MEASUREMENT
Application note

Measuring electron temperature using Nanonis Tramea
Eduardo Barrera, Kyle Willick, Jonathan Baugh, University of Waterloo, Canada

Introduction
The Nanonis Tramea Quantum Transport Measurement
System (QTMS) was used to measure electron transport
through an electrostatically defined Gallium Arsenide(GaAs) quantum dot in an Oxford Instruments Triton
200 dilution refrigerator. The high-speed demonstrated
by Nanonis Tramea allowed for a significant reductionin the measurement acquisition time and the low
noise environment of the Oxford Instruments dilution
refrigerator combined with the Tramea system, allowed
us to measure an electron temperature of 35 mK. Thiswas equal to the base temperature of the cryostat withcustomised wiring installed.

Triton and Nanonis Tramea

Equipment used
Oxford Instruments Triton 200 dilution refrigerator
Nanonis Tramea with 3D sweeper module
DL-1211 current preamplifier

BackgroundA single quantum dot is ideal for device thermometry at millikelvin temperatures due to the strong temperaturedependence of the zero-bias conductance peak width and height in single-level transport. This is described bythe equation:

where G is the conductance through the dot, h is Planck’s constant,e is the electron charge, kB is the Boltzmann constant,
C2 is an amplitude fitting parameter, Te is the electron temperature,
α is the gate lever arm, Vo is the applied gate voltage
at which the peak is maximum (resonant tunnelling),and Vg is the plunger gate voltage.

MEASUREMENT
Application note

Experimental set-up
The GaAs quantum dot was fabricated on Al0.33Ga0.66As/GaAs heterostructure wafer, where the two dimensional
electron gas (2DEG) is located 110 nm from the surface. The heterostructure has a 10 nm Silicon (Si) cap and aδ-doping layer buried 70 nm from the surface (n-type doping = 5x1011 cm-2). The quantum dot is formed by applying
negative voltages on a set of titanium gold, Ti/Au (20/20 nm), metal gates, shown in Figure 1. These gates deplete
the buried 2DEG such that a small amount of charge is isolated in a region of approximately 100 nm2. The sample
was made at the Quantum NanoFab facility at the University of Waterloo.
An image of the device was taken using scanning electron microscopy (SEM) and is shown in Figure 1, also showing
a schematic of the experimental setup with electrical connections to Nanonis Tramea. The plunger gate (Vg), source(S) and drain (D) are shown. A customised filter in the MHz range was mounted on the mixing chamber of the Oxford
Instruments Triton 200 using copper powder loaded epoxy on the PCB board. Additional low pass RC filters werealso mounted on the cold plate at 150 mK to provide filtering down to 25 kHz and room temperature filters with acut off frequency of 1.5 Hz were used outside Triton. A voltage divider is added to the source output voltage.

Figure 1. A schematic of the measurement setup. The GaAs
quantum dot location is shown in the dotted white circle.

The GaAs quantum dot device was mounted on the cold finger of an Oxford Instruments Triton 200 dilution
refrigerator. With customised DC wiring, coaxial cables and extra radiation shielding of the mixing chamber, atemperature of 35 mK was recorded as the base temperature, measured using a calibrated ruthenium oxide
thermometer, mounted on the mixing chamber. All voltages were supplied by Nanonis Tramea and the output
current from the device was amplified using a DL-1211 current preamplifier (battery-operated), whose output wasconnected to a Tramea input channel.

Experimental results
After tuning the gate voltages to define the quantum dot, a clear conductancepattern referred to as ‘Coulomb diamonds’ shown in Figure 2, was observed.
The experimental data was fit to the equation described previously, using theexperimentally determined α, shown in figure 2, and three fitting parameters:
Vo, Te, and C2. The lever arm α is a conversion factor between energy and gate
voltage and is calculated as the ratio between the energy and gate voltage
difference between adjacent conductance Coulomb peaks and the charging
energy of the quantum dot.

MEASUREMENT
Application note

Experimental results

Figure 2: Conductance throughthe GaAs quantum dot measured
at a lattice temperature of
35 mK. The conductance shows
clear Coulomb diamonds.

Figure 3: Conductance arounda Coulomb diamond vertex
measured using an integration
time of 1 ms. The totalacquisition time was 90 seconds.

Figure 4: Conductance around thesame Coulomb diamond vertex
measured using an integration timeof 50 ms. The total acquisition timewas 35 minutes.

Figures 3 and 4 show a close-up of a single Coulomb diamond vertex measured with integration times of 1 ms and50 ms (total acquisition time of 90 seconds and 35 minutes), respectively. The fact that both the voltage outputs andcurrent inputs for the measurement were handled by Nanonis Tramea, removed the usual experimental barrier ofcommunicating with a range of instruments connected over slow communication buses. This allowed for a decreased
acquisition time and enabled quick device tuning and exploration of the gate voltage parameter space.

Figure 5: Zero-bias conductance peak fit at a mixing
chamber temperature of 35 mK. The electron
temperature is estimated to be 35.5 ± 1.3 mK. The Inset
shows the conductance around the Coulomb diamondvertex which is used to extract the zero-bias conductancepeak (shown by dashed black line). A constant DC
voltage offset on the input of the current preamp causes
the observed bias offset of about 170 µV.

Figure 6: Experimentally measured
relationship between the estimated electron
temperature vs. the mixing chambertemperature of the dilution refrigerator.
The two temperatures are equal within
uncertainty down to the base temperature of35 mK, indicating that voltage noise from themeasurement setup is negligible.

At the base temperature of 35 mK, a selected conductance peak, shown in Figure 5,
was fit to the equation on page 1, giving an electron temperature of 35.5 ± 1.3 mK.
This fitting procedure was repeated for 5 different mixing chamber temperatures TMC,
controlled by a resistive heater on the mixing chamber plate.

MEASUREMENT
Application note

Experimental results
The resulting electron temperatures are plotted as a function of TMC in Figure 6. The agreement between the latticeand electron temperatures, extending all the way to the base temperature, indicates that Nanonis Tramea voltage
noise levels are negligibly small in this experimental context.

Conclusion
In conclusion, Nanonis Tramea enables high-speed control over several output voltages with a negligible amountof electrical noise introduced into the measured device, which is essential in quantum transport measurements ofquantum dots and other devices. The high-precision, high-bandwidth capabilities of the Tramea system could becombined with automation/machine learning algorithms to efficiently auto-tune and calibrate quantum devices fordesired experiments. The high speed capability of the Tramea combined with the stable millikelvin environmentof the Oxford Instruments Triton 200 dilution refrigerator meant an electron temperature of 35 mK could bemeasured using a GaAs quantum dot.

About Triton and Nanonis Tramea
The ultra-low temperatures andhigh magnetic fields provided by theTriton dilution refrigerator make ita key research tool in revealing thequantum properties of many materials
of interest. The Triton systems alreadylead the way in experiment-readinesswith high-density RF and DC wiring
capability, unique sample exchangemechanisms, and unbeatablesuperconducting magnet integration.
SPECS’ Nanonis Tramea QTMS is anatural complementary partner to theTriton, with its fast, multi-channel,multi-functional capability. The systemenables quantum measurements to be
carried out on a variety of samples, as
shown in this application note.

Nanonis Tramea
multifunctional,
low noise, low drift
and high resolution
electronics.

The latest Triton dilution refrigerator with increased
experimental space and cooling power.

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September 2018, Issue 1