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lecture18

lecture18 - 6.720J/3.43J Integrated Microelectronic Devices...

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Unformatted text preview: 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 18-1 Lecture 18 - Metal-Semiconductor Junction (cont.) March 16, 2007 Contents: 1. Metal-semiconductor junction outside equilibrium (cont.) Reading assignment: del Alamo, Ch. 7, § 7.2.3 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 18-2 Key questions • In a metal-semiconductor junction under bias, is there current flow? If so, how exactly does it happen? • What are the key dependences of the current in a metal-semiconductor junction? 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]. 1. Metal-semiconductor junction outside TE 6.720J/3.43J - Integrated Microelectronic Devices - Spring 2007 Lecture 18-3 (cont.) I-V Characteristics Few minority carriers anywhere → majority carrier device Bottleneck: transport through SCR q j Bn E F q j Bn J e =0 a) equilibrium E c E F E v J e E f q j Bn q( j Bn-V) b) forward bias E c E fe E v J e c) reverse bias E c E fe E v • in forward bias, J ∝ e qV/kT • in reverse bias, J saturates with V E f q j Bn q( j Bn-V) 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 18-4 Balance between electron drift and diffusion in SCR: • TE: perfectly balanced • forward bias: E ↓ ⇒ diffusion > drift • reverse bias: E ↑ ⇒ diffusion < drift Net current due to imbalance of drift and diffusion ⇒ Drift-diffusion model Start with electron current equation: dn qn dφ dn J e = qµ e n E + qD e = qD e ( − + ) dx kT dx dx Multiply by exp( − qφ ): kT qφ qn dφ qφ dn qφ J e exp( − ) = qD e [ − exp( − ) + exp( − )] kT kT dx kT dx kT d qφ = qD e [ n exp( − )] dx kT 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 18-5 Integrate along the depletion region: • left-hand side: J e J (negligible hole contribution), and J independent of x : x d qφ x d qφ J e exp( − ) dx = J exp( − ) dx 0 kT 0 kT • right-hand side x d d qφ qφ x d qD e [ n exp( − )] dx = qD e n exp( − ) | 0 dx kT kT For left-hand side, use φ ( x ) obtained earlier: x 2 2 x φ ( x ) = − ( φ bi − V )( 2 − + 1) for 0 ≤ x ≤ x d x d x d For right-hand side, use boundary conditions:...
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lecture18 - 6.720J/3.43J Integrated Microelectronic Devices...

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