Insulator has negative temperature coefficient. Intrinsic Semiconductor has negative temperature coefficient. Extrinsic Semiconductor has positive temperature coefficient. Metal has positive temperature coefficient. Resistance of semiconductor decreases exponentially in case of insulator it is linearly decreasing. In metal forbidden band gap Eg between conduction and valance band is zero, i.e, two bands are overlapped
Band gap of insulator is 6 ev (diamond). Semiconductor bandgap is equal to 1 ev. At very low temperature semiconductor act as insulators (say 0k). At 0k temperature germanium and silicon Eg are 0.7 and 1.21 ev respectively. By doping forbidden gap of Ge becomes 0.01 eV and Si becomes 0.05 eV. Electron volt is a unit of energy. Ionisation energy is low in germanium than silicon. Germanium has 32 electron, 32 proton and 40 neutron. Total carrier flow in semiconductor is sum of drift, diffusion and recombination flow. Metal is unipolar and semiconductor is bipolar.
Germanium have higher electron and hole mobility than silicon. Electron mobility is three times higher than hole mobility. Mobility of carriers decreases with increase in temperature. When temperature increases from 0 K, there is finite probability that some of the electrons below Fermi level moves above the Fermi level which is given by Fermi Dirac statistics. At any temperature minimum 50 % of electrons will occupy in Fermi level. In intrinsic semiconductor Fermi level lies in the central of forbidden gap.
Silicon and germanium are tetra valent atoms. Suitable pentavalent impurities are phosphorous, antimony, arsenic bismuth (PAAB). By doping with pentavalent atom no of electrons increases and holes decreases. Trivalent impurities are boron, aluminium, gallium and indium (BAGI). During pentavalent doping a new discrete energy level formed just below the conduction band. During trivalent doping a new discrete energy level formed just above the valence band
When doping increases (conductivity increases) in p type (pentavalent) Fermi level goes down, in n type Fermi level goes up. When temperature increases (conductivity decreases) in p type Fermi level goes up, in n type Fermi level goes down. According to law of mass action product of number of electrons in the conduction band and holes in valance band is a constant. Gold is used as recombination agent in semiconductor. Carbon is not used as semiconductor because ionisation energy is very high. If donor and acceptor concentration are same then depending up on the temperature, semiconductor become P or N
Semiconductor is damaged by strong current because of excess electron. Impurity atom profile of a semiconductor is complimentary error function. Excess carriers can be created in n type material by exposing one end of the specin with light, current flow at that time is occurred by diffusion. A long specimen of p type semiconductor is electrically neutral. Law of conservation of charge – continuity equation
Einstein’s equation related to thermal voltage. Mobility of electrons in semiconductor is defined as the drift velocity per unit electric field. Mobility of electron decreases with increase in doping because relaxation time of electron increases with doping