what is Lambda in the parameters of transistor MOS

hello all;

can someone saying me : What is the relation between L , W and Lambda λ in the designing of transistor MOS

best regard

λ is a process technology parameter. for a given process λ is inversely proportional to the length selected for the channel. in practice increasing Vds does affect the channel. this phenomenon called channel length modulation.

As mentioned in the previous reply, as a result of channel length modulation the mosfets have a finite output resistance (rds= 1/ (lambda x Ids )) - as opposed to the ideal case inwhich they could operate as a perfect current source in saturation with rout = infinity. One of the main effects of lamda is in calculating the gain of a transistor (A= gm x rds). Note that lamda is dependent on the channel length and therefore we wouldnt like to use it in calculations (since it is not constant). we would rather use the parameter Ve which is constant in a technology (it is different for pmos and nmos in that technology), so we could use the relationship (lambda=1/(Ve x L)) and therefore rds becomes rds= (Ve x L)/ Ids.
so the gain of a single transistor becomes A= (2 x Ve x L)/ (VGS-Vt). Note that gm= (2 x Ids)/(VGS-Vt). Therefore the voltage gain (A) can be controlled by L and VGS. The current gain (gm) can be controlled by Ids and VGS. lower VGS-Vt and higher L would give higher A.
Note that both decreasing VGS and increasing L would effect other parts of circuit performance but lets leave that alone since its not part of the question.