Energy Band View of Semiconductors Conductors semiconductors insulators Why is it that when individual atoms get close together to form a solid such as copper silicon or quartz they form materials that have a high variable or low ability to conduct current Understand in terms of allowed empty and occupied electronic energy levels and electronic energy bands Fig 1 shows the calculated allowed energy levels for electrons vertical axis versus distance between atoms horizontal axis for materials like silicon Fig 1 Calculated energy levels in the diamond structure as a function of assumed atomic spacing at T 0o K From Introduction to Semiconductor Physics Wiley 1964 In Fig 1 at right atoms are essentially isolated at left atomic separations are just a few tenths of a nanometer characteristic of atoms in a silicon crystal If we start with N atoms of silicon at the right which have 14 electrons each there must be 14N allowed energy levels for the electrons You learned about this in physics in connection with the Bohr atom the Pauli Exclusion principle etc If the atoms are pushed together to form a solid chunk of silicon the electrons of neighboring atoms will interact and the allowed energy levels will broaden into energy bands When the actual spacing is reached the quantum mechanical calculation results are that at lowest energies very narrow ranges of energy are allowed for inner electrons these are core electrons near the nuclei a higher band of 4N allowed states exists that at 0oK is filled with 4N electrons then an energy gap EG appears with no allowed states no electrons permitted and at highest energies a band of allowed states appears that is entirely empty at 0oK Can this crystal conduct electricity NO it cannot conductor electricity at 0o K because that involves moving charges and therefore an increase of electron energy but we have only two bands of states separated by a forbidden energy gap EG The lower valence band is entirely filled and the upper conduction band states are entirely empty To conduct electricity we need to have a band that has some filled states some electrons and some empty states that can be occupied by electrons whose energies increase Fig 2 shows the situation at 0o K for left a metallic solid such as copper and right a semiconductor such as silicon The metal can conduct at 0o K because the uppermost band contains some electrons and some empty available energy states The semiconductor cannot conduct it is an insulator If we raise the temperature of the semiconductor some electrons in the filled valence band may pick up enough energy to jump up into an unoccupied state in the conduction band Thus at a finite temperature a pure intrinsic semiconductor has a finite electrical conductivity Fig 2 Electronic energy bands for a metallic conductor at T 0o K b insulator or intrinsic semiconductor at 0 o K How much conductivity can a pure intrinsic semiconductor exhibit This depends on how much thermal energy there is and the size of the energy gap EG Mean thermal energy is kT where k Boltzmann s constant 1 38 x 10 23 J K and T is the absolute temperature In electron volts this is kT qe or 26 millivolts for room temperature 300o K For silicon EG 1 12 eV at 300o K This leads in pure intrinsic Si to a carrier concentration ni 1010 carriers cm3 at 300o K Adding Impurities Doping to Adjust Carrier Concentrations Adjust carrier concentrations locally in semiconductor by adding easily ionized impurities to produce mobile electrons and or holes To make silicon N type Add valence 5 phosphorous P atoms to valence 4 silicon Fifth electron is easily freed from the atom by a little thermal energy 0 045 eV for phosphorous to create donate a mobile electron Fig 3a shows the donor energy level just below bottom of conduction band To make silicon P type Add valence 3 boron B to silicon An electron at the top of the valence band can pick up enough thermal energy to release it from the silicon so it attaches to a boron atom completing its outer ring of electrons In the band picture Fig 3b this is represented by an acceptor energy level 0 045 eV above the top of the valence band Fig 3a Electronic energy band for n type semiconductor Ge with donors only Fig 3b Electronic energy band for p type semiconductor Ge with acceptors only
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