On the Adequacy of the Transmission Line Model to Describe the Graphene–Metal Contact Resistance

Abstract

The contact-end-resistance method is applied to TLM structures to characterize in-depth the graphene-metal contact and its dependence on the back-gate bias. Parameters describing the graphene-metal stack resistance are extracted through the widely used transmission line model. The results show inconsistencies which highlight application limits of the model underlying the extraction method. These limits are attributed to the additional resistance associated to the p-p + junction located at the contact edge, that is not part of the conventional transmission line model. Useful guidelines for a correct application of the extraction technique are provided, identifying the bias range in which this additional resistance is negligible. Finally, the contact-end-resistance method and the transmission line model are exploited to characterize graphenemetal contacts featuring different metals.

Dependable Contact Related Parameter Extraction in Graphene–Metal Junctions

“…R CE ranges from 10.5 to 12 Ω with respect to L CH at a fixed V BG , demonstrating that R CE is more or less unaffected by the channel resistance outside the contact. [ 33,54 ] The R CE measurement was also carried out in ambient air at V BG = 0 V (Figure 5d) and was found to be very consistent with the results in vacuum, which indicates that R CE is unaffected by the channel conductivity and, thus, by the measurements conditions (in this case graphene is protected from water molecules by the contact on the top). Finally, R CE is rather independent of V BG .…”

“…In such a situation, additional measurements are required to extract reliable contact related parameters at the G-M junction, namely the R CE technique. [33,38] R CE can be measured directly by forcing a known current between contacts 1 and 2 and measuring the generated voltage drop across the G-M stack, while imposing a null current on contact 3 as shown in Figure 1a. In this way, R CE is measured by the use of the additional contact 3, since by forcing a null current, there is no additional voltage drop between contacts 2 and 3.…”

“…It has been suggested and demonstrated that the classic TLM may be inappropriate under certain conditions for characterizing G-M contacts. [31][32][33][34][35] Since the sheet resistance of the graphene channel (R SH ) is a dominating component of the total resistance of the device (R T ), and since the TLM technique is based on the comparison of the R T values of the graphene field effect transistors (GFETS) inside the TLM structure, slight changes in R SH along the TLM array will lead to erroneous R C values. In addition, the R SH is different from the sheet resistance of graphene under the metal contact (R SK ) due to the G-M interactions that dope graphene, [27,36,37] and this should be accounted for in the extraction of the parameters describing the G-M junction.…”

DFT study of graphene doping due to metal contacts

“…Furthermore, despite the similar graphene quality between the different samples (not shown) [8], the R C values do depend on the metal contact, with larger R C values for Ni and smaller R C values for Au. This indicates that the M-G interactions influence the electrical properties of the M-G contact, which is not a surprising result [9].…”

“…However, metal-graphene (M-G) contacts still severely degrade the electrical performance of graphene based devices because of the large contact resistance (R C ). For instance, R C largely degrades the output conductance and the maximum oscillation frequency of graphene-FETs (GFETs) [1], [3]. Thus, to boost the graphene technology, design strategies to optimize R C are urgently required to make graphene a viable solution for high performance electronic devices [4].…”