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 EE42 100 Spring 2006 Week 9a Prof White 1 Fig 1 Calculated energy levels in the diamond structure as a function of assumed atomic spacing at T 0o K From EE42 100 Spring 2006 Week 9a Prof White Introduction to Semiconductor Physics Wiley 1964 2 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 EE42 100 Spring 2006 energy bands Week 9a Prof White 3 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 Week 9a Prof White Can this crystal conduct electricity 4 EE42 100 Spring 2006 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 EE42 100 Spring 2006 Week 9a Prof White 5 energies increase Metals pure silicon at 0K and 300K and doped silicon A Conductors such as aluminum and gold can conduct at low temperatures because the highest energy band is only partly filled there are electrons and there are empty states they can move into when caused to move by an applied electric field B Silicon at 0K can t conduct because the highest band containing electrons is filled C Pure silicon at room temp is slightly conductive since thermal energy can raise some electrons to the mostly empty conduction band D Silicon doped with donors like P or As can conduct and become n type better than pure silicon at room temp since it doesn t take much energy to free a valence electron so it can enter the conduction band E Silicon doped with acceptors like B can conduct and become p type at room temp since it doesn t take much energy to free a valence electron and create a hole in the valence band EE42 100 Spring 2006 Week 9a Prof White 6 A Metal B Pure Si 0K C Pure Si at 300K D n type Si E p type Si Conduction band Donor level Forbidden energy band energy gap Acceptor level Valence band EE42 100 Spring 2006 Week 9a Prof White 7
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