graph to its original scale.
STEP 3: Creating Impurity States
Add impurity atoms to the "Regular Solid" by clicking on the "Impurity" tab. The screen of the program shows the default parameters of the impurity atom (Depth = 100eV, Width = 0.1nm).
- Changing the Depth of the Impurity Atom: Change the depth of the impurity atom using the "Depth" (eV) slider in the "Impurity" tab below the potential energy graph. The depth can be varied from 0eV to 400eV. Usually a donor impurity atom is characterized by a well that is slightly deeper than that of the regular solid atom, and an acceptor impurity atom is characterized by a well that is slightly shallower than that of the regular solid atom.
- Changing the Width of the Impurity Atom: Change the width of the single potential well using the "Width" (nm) slider in the "Impurity" tab below the potential energy graph. The width can be varied from 0.05nm to 0.2nm. Usually a donor atom is characterized by a well that is slightly wider than that of the regular solid atom, and an a acceptor impurity atom is characterized by a well that is slightly narrower than that of the regular solid atom.
- Changing the Impurity Concentration: Increase the concentration of impurity atoms in the "Regular Solid" by moving the "Impurity Concentration" slider from its default value of 0 (impurity atoms in 10 regular solid atoms) to any number up to 10. Impurity atoms (shaded green) appear amidst the regular solid atoms (shaded blue).
- Determining the Allowed Energies: After altering the parameters of the Impurity, click the "Find Energies" button. The allowed energy levels for the regular solid appear in red, while those corresponding to the impurity atoms appear in green.