The Transfer Length Method or the "Transmission Line Model" (both abbreviated as TLM) is a technique used in semiconductor physics and engineering to determine the specific contact resistivity between a metal and a semiconductor. 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.
General description The goal of the transfer length method (TLM) is the determination of the specific contact resistivity ρ C {\displaystyle \rho _{C}} of a metal-semiconductor junction. 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. In this case the contact resistivity ρ C {\displaystyle \rho _{C}} can be defined as the voltage difference Δ V {\displaystyle \Delta V} across the interfacial layer between the deposited metal and the semiconductor substrate divided by the current density J {\displaystyle J} which is defined as the current I {\displaystyle I} divided by the interfacial area A {\displaystyle A} through which the current is passing:
ρ C = Δ V J = ( V S e m i c o n d u c t o r − V M e t a l ) A I {\displaystyle \rho _{C}={\frac {\Delta V}{J}}={\frac {(V_{Semiconductor}-V_{Metal})A}{I}}}
In this definition of the specific contact resistivity V S e m i c o n d u c t o r {\displaystyle V_{Semiconductor}} refers to the voltage value just below the metal-semiconductor interfacial layer while V M e t a l {\displaystyle V_{Metal}} represents the voltage value just above the metal-semiconductor interfacial layer. There are two different methods of performing TLM measurements which are both introduced in the remainder of this section. One is called just transfer length method while the other is named circular transfer length method (c-TLM).
TLM
To determine the specific contact resistivity ρ C {\displaystyle \rho _{C}} 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. The definition of the rectangular pads can be done by utilizing photolithography while the metal deposition can be done with sputter deposition, thermal evaporation or electroless deposition. In the image to the right the distance between the pads d i {\displaystyle d_{i}} increases from the bottom to the top. Therefore, when the resistance between adjacent pads is measured the total resistance R T o t {\displaystyle R_{Tot}} increases accordingly as it is indicated in the graph beneath the depiction of the metal pads. In this graph the abscissa represents the distance d {\displaystyle d} between two adjacent metal pads while the circles represent measured resistance values. The total resistivity R T o t {\displaystyle R_{Tot}} can be separated into a component due to the uncovered semiconductor substrate and a component that corresponds to the voltage drop in two metal-covered areas. The former component can be described with the formula R S Z d i {\displaystyle {\frac {R_{S}}{Z}}d_{i}} , whereas R S {\displaystyle R_{S}} represents the sheet resistance of the semiconductor substrate and Z {\displaystyle Z} the width of the metal pads. The other component that contributes to the total resistance is denoted by 2 R C {\displaystyle 2R_{C}} because when two adjacent pads are characterized two identical metallized areas have to be considered. This means that the total resistance can be written in the following functional form, with the pad distance d {\displaystyle d} as independent variable:
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