Peak Mobility of Silicon Metal-Oxide-Semiconductor Systems

Abstract

The density dependence of the mobility of Si (100) inversion layers is calculated within a multiple-scattering theory. Two scattering mechanisms are included. Because of surface-roughness scattering and charged-impurity scattering, a peak mobility fx m is found at a characteristic electron density n m . The inclusion of a mobility edge for low electron densities sharpens the peak structure drastically in comparison with the linear scattering theory. The comparison of calculated mobilities with experimental results gives good agreement in the full measured density range.PACS numbers: 73.25.+ i, 73.40.Qv Mobility measurements in inversion layers are a widely used method to characterize the samples. 1 The reason for this is the specific electron-density dependence of the mobility. With increasing density n the mobility grows and reaches a maximum at a density of about some 10 12 cm" 2 and then decreases for higher density. The origin of the increasing mobility is the screening of the charged impurities, and the later decreasing mobility is due to increased surface-roughness scattering. 2 The peak mobility can characterize the sample. Systematic measurements, done by drifting Na + ions to the Si-Si0 2 interface, have shown 3 that the peak mobility is decreased with increasing density of the Na + impurities n t and that the peak position goes to higher n values.In the following, I give a new treatment of this effect by taking into account scattering by charged impurities and surface-roughness scattering within a nonlinear theory. The strongly peaked structure of the mobility-versus-density data is described by a mobility edge for low density. For high impurity densities the multiple-scattering effects influence the mobility for all electron densities. So for a quantitative description of the peak position a nonlinear theory is necessary. Good agreement of the density dependence of the mobility is reached within our frame for the first time.For the calculations of the mobility for temperature zero I use the self-consistent current-relaxation theory of Gotze 4 generalized to an interacting electron gas. 5 The static scattering rate a determines the mobility / LC = e/ma and the static conductivity cr = nefjt. e is the electron charge and m is the transport mass of the electron. Via a mode-coupling equation 5 a is given as(\U(q)\ 2 ) is the random potential, which is specified later. </>°(q,z) is the density relaxation function of the free-electron gas for wave vector q and complex fre-quency z = /a, given as </>°(q,z) = [Z°(q,z) -g°(q) ]/z. X°(q,z) is the two-dimensional Lindhard function, 6 g°(q) sss X 0 (q,z= s 0) 9 and for the local-field corrections I use the expression G(q) = q/2g v (q 2 -\-kf) l/2 . 7 g v is the valley degeneracy, V(q)F(q)is the effective electron-interaction potential given by V(q) = 27re 2 / (e L q), the Fourier transform of the Coulomb potential, and F(q) is a form factor due to the finite extent of the wave functions perpendicular to the surface [Eq.(2.52) of Ref. 1]. e L is the mean backgr...

Role of background impurities in the single-particle relaxation lifetime of a two-dimensional electron gas

“…The calculations of τ qr for finite thickness samples also highlight a problem with clean samples that are thinner than ∼ 1µm, such as heterostructure epilayers: τ qr hasn't yet saturated to τ ∞ qr , so the standard assumption of an infinite heterostructure thickness [19,28,29,30] results in an overestimation of the renormalised single-particle scattering rate 1/τ ∞ qr . This result clearly demonstrates that the scattering potential U (q) must take into account the finite thickness of the heterostructure for accurate comparison with experimental data.…”

“…However the transport lifetime is convergent since it is less sensitive to small angle scattering events. The non-physical assumption of an infinitely thick sample has been a common assumption in previous calculations of background impurity scattering [19,23,28,29,30].…”

Zero-magnetic-field collective insulator phase in a dilute 2D electron system

“…The SPL description is more appropriate when L^ is^ a. We probed the role of disorder quantitatively by using Gold's calculation [17] for the mobility of Si(lOO) inversion layers. It yields a satisfactory description of jjP^^^ vs n^ for our samples.…”

Transport Properties of A Quasi-two-dimensional Electron Gas in InP/In\(_{1 - x}\)Ga\(_{x}\)As/InP Quantum Wells : Correlation and Magnetic Field Effects

“…We find that the resistivity shows strong low-temperature dependence at low density in both G(q) models. It was shown that MSE can account for a MIT at low electron density where interaction effects become inefficient to screen the random potential created by the disorder [12][13]. When the MSE are included, the mobility can be calculated as µ MSE = µ(1 − A) where the parameter A is given in Refs.…”