• Electrical and Mechanical noise reduction setup. Also read this link.

Drude's model

In this lab, you will explore the phenomena of quantized conductance in a gold quantum point contact repeatedly created at room temperature. From the experiment, you will understand the importance of quantum mechanics at the nanoscale. You will also learn the typical electrical characterization techniques in condensed matter Physics and nano science fields.

More information can refer to Wikipedia: https://en.wikipedia.org/wiki/Conductance_quantum

You should also read refs about quantum tunneling. Quantum tunneling happens when the two metal electrodes are in a distance of a few nanometers. You will observe the quantum tunneling current right after the breakage of the gold point contact. Based on quantum tunnleing, Scanning Tunneling Microscope (STM) was invented and STM can help us to see individual atoms at real space.

• Current amplifier for small current measurement (understand pA, nA and uA current scales)
• Stepper motor for low precision movement of gold tip (about 100 nm resolution).
• Piezo driver and piezo actuator to control the high precision movement of gold tip (about 0.1 nm resolution).

• Data acquisition setup, labview program to control the hardware

Quantum conductance can also refer to Wikipedia: https://en.wikipedia.org/wiki/Conductance_quantum

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).

• Piezo driver and piezo actuator to control the high precision movement of gold tip.

The experimental setup: 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.

Explain why the current decrease with the withdraw of the tip, the quantum steps, and the tunneling current between two nanoscale electrodes after the point contact is broken.

Other interesting discovers in your experiments.

• 1.4765331-Quantum_step_ref1.pdf: ref 1

• Quantized_Conductance_ref_2.pdf: ref 2

• laetitia-report_ref_3.pdf: ref 3

Lab Assignment: Quantized Conductance Lab

Theory

Setup and calibration

Part A: Data Collection

Part B: Data Analysis

Materials and Equipment:

The list of necessary equipment is:

• Current amplifier for small current measurement
• Stepper motor for low precision movement of gold tip.
• Piezo driver and piezo tube actuator to control the high precision movement of gold tip.
• Data acquisition setup, labview program
• Electrical and Mechanical noise reduction setup

Title

Article text.---+ Lab Assignment: Cosmic Ray Lab

In this lab you will measure the cosmic ray flux as a function of the zenith angle and determine its shape by fitting your data with a function that represent theoretical expectations. Does it conform to those expectations?

Setup and calibration

Before you begin your flux measurements you should become familiar with the experimental apparatus. To do this we'll first perform a calibration of the Cosmic Telescope, basically determine what high voltage to use for the PMT input and then take measurements of count rates before we plunge into our flux measurements.

First: Connect the HV supply to the PMTs and use the oscilloscope to find the output signal from the PMT. You will likely need to adjust the time scale or sweep (horizontal axis) and the voltage scale (vertical axis) on the scope. We expect output signals from the PMT to be 10-20 ns long and the output voltage to be a few millivolts for the Cosmic Ray telescope setup. You'll also need to set up the scope to self trigger on the output pulse; set the trigger to trigger on the channel the PMT output is on. Note that the output will only trigger the scope if it exceeds a set discriminator (disc) threshold (the "level" knob located on the trigger portion of the scope). Adjust the level knob to some fraction of the PMT's average output voltage. Since our PMT output voltage is negative you'll want to set the threshold below 0 V to display any events.

Once you have your scope displaying multiple PMT pulses and have ascertained a reasonable value for your discriminator threshold you can take the PMT output and redirect it to the discriminator NIM module. As with the disc threshold on the scope the disc threshold on the NIM Module is used to filter out noise pulses from signal pulses. You can adjust the disc threshold on the NIM module by turning the tiny set screw hidden inside the whole labeled "THR". The threshold voltage can be read with a multimeter with leads connected to ground and the disc reading pad.

Before you proceed with the experiments, PART A and B below lets first determine the proper input voltage to run the PMTs at, given the chosen disc threshold settings that you've selected. We do this to insure that the PMT pulses and thus count rates are stable across a sizable range of input voltages which may drift over the course of the experiment. We'll do this by measuring the count rate as a function of input voltage and look the input voltage that corresponds to start of the count plateau.

Begin by setting up the cosmic telescope by connecting the PMT output to the NIM discriminator then connect the disc output to the counter. Set the counter time window to collect a few 100 events. Make sure that you are counting real signals by insuring that the disc is set sufficiently high, check with the scope. Take count reading at various PMT input voltage and plot the results. Please DO NOT go beyond 2000 VOLTS. What you should see is that the count rates varies a lot when the voltage is set too high or too low. You'll want to use the a random event source, like the Sr 90 to insure you have real triggers instead of noise with proper disc setting. DO this for BOTH PMTs and provide in your lab report the plots you create.

Part A: Observation of Poisson and Gaussian distributions in radioactive decay of Sr 90.

You will only need to use one of the scintillator/PMTs for this part of the experiment. Decide on how to best setup your cosmic telescope viz. discr setting and HV input from the calibration setup above.

Using a random source, that ⁹⁰ Sr is as good a random source as any. Take 100 measurements with the count time interval set to collect on average 1 event per time interval. Histogram the results. Your histogram will have on the horizontal axis the number of counts per interval and on the vertical axis the number of times you record a particular number of counts. How is the data distributed? Then repeat the exercise but now use 100 events per time interval. You can adjust any of the experimental conditions you control to achieve these measurements. You can change the distance between the source and the scintillator or adjust the discriminator level. What ever you do make sure you retain the randomness of the events by insuring you are not picking up PMT or other sources of noise. There is no need to fit the distributions in this part of the lab but please do feel free to comment on what you observe.

Part B: Cosmic Ray Flux

Using both PMTs, both of which you should have already plateaued and are running in optimal configuration for your experiment, perform the flux vs. angle measurement. Here you'll need to use the coincide NIM module inline between the discriminator outputs and the counter. The coincidence counter will trigger and output a NIM pulse when it detects two NIM pulses. This particular coincidence counter uses the size of the input pulse to select the size of the window it will use to determine if there is a coincidence, check the manual for the device if you are interested in details, something you'll have to find online. As you take data do plot the distribution. In the SLAC paper, linked below you'll see an estimate of the count rate. Make sure your count rate is consistent with your expectation. It typically takes 20 minutes to take one reading and you don't want take 10 of these 20 min reading to find out you did something wrong. and fit a function form to your data and discuss what you see. There is a nice write up on this part that you can access as a reference. See document from SLAC linked below.

Equipment:

Our Cosmic Ray Telescope consists of a piece of plastic (organic) scintillator made out of material that when exposed to charged particles reacts by emitting light. The light travels through the transparent plastic material, reflecting from surfaces until eventually some of the photons emerge at the front face of the PMT. The PMT is an electronic device based on the photoelectric effect that first converts a small number photons, into an amplified electrical signal sufficiently large to be easily recorded by standard laboratory equipment. You should provide in your write up an a short description, longer than this, of how this works. You should also include a paragraph or two about cosmic rays, what are they where do they come from and what does our detector actually "see".

The list of necessary equipment is:

• Scintillation counters each with its own PMT (Cosmic Ray Telescope: Note for this experiment you will need to use both counter)
• High Voltage Supply (to power the PMT)
• NIM module Discriminator (to decide whether the signal is a true PMT pulse and not noise)
• NIM module Linear Fan In Fan Out (this allows you to duplicate RF signals from the PMT and NIM modules
• NIM module Counter/timer (to count the number of NIM output signals)
• NIM module Quad Coincide (produces a NIM output when two signal arrive within an interval of time determined by module's internal logic)
• Oscilloscope (to examine the output of the PMT and help set discriminator levels etc.)
• ⁹⁰Sr radioactive source

Include in your introduction a breif description of the important components of the apparatus you used to conduct this experiment:

1. The Scintillator: Look up references on how organic or plastic scintillators work. The scintillator you are using is I believe a Bicron BC 400 series plastic scintillator
2. The Photomultiplier: Describe how a PMT works. You should provide as much detail as you need to demonstrate that you understand how this device functions and why it is used.
3. The High Voltage supply, Just noting that one is used is probably sufficient.
4. The data acquisition equipment: The various NIM modules you used in your experiment. You should be familiar with the operation of each and report on their use and function in your write up.
5. The Oscilloscope: No description required but you may want to explain who you used it.

Analysis

Histogram your flux measurments, number of counts vs. angle w.r.t zenith and fit the distribution with an appropriate probability distribution funciton. Discuss the results and the goodness of fit.

GradingRubric

• slac-tn-95-001.pdf: SLAC Cosmic Ray Telescope paper

-- Jorge Rodriguez - 2018-01-08

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