Electronic- Intrinsic Semiconductors Flashcards
Families of semiconductors
Group 4 Si and Ge.
Group 3 Al to In bonded to group 5 N to Sb.
Group 6 S to Te bonded to last TM group Zn to Hg
Describe the bonding in silicon
Bands correspond to sp3 hybridised molecular orbitals. These have a tetrahedral symmetry appropriate to crystal structure. Has diamond lattice structure. There are 4 levels per atom in the first band
What other crystal structure can semiconductors have?
Zinc blend. Group 3 and 5 bonded semiconductors
How to work out critical wavelength for semiconductor
This is where a photon is absorbed to excite and electron from the valence to conduction band. Know the band gap.
λc=hc/Eg
This is maximum wavelength (min energy) of photon
How to tune the band gap of a semiconductor
Can vary the ternary composition. Can make not whole number ratio between elements in compound. Changes the lattice constant a. Generally decreasing a increases the band gap
What happens when a semiconductor is at 0K
The valence band of the semiconductor is full. It is an insulator because there are no empty levels in the VB, no overlapping bands, no thermal energy to excite any electrons across band gap into empty levels in conduction band
What happens to semiconductors above 0K?
Some electrons can be promoted to conduction band due to thermal energy. When in CB, behave like free electrons in a metal (easily accelerated by electric field as there are many empty levels).
Other ways of making semiconductors conduct
Light of appropriate wavelength can excite electrons leading to temporary conduction (photoconductivity). Electrons with high potential can be injected into CB from another material
What does an excited electron from the VB leave behind?
A positively charged hole in the VB
E-k curves for valence and conduction bands
Not straight lines. VB starts low then curves up a bit before levelling off at π/a. Conduction band starts at π/a and above end of VB. similar shape but stretched vertically. Solutions for particular bands are periodic with every 2π/a change with k. Means the band gap is not constant it depends on k (will be vertical distance between VB and CB at any k).
What is a direct band gap material?
Where the minimum CB energy aligns (same k) with the maximum energy in the VB
Effective masses of electrons and holes in semiconductors
Symbol m* with subscript e or h. The effective mass of an electron is not the same as the mass of a free electron and not equal to the mass of its corresponding hole. Because of interaction of the electron with the crystal lattice
Energy of CB formula
ECB=hbar^2k^2/2me*
hbar is h/2π
Energy of valence band formula
EVB=hbar^2k^2/2mh*
Band diagram for T>0K
Energy vs F(E) fractional occupancy. Small amount of conduction electrons above band gap at low fraction. Equal area omitted in VB at high fraction for holes. No electrons in band gap. Ef half way up Eg
How to determine population of electrons in CB
Probability of occupation of the state times number of available energy states
Formula for Fermi function
F(E)=1/(exp(E-Ef/kBT)+1)
Approximately
exp(-(E-Ef)/kBT)
Formula for density of conduction electron states
ρ(E)=((8rt(2π)m^3/2)/h^3)rt(E-Eg)
To find Ncb integrate from Eg to infinity
Formula for number of electrons in CB per unit volume, ne (=Ncb)
ne=2((me*kBT/2πhbar^2)^3/2)(exp(-Eg/2kBT)
Same formula for holes (np) but with mh*
Formula for intrinsic carrier density
ni=rt(nenp)
Number of e times number of holes
How does intrinsic carrier concentration vary with temperature?
It increases steeply at first and then starts to level off (constant curve)
What is the band gap for Si?
1.12eV
How does conductivity work in Si?
An electron in the CB behaves like a free electron in a metal. The hole it leaves behind moves by VB electrons filling it and leaving a different hole
Why does increasing temperature not decrease conductivity like in metals?
The effect of scattering (reduction in mean free path) is much smaller than the effect of the number of charge carriers rapidly increasing with temperature
