Question about lambda in NMOS and PMOS

hi,guys
in prof.RAZAVI's book "design of analog cmos integrated circuit", he said that given the same bais current and size, NMOS has the smaller λ. in my opinion, if using N-well process, the doping profile of N-wel is larger than substrate. the
λ =(1/Leff)*(ΔXd/ΔVds), then when NMOS and PMOS has the same Leff, to the same ΔVds, the PMOS will have smaller ΔXd, then has smaller λ.
hope for your reply!
with regards
wanily

question about lamda

pmos will have smaller delta Xd, is that true?

Re: question about lamda

1. Nmos and Pmos with same dimensions do not necessarily have the same doping profile at the drain. They usually don't, due to different doping materials, leading do different doses and implant energies, so the depletion region into the channel can still be, in fact, larger in nmos than in Pmos.
2. Razavi says in P. 37 that "for given dimensions and bias current sources" Nmos exhibit a higher output resistance. So, for Nmos and Pmos to have the same current means that Nmos needs a lower overdrive voltage than Pmos due to a higher mobility, that is why it needs a lower Vds to keep in saturation, leading to Less ΔXd in Nmos than in Pmos.
3.Because less overdrive current is needed in Nmos to maintain saturation, there is less lateral elecrtric field penetrating into the bulk, hence the inversion layer is not as "thick" as with higher Vg (as in Pmos). That is why the N-channel can be more resistive, leading to a higher output resistance.

Hope this helps,

Sharas

question about lamda

pmos should have smaller lamda

Re: question about lamda

hi, Sharas
to a PN junction,d(Xd)/d(VR) is proportional to (VR+ψ0)^(-1/2), we can regards the channel length modulation as a PN junction depletion problem.
as your words, NMOS has the smaller Vov, then d(Xd)/d(VR) of NMOS is larger than PMOS. it show that NMOS has smaller Rout given the same bais current and size.