Tunneling regime

Since our motivation was to use the break-junctions as the electrodes, the tunneling regime is the most important in our works. According to Eq. 2.4 in chapter 2, the logarithm of conductance should depend linearly on the distance (also the motor counts or the time in our measurement, because of the direct relationship between them). This result has already been obtained in vacuum, in ambient and at low or room temperatures ^15-18.

But in aqueous condition, the tunneling current is not the only contribution to the conductance, as we discussed in the previous section. So, the conductance behavior in the so called “tunneling regime” is more complicate.

Figure 3.3 shows typical resistance traces versus distance of a break junction in aqueous solution. We used TE buffer as the solution since the ions in TE buffer is useful to keep the B-conformation of the DNA structure stable. The ions in the aqueous solution enhance the influence of the ion diffusion effect in the conductance.

As shown in Figure 3.3, the logarithm of the conductance has a linear relation to the distance of the electrode junction when the distance is smaller than 0.6 nm (region I).

For larger distance, the current from the electrochemical effect plays the dominant role in the charge transport between the two electrodes, which happens not only at the very end of the tip but the whole gold electrodes. Therefore, the distance dependence of this signal is much less to that of tunneling current, which is exponentially attenuated with the distance. That’s why in region II, the resistance remains roughly

linear and reversible when the scan voltage is below 200 mV, as discussed in the previous section, we conclude that no new material is deposited. The leakage current does not break the MCBJs.

Since the DNA molecules we used are more than 1nm long, the d > 0.6 nm region is the most interesting region for us to investigate in detail. Although it is possible that the DNA molecules do not bind to the very end of the electrodes, making the binding of DNA to the electrodes possible even when the distance is less than 0.6 nm, the tunneling signal of the metal electrodes in this case is so high that it might exceed the charge transfer mediated by DNA molecules.

0.0 0.5 1.0 1.5 2.0

100k 1M 10M 100M 1G 10G 100G

R/ Ω

d/nm

close open

Region I Region II

S4-3

0.0 0.5 1.0 1.5 2.0

100k 1M 10M 100M 1G 10G 100G

R/ Ω

d/nm

close open

Region I Region II

S4-3

R[

Ω

d[nm]

Figure 3.3: Typical open (black) and close (red) curves of break junction in TE buffer solution. In the open curve, it is hard get correct distance between electrons from the motor counts. At later stage of the opening process, the resistance is increased to a certain plateau resistance (we call it Rp). Then the junction is closed (shown as the red curve). The resistance will not change until the distance is lower than 0.6 nm. When the distance is lower than 0.6 nm, the logarithm of conductance has linear relation to the distance of the electrode junction.

These results are very important for the further measurement of DNA conductance

in aqueous solution. We can assume that if the conductance mediated by DNA is smaller than that of the electrochemical effect, the charge transfer signal will be covered by the one from the solution. On the other hand, if the conductance mediated by DNA is higher than that from the electrochemical effect in the buffer solution, it is possible to obtain useful signals in solution. This part of work will be discussed in chapter 4.

As the principle of break junction, we can get the distance-counts relationship from the conductance vs. counts curve, from Eq. (2.5), given the work function. But the work function depends on the environment even for the same material. Many experimental and theoretical investigations suggest the work function of gold (bulk and nano tips) in aqueous solution is lower than that in vacuum^{10, 11}. In this experiment we can compare the work function in different conditions from Eq. (2.5).

*φ

From this equation we can easily get:

K2

where K and k are the slopes in conductance vs. distance curves and conductance vs.

motor-counts curves, respectively. φ0, K0 and k0 are the values in vacuum or air, while φ, K and k are values in solution. It is also assumed here that the counts-distance relationship should be same for the same junction. So comparing the k values in different environment, we can get the comparative value of the work function in different conditions.

We compare the slopes of logarithm in air condition and in water conditions, and found the obvious difference between them, as showed in Figure 3.4. Give the measured value k0 in air and kin water,

that in air condition in our experiment. This result is coincident to the experiment and theoretical results of the former works ^{10, 11}. We also compare the work function in solution in different bias voltage. It shows that the work function is independent to the bias voltage when the bias voltage is below 0.4Ｖ.

-316.0M -312.0M -308.0M

1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

-304.0M -300.0M -296.0M

G/Go

Motor Counts

in buffer solution in air

In buffer

In air

-316.0M -312.0M -308.0M

1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1

-304.0M -300.0M -296.0M

G/Go

Motor Counts

in buffer solution in air

In buffer

In air

G[Go]

Figure 3.4: Logarithmic plot of closing curves in air (red) and in water (black) in the tunneling region, along with exponential fits used to estimate the counts–distance relation. Only two curves for each condition are selected here for the purpose of clarity. The dashed lines are linear fit of the curves. It is clear that the slope of the fit line in buffer solution is smaller than that in air with the same junction (s4-6).

We should point out that this simple principle is not easy to carry out in our experiment. The mean difficulty is to measure the same junction in all conditions (in buffer solution, in air and in vacuum). The life time of one junction is not long enough especially in aqueous solution.