Steady-state currents of the scanning electrochemical microscope (SECM), wh
ich can be used to convert approach curves to topographical information, ar
e considered in four cases, corresponding to the combination of positive an
d negative feedback on the substrate surface with either a finite or infini
te glass insulator around the disc electrode. If the substrate is an insula
tor and both substrate and insulator extend to infinity (case I), steady-st
ate cannot be attained. When the bulk concentrations can be assumed to be r
estored at a finite distance (the glass radius), both the negative (case II
) and positive (case IV) feedback steady-state currents can be analytically
found by using properties of the Bessel functions in the solution of a dua
l series equation. The strong influence of the glass radius on the current
in case II can be taken into account in the exact computation and in simple
approximate expressions. Positive feedback with an infinite domain (case I
II) can be solved with a dual integral equation. All solutions can be easil
y computed with modern software. Moreover, very simple and accurate approxi
mate expressions (from the literature and new suggestions) are assessed and
compared. A consistent way of linking the theoretical and experimental nor
malized currents for finite glass radii is suggested in terms of the values
of the currents corresponding to an infinite distance between the electrod
e and the substrate. An expression to estimate the electrode radius from th
e insulator radius and the current with no feedback is suggested.