content_image/414001.jpg content_image/414008.jpg content_image/414007.jpg content_image/414010.jpg content_image/414011.jpg content_image/414004.jpg content_image/413993.jpg content_image/413994.jpg content_image/413996.jpg content_image/414000.jpg content_image/414002.jpg content_image/414006.jpg content_image/414012.jpg content_image/413995.jpg content_image/414003.jpg content_image/414005.jpg content_image/414009.jpg
scattering. At very low electron densities this screening becomes weaker and the scattering will finally increase so that the resistivity should be higher in this regime. These effects have not been taken into account in the frame of the current work, as we like to present the basic effects due to charging of trap states. 

Althogether, our detailed numerical calculations within the dipol trap model show that a pronounced metallic state can be caused by trap states at an appro- priate energy level inside the oxide of Si-MOS structures. For the realistic assumptions of energetic broadening and narrow spatial distribution near the oxide-semiconductor interface, the behavior is in close agreement with exper- imental observations. 

Work was supported by the Austrian Science Founda- tion (FWF) project no. P16160. We thank our former colleague A. Prinz to perform first calculations within the Altshuler-Maslov Trap model. 

Appendix A: Temperature behavior of the chemical potential and of the effective electron energy for low temperatures 

First we show that 

<img src='content_image/414001.jpg'>

holds for µ$_{E}$$_{0}$ ( T ) from Eq. (31). In our calculations we use the temperature T and the electron density in the inversion layer n$_{s}$ as independent variables. So it is al- lowed to set n$_{s}$ = const. and therefore also ε$_{F}$$_{0}$ = const. while varying T, see Eq. (32). 

For simplicity we introduce the auxiliary variable 

and the function 

With the chain rule we find 

<img src='content_image/414008.jpg'>

So Eq. (A1) is equivalent to 

From Eq. (31) we get 

## ACKNOWLEDGMENTS 

<img src='content_image/414007.jpg'>

<img src='content_image/414010.jpg'>

<img src='content_image/414011.jpg'>

<img src='content_image/414004.jpg'>

The first two derivatives are 

<img src='content_image/413993.jpg'>

<img src='content_image/413994.jpg'>

The second derivative contains only terms of the form 

Differentiating g$_{a,b}$ yields 

<img src='content_image/413996.jpg'>

therefore all higher derivatives d $^{n}$M dx n also contain only terms g$_{j,k}$ with j ∈ { 1 , 2 , . . . , n } and k ∈ { n + 1 , n + 2 , . . . , 2 n − 1 } . Now we can multiply the nu- merator and the denominator of g$_{j,k}$ with exp ( − j/x ) and write 

<img src='content_image/414000.jpg'>

with y = j/x . Applying the rule of L’Hospital k times we get 

<img src='content_image/414002.jpg'>

The limit for the first derivative also vanishes 

so Eq. (A5) holds and 

With help of Eq. (A1) we show now that 

<img src='content_image/414006.jpg'>

holds for Eq. (38). 

For not too small η the Fermi-Dirac integral F j ( η ) can be approximated by 32 

For low temperatures µ$_{E}$$_{0}$ approaches ε$_{F}$$_{0}$ and therefore it is positive, so from Eq. (38) we get 

<img src='content_image/414012.jpg'>

<img src='content_image/413995.jpg'>

<img src='content_image/414003.jpg'>

<img src='content_image/414005.jpg'>

<img src='content_image/414009.jpg'>

