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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: Jesús 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: Jesús 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 = π 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: Jesús 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 , τ c : average time between collisions [ s ]. Then: l c = v th τ c Cite as: Jesús 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
 Condensed matter physics, Integrated Microelectronic Devices, Jesús del Alamo

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