Semiconductor physics:

The charge, or quantity of negative electricity is 1.60*10-19 C.
The number of electrons per second represents current, I.
The charge of a positive ion is an integral multiple of the charge of the electron.
Hole is an effective charge carrier.
The force, f on a unit positive charge, q is an electric field is the electric field intensity, at that point (f = q ).
The potential V of point B at x with respect to point A at x1 is the work done against the field in taking a unit positive charge from A to B.


The electric field equals the negative gradient of the potential , ?= - dV/dx
Electron volt (eV) is the unit of work or energy(electric, mechanical, thermal, etc.,)
For germanium EG is 0.785 eV, for silicon 1.21 eV.
Semiconductors have property of negative temperature coefficient of resistance.
A semiconductor in which electrons and holes are solely created by thermal excitation is called a pure or intrinsic semiconductor.
In intrinsic semiconductor the number of holes is always equal to the number of electrons.
Hole may serve as a carrier of electricity comparable in effectiveness with free electron.
If impurities added to pure semiconductor then it is called extrinsic semiconductor. This process is called doping.
The current in a conductor is due to flow of electrons, whereas the current in a semiconductor results from the movement of both electrons and holes.
The transport of the charge in a crystal under influence of an electric filed result in drift current.
Diffusion current is the result of a non-uniform concentration gradient.
The drift velocity is proportional to applied electric filed intensity .
= µ , where µ (square meters per volt second, m2/vs) is called mobility of the electrons.
The current desist J is the current per unit area of the conducting medium.
The above equations defines Ohm's law, the conduction current is proportional to the applied voltage.
Power density , power dissipated within the metal by electrons is J = ? 2
If the dopant has five valance electrons those will call donor or n-type impurities ex. Antimony, phosphorus and arsenic.
If intrinsic semiconductor doped with n type impurities, the electrons will increase, holes will decrease. This type material is called as n-type semiconductor.
If the dopant has three valance electrons those will call acceptor or p-type impurities ex. Boron, gallium and indium.
If intrinsic semiconductor doped with p type impurities, the holes will increase, electrons will decrease. This type material is called as p-type semiconductor.
The product of free negative and positive concentrations is a constant independent of the amount of donor and acceptor impurity doping. This is called mass-action law.
np = ni²
Metal is unipolar where as semiconductor is bipolar (two charge carrying particles).
If a specimen carrying a current I is placed in a transverse magnetic filed B, an electric filed is induced in the direction perpendicular to both I and B. This phenomenon, known as the Hall Effect.
Hall Effect is used to determine type of semiconductor (p or n) and carrier concentration.
By Hall Effect can measure mobility.
Hall Effect applications: magnetic field meter, Hall Effect multiplier.
Thermistor has a negative temperature coefficient of resistance.
Silicon and germanium not used as thermistors because their properties are too sensitive to impurities.
A heavily doped semiconductor can exhibit a positive temperature coefficient of resistance. Such device called sensistor.
If radiation falls upon a semiconductor, its conductivity increases.
In Hall Effect the output voltage produced across the crystal is due to movement of charge carriers toward one end.
The voltage measured between the two faces is called hall voltage.
Hall voltage is zero for intrinsic semiconductor.
Hall coefficient depends on the type of material.
Hall Effect probes are used for measurement of DC current in a wire.
Fermi level is a measure of probability of occupancy of electrons or holes in the allowed energy states.
In pure semiconductor the Fermi level is at the middle of the conduction and valence band.
In n type semiconductor the Fermi level is just below the conduction band.
In p type Fermi level is just above the valance band.
In a heavily doped n- type semiconductor the Fermi level is in the conduction band, similarly in a heavily doped p- type semiconductor the Fermi level is in the valance band.
Fermi Dirac function f(E) gives the probability that a quantum state with energy E is occupied by an electron.
Fermi level EF represents the energy state with 50% probability of being filled if no forbidden band exists.
If E >> EF then f(E) = 0, means there is zero probability of finding an occupied quantum state of energy greater than EF.
If E << EF then f(E) = 1, means all quantum levels with energy less than EF are occupied.
Silicon and germanium are called indirect band gap semiconductor where as gallium arsenide is called direct band gap semiconductor.

Diode fundamentals.

If a junction formed between a sample of p type and one of n type semiconductor, this combination possesses the properties of a rectifier (diode).
At this junction, one side has a high concentration of holes whereas the other side has high concentration of electronics due to this movement of charge carriers takes and this phenomenon is called diffusion.
The potential barrier (depletion region) is negative on p side and positive on n side which restricts the recombination of electrons with holes.
Within this narrow space charge layer there are no mobile carriers (no holes and no electrons).
If we want charge carriers to cross the junction, then an external voltage of appropriate polarity has to be applied in order to overcome the opposition of the barrier potential known as cut-in voltage.
In semiconductor both diffusion and conduction currents exist simultaneously.
The reverse saturation current depends on temperature and independent of magnitude of reverse bias.
Doping inversely proportional to the square root of the potential width.
Depletion region opposes flow of majority carrier and assist the flow of minority carriers across the junction (drift currents).
Charge density is depends on amount of doping.
Pn junction device s bipolar device.
Diode characteristics:
Volt equivalent of temperature is VT = T/11600 = 26 mV.
At high currents, the diode behaves more like a resistor than diode, and the current increases linearly rather than exponentially with applied voltage.
The electron in germanium 3 times faster than silicon, for high frequency applications germanium is suitable.
The value of reverse saturation current is about double in magnitude for every 10o C rise in temperature.
The generation and recombination process occur simultaneously. But generation rate is higher than the rate of recombination in extrinsic semiconductor.
In intrinsic semiconductor both rates same.
Static resistance R of a diode is defined as the ratio V/I of the voltage to the current. It is not useful parameter because of its wide variation due to V and I.
Dynamic resistance of a diode is defined as the slope of the V-I characteristics of the diode.
Dynamic resistance inversely proportional to the forward current.
Capacitive effect at junction due to uncovered charge with applied voltage is called transition or space charge capacitance, CT.
The CT is not constant, but depends upon the magnitude of reverse voltage.
The rate of change of injected charge with voltage called diffusion or storage capacitance CD in forward bias.
CD is much larger than CT in forward bias.
The CD is proportional to the current.

Diode fundamentals

Semiconductor physics