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#### L31_MOScap

Course: ECE 440, Fall 2008

School: University of Illinois,...

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440: ECE Lecture 31 MOS Capacitor Today: MOS capacitor = a parallel plate capacitor (i.e. the MOSFET without Source/Drain regions... for now) GATE xo VG + _ Si In nMOS device: n+ gate, p-substrate In pMOS device: p+ gate, n-substrate (but, gate = metal by Intel at 45 nm tech node, ~ Q1 2008) What are Source/Drain regions in nMOSFET, pMOSFET? Illinois ECE440 Prof. Eric Pop 1 We're almost ready to...

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440: ECE Lecture 31 MOS Capacitor Today: MOS capacitor = a parallel plate capacitor (i.e. the MOSFET without Source/Drain regions... for now) GATE xo VG + _ Si In nMOS device: n+ gate, p-substrate In pMOS device: p+ gate, n-substrate (but, gate = metal by Intel at 45 nm tech node, ~ Q1 2008) What are Source/Drain regions in nMOSFET, pMOSFET? Illinois ECE440 Prof. Eric Pop 1 We're almost ready to understand the metal/high-K MOSFET (but we'll come back to it later too): Source: intel.com Let's focus on the "traditional" nMOSFET. Draw band diagram in equilibrium (V=0). Illinois ECE440 Prof. Eric Pop 2 We drew this as an n+ gate MOS, but remember the gate can also be metal! Then the metal gate work function M matters: Define the bulk (body) potential: 1 kT N sub F = ( Ei - EF ) = ln n q q i Define the surface potential: 1 s = ( Ei ,bulk - Ei , surf ) q Illinois ECE440 Prof. Eric Pop 3 What happens if we apply a gate voltage? V < VFB V = VFB VFB < V < VT VT < V There are two "magic voltages" here: 1) The flat-band voltage, VFB = voltage we need to put on gate to get E-field = 0 everywhere (flat bands). Note, this can be zero, but generally depends on gate work function or doping: qVFB = The threshold voltage, VT = voltage we need to put on gate to get as many electrons at the surface as there are (majority) holes in the p-type bulk. I.e. silicon surface is "inverted". 2) Illinois ECE440 Prof. Eric Pop 4 In general, the voltage applied on the will gate be: VG = VFB + Vox + s Where Vox = Eoxd = voltage dropped across oxide And s = voltage dropped in the silicon (surface potential) Q: what is Vox when V = VFB? Three interesting regions of MOS operation: Accumulation Depletion Inversion Let's take them one by one: Illinois ECE440 Prof. Eric Pop 5 Accumulation: V < VFB, holes accumulate at surface M 3.1 eV O S | qVox | Ev |qVG | |qS| is small, 0 Ec EFS Ev 4.8 eV VG VFB + Vox GATE + + + + + + d Qacc (C/cm2) p-type Si Illinois ECE440 Prof. Eric Pop 6 Depletion: VFB < V < VT, holes pushed back in the substrate. Surface is depleted of mobile carriers All surface charge is due to fixed dopant atoms M qVox O W S Ec 3.1 eV Ec= EFM Ev 4.8 eV qS EFS Ev qVG Again, we apply depletion approximation we used for p-n diode: assume abrupt displaced charge (rectangular). Draw: Illinois ECE440 Prof. Eric Pop 7 Charge density in depleted region: -qN A d qN = - A dx Si Si (0 x W ) Poisson's equation in depleted region: (0 x W ) Integrate twice (from bulk x = W to surface x = 0) to obtain surface S or depletion depth W: To find S as a function of gate V we need all voltage drops. Across oxide: Vox = Eoxd = Qdep/Cox where Qdep is the total charge in the silicon (on the silicon "plate" of the oxide capacitor): Qdep = -qNAW = Finally, VG = VFB + S + Vox = We can now solve from the surface potential vs. gate voltage: qN A si S = 2 2Cox Illinois ECE440 2Cox (VG - VFB ) 1+ - 1 qN A si 2 Prof. Eric Pop 2 8

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