Editing MOSFET (section)

=== Body effect ===
[[file:Inversion with source-body bias.png|thumb|upright=1.2|[[Band diagram]] showing body effect. ''V''<sub>SB</sub> splits Fermi levels F<sub>n</sub> for electrons and F<sub>p</sub> for holes, requiring larger ''V''<sub>GB</sub> to populate the conduction band in an nMOS MOSFET.]]

The occupancy of the energy bands in a semiconductor is set by the position of the [[Fermi level#"Fermi level" in semiconductor physics|Fermi level]] relative to the semiconductor energy-band edges. Application of a source-to-substrate reverse bias of the source-body pn-junction introduces a split between the Fermi levels for electrons and holes, moving the Fermi level for the channel further from the band edge, lowering the occupancy of the channel. The effect is to increase the gate voltage necessary to establish the channel, as seen in the figure. This change in channel strength by application of reverse bias is called the "body effect."

Using an nMOS example, the gate-to-body bias ''V''<sub>GB</sub> positions the conduction-band energy levels, while the source-to-body bias V<sub>SB</sub> positions the electron Fermi level near the interface, deciding occupancy of these levels near the interface, and hence the strength of the inversion layer or channel.

The body effect upon the channel can be described using a modification of the threshold voltage, approximated by the following equation:

: <math>V_\text{TB} = V_{T0} + \gamma \left( \sqrt{V_\text{SB} + 2\varphi_B} - \sqrt{2\varphi_B} \right),</math>

where ''V''<sub>TB</sub> is the threshold voltage with substrate bias present, and ''V''<sub>T0</sub> is the zero-''V''<sub>SB</sub> value of threshold voltage, <math>\gamma</math> is the body effect parameter, and 2''φ''<sub>B</sub> is the approximate potential drop between surface and bulk across the depletion layer when {{nowrap|''V''<sub>SB</sub> {{=}} 0}} and gate bias is sufficient to ensure that a channel is present.<ref name=inversion>

For a uniformly doped p-type substrate with bulk acceptor doping of ''N<sub>A</sub>'' per unit volume,
: <math>\varphi_B = \frac{k_B T}{q} \ln \left(\frac{N_A}{n_i}\right) \ , </math>

with ''n<sub>i</sub>'' the intrinsic mobile carrier density per unit volume in the bulk. See, for example, {{cite book |title=Mosfet modeling for VLSI simulation: theory and practice |first=Narain|last=Arora |chapter=Equation 5.12 |chapter-url=https://books.google.com/books?id=SkT2xOuvpuYC&pg=PA173 |page=173 |isbn= 9789812707581|year=2007 |publisher=World Scientific}}</ref> As this equation shows, a reverse bias {{nowrap|''V''<sub>SB</sub> > 0}} causes an increase in threshold voltage ''V''<sub>TB</sub> and therefore demands a larger gate voltage before the channel populates.

The body can be operated as a second gate, and is sometimes referred to as the "back gate"; the body effect is sometimes called the "back-gate effect".<ref>{{cite web |url=http://equars.com/~marco/poli/phd/node20.html |title=Body effect |publisher=Equars.com |accessdate=2012-06-02 |url-status=dead |archiveurl=https://web.archive.org/web/20141110225738/http://equars.com/~marco/poli/phd/node20.html |archivedate=2014-11-10 }}</ref>