where J$_{1}$ is the current density at B = B$_{1}$ , generates a power-law also in the thickness dependence: J$_{sf}$ ( d ) = J 1 / (1+ α ) 1 ( µ$_{0}$γd B$_{1}$π ) − α/ (1+ α ) . (6) Figure 2 compares simulations and Eqn. 6. We find by least squares fitting γ ≈ 1 . 2, in agreement with the above result. Note further, that this pre-factor represents only a constant vertical shift in Fig. 2 and that the dependence on the thickness, which is in excellent agreement with the numerical simulations, is thus entirely the result of Eqn. 4. After confirming the analytical solution for a power-law J$_{c}$ ( B ) we can analyze experi- mental data. Fits to J$_{sf}$ ( d ) curves are, for example, available from Ijaduaola et al. $^{5}$, who finds J$_{sf}$ ( d ) ∝ d − 0 . 4 in all but the thinnest film. According to Eqns. 5 and 6 the exponent α of J$_{c}$ ( B ) translates into an exponent of α/ (1 + α ) in the thickness dependence. We infer α = 0 . 6, which is reasonably close to α ≈ 5 / 8 determined in measurements of J$_{c}$ ( H ) at applied fields much above the self-field, where J$_{c}$ ( B ) and J$_{c}$ ( H ) are identical. The J$_{sf}$ ( d ) de- pression observed in this work can therefore be explained without any additional assumption by continuing the power-law J$_{c}$ ( B ) down to the low self-fields of the sample. Another popular parametrization of J$_{c}$ ( B ) is a generalized form of the Kim model which reproduces a power-law if B ≫ B$_{0}$ and is constant if B ≪ B$_{0}$ . The maximum cur- rent density of J$_{c}$ ( B = 0) = J$_{0}$ limits the self-field of the sample to about 1 . 2 µ$_{0}$J$_{0}$d/π , which is roughly 14 mT at 3 µ m (the thickest film of the simulations) if we assume J$_{0}$ = 10 $^{10}$Am − $^{2}$. Thus we expect that the self-field, which increases linearly with thickness, significantly af- fects J$_{sf}$ ( d ) only if it is comparable to or exceeds B$_{0}$ . Calculations for three different values of B$_{0}$ are given in Fig. 3 and show the expected behavior: The self-field of the thinnest sample is approximately half of B$_{0}$ = 1 mT and causes a noticeable J$_{c}$ decrease, whereas the self-field of the sample is insignificant and J$_{c}$ ( d ) approximately independent of thickness, if B$_{0}$ = 100 mT. The intermediate B$_{0}$ = 10 mT shows a transition from the first to the second case; in the thinnest films J$_{sf}$ ( d ) is nearly constant and the depression evolves as the thickness (and the self-field) increases. The (numerical) solution of Eqn. 4 accounts for all three situations and matches perfectly the simulations using again γ ≈ 1 . 2. 5 J$_{c}$ ( B ) = J$_{0}$ (1 + B/B$_{0}$ ) α , (7)