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ee3161 spring10 hw2 - Pierret pp 105-138 Lecture Note 5...

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U NIVERSITY OF M INNESOTA EE3161 Semiconductor Devices Sang-Hyun Oh Lecture Note 5 Carrier Dynamics 1 Light absorption Generation/recombination Capacitor analogy Photo-generation Minority carrier diffusion Examples Quasi Fermi level Pierret pp. 105-138
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U NIVERSITY OF M INNESOTA EE3161 Semiconductor Devices Sang-Hyun Oh Cover Image: Carrier Dynamics 2 “Crossing the border” Positive holes from the p-side (red) of a semiconductor (GaAs) p-n junction increasingly diffuse into the n-side (blue) as voltage across the junction is increased. Imaged with a scanning tunneling microscope (STM) at a resolution of ~10 nanometers. Shoji Yoshida et al. Phys. Rev. Lett . 98, 026802 (2007)
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U NIVERSITY OF M INNESOTA EE3161 Semiconductor Devices Sang-Hyun Oh Themes The main topic of our course is to apply a voltage to a device to inject holes and electrons; then watch how the conductivity is changed. It’s simpler to first put the excess carriers in the semiconductor by photo-excitation . From Pierret: “Minority carrier diffusion into a sea of majority carriers might be likened to a small group of animals attempting to cross a piranha-infested stretch of the Amazon River.” Their distribution falls off exponentially. 3
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U NIVERSITY OF M INNESOTA EE3161 Semiconductor Devices Sang-Hyun Oh Light Absorption 4 I ( x ) I ( x + dx ) = α dx I ( x ) dI I = I =
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U NIVERSITY OF M INNESOTA EE3161 Semiconductor Devices Sang-Hyun Oh Illumination Assume that light is uniformly incident on the surface of a semiconductor. If α L 1, then light is absorbed uniformly throughout the semiconductor G L = #/vol/sec of electron-hole pairs generated. 5
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U NIVERSITY OF M INNESOTA EE3161 Semiconductor Devices Sang-Hyun Oh Absorption vs. Bandgap Quiz: 6 Silicon E g =1.12 eV Ge E g =0.66 eV GaAs E g =1.42 eV E g E photon ? When each semiconductor material is
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U NIVERSITY OF M INNESOTA EE3161 Semiconductor Devices Sang-Hyun Oh Notation n = carrier concentration under arbitrary conditions. n 0 = equilibrium carrier concentration n = (n - n 0 ) = excess carrier concentration G L =external light that generates electron-hole pairs 7
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U NIVERSITY OF M INNESOTA EE3161 Semiconductor Devices Sang-Hyun Oh Energy Picture (# additional electrons) = (# additional holes) 8 G L = G L ( x, λ ) = n ( x, t ) t light = p ( x, t ) t light
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U NIVERSITY OF M INNESOTA EE3161 Semiconductor Devices Sang-Hyun Oh Law of Mass Action: Revisited The equilibrium carrier concentration is not a static concept, but is the average result of the balance between competing dynamic processes (i.e. generation and recombination). For a given semiconductor material, the thermal generation rate of electron-hole pairs, G i,th (T) , depends only on temperature (intrinsic material). The rate of recombination events, R i (n 0 ,p 0 ,T) , however, will in general depend on both electron and hole concentration, and the temperature.
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