Transfer length method

[1][2][3] TLM has been developed because with the ongoing device shrinkage in microelectronics the relative contribution of the contact resistance at metal-semiconductor interfaces in a device could not be neglected any more and an accurate measurement method for determining the specific contact resistivity was required.

[4] The goal of the transfer length method (TLM) is the determination of the specific contact resistivity

To create a metal-semiconductor junction a metal film is deposited on the surface of a semiconductor substrate.

The TLM is usually used to determine the specific contact resistivity when the metal-semiconductor junction shows ohmic behaviour.

across the interfacial layer between the deposited metal and the semiconductor substrate divided by the current density

an array of rectangular metal pads is deposited on the surface of a semiconductor substrate as it is depicted in the image to the right.

between two adjacent metal pads while the circles represent measured resistance values.

This means that the total resistance can be written in the following functional form, with the pad distance

arises because of the voltage drop at the metal-semiconductor interface as well as in the semiconductor substrate underneath.

This means that during a total resistance measurement, the voltage drops exponentially (and hence also the current density) in the metallic regions (see also theory section for further explanation).

[8] As it is derived in the next section of this article the majority of the voltage drop underneath a metallic pad takes place within the length

The original TLM method as described above has the drawback, that the current does not just flow within the area given by

This means that the current density distribution also spreads to the vertical sides of the metallic pads in the figure in the TLM section, a phenomenon that is not considered in the derivation of the formula describing

[1] In the last section the basic principle of TLM was introduced and now more details about the theoretical background are given.

Therefore, in the image to the right a resistor network is illustrated that describes the situation when a voltage is applied between two adjacent metallic pads.

) represent the resistance due to the semiconductor substrate and the vertical resistor elements (

This methodology is also used for the derivation of the telegrapher's equations which are used to describe the behaviour of transmission lines.

Because of this analogy, the described measurement technique in this article is often called the transmission line method.

[1] By using Kirchhoff's circuit laws the following expressions for the voltage as well as for the current within the above considered length element (read square in the figure in this section) are obtained for a steady state situation where both voltage and current are not a function of time: By taking the limit

Two boundary conditions can be obtained by defining the voltage as well as the current at the beginning of a metallic pad area as

are obtained by using the four stated boundary conditions:[4] 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

: The last equation describes the voltage drop across the region covered by a metallic pad (compare with the figure in this section).

[3][8][4] 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.

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).

To obtain values for the total resistance corresponding to each c-TLM pad, current-voltage measurements were performed across each gap spacing.

The plot to the left shows the recorded measurement data, whereat the green arrow indicates an increase of the gap length.

The curves are linear (which proofs that there is an ohmic contact between the metal and semiconductor layer) and the value of the total resistance for each c-TLM pad is obtained by taking the inverse of the slope.

Before proceeding the matrix-vector equation is written in a more compact form: The goal is to find values of

A plot to the left shows the measured resistance values in dependence of the gap length together with the fitting function corresponding to the determined coefficients

The following GNU Octave script corresponds to the performed measurement series and also includes the obtained resistance values.

Graphical description of the transfer length method (TLM)
Pad structure for circular transmission line measurements (c-TLM)
Resistor network for derivation of the TLM differential equations and a plot of the voltage drop across two adjacent measurement pads
Infinitesimal resistor network for the derivation of the c-TLM differential equations
Modified Bessel functions of the first kind, I α ( x ) , for α = 0, 1, 2, 3
Modified Bessel functions of the second kind, K α ( x ) , for α = 0, 1, 2, 3
Current-voltage plots corresponding to c-TLM measurement series. The green arrow indicates an increase of the gap spacing from 20 μm to 200 μm.
Plot of the total resistance versus gap length corresponding to a c-TLM measurement series. The circles represent the measurement data while the curve represents a fit according to the text.