CN7-doping - Doping and Equilibrium Statistics 1 Outline...

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1 1 Doping and Equilibrium Statistics 2 Outline ± Introduction ± “Equilibrium” and “detailed balance” ± Carrier concentrations and the Fermi level ± The intrinsic material limit as a reference ± Extrinsic materials, dopants, compensation doping and carrier concentrations ± Deviations from ideal behavior ± Summary
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2 3 Introduction In a typical equilibrium calculation in a quasi-bulk region we might for example (and note the order) 1. determine the majority carrier type (the ones there are more of) and concentration from the nature and number of impurities (such as later required to determine conductivity), 2. then determine the minority carrier type and concentration from the majority carrier concentration and temperature (so as to establish a reference for non-equilibrium calculations), 3. and then find the Fermi level position relative to the band edges (so as, for example, to later determine were the band edges will be as a function of position in a MOSFET in equilibrium and then under applied voltages.) In what follows I show you how to do those things (not in parentheses) … but not in that order . 4 Equilibrium and “detailed balance” So just what is this “equilibrium” condition? In “ equilibrium ,” by definition detailed balance ” is satisfied: on average each and every physical process, in detail, is precisely balanced by its inverse … of more plainly if less precisely, absolutely nothing is happening . E.g., there is no current flow of either carrier type independently, there is no light being emitted or absorbed, there is no heat being conducted, emitted or absorbed, etc. The requirement for detailed balance for a system of interacting particles in equilibrium (electrons, holes, phonons, photons, etc.) actually leads to the Fermi distribu- tion for the carriers (and Bose-Einstein statistics for the photons and phonons). For any other carrier distribution the system will not be balanced in detail and something will be happening .
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3 5 Equilibrium is not simply “steady-state ;” steady state only implies that that there are no changes in time in the rate at which whatever is happening, happens … (… although if something is in equilibrium it is also in steady- state). 6 So why do we care about equilibrium? Aren’t we most interested in devices when they are actually doing there job of conducting current and/or emitting light, etc? Equilibrium is a critical limiting/boundary condition : o We, e.g., may apply an electric field to drive the system out of equilibrium and allow, e.g., current to flow, and the system will respond by emitting lattice vibrations (phonons) and/or light (photons) that drive it back towards equilibrium … (… where the balancing of these processes can lead to steady-state non-equilibrium conditions, as TBD later.) o Often times, even under non-equilibrium conditions, the carrier populations will still be very near equilibrium particularly near contacts where interactions with the huge numbers of carriers in the contacts very efficiently drive the system towards equilibrium.
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CN7-doping - Doping and Equilibrium Statistics 1 Outline...

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