The feedback controlled electrobreakdown processes are performed by a measure-ment control program developed by myself. It was written in C# object oriented programming language. The breakdown timescale during the electromigration in metals is few tens of milliseconds [174], it would not require fast operation. How-ever this program is also used for the electrobreakdown of graphene stripes whose breakdown timescale is several orders of magnitude shorter. It is in the order of few 100µs [116, 175], thereby fast feedback control is needed. During the bias voltage ramp the acquisition rate of resistance must happen suciently frequently to detect and react to the sudden change. When the critical resistance jump is observed the bias voltage has to be dropped to low voltage region. However the specications of the DAQ and the PC control do not allow fast feedback process, the communication between the two devices could take even several10ms. If a high voltage was applied on the sample during this period of time, the breakdown could proceed further. In order to eliminate this kind of delay time of the feedback control, the breakdown process is performed by voltage pulses. The pulses are applied periodically, whose periodicity has a minimal value of≈20ms which corresponds to the aforementioned limit of the communication.
Figure 3.3.a shows the electromigration process of a800nm long and100nm wide silver nanowire performed by my measurement control program. The breakdown was performed in cycles and after each cycle the resistance was a bit higher (see Figure 3.3.b). In this specic case after 80 cycles I increased the resistance from 62 Ω to 900 Ω. The cycles mean voltage ramps until the precursor of the breakdown, which is a sudden fall in the current. However, in contrast to the similar measurement protocols, in case of my program the voltage ramp is not the continuous increase of bias voltage, rather discrete points as it can be seen in the inset of Figure 3.3.a, which shows the last part of the rst cycle. Each point corresponds to an applied voltage pulse. The height of the pulse (Vhigh) is presented on the x-axis, while the current measured during the pulse (Ihigh) is indicated on the y-axis. These pulses are applied
Figure 3.3: Feedback controlled electromigration of a silver nanowire performed by voltage pulses. The amplitude of the voltage pulse (Vhigh) was increased until the pre-cursor of the breakdown, afterwards a new voltage ramp cycle was started. Meanwhile the current was measured simultaneously (Ihigh). The inset shows the last part of the rst cycle. b) Evolution of the low bias resistance during the breakdown cycles. The initial resistance was 62 Ω and after 80 cycles it was increased to 900 Ω. Schematics on the top illustrates the structure of the silver nanowire at the dierent stages of the breakdown process.
periodically and these periods are the basic units of my program. In each period the resistance of the junction is calculated and the pulse amplitude is raised by a xed value (Vstep = 1mV) if there was no feedback event. In the other case, if feedback event is detected the next pulse is applied with low amplitude (Vlow) and thereby a new cycle starts. The schematics at the top of Figure 3.3.a illustrate the structure of the silver nanowire at the dierent stages of the electromigration. If the resistance of the metal junction is close to the conductance quantum, 1G0=(12.9 kΩ)−1, the two sides are connected by only few atoms [176]. Applying this electrobreakdown technique I can break a nanofabricated 100nm wide and 400−1000nm long silver nanowire in controlled way with100% yield. In case of asymmetric silver structure, presented in Chapter 4, the yield of the electromigration is lower due to the better
heat conduction of the electrodes and the mechanical stress buildup along the wire [177], but it is still about50%.
The block diagram of my measurement control program is shown in Figure 3.4.a.
After the rst initialization of variables and input/output channels (Panel 1-5) the program enters into the periodic pulse generation routine which is realized by a software timer (Timer tick panel). A period starts with applying the output voltage signal, which is illustrated on the Signal generation panel. The breakdown is induced by the voltage pulse in the middle of the signal. Before and after this voltage pulse the resistance is measured at low voltage level (Rlow) by recording I-V characteristics with Vlow=10−100mV amplitude. In the rst cycle the height of the pulse (Vhigh) is the same as the amplitude of the triangular signals (Vlow). The length of the pulse (τpulse) can be tuned from few µs to several seconds, while the low level I-V measurements have xed1ms length. Therefore the total length of the signal is in the order of few ms if the pulse length is not longer than1−2ms. While the output signal is applied the current is measured simultaneously. After applying the output signal the program reads the acquired current data and calculates the relevant parameters such as Ihigh, Rhigh, Rlow. After plotting and saving the data the program check whether the resistance reached the threshold limit. The threshold value means the desired nal resistance value, where we would like to stop the breakdown procedure.
