Temperature Effects Semiconductors Fermi level doped semiconductor =‖ from the donor state ntermediate Temperatures to dopant concentration qual/ d Enough thermal energy to E, Altav-Er xcite an effective amount of alence e-s into the p-types behave similarly nduction band with temperatur Analogy Between pH and Fermi Level E) Extent of ionization Weak Acid- Acceptor Analogy A台h"+A lutions and the HA←H+A [H+IA-I play analogous HAl oles in pK,=-log K in the two media When pH=pk. E,=acceptor energy leve/ s When Er- ea LAJ- IA-I Energy Levels for Impurities in Silicon Interaction of light and Electrons shallow 一Pm040一n·8pm aDsorption Donors 0s一0怕 Spontaneous Acceptors oM emIssIo shallow
2005-11-11 6 Temperature Effects undoped Extrinsic n-type Semiconductors Low Temperatures Thermal energy is insufficient to excite electrons from the donor state Intermediate Temperatures e -’s from donor state are excited into the conduction band. e- concentration equal to dopant concentration. High Temperatures Enough thermal energy to excite an effective amount of valence e-’s into the p-types behave similarly conduction band with temperature Fermi Level Ef metal Ef undoped semiconductor Ef Ef p-type semiconductor n-type semiconductor Ed Ea The pH of aqueous solutions and the Fermi level in semiconductors play analogous roles in determining the extent of ionization in the two media. Analogy Between pH and Fermi Level (Ef ) Extent of Ionization: Weak Acid - Acceptor Analogy When pH = pKa [HA] = [A- ] Acid-base system Semiconductor When Ef ~ Ea [A] ~ [A- ] Ea = acceptor energy level a a a pK log K [HA] [H ][A ] K HA H A = - = « + + - + - + - A « h + A Energy Levels for Impurities in Silicon Donors Acceptors e - h+ shallow shallow deep Interaction of Light and Electrons absorption Spontaneous emission Stimulated emission
Optical Properties of Semiconductors Semiconductor Glossary mission Direct Bandgap Semiconductor: semiconductor in which the ottom of the conduction band and the top of the valence se, energy ased during band-to-band electron recombination with g GaAs, InP, ete. Indirect Bandgap Semiconductor semiconductor in which m longest wavelength absorption to promote e corresponds to E a上=1、 i hifted with respect to the top of the electron recombina th a hole is converted primarily TE is energy between"HOMO"of valence band and into phonon 'e. g. Si, Ge, GaP LUMo"of conduction band Bandstructure in Three dimensions Bandstructure in Three dimensions easily drop from the conduction band to the valence band by reet semiconductor we have seen that the bottom of the n band and the top of th ce this would violate momen to t by the size of its energy gap E instead the electron must simultaneously emit a photon and exchange recombination is therefore analogous to the level transitions that ng is very small, so indireet In atomic systems rn out to be much poorer emitters of light than direct one ELectronhole Recombination in a direct semiconductor such as GaAs nElectrorrhole recombination in an indireet a An electron drops from the conduction band g and momentum. an aNote that in the figure shown here the initial his is an important property of direct 地四山Su semiconductors Bandstructure in Three dimensions Luminescence from the valence band into then cegs to recombination is (GaAs) alence-band stat Both direct and indirect se luctors may therefore be used as The absorption of these materials strongly absorptionof light by direct (left)and indirect (right) semiconductor
2005-11-11 7 Optical Properties of Semiconductors longest wavelength absorption to promote ecorresponds to Eg Eg is energy between “HOMO ”of valence band and “LUMO”of conduction band Eg Absorption Emission Eg Semiconductor Glossary Direct Bandgap Semiconductor: semiconductor in which the bottom of the conduction band and the top of the valence band occur at the momentum k=0; in this case, energy released during band-to-band electron recombination with a hole is converted primarily into radiation (radiant recombination); wavelength of emitted radiation is determined by the energy gap of semiconductor. e.g. GaAs , InP, etc. Indirect Bandgap Semiconductor: semiconductor in which bottom of the conduction band does not occur at effective momentum k=0, i.e. is shifted with respect to the top of the valence band which occurs at k=0; energy released during electron recombination with a hole is converted primarily into phonon; e.g. Si, Ge, GaP. An important property of direct semiconductors is that electrons may easily drop from the conduction band to the valence band by emitting a photon This process is known as electron-hole recombination since the electron drops to occupy a hole state in the valence band Þ the energy of the photon emitted by the semiconductor is determined by the size of its energy gap Þ recombination is therefore analogous to the level transitions that occur in atomic systems Bandstructure in Three Dimensions E k PHOTON Electron-hole Recombination in a direct semiconductor such as GaAs An electron drops from the conduction band to the valence band and its excess energy is emitted in the form of a photon Note that in the figure shown here the initial and final wavevector states are the same … this is an important property of direct semiconductors In indirect semiconductors, we have seen that the bottom of the conduction band and the top of the valence band occur at different points in k-space An electron cannot therefore drop from the conduction band to the valence band just by emitting a photon since this would violate momentum conservation Þ instead the electron must simultaneously emit a photon and exchange momentum with the crystal lattice Þ the probability of this double process occurring is very small, so indirect semiconductors turn out to be much poorer emitters of light than direct ones Bandstructure in Three Dimensions E k PHOTON Electron-hole recombination in an indirect Semiconductor In order to conserve energy and momentum, an electron must drop to the valence band by emitting a photon and exchanging momentum with the crystal Because this process has a low probability, indirect semiconductors such as Si or Ge cannot be used in optoelectronic applications as light emitters The opposite process to recombination is electron-hole generation in which an electron is excited from the valence band into the conduction band by absorbing a photon Since this process also must conserve momentum the electron is excited into a state with the same k-value as the initial valence-band state Þ Both direct and indirect semiconductors may therefore be used as photodetectors to detect electromagnetic radiation Þ The absorption of these materials strongly increases once the photon energy exceeds the direct band gap Bandstructure in Three Dimensions E k PHOTON absorptionof light by direct (left) and indirect (right) semiconductors E k PHOTON Luminescence