# When does the NMOS form the channel? VGS > VTH or VGB > VTH?

When does the NMOS form the channel? VGS > VTH or VGB > VTH? I see that textbook talks about VGS > VTH, channel formed, but the capacitor is formed between the gate and the body, so i think it should be VGB >VTH?

When does the NMOS form the channel?

An n-channel mosfet forms channel when $$V_{GS} > V_{TS}\tag1$$ or when $$V_{GB} > V_{TS} + V_{SB}\tag2$$ (Both conditions are actually same)

Where $V_{TS}$ is the threshold voltage with source as reference terminal and is given by: $$V_{TS} = V_{T0} + \gamma(\sqrt{\phi_t+V_{SB}}-\sqrt{\phi_t})$$

$\gamma$ and $\phi_t$ are device parameters (see body effect). $V_{T0}$ is the threshold voltage with source and bulk shorted ($V_{SB}=0$). The threshold voltage given in datasheet is $V_{T0}$ .

The point I want to make is that you can not say that a mosfet will form channel if either $V_{GS}$ is greater than a particular voltage or $V_{GB}$ is greater than a particular voltage without the knowing the voltage between source and bulk, $V_{SB}$.

For example, for an n-MOS of threshold voltage 3V, $V_{GB} = 4V$ does not ensure channel formation if source terminal is at a higher potential than bulk (or body) terminal.

With respect to which reference terminal threshold voltage is defined?

One can actually defined two threshold voltages- $V_{TS}$ with respect to source and $V_{TB} (= V_{TS} + V_{SB})$ with respect to bulk. Text books and articles, especially circuit related, usually defines it with respect to source terminal.

Indeed Vbg > Vth is really the condition above which a channel is formed.

I think that in the case that Vgs > Vth is used, the simple explanation is that it is assumed that the Source is shorted to the Bulk so: Vgs = Vgb

When the source is not shorted to Bulk and Vsb > 0 body effect will increase Vth so I think using Vbg > Vth is prefered.