If it is false the program stays in the loop and checks the feedback condition. Finally according to the feedback the new output signal is generated and new period begins.
If the junction resistance exceeds the threshold value the timer is stopped and no other pulse is applied. The timer interval must be longer than the sum of the length of output signal and the calculation time, but it has the minimum value of20ms due to the aforementioned communications between the instruments.
The feedback condition corresponds to the relative change of one of these three quantities: ∆Rhigh\Rrefhigh,∆Rlow\Rreflow or∆Ihigh\Ihighref . Before starting the electromi-gration we have to choose which parameter is monitored. If the relative change of the chosen parameter exceeds a critical value, feedback event occurs. This critical value can be set on the graphical user interface. In case of the metal junctions there are no substantial dierences between these three quantities, for graphene this issue is studied in Section 5.4. Typically a smaller value (1-5%) must be given at the begin-ning of the process and as the resistance grows, it can be increased. Furthermore, in case of graphene large resistance changes can be caused by the Joule-heating induced cleaning, which is easily confused with the breakdown precursor. In order to avoid the false feedback events the resistance changes can be calculated by dierent refer-ence values (initial value, global extremum or extremum of the last few hundreds of mV). If we would like to suppress the slow resistance changes due to other eects, like
Joule-heating induced cleaning, the reference value should be the maximum current or minimum resistance of the last100−200mV voltage interval.
Since the applied waveform has complex shape it is essential to synchronize the timing of the output and input channels. It is realized by a common hardware start trigger. Both the input and the output tasks start to run if a rising edge appears on a programmable function interface (PFI) digital port. When the sampling is over, both tasks wait for another start trigger, meanwhile the output is set to zero bias.
The trigger signal is generated by the program at the end of the timer period when the new output signal is generated. Figure 3.4.b shows the graphical user interface of the program. The parameters, such as Vlow, Vstep, τpulse, threshold resistance, feedback conditions etc. can be set here. During the breakdown procedure the actual resistance and current is plotted on a graph and the breakdown can be stopped manually as well.
Besides the feedback controlled electrical breakdown process, I also implemented the further parts of sample characterization into the measurement control program (see Figure 3.4.a). The measurement automation enables us to perform the electrical characterization quicker and more uniformly which results in higher statistics. In case of graphene devices, discussed in Chapter 5 and 6, before the electrical breakdown it is necessary to measure the back gate dependent resistance of the graphene to determine its quality. During the gate measurement the back gate voltage, supplied by a DAQ controlled voltage amplier, is varied, while I-V curves are measured at each gate voltage. The frequency and the amplitude of the gate and bias voltages can be set up on the graphical interface. The detailed analysis of the gate depen-dent resistance is discussed in Section 5.1.3. After the breakdown of the metal or graphene constriction the electrical characterization of the tunnel contact follows by measuring I-V traces. During these measurements very low current signals (few tens of pA) have to be acquired, thus the proper shielding and low noise setup are needed.
These measurements can be performed by either multi-channel or Femto DLPCA-200 current ampliers. The detailed study of the tunneling measurements is presented in Section 5.2.2. The same panel was used for the electroforming process or record-ing hysteric memristor I(V) traces if the bandwidth of this setup (≤ 500kHz) was suitable. The characterization of resistive switches requires various triangular sig-nals, for this reason on the graphical interface we can set several parameters, such as the frequency, initial voltage sweep direction or the positive and negative bias limits. After stable resistive switching was established by the I-V measurements, the voltage dependence and the timescales of switching mechanism were investigated by pulsed measurements. During this study a series of voltage pulses are applied while the current is recorded real time. On the interface of the program we can set
Figure 3.4: a) Block diagram of the measurement control program used for the elec-trical characterization and electrobreakdown process. b) The graphical user interface of the breakdown panel.
among others the length and the amplitude of the pulses or the duty cycle. In case of SiO2 resistive switches due to the high ON/OFF current ratio, the memristor I-V or pulsed measurements can be performed by only the multi-channel current amplier.
The measurement control program can partially process the measured data as well.