Thank you to everyone who attended the "Nanostructure transport characterization" Webinar. It was my first webinar and it was an amazing experience for the whole team. We received a lot of questions and in this post I will answer most of them by grouping them into four categories:
- Measurement tools available with the MFLI and other Zurich Instruments lock-in amplifiers
- Lock-in measurement considerations: connecting the lock-ins and the external reference, simultaneous current and voltage measurements using the MF-MD option, filter settings
- Quantum dot (QD) lock-in characterization
- Fast lock-in measurements and RF-reflectometry
I will add as many references as possible throughout and based on your feedback so far plan another event that will cover one of these aspects in more detail. It would be great to have one of the experts on board so we can have another webinar in more live circumstances so you can ask questions yourselves and we can have a lively conversation. Let's get started!
One set of questions referred to the tools that we use in our lock-ins and how they help improve the measurements. The best thing about the tools is that they are always there and you can use them before, during and after the measurements. Available tools are shown in Figure 1.
Figure 1: The block-diagram of available tools in the MFLI Lock-in Amplifier and their main data sources raw or demodulated. In both cases the representation in time and frequency domain is available.
Figure 1 shows the point of data analysis in the time and frequency domain. Oscilloscope represents raw data in time and frequency domain. Demodulated data is acquired using the DAQ module that works together with the imaging module for 2D plots. The Plotter represents demodulated data in real-time and can be used for analysis by calculating the mean and standard deviation of the demodulated data, for example. The data can be viewed in the frequency domain as well by calculating the fft on the raw data in the Oscilloscope tool and demodulated data in the Spectrum tool. Finally, the Parametric Sweeper tool sweeps several parameters available such as frequency and amplitude and plots any instrument output parameters such as amplitude and phase of a single or multiple-demodulators. For more information see our page on LabOne where you will find the API information as well as system support.
Many questions referred to the two lock-in amplifiers connected to measure the Hall effect as an example. The first requirement to perform these measurements is lock-in synchronization. The signal frequency and all lock-in frequencies have to be identical for the lock-in to output the desired result. There are several ways to synchronize devices:
- Use the TTL I/O in the back of the lock-ins
- Use the AuxIn as ExtRef port on the front panel
- Use the MDS synchronization that synchronizes lock-in clocks and time stamps
For more information please refer to the MFLI User Manual Chapter 3.2. External Reference.
Figure 2: a) An example of 2 MFLIs synchronized using the MDS option. b) An example of the MFLI synchronized via AuxIn to an external chopper reference frequency.
In one of my slides, I show that the current can be measured concurrently with the voltage. This is the case if that lock-in is equipped with the Multi-Demodulator MF-MD option enabling 4 instead of one demodulator. This means you can measure 4 signals using the 4 oscillators at the same time. The assignment of the measurement port and frequency can be changed depending on your measurement need as shown in the diagram of Figure 3. See more in the MFLI User Manual Chapter 4.4.
Going back to Hall effect measurements, it is important that the two lock-ins have the common ground. When you measure the current it’s important to take care that the current input serves as a sink and no current leaks to the ground. Read more about the ground loops and how to tackle the issue in this blog post where the issue is addressed for another platform but the topic is universal.
Figure 3: Diagram of the MF-MD option.
In practical terms, this means that you can set the DC (f=0) for oscillator 1, and AC (f - arbitrary) for oscillator 2 and selected inputs can change from I and V for DC signal and I and V for AC signal. That way we can measure current and voltage dc and ac characteristics with only one lock-in device. There is a difference between setting an oscillator to DC (f=0) and adding a DC bias. Oscillator set at the DC will measure the DC part of the signal, whereas adding the DC offset to the signal will change that measurement. Not that and AC high pass filter will remove all the DC components.
Figure 4: MFLI lock-in Tab with MF-MD option. Red square depicts oscillator frequency setting. Blue square depicts the input selection setting.
With the MF-MD option, the possibilities are vast – you can change the harmonic order at any time and thus measure higher harmonics of the same oscillator