The Transfer Length Method or the "Transmission Line Model" (both abbreviated as TLM) is a technique used in
semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...
and
engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
to determine the
specific contact resistivity between a
metal
A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typicall ...
and a semiconductor.
TLM has been developed because with the ongoing device shrinkage in
microelectronics
Microelectronics is a subfield of electronics. As the name suggests, microelectronics relates to the study and manufacture (or microfabrication) of very small electronic designs and components. Usually, but not always, this means micrometre-sc ...
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
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
can be defined as the voltage difference
across the interfacial layer between the deposited metal and the semiconductor substrate divided by the current density
which is defined as the current
divided by the interfacial area
through which the current is passing:
:
In this definition of the specific contact resistivity
refers to the voltage value just below the metal-semiconductor interfacial layer while
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
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
In integrated circuit manufacturing, photolithography or optical lithography is a general term used for techniques that use light to produce minutely patterned thin films of suitable materials over a substrate, such as a silicon wafer, to protect ...
while the metal deposition can be done with
sputter deposition
Sputter deposition is a physical vapor deposition (PVD) method of thin film deposition by the phenomenon of sputtering. This involves ejecting material from a "target" that is a source onto a "substrate" such as a silicon wafer. Resputtering is re ...
,
thermal evaporation or
electroless deposition.
In the image to the right the distance between the pads
increases from the bottom to the top. Therefore, when the resistance between adjacent pads is measured the total resistance
increases accordingly as it is indicated in the graph beneath the depiction of the metal pads. In this graph the
abscissa
In common usage, the abscissa refers to the (''x'') coordinate and the ordinate refers to the (''y'') coordinate of a standard two-dimensional graph.
The distance of a point from the y-axis, scaled with the x-axis, is called abscissa or x coo ...
represents the distance
between two adjacent metal pads while the circles represent measured resistance values.
The total resistivity
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
, whereat
represents the
sheet resistance
Sheet resistance, is a measure of resistance of thin films that are uniform in thickness. It is commonly used to characterize materials made by semiconductor doping, metal deposition, resistive paste printing, and glass coating. Examples of thes ...
of the semiconductor substrate and
the width of the metal pads. The other component that contributes to the total resistance is denoted by
because when two adjacent pads are characterized two identical metallized areas have to be considered. This means that the rotal resistance can be written in the following functional form, with the pad distance
as independent variable:
:
If the contribution of the metal layer itself is neglected then
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).
As it is derived in the next section of this article the majority of the voltage drop underneath a metallic pad takes place within in the length
which is defined as the transfer length
.
Metaphorically speaking this means that the main part of the area underneath a metallic contact through which current enters the metal via the metal-semiconductor interface is given by the transfer length multiplied with the width of the pad
. This situation is also depicted in the figure in this section where the current density distribution underneath two adjacent metal pads during a resistance measurement is depicted with a green colouring.
All in all this means that (if the metal pad length
is much larger than the transfer length) that a relation between
and
can be stated:
:
Since
can be extracted from a linear fit through the data points and
can be obtained from the y-intercept of the linear fit an estimation of
is possible.
Circular TLM
The original TLM method as described above has the drawback, that the current does not just flow within the area given by
times
. 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
.
To account for this geometrical issue instead of rectangular metallic pads, circular pads with radius
are used which are separated from a holohedral metallic coating by a distance
(see figure to the right). When the total resistance between circular pad and holohedral coating is measured three distinguishable components contribute to the measured value, namely the gap resistance
and the contact resistances at the inner and outer end of the gap area (
and
). This is expressed in the following formula:
:
As will be derived in the theory section an expression for
that allows the extraction of
from experimental data as long as
is much larger than
:
: