← All parts of this equation

Equation 6 · Part 3 · How Advanced Semiconductor Fabrication Actually Works

Symbol T

S=kTqln⁡(10)(1+CdepCox),S = \frac{kT}{q}\ln(10)\left(1 + \frac{C_{\mathrm{dep}}}{C_{\mathrm{ox}}}\right),
TT

What this part means

T occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

T occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

The reason that fourth side matters can be written down directly. A transistor’s subthreshold swing — how many millivolts of gate voltage it takes to change the drain current by a factor of ten — is well approximated by S=kTqln⁡(10)(1+CdepCox)S = \frac{kT}{q}\ln(10)\left(1 + \frac{C_{\mathrm{dep}}}{C_{\mathrm{ox}}}\right). 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,…

Read this part in the article →

Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

Open the illustrated variables: a letter stands for a value guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.