Shot Noise Thermometer

Outline

Introduction

The Shot Noise Thermometer, or SNT is a primary thermometer based on the noise from a tunnel junction that was recently invented here at Yale.  The proof of concept results were published in the journal Science in June of 2003, and received some attention in the press.  Below we explain the basic operation of the SNT and provide some other useful information about metrology and thermometry.

Noise and the SNT

Cartoon depiction of a tunnel junction.  An external bias forces a direct current to flow, which causes a noise signal from which the temperature may be determined.

All electrically conducting materials at finite temperature exhibit electrical fluctuations from the thermal agitation of the electrons in the material. These fluctuations manifest themselves as white noise, and have a total power proportional to the temperature of the material. Johnson noise thermometry, which has been the subject of decades of study, involves measuring the power of this signal and calculating the temperature of the material being measured. Johnson noise thermometry is made challenging by the fact that the signals involved are very small. Accurate measurements of Johnson noise signals require the use of high gain amplifiers, which can be very difficult to calibrate accurately. Any error in the calibration of the amplifier translates to an error in the measured noise power at the input and hence an error in the measured temperature. This problem becomes more pronounced at higher frequencies, which limits significantly the speed with which a traditional Johnson noise measurement can be done accurately.

Atomic force microscope (AFM) image of aluminum-aluminum oxide-aluminum tunnel junction used for SNT experiments.  Note the double image from the two evaporation angles used in fabrication. Click here for more fab images

At the heart of the Shot Noise Thermometer (SNT) is a tunnel junction. A tunnel junction consists of a pair of metal electrodes separated by a thin insulating film. When current flows through the junction, electrons cross the insulating film using quantum mechanical tunneling. The current in a tunnel junction thus consists of a sequence of many single-electron current pulses. In many ways a tunnel junction acts just like a resistor, and like any resistor, when left alone it produces noise that is proportional to the temperature of the junction (Johnson noise). In addition to Johnson noise, however, tunnel junctions produce another kind of white noise called shot noise. Shot noise is present in any device where current consists of discrete electron tunneling events such as an electron passing across the tunnel barrier in a junction or being emitted from a metal electrode in a vacuum tube. The total noise power from shot noise is independent of temperature and is proportional to the current that flows through the junction.

Photograph of SNT setup used for first generation experiments.

The Shot Noise Thermometer, or SNT, consists of a tunnel junction with both direct current and high frequency leads, and amplifiers to measure the noise signal. The DC leads are used to vary the voltage across the junction and hence how much current flows through the junction. The DC voltage and noise power are simultaneously measured for several voltages, and the data are fit to the predicted voltage dependence of the noise, with temperature as a fit parameter. This is a self-calibrating temperature measurement in the sense that the gain of the noise amplifiers is fit from the data and need not be calibrated independently. This leads to a major advantage over traditional Johnson noise measurements both in simplicity and in the fact that it allows the use of much higher frequency amplifiers, which translates to a much faster measurement.

The potential importance of the SNT is twofold. First of all, by relating temperature to voltage in a simple way, it has the potential to be used as a part of future temperature standards or as a check of present standards. We have not yet demonstrated the accuracy of the SNT to the level required to fulfill the rather stringent requirements of a true standard , but we believe our method is a promising one and are working toward demonstrating the needed accuracy. Secondly, the SNT provides a new kind of practical thermometer that can repeatably operate with high accuracy at low temperatures, yet also work up t o room temperature. This is very useful to low temperature physicists, who commonly work with temperatures ranging from 300 kelvin (room temperature) through less than 0.01 kelvin and need to know the temperature throughout that entire range.

There are several sensors on the market that share some but not all of the benefits of the SNT for general use. The most common sensors are resistive thermometers, which are just resistors the value of which changes with temperature in a known (but never calculable!) way. These typically have limited range, and have to be calibrated periodically due to drift. At the low end of the temperature scale another thermometer that also uses tunnel junctions is the Coulomb Blockade Thermometer (CBT), which has been commercialized into a product (http://www.nanoway.fi). We believe that the SNT can be made into yet another truly practical thermometer for everyday use in low temperature physics labs, and are intend adapt the SNT for such use.

Metrology: the science of measurement, and temperature standards

There are two issues at stake when discussing the measurement of any quantity. First , there is the practical matter of measuring the relevant quantity to the needed precision and accuracy for the application at hand, which I will discuss below. Second, there is the issue of the actual definition of the unit one is comparing to. Standards labs such as the National Institute of Standards and Technology (NIST) in the U.S. and the National Physical Laboratory (NPL) in England are responsible for maintaining these standards and disseminating them to other labs and instrument manufacturers around the world. The collection of the internationally accepted units is called SI, or System International. For more information on SI , see the NIST site at http://physics.nist.gov/cuu/Units/.

The SI unit for temperature is the kelvin. The actual definition of the kelvin is rather abstract, and is based on absolute zero being defined as 0 kelvin and the triple point of water (the temperature at which water vapor, liquid and ice coexist) being defined as 273.16 kelvin. In addition to this formal definition there exists a standard called ITS-90 (the international temperature scale of 1990) which is the basis of the practical temperature standard maintained by the standards labs. ITS-90 is a collection of reproducible fixed temperatures, such as the triple points of various substances, and measurement methods that define a practical temperature scale from 0.65 K to over 1000 K. From 0.0009 K to 1 K the only existing semi-official temperature scale is the PLTS-2000, or provisional low temperature scale of 2000. Both of these scales are known to have deviations from the ideal thermodynamic temperature. There is a need to find better ways to relate the temperature of the practical scales to the true thermodynamic temperature in order to improve these scales.

Press

The SNT received some attention in the popular press.  Click the links below to see copies of articles covering the SNT:

Links

Temperature Metrology

Commercial/Practical Thermometry

Figures

Questions/comments on this page or project to lafe.spietz@yale.edu