lec4 - 6.012 - Microelectronic Devices and Circuits - Fall...

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6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 4-1 Lecture 4 - PN Junction and MOS Electrostatics (I) Semiconductor Electrostatics in Thermal Equilibrium September 20, 2005 Contents : 1. Non-uniformly doped semiconductor in thermal equi- librium 2. Quasi-neutral situation 3. Relationships between φ ( x ) and equilibrium carrier concentrations ( Boltzmann relations ), ”60 mV Rule” Reading assignment: Howe and Sodini, Ch. 3, §§ 3.1-3.2
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6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 4-2 Key questions Is it possible to have an electric feld inside a semicon- ductor in thermal equilibrium? IF there is a doping gradient in a semiconductor, what is the resulting majority carrier concentration in ther- mal equilibrium?
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6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 4-3 1. Non-uniformly doped semiconductor in ther- mal equilibrium Consider frst uniformly doped n-type Si in thermal equi- librium: N d N d (x)=N d x n-type lots oF electrons, Few holes Focus on electrons n o = N d independent oF x Volume charge density [ C/cm 3 ]: ρ = q ( N d - n o )=0
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6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 4-4 Next, consider piece of n-type Si in thermal equilibrium with non-uniform dopant distribution : N d N d (x) x What is the resulting electron concentration in thermal equilibrium?
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6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 4-5 Option 1 : Every donor gives out one electron n o ( x )= N d ( x ) n o, N d n o (x)=N d (x)? N d (x) x Gradient of electron concentration: net electron diffusion not thermal equilibrium!
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6.012 - Microelectronic Devices and Circuits - Fall 2005 Lecture 4-6 Option 2
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lec4 - 6.012 - Microelectronic Devices and Circuits - Fall...

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