conductivity, the dierence between the lowest and highest value is about2eV. The nite element simulation further veried our proposal that in ambient electroburn-ing takes place, while in vacuum the sublimation of the carbon atoms breaks the junction.
κg,ρgox 2κg, ρgox 0.5κg,ρgox
κg (WK−1m−1) 1000 2000 500
ρgox (1·10−8 m2K/W ) 1 1 1
Ea (eV) ambient 1.19±0.23 1.10±0.20 1.27±0.25 Ea (eV) vacuum 8.1±1.8 6.9±1.5 9.0±2.0
Table 5.5: The corrected activation energy values considering the exact device geom-etry in nite element simulation.
resistance the temperature prole around the constriction will be narrower and it reduces the cleaning eect.
Figure 5.17.a shows EB process of a pre-cleaned sample by applying 6V bias voltage in vacuum. The slight variation of the resistance curves indicate that most of the contamination is removed, but there are still some kinks. The Joule-heating caused resistance growth at high bias can be clearly seen. The corresponding current (Ihigh) is shown in Figure 5.17. b, the last 150mV is plotted in the inset. It shows nearly monotonically increasing behavior, but as the precursor of the breakdown the current drops o in the last few tens mV. To control the electrobreakdown in more reliable way I examined which parameter is the most sensitive to the breakdown event. To reduce the eect of cleaning, current saturation or any long-term resistance change it is a common method to monitor the change of the resistance or current only in the last few hundreds millivolts. The relative change of Rlow, Rhigh, and Ihigh in the last 100mV bias window is presented in Figure 5.17.c as the function of the pulse amplitude. In case of Rlow there is no observable precursor before the breakdown. It could be the consequence of the higher noise level of Rlow. In contrast,
∆Rhigh (middle panel) shows less variation, but it has a constant oset due to the Joule-heating. A sudden increment can be detected right before the breakdown, however despite the pre-cleaning procedure, it is still in the range of the uctuations.
Finally the current change is presented in the third panel, which shows the most robust precursor of the breakdown. It is closely related to∆Rhigh, but it scales down with the ratio of the examined bias window (100mV) and the actual bias. At low bias, where the cleaning is the dominant eect, larger resistance change is needed to decrease the current by1−2 % than in larger voltage regime where the breakdown occurs. In conclusion the high level current is the best parameter to monitor if we would like to actively control the breakdown process.
Besides the feedback method, the sample geometry was also optimized to reduce the eect of cleaning. By using bow-tie geometry other research groups could control the breaking process [175, 251]. It could be related to the more localized heating, the temperature prole is narrower and smaller graphene part is involved in the cleaning before the breakdown. The samples with bow-tie constriction were made with dierent narrowest cross-section from 100nm to 350nm with 50nm steps (see Figure 5.3).
Figure 5.18.a shows the current during the controlled breakdown of a bow-tie sample with minimal cross-section of 250nm under ambient condition. The rst cycle is highlighted by red. The breakdown was performed by 100µs long voltage pulses. In the rst cycle the feedback event occurred when the current dropped by 2% in the last 100mV. As the EB progressed higher current change value had to be
Figure 5.17: a) Measured low and high level resistances and b) high level current during the electrobreakdown process of a cleaned graphene sample. The resistance curves show only slight changes. c) Relative changes of the resistances and the cur-rent in the last 100mV increment of the pulse amplitude. The measurements were performed by me in Budapest, the graphene was grown in Basel and the sample was fabricated by me in Budapest at MTA EK MFA.
set, otherwise the resistance did not increased from cycle to cycle. As the graphene connection gets narrow both the threshold voltage and the current decrease. Figure 5.18.b shows the power of pulses (P=Ihigh·Vhigh) during the same EB process. The power also decreases in every cycle.
Before the EB, there was no cleaning process. Although the sign of the cleaning can be observed (kinks in the red curves), but it is below the feedback limit. The electrobreakdown processes were controllable independently of the minimal width.
The new sample geometry allow us to control the breakdown process without any hazardous cleaning pre-treatment.
Figure 5.18: The recorded a) current and b) power during controlled electrobreakdown of a bow-tie shaped constriction with minimal width of 300nm under ambient con-dition. Both the current and the power drop o when the breakdown process starts.
c) Evolution of the low bias resistance during the breakdown cycles. d) The critical power of the rst bias ramp cycle as the function of the minimum cross section of the bow-tie constriction (dots). The lines correspond to the simulated isotherms on the power-width graph. The measurements were performed by me in Budapest, the graphene was grown in Basel and the sample was fabricated by me in Budapest at MTA EK MFA.
As we saw in Section 5.3, the main parameter of the breakdown is the temperature and thus the applied power. To verify this phenomena for the bow-tie samples as well I collected the critical power of the rst cycles during the EBs. All measurements were performed under ambient conditions and 3-5 samples were broken at each constriction widths. The geometry of the graphene is well dened only before the rst feedback
event, thus the further cycles are not investigated in this regard. The pulselength was 100µs for all cases. Figure 5.18.c shows the measured power (black dots) as the function of the constriction width. A clearly visible trend is observed, the wider samples, the higher power is needed to induce the breakdown process. In order to interpret this result I have calculated the temperature by nite element simulation using the exact geometry. The colored lines in the same gure show the isotherms.
The experimental data t well in the range of 950±100◦C. This nding conrms that the graphene breaks around at xed temperature if the pulse length is also xed.
The controlled electrobreakdown allows us to increase the resistance of the graphene junction from step to step. However as the resistance raises large current uctuation and jumps appear and the process becomes less controllable (see in Figure 5.19.a).
This behavior could be caused by the uctuation of carbon atoms at the nanojunc-tion region or the contaminananojunc-tion of the nanogap. The current change ratio has to be set to high value (e.g. >80 %) or the feedback control has to be switched o to increase the resistance further. Finally the formed gaps typically have lower resis-tance than we get by the uncontrolled breakdown. Figure 5.19.b shows a tunnel I-V characteristic whose low bias resistance is ≈ 8.9MΩ and the distribution of tunnel resistance for larger statistic is shown in Figure 5.19.c, they are in the range of1MΩ -1GΩ. To determine the cleanness of the nanogaps, gate dependent I(V) character-istic measurements were performed at room temperature. However the contacts were not stable during the measurements, there were some structure in the gate responses, but they were not reproducible. For more accurate investigation low temperature measurement is needed to suppress the thermal instability.