CN5-energy-bands - Energy Bands and Bandstructure 1 Outline...

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1 1 Energy Bands and Bandstructure 2 Outline ± Energy bands ± Very simple view of charge current conduction in energy bands ± Metals, vs. semiconductors vs. insulators ± Bloch functions and band structure ± Symmetries in the bandstructure and Brillouin zones ± Semiconductor bandstructures ± Metals, vs. semiconductors vs. insulators revisited ± Strain and semiconductor properties ± Summary
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2 3 Reminders (incomplete) ± There are three variations of cubic lattice, all of which are relevant for semiconductors ± fcc lattice semiconductor crystals have a two atom basis (two atoms within the primitive unit cell) with atoms bonded in a tetrahedral arrangement to their four nearest neighbors ± For an arbitrary direction [abc] in a fcc (or sc or bcc) lattice there are 48 equivalent directions obtained by changing the order of the indices and/or there signs . .. or less if one or more of the indices is zero or two or more indices are the same . 4 ± Two observables can be known precisely simultaneously if and only if the particle can be in an eigenstate of both of the two corresponding operators simultaneously, which is only possible if the corresponding QM operators commute, and which is the “ Heizenberg Uncertainty Principle ” (e.g., position and momentum, can not be know simultaneously). ± The observable properties of particles in (true) energy eigenstates do not evolve in time at all so that these state are often called “stationary states.” ± If a particle is not in an energy eigenstate, its observable properties will evolve in time .
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3 5 Reminders (incomplete) ± Electrons are Fermions (with spin ± ½ ħ )and are thus subject to : ¾ the “Pauli Exclusion Principle” ¾ Fermi statistics in equilibrium ± The overlapping of “initially” separate QM systems produces: ¾ energy level splitting, ¾ and associated “covalent” bonding and antibonding forces . 6 ± Atoms in Column IV atoms such as Si and Ge have 4 “outer shell” electrons, … … while a 50-50 mix of column III atoms such as Ga and In with 3, and column V atoms such As and P with 5 also have an average of 4 outer- shell electrons per atom … ± … and, not surprisingly, crystals formed from these atoms or atom combinations have similar, although certainly not identical, properties.
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4 7 Energy bands and band filling Remember the mixing and resulting splitting of the electronics states of two hydrogen atoms as they are brought together, and of course the covalent bonding that holds them together as a molecule? Here we consider what happens where say Avogadro’s number give or take a few orders of magnitude of more complex atoms are brought together to form a crystal … … and a particular twist in the process that defines semiconductors and insulators.
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This note was uploaded on 02/03/2009 for the course EE 339 taught by Professor Banjeree during the Spring '08 term at University of Texas at Austin.

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CN5-energy-bands - Energy Bands and Bandstructure 1 Outline...

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