Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 1 Chapter III June 1, 2015June 1, 2015June 1, 2015 Carrier Transport Phenomena

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 2 Mobility From equipartition principle, the average thermal energy of a conduction electron is kT/2 units of energy per degree of freedom. Therefore, the kinetic energy of the electrons is From equipartition principle, the average thermal energy of a conduction electron is kT/2 units of energy per degree of freedom. Therefore, the kinetic energy of the electrons is where v th is the thermal velocity of electrons and is 10 7 cm/s at room temperature for Si or GaAs. where v th is the thermal velocity of electrons and is 10 7 cm/s at room temperature for Si or GaAs.

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 3 The mean free path of electrons in Si is cm, and mean free time,, is /v th = s

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 5 Lattice Scattering and Impurity Scattering Probability of a collision taking place per unit time, Probability of a collision taking place per unit time, or or

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 8 Resistivity

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 16 The Hall Effect

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 18 In fact,

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 19 Diffusion Current

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 22 Einstein Relation

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 23 Current Density Equations

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 24 Generation and Recombination Processes In thermal equilibrium, the relationship pn=n i 2 is valid. If excess carriers, by such as optical excitation or forward-biasing a p-n junction, are introduced to a semiconductor so that pn>n i 2, we have a nonequilibrium situation. The process of introducing excess carriers is called carrier injection. The process of restoring the system to equilibrium is recombination of the injected minority carriers with majority carriers. The released energy that results from the recombination process can be emitted as a photon (radiative recombination process) or dissipated as heat to the lattice (nonradiative recombination process). In thermal equilibrium, the relationship pn=n i 2 is valid. If excess carriers, by such as optical excitation or forward-biasing a p-n junction, are introduced to a semiconductor so that pn>n i 2, we have a nonequilibrium situation. The process of introducing excess carriers is called carrier injection. The process of restoring the system to equilibrium is recombination of the injected minority carriers with majority carriers. The released energy that results from the recombination process can be emitted as a photon (radiative recombination process) or dissipated as heat to the lattice (nonradiative recombination process).

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 25 Recombination Mechanisms Shockley Read Hall recombination

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 26 Direct Recombination where G is generation per unit volume and =g/A, g(x)= α(λ) exp[-α (λ)x] where g is generation per unit length of light path.

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 35 for Boltzmann approximation

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 41 Here R is U described in Eq (48) [Eq (48)]

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 43 This recombination process is also called Shockley Read Hall recombination (SRH).

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 44 EtEt

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 45 (energy) Defect energy levels for some elements in Silicon

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 46 E t of Au: 0.54 eV E t of Ti: 0.2 eV

Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 47 Auger Recombination

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 49 Auger recombination dominates when doping concentration is greater than atms/cm -3.

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 51 Surface Recombination

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 53 Continuity Equation

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 56 Steady State Injection from One Side

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 58 Minority Carriers at the Surface

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 60 The Haynes-Shockley Experiments

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 62 Thermionic Emission Process qχ : electron affinity: the least amount of energy required to remove an electron from a solid.

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 64 Tunneling Process of Electrons

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 68 High Field Effect

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 73 Avalanche Resulting in Breakdown in p-n Junction

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Department of Aeronautics and Astronautics NCKU Nano and MEMS Technology LAB. 75 The number of electron-hole pairs generated by an electron per unit distance traveled is called the ionization rate of the electron, α n. The electron-hole pair generation rate G A is given by: