1) Body effect:

• Generally, source and body (bulk or substrate) of nmos is shorted together and connected to ground. But if body is connected to some other potential with respect to source then body effect will occur.
• Consider an nmos whose Vs = VD = 0 and VG is somewhat less than VTh, so that depletion region is formed under the gate but no inversion layer exists.

• Let us assume that negative voltage is applied to bulk w.r.t. source.

  

• As VB becomes negative, more holes are attracted to the substrate connection, leaving a larger negative charge behind i.e. depletion region becomes wider.

• We know that threshold voltage is a function of the total charge in the depletion region because gate charge must mirror Qd (charge in depletion region) before an inversion layer is formed.
• Thus as VB drops, Qd increases and hence VTh also increases. This is called body effect or backgate effect.

• The VTh with body effect can be given as –

  

2) Channel length modulation:

• We assume that in saturation region, drain current ID is constant w.r.t. changes in VDS. But actually the length of channel gradually decreases as potential VDS increases i.e. channel length is function of VDS.
• This effect is called channel length modulation effect.

• The drain current saturation region considering channel length modulation effect is given by,

  Where λ is called channel length modulation parameter.

• The transconductance considering channel length modulation effect is given by,