Formation mechanism and resistance fluctuations of atomic sized junctions

In this thesis we focus on:
(a) Feedback controlled electromigration in four-terminal nano-junctions, where a new technique to control electromigration in Au nano-junction is presented. The observation during electromigration in nano-junction is discussed.
(b) Scaling of 1/f noise in tunable break-junctions, where 1/f voltage noise of gold nano-contacts formed by electromigration and mechanically controlled break-junctions is studied. The voltage noise is measured for resistance value of the nano-contacts from 10Ω (many channels) to 10 kΩ (single atom contact).
We present a successful technique to implement smooth EM in gold nano-junctions. By using a fast feedback voltage source (response time < 0.5 μs) over a four-terminal nano-junction, the voltage drop over the junction can be exactly measured and controlled. Hence the current density in the junction, which is the key parameter of EM, is under control as well. This technique solves the previous problem of thermal runaway in
the junction. It highly increases the speed and the success rate of nanogaps formation. During EM we are able to evaluate the temperature in the junction. In our junctions the temperature required to trigger EM is over 100 °C. If we think about molecular electronics, the usual way is to assemble the molecules on the junction surface before EM. From our estimation of temperature the molecules may get destroyed during EM. A transition from
diffusive to ballistic regimes is observed while the junction cross-section is shrunk by EM. In quasi-ballistic regime we can not estimate the temperature by junction resistance measurement, because the resistance depends only slightly on temperature in quasi-ballistic regime. We expect that the temperature is still enhanced in the junction. But at the very small constriction where the gap is formed, there is no enhancement of temperature.
Hence we suggest to assemble the molecules after the first transition into regime II, then open the gap by starting EM again. Very surprisingly, EM proceeds in the quasi-ballistic regime as well. However EM is much slowed down there. The decrease of conductance in quantized steps of G0 is observed at the end of the regime II.
Due to smooth EM in nano-junctions, we are able to investigate resistance fluctuation (1/f noise) in the junction as function of junction resistance. The 1/f noise is measured and compared in both electromigrated junctions and MCBJ (Mechanically Controlled Break Junctions). The scaling of 1/f with junction resistance is very similar in both electromigrated junctions and MCBJ. The cross-over from diffusive to ballistic regime is visible in measured noise magnitude. The noise magnitude scales with junction resistance in power 3 in diffusive regime and power 1.5 in ballistic regime. We are able to conclude the 1/f noise in the junctions is generated in Bulk, which is true even for the very small junctions where only few conduct channels available. Hooge's parameter α extracted from the noise data compares very well with parameters reported in the literature.
This thesis is structured as follows:
• Chapter 1 gives a brief review about the conductance of metals in diffusive, ballistic and quantum regimes. The theory background for electromigration and its driving force is introduced. As the basics to understand noise measurements, we discuss two types of noise, i.e. thermal noise and 1=f noise, which we measured in our experiment. The mathematic basis for noise analysis is given as well.
• In Chapter 2 we describe first the general sample fabrication methods and processes. As an important technical basis in our experiments, we presents our new technique of feedback controlled electromigration in details. The setup to perform electromigration and its calibration is described as well. For noise measurements we explain the procedure and setup for noise measurement. The important step of setup calibration is discussed in depth.
• In Chapter 3 we discuss the physical aspects more in depth in nano-junction during the narrowing of the junction cross-section by electromigration. We show the results of noise measurement in electromigrated and mechanically controlled break-junctions. The transition from diffusive to ballistic regime in nano-junction is observed during electromigration and proved by the noise measurement.
• Chapter 4 summarizes this thesis. The ideas and possibilities to explore further experiments based on our current experience are suggested.