An experimental set-up to probe the quantum transport through a single atomic$/$molecular junction at room temperature

Abstract

Understanding the transport characteristics at the atomic limit is the prerequisite for futuristic nanoelectronic applications. Among various experimental procedures, mechanically controllable break junction (MCBJ) is a well-adopted experimental technique to study and control atomic or molecular scale devices. Here, we present the details of developing a piezo-controlled table-top MCBJ set-up, working at ambient conditions, along with the necessary data acquisition technique and analysis of the data. We performed the conductance experiment on a macroscopic gold wire, which exhibits a quantised conductance plateau upon pulling the wire. Conductance peak up to ~ 20G₀ (G₀ = 2e²$/$h where e is the electronic charge and h is the Planck’s constant) could be resolved at room temperature. A well-known test bed molecule, 4,4′-bipyridine, was introduced between the gold electrodes and the conductance histogram exhibits two distinctive conductance peaks, confirming the formation of a single molecular junction, in line with the previous reports. This demonstrates that our custom-designed MCBJ set-up can measure the quantum transport of a single molecular junction at ambient conditions.

Appendices

Appendix A: Calibration between the displacement (or electrode separation) and the voltage applied to piezoelement

Experimentally, distance between two electrodes is manipulated by applying a voltage to the piezoelectric actuator. Adopting the procedure from ref. [67], exponential dependence of the current on the vacuum gap is used to make a rough calibration of the gap size. Linear relation between the piezoexpansion that means the voltage at piezo (${V}_{\mathrm{piezo}}$) and gap size ($\Delta$) (i.e. electrode separation or displacement) helps to define a simple calibration constant $(c)$,

$$c= \frac{\Delta }{{V}_{\mathrm{piezo}}}.$$

(A1)

Tunnel current (I) between two electrodes which are separated by a distance $\Delta$ (provided the applied voltage V₀ is smaller than the work function of the electrodes) can be expressed as [68]

$$I \left({V}_{0}\right)=k{V}_{0}{\mathrm{e}}^{-2\Delta \sqrt{2m\phi /{\mathrm{\hslash }}^{2}}},$$

(A2)

where m is the mass of the electron, $\phi$ is the work function of the electrode, $k$ is a constant related to the area of the electrode and to the electron density of states at the Fermi level and $\hslash$ is the reduced Planck constant. Resistance of the tunnel junction is thus,

$$R= {R}_{0}{\mathrm{e}}^{2\Delta \sqrt{2m\phi /{\hslash }^{2}}}.$$

(A3)

Combining eqs (A1) and (A3), we can write,

$$R= {R}_{0}{\mathrm{e}}^{2{c}\mathrm{V}_{\mathrm{piezo}}\sqrt{2m\phi /{\hslash }^{2}}}.$$

(A4)

Slope m of the logarithmic resistance with respect to the piezovoltage is thus

$$m=\frac{\partial (\mathrm{ln}R)}{\partial {V}_{\mathrm{piezo}}}=\frac{\partial (2{c}\mathrm{V}_{\mathrm{piezo}}\sqrt{2m\phi /{\hslash }^{2}})}{\partial {V}_{\mathrm{piezo}}}= \frac{\sqrt{2m\phi }}{\hslash }2c ,$$

(A5)

$$ {\text{Calibration}}\,{\text{constant}},c = \frac{m*\hbar }{{2\sqrt {2m\phi } }}. $$

(A6)

This expression is indeed very simple and clean electrodes follow an exponential behaviour (shown in figure 7a) of the current as a function of ${V}_{\mathrm{piezo}}$, which would make this a suitable method to calibrate the gap size with voltage applied to the piezoelectric actuator. A histogram of calibration constant (shown in figure 7b) is prepared using slopes, calculated from a large number of conductance traces. Then, most frequent $c$ value is obtained by Gaussian fitting to this histogram and is used further to calibrate. However, major source of inaccuracy in this method comes from the value of work function used which is very much sensitive to the fine-structure details of the junction [69] and also the local environment [70].

Figure 7

(a) Conductance traces of gold atomic junction where conductance is presented in terms of piezovoltage (V_piezo). Region used for calculating the calibration constant is marked by the black dash line. (b) Histogram of the calculated calibration constant, obtained from 10,000 traces of clean gold junction. Red line plot is the Gaussian fitting which elicits the most possible calibration constant ~ 0.053 Å/$\mathrm{mV}$.

Appendix B: Gold atomic junction at higher conducting configuration

See figure 8.

Figure 8

One-dimensional conductance histogram of the gold atomic junction till conductance value upto 20G₀, constructed from the same 10,000 traces used in figure 4, using 200 bins. High conductance peaks can be resolved even upto ~ 20G₀.