and is given by . Two boundary conditions can be obtained by defining the voltage as well as the current at the beginning of a metallic pad area as and respectively. In a formal manner this means that and when using the settings in the figure in this section. By using the pair of coupled differential equations above two more boundary conditions are obtained, namely and which is the inverse of the previously defined transfer length . Eventually two equations, describing the voltage and the current as a function of distance are obtained by using the four stated boundary conditions: When a measurement is performed, it can be assumed that no current is flowing at the opposing end of each metallic pad, which in turn means that . This allows a further refinement of the equation describing the voltage when using the relation : The last equation describes the voltage drop across the region covered by a metallic pad (compare with the figure in this section). By realizing that the resistance value can be expressed with and by setting in the last formula an expression can be found that relates to the specific contact resistivity : The last equation allows the calculation of by utilizing experimental data. Since goes to 1 as increases and is significantly larger than the transfer length often the estimation is used instead of the strictly derived equality. This is identical to what was stated in the general description section. In summary the voltage as well as the current as a function of distance in the region of a metallic pad has been derived by utilizing a model that is similar to the telegrapher's equations. This enabled to find an expression that allows the calculation of the specific contact resistivity of the metal-semiconductor junction by using the experimentally found quantities and and the width of a metallic pad. Circular TLM The physical idea of deriving differential equations for the c-TLM method is the same as for TLM but polar coordinates are used instead of cartesian coordinates. This changes the resistor network that describes the metal covered area as can be seen in the figure to the right. Like for TLM by using Kirchhoff's circuit laws two coupled differential equations are obtained. When the current is eliminated a different equation for the voltage is obtained: A general solution to this type of differential equations is given as