Last time: Concentration of electrons in conduction band Top of conduction band Volume concentration of electrons with energy ~E in interval of energies de. Total volume concentration of electrons: Top of conduction band Fermi-Dirac distribution Volume concentration of allowed energy levels with energy ~E in interval of energies de. Density of states Probability of having electron at state with energy E. 1
Boltzmann s approximation Can not be taken analytically ll Fortunately for for Effective density of states at band edge 2
Electron and hole concentrations. 3
Intrinsic semiconductors 4
Doped Semiconductors N-type P-type 5
Metal Semiconductor Junction Metal N-Semiconductor Vacuum level (minimum energy of electron that is free from crystal) Electron affinity Work function When these two materials are brought into contact the electrons will try to lower their energy by going to material with bigger work function. This will continue until electric field created by separated charges stops this charge transfer. For instance, if Φ M > Φ S certain number of electrons will leave semiconductor and move to metal. 6
Metal Semiconductor Junction Schottky contact. When new equilibrium i is established there is no current and Fermi level l is flat. Metal N-Semiconductor Schottky barrier Built-in potential (energy barrier that stopped electron transfer) Depletion region (region with dramatically reduced concentration of mobile electrons) Surface charge concentration on semiconductor side of junction. (Depletion region charge) 7
Schottky contact under reverse bias. The external voltage is trying to move electrons from metal to n-semiconductor. BUT Schottky barrier prevents electrons from going, hence, no appreciable current is expected. Only depletion region width increases: Junction capacitance per unit area decreases: 8
Schottky contact under forward bias. The external voltage is trying to move electrons from n-semiconductor to metal. Barrier for electron transport from n-semiconductor to metal is reduced. Depletion region width decreases. Current will flow: Richardson constant 9
Schottky diode Current Voltage (IV) Characteristics. Anode Cathode In our example considered + - small 10
Ohmic contact. Metal n+ - semiconductor Heavily doped Almost linear very steep IV. Depletion region is very thin (<<100 nm) 11
More realistic diode IV. + - + - Becomes linear at large currents + - Junction IV Load line 12
Diode models. Ideal diode: Constant voltage drop model. Battery + resistance model. 13
Diode small signal model. Differential resistance Differential resistance depends on bias. 1. Large currents:: 2. Small currents: Diodes also have small-signal capacitances. We already know junction capacitance. 14
Example 1: Clipper Diode based limiting circuits. Diode takes care of all extra current and thus limits output voltage. Example 2: Double clipper Example 3: protection Limits maximum negative V BE 15
Clamped capacitor. Circuit restores DC component of the signal measure of duty cycle. 16
pn Junction. When these two materials are brought into contact the electrons will go from n to p and holes from p to n regions by diffusion. They will be leaving behind immobile charges of ionized donors and acceptors. The corresponding electric field will eventually stop diffusion currents. 17
pn Junction band diagram. Donor concentration Acceptor concentration Surface charge densities on both sides of pn-junction Built-in potential 18
pn Junction under reverse bias. External field is trying to move electrons from p to n and holes from n to p. Almost no current can flow since there is small number of electrons in p and holes in n regions Junction capacitance decreases 19
pn Junction under forward bias. External field is trying to move electrons from n to p and holes from p to n. Current should be expected. 20
Current of pn junction under forward bias. Reverse saturation current Observe accumulation of mobile charges on both sides on pn-junction under forward bias 21
IV of pn junction diode. Nonideality factor 22