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Unformatted text preview: 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 61 Lecture 6 Carrier drift and diffusion February 16, 2007 Contents: 1. Thermal motion and scattering 2. Drift 3. Diffusion Reading assignment: del Alamo, Ch. 4, 4.14.3. Cite as: Jess del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 62 Key questions Are carriers sitting still in thermal equilibrium? How do carriers move in an electric field? What are the key dependencies of the drift velocity? How do the energy band diagrams represent the pres ence of an electric field? How does a concentration gradient affect carriers? Cite as: Jess del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 63 1. Thermal motion and scattering We can think of carriers as particles in an ideal gas. At finite T , carriers have finite thermal energy. All this energy resides in the kinetic energy of the particles. Carriers move in random directions: no net velocity, but average carrier velocity is thermal velocity : 8 kT v th = m c Where: m conductivity effective mass [ eV s 2 /cm 2 ] c m accounts for all interactions between the carriers and c the perfect periodic potential of the lattice. For electrons in Si at 300 K ( m ce = 0 . 28 m o ) and v the 2 10 7 cm/s Cite as: Jess del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 64 But... semiconductor crystal is not perfect: the Si atoms themselves are vibrating around their equilibrium position in the lattice there are impurities and crystal imperfections As carriers move around, they suffer frequent collisions: Define: Mean free path , l c : average distance travelled be tween collisions [ cm ]. Scattering time , c : average time between collisions [ s ]. Then: l c = v th c Cite as: Jess del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY]. 6.720J/3.43J Integrated Microelectronic Devices Spring 2007 Lecture 65 Scattering mechanisms: 1. lattice or phonon scattering : carriers collide with vibrating lattice atoms (phonon absorption and emis sion) some energy exchanged ( tens of meV ) 2. ionized impurity scattering : Coulombic...
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 Spring '07
 JesúsdelAlamo

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