8 (a) (b) 10 −1 10 0 10 1 10 2 10 −3 10 −2 10 −1 10 0 10 1 T (K)  (h/e 2 ) 0 5 10 15 20 1 2 3 4 5 6 T (K)  (h/e 2 ) (c) (d) 10 −1 10 0 10 1 10 2 10 −3 10 −2 10 −1 10 0 10 1 T (K)  (h/e 2 ) 0.95 1 1.05 10 −3 10 −2 10 −1 10 0 10 1 n$_{s}$/n$_{sc}$  (h/e 2 ) Figure 6. Behavior of the resistivity ρ depending on the temperature T and the 2D electron density in the inversion layer n s . Full lines: saddle-point approximation, point symbols: numerical integration, dashed lines: low temperature approximations. On the curves in a) - c) n s and in d) T is constant. Critical density n sc = 10 11 cm $^{$_{−}$2}$. a) logarithmic and b) linear display of ρ ( T ) with parameters: n s = 0 . 75 , . . . , 1 . 25 × n sc in steps of 0 . 05 × n sc in top down order for the individual curves, c) logarithmic view of ρ ( T ) with top down parameters: n s = 0 . 95 , . . . , 1 . 05 × n sc in steps of 0 . 01 × n sc , d) ρ ( n s ) with parameters T = 0 , 0 . 2 , 0 . 5 , 1 , 2 , 5 , 10 , 20 K in bottom up order. and Stern (AFS) 28 and neglect the exchange interaction and correlation effects and use the Ritz variational prin- ciple. (In the mentioned article also more sophisticated methods for the calculation of ε$_{0}$ are given.) For convenience we introduce a new coordinate system z = − Z , i. e. the z -axis is perpendicular to the OS inter- face, positive z -values correspond with the semiconduc- tor side. For the electrons in the inversion layer the bent conduction band of the semiconductor together with the step at the interface builds the quantum well. We use the Fang-Howard envelope wave function according to AFS 34 0 2 4 6 8 10 10 20 30 40 50 60 n$_{s}$ (10$^{11}$cm −2 ) 0  (meV) ϕ ( z, b ) = {√ b 3 2 z exp ( − bz 2 ) for z ≥ 0 0 for z < 0 . (48) Figure 7. Ground state energy of the inversion layer ε 0 versus the density of electrons in the inversion layer n s for three temperatures, top-down: T = 0 , 200 , 300 K . The parameter b is varied in order to make the total energy per electron minimal. For the potential several approximations are taken, see App. B for details. In Fig. 7 the ground state energy ε$_{0}$ versus the elec- tron density n$_{s}$ is shown, ε$_{0}$ decreases with decreasing n$_{s}$ . Now we hold the difference between trap energy and con- duction band edge at the interface ε$_{TsCs}$ = E$_{Ts}$ − E$_{Cs}$ = E$_{Ts}$ − µ + µ$_{E}$$_{0}$ + ε$_{0}$ constant (instead of ε$_{Ts}$$_{0}$ as before).