The Full scaling technique attempts to preserve the magnitude of internal electric fields in the MOSFET, while the dimensions are scaled down by factor of ‘s’.
In Constant voltage scaling, all dimensions of the MOSFET are reduced by a factor of ‘s’, but power supply & terminal voltage remain unchanged.
Device density is the area i.e. Area = L.W, therefore after scaling it becomes, Area’ = Area/ $s^2$
Also current density is given by J = $I_D$/Area. Therefore for Full scaling, J’ = s.J and for Constant voltage scaling, J’ = $s^3$ .J
In Constant voltage scaling, drain current density and power density are increased which may eventually cause serious reliability problem for the scaled transistor such as electro-migration, hot carrier degradation, oxide breakdown & electrical overstress.