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Lab Assignment: Quantized Conductance LabQuantum mechanics states that electrons behave like waves. Howver, in macroscopic systems, we rarely observe their wavelike properties. For example, the electron transport in bulk metal can be well-expalined by the classical Drude's model![]() TheoryPlease read the references(see the three attachments at the bottom of this page) to understand the quantized conductance through classical Physics (Drude model) and Quantum Physics. Quantum conductance, denoted by the symbol G0, is the quantized unit of electrical conductance. It is defined by the elementary charge e and Planck constant h as G0=2e^2/h=7.7480917310(18)×10−5 S≈1/13 kΩ More information can refer to Wikipedia: https://en.wikipedia.org/wiki/Conductance_quantum![]() ![]() ![]() Setup and calibrationBefore the experiment, you need to understand the theory and principle of the experiment. You will be supervised by a graduate student to use the experimental setup and collect data. Please follow the instruction of the graduate student. You will learn: 1. How to prepare sharp(a few nanometer at the tip) gold tip and clean both gold tip and gold substrate 2. How the experimental setup works (electric circuit, noise reduction...). 3. Data acquisition using DAQ card (from national instrument) and customed labview programs 4. How to repeatedly acquire a large number of the conductance-distance (I-d) curves. 5. Statistical data analysis, build histogram, perform Gaussian fits to the histogram. 6. Develop understanding of quantum mechanics | ||||||||
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Part A: Data CollectionObserve quantum steps in the current vs distance (I-d) curve. You should be able to see at least one conductance (conductance=current/voltage) step at G0=2e^2/h≈77.5 microsiemen (uS) or R0=1/G0=12.9 kΩ, There are typically more than 1 steps, appearing at 1G0, 2G0, ... Learn how to optimize the experimental conditions, i.e., tip approach and withdraw speed of the tip, applied bias, environment (in air and in solution). Build histograms from 50, 100 and 200 I-d curves at 0.1V bias. Compare the shape of peaks and understand how the statistics play the role. Collect about 200 withdraw conductance curves (more is better) at different biases, 0.05V, 0.1V, 0.2V.Part B: Data AnalysisYou will use the labview programs to build conductance histograms from hundreds of I-d curves you collected. You need to understand how to covert the current unit Amper to quantume conductance unit G0 and how to convert individual I-d curves to G-d curves, then to a conductance histogram (pay attention to the bin size). After buding conductance histograms, you will perform Gaussian fits to the conductance peaks in the histograms. You will discuss the goodness of fit using reduced chi-square.Materials and Equipment:The list of necessary equipment is:
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Write Up
You need to explain the experiment principle and theory, quantum conductance, quantum tunneling.
The experimental setup: Simple diagram of electrical circuit of electrical measurement. How the gold point contact was repeatedly formed, the Piezoelectric effect. The precise control of distance by Piezo actuator.
Results and discussions:
The cleanness of the tip and substrate is important to achieve better results. The size of gold atom? Why the electron transport through the gold wire with the width of one or a few gold atoms be limited?
For individual conductance curve (or G-d cruve), explain why the current decrease with the withdraw of the tip. Explain the quantum steps, the sharp drop of the conductance after the step, also the quantum tunneling current between two nanoscale electrodes after the point contact is broken.
Other interesting discovers in your experiments.
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