follows, whereat and are unspecified constants and is . The functions and are zero-order modified Bessel functions of the first and second kind respectively. By utilizing the coupled differential equations above and the differentiation rules for modified Bessel functions (, ) an expression for the current can be obtained. The functions and are first-order Bessel functions of the first and second kind respectively. Now after having obtained expressions for the current as well as for the voltage, expressions for the contact resistances corresponding to the inner and outer boundary of the gap area have to be found (compare with the schematic illustration of the measurement metallization in the general section). The contact resistance at the inner boundary is given by and during a measurement the current in the middle of the circular metallic pad is zero (). Since the modified Bessel function tends to infinity when tends to zero (see figures to the right), the constant has to be zero because the voltage can not be infinite. Considering this, the contact resistance at the inner boundary of the gap area equates to: In a similar manner an expression for the contact resistance at the outer boundary of the gap area can be found when is replaced with (compare with the drawing in the general section). Here, also a boundary condition for the current can be given, namely . This means that A has to be zero because the function tends to infinity (see figure to the right) as goes to infinity. In turn this means that the contact resistance at the outer boundary of the gap area is given by: The resistance due to the gap area itself can be found by considering the horizontal differential resistor in the figure in this section and by integrating from to . By adding , and an expression for the total resistance can be given: When the outer and the inner radius are much larger than the transfer length the quotients of the modified Bessel functions are approximately one. This means that when is substituted with the same formula for as given in the general section is found, which can be used for extracting and from experimental data: See also References Further reading Semiconductors