How does TLM help to extract contact resistance, specific contact resistivity and re-modeling of TLM for electronic device evaluation?

 

Transmission line method (TLM)

For the semiconductor industry, small and faster device operation is demanded. There are so many factors associated with device performance. The contact resistance in a device is one of them. The typical value of contact resistance of electronic devices is around (10E-8 to 10E-6)  [Ohm-cm²] which is widely reported in many kinds of literature. It usually depends on the contact area. We termed it specific contact resistivity (ρc). This is a figure of merit for ohmic contact and determines interface quality. Mostly, the transmission line method (TLM) is used to extract the contact resistivity. It is made of metal contacts developed in the conducting area. This area has a specific length (Le), and width (W) at the different spacing between them. Figure 1 shows a conceptual model for Metal electrode and semiconductor contact. 

Figure 1: Transmission line method for metal and conducting channel interface

Here, I would like to discuss the basic TLM modeling and subsequently re-modeling of the TLM to fit device structure in a simplified way. So, to measure mainly Ohmic contact in a planner device contact (figure 1), we consider, that the sheet resistance of the channel layer is ((ρ_s), the resistance per unit length, R=((ρ_s/W), and potential at metal 0, with potential v(x) and current i(x) at the position x of the channel are,

The Lt is crucial for designing electrode length. We usually call it to transfer length. We can consider total resistance RT between the two metal electrodes (figure 2). The transfer length mainly determines specific contact resistivity. It is defined such that 63% of the current flows into contact. If the lateral contact becomes larger enough than the transfer length, then the contact behaves like semi-infinite contact. It is natural decreasing transfer length contact resistance increases. 

Figure 2: TLM modeling between two contact points

Anyway, if the spacing between two metal electrodes is (L) and total resistance follows a linear relationship, we can extract sheet resistance from the slope and contact resistance from the intercept and hence specific contact resistance by (7) or (8). The total resistance becomes,  it is already seen from the measured TLM where we can extract contact resistance from different L-dependent I-V plots as shown in figure 3, and the important parameters like sheet resistance and contact resistance are extracted from the linear fitting as clearly shown in figure 3. 

Figure 3: From I-V the contact resistance extraction and fitting.

However, if device processing makes an uneven distribution of channel material thickness between the contacts  (figure 4), re-modeling of the contact has to be carried out. Here, we simply re-model the TML as shown in figure 4.  From the TLM result and the re-model structure, we can know the sheet resistance ρs2 of a channel between the metal electrode and using the ρs2, we find sheet resistance ρs1  of the channel underneath the metal electrode. This can be written in the following form:

Figure 4: Re-modeling of TLM with uneven channel thickness due to device processing

Where d1 and d2 are channel material thickness underneath the metal electrode and between metal electrodes respectively. I think many researchers face similar problems during developing device structure and unconsciously misinterpret the measured data which results in the failure of their efforts. I hope that my critical thinking about the re-modeling of TLM will help people in device physics to excel in their work properly. Therefore, I would like to welcome people who are really interested in such critical considerations for their work for the development of science and technology. You may also have an interest in ferromagnetic phase transition-related problem solving, or Schottky diode evaluation for power device applications. These are available in my blog also, please check here.