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Equation 8 · How Advanced Semiconductor Fabrication Actually Works

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CoxC_{\mathrm{ox}}

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the gate’s own oxide capacitance. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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CoxC_{\mathrm{ox}}

Symbol C_ox

the gate’s own oxide capacitance.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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where CdepC_{\mathrm{dep}} is the capacitance of the depletion region the gate does not fully control and CoxC_{\mathrm{ox}} is the gate’s own oxide capacitance. As CdepC_{\mathrm{dep}} falls toward zero, S falls toward its physical floor of about 60 millivolts per decade at room temperature. Wrapping the gate fully around the channel is, in this equation, a direct attack on CdepC_{\mathrm{dep}} : there is no substrate face left for the depletion region to leak through, because there is no substrate face left at all. A review of nanosheet and nanowire scaling states the qualitative result plainly — gate-all-around structures have better short-channel suppression than the FinFETs they are replacing — while…
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where CdepC_{\mathrm{dep}} is the capacitance of the depletion region the gate does not fully control and CoxC_{\mathrm{ox}} is the gate’s own oxide capacitance. As CdepC_{\mathrm{dep}} falls toward zero, S falls toward its physical floor of about 60 millivolts per decade at room temperature. Wrapping the gate fully around the channel is, in this equation, a direct attack on CdepC_{\mathrm{dep}} : there is no substrate face left for the depletion region to leak through, because there is no substrate face left at all. A review of nanosheet and nanowire scaling states the qualitative result plainly — gate-all-around structures have better short-channel suppression than the FinFETs they are replacing — while adding a qualification often left out of promotional accounts: the advantage over a fin only shows up once the vertical spacing between stacked sheets is kept below the sheet’s own width, and that spacing is itself bounded below, at around 7 to 8 nanometers, by how thin the gate oxide and metal-gate stack can be made and still work [ 8 ] . The same review notes a real cost on the other side of the ledger: nanosheet and nanowire channels tend to show lower carrier mobility than a conventional planar channel, an effect that worsens at sheet or wire widths below about 10 nanometers because of increased surface-roughness scattering [ 8 ] . Gate-all-around is not a strictly better geometry; it is a geometry that trades mobility for electrostatic control, and the trade only pays off inside a specific dimensional window.

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