| Valence Band definition | Highest Occupied Band |
| Conduction Band Definition | Lowest Unoccupied Band |
| Band Gap Definition | minimum energy separation between the two bands
the energy gap between the valence band maximum and conduction band minimum |
| Direct vs indirect bandgap | In a direct band gap semiconductor the valence band maximum has the
same wavevector as the conduction band minimum, for an indirect band gap it does not |
| Electronic transitions for a direct bandgap semiconductor | Only energy (no momentum needs to be supplied) is needed to promote electron, and so this can easily be supplied by photons of the appropriate energy (at least band gap energy). This means light absorption/emission are both strong for direct bandgaps |
| Electronic transitions for an indirect bandgap semiconductor | An electronic transition here involves a change in electron momentum. To conserve momentum during light absorption phonons from the crystal must therefore be either created or destroyed. This means light absorption in indirect bandgap semiconductors is weaker. |
| Alloying: What is it, why is it done and what is the equation of alloying? | Alloying is the process of mixing two different components to form a solid solution. It is done to tune the band gap to a desired energy. Band gap equation is
Eg,AB = xEg,A + (1 − x)Eg,B − bx(1 − x), where x is the fraction of A in the alloy, and b is the bowing parameter. |
| Vegard’s law | Lattice parameter in an alloy follows this equation:
a_AB = xa_a + (1-x)a_b |
| Why do we need to be conscious of lattice parameter for devices. | Devices feature a THIN layer of semiconductor on top of a substrate, for cheapness. If there is a large difference in lattice parameter between substrate and film then significant strain can build up in the latter, leading to poorer quality devices. |
| Effective mass | As an electron moves through a crystal it will undergo Coulomb scattering with other electrons and atomic nuclei. In free space, a force applied on an electron can be related to it's acceleration using Newton's 2nd Law, however due to coulomb scattering, the applied force is not the only force. The effective mass is the mass required for the electron to have an acceleration a with applied force F. It is calculated using h_bar^2/(d^2E/dk^2) |
| pn junctions - condition for charge neutrality | NaWp = NdWn |
| Relating Charge density to E field to electric potential (pn junctions) | ∇.E = p(x)/εrε0
-∇Φ = E |
| Charge density for pn junctions | -eNa on p-side (ionised acceptors on the p-side are negatively charged)
eNd on n-side |
| Assumptions when finding potential for pn junctions | ?(wn) = ?_(bi) (Built in potential)
?(-wp) = 0 |
| Spontaneous polarisation of the ferroelectric phase | (∂GFE/∂P) =0 |
| Clausius-Mossotti Relation | Nα/3ε0 = (εr-1)/(εr+2) |
| Relationship between polarisation and local E field | P = NαE_(local) |
| Electric Susceptibilty | X = P/ε0 E |
| Difference between type 1 and type 2 superconductors | Type 1 - 1 critical B field so superconducting and normal states can't coexist
Type 2 - lower and upper critical B field, meaning there's a mixed/vortex phase region where states can coexist |
| Bias current density | J = J0 (exp(-eV/kT)-1) |
| Importance of Tc in Polariation (from condensate energy) | Above Tc, equation for Ps does not give real solutions |
