In order to investigate the metallic state in high-mobility Si-MOS structures, we have further developed and precised the dipole trap model which was originally proposed by B. L. Altshuler and D. L. Maslov [Phys. Rev. Lett. 82, 145 (1999)]. Our additional numerical treatment enables us to drop several approximations and to introduce a limited spatial depth of the trap states inside the oxide as well as to include a distribution of trap energies. It turns out that a pronounced metallic state can be caused by such trap states at appropriate energies whose behavior is in good agreement with experimental observations. Institute for Semiconductor Physics, Johannes Kepler University, 4040 Linz, Austria; and Christian Doppler Labor for Surface Optics, Johannes Kepler University, 4040 Linz, Austria Institute for Semiconductor Physics, Johannes Kepler University, 4040 Linz, Austria Dipole trap model for the metallic state in gated silicon-inversion layers T. Hörmann G. Brunthaler ∗ I. INTRODUCTION arXiv:1001.0205v1 [cond-mat.str-el] 1 Jan 2010 PACS numbers: 71.30.+h; 73.40.Qv; 72.10.Fk Keywords: Metal-insulator transition; Si-MOS structures; Scattering model The discovery of the metal-insulator transition (MIT) in two-dimensional (2D) electron systems in 1994 1,2 has attracted large attention, as it was in apparent con- tradiction to the scaling theory of localization 3,4 which states that in the limit of zero temperature, a metal- lic state should exist only in three dimensional systems, whereas in two dimensions disorder should always be strong enough to induce an insulating state. The MIT in high-mobility n-type silicon inversion layers shows a strong decrease of resistivity ρ towards low temperature T for high electron densities, manifesting the metallic re- gion, whereas a strong exponential increase of ρ demon- strated the insulting regime for low densities. A similar but weaker behavior was observed in many other semi- conductor systems at low densities and low temperatures (e. g. p -GaAs, 5 n -GaAs, 6 SiGe, 7 AlAs $^{8}$) Several models were suggested in order to explain the unexpected finding of metallic behavior in 2D. The most important ones are i) temperature-dependent screening, 9–14 ii) quantum corrections in the diffusive regime, 15–18 and iii) quantum corrections in the ballistic regime. 19,20 Numerous argumentations for the different models are given in literature, 21–25 but a clear decision for one of them could not been drawn yet. As an alternative, Altshuler and Maslov (AM) intro- duced the dipol scattering scenario for Si-MOS struc- tures in which charged trap states in the oxide layer form dipols together with the image charge of the screening 2D electrons. 26 The interplay between the gate voltage dependent energetic position of the trap states and the height of the chemical potential may lead as well to a metal-insulator transition in that system. It should not be assumed that the dipol scattering effect is active alone, as the temperature dependence of screening and quantum corrections will surely contribute at low temperatures, but the charging of trap states might be the generator of the particularly large effect in Si-MOS structures. It a8) the chemical potential µ in the 2D layer has (A) either the same temperature dependence as in the bulk a7) the energy of the trap state E$_{T}$ is fixed relative to the quantization energy E$_{0}$ of the 2D ground state inside the inversion potential, and a6) a parabolic saddle-point approximation for the ef- fective potential between the Si/SiO2 interface and the metallic gate was used in order to perform analytical cal- culations, a5) the scattering efficiency of the 2D electrons is de- scribed by a dipole field of the trap charge and its mirror charge, a4) a charged trap state is screened by the 2D electrons so that the resulting electrostatic potential can be de- scribed by the trap charge and an apparent mirror charge with opposite sign on the other side of the interface, a3) the states occupied with electrons behave neutral and cause no scattering of 2D electrons whereas the un- occupied states are positively charged and lead to scat- tering (AM work in the hole trap picture, but we describe occupation in terms of electrons), a2) the spatial density distribution in the oxide is ho- mogeneous, a1) the trap states possess a δ -like distribution in en- ergy (i. e. have all the same energy), For the analytical calculations AM made a number of assumptions. These are: AM could show within their analytical calculations that a trap level at energy E$_{T}$ which is either filled or empty, depending on its position relative to the Fermi energy E$_{F}$ , can lead to a critical behavior in electron scattering if E$_{T}$ and E$_{F}$ are degenerate. This dipole trap model is able to explain the main properties of the metal- insulator transition in gated Si-MOS structures. is known that the misfit at the silicon/silicon-oxide in- terface produces charged defect states in the thermally grown oxide layer. 27–29 Arguments on the importance of trap states in Si-MOS structures were also given by Klap- wijk and Das Sarma. 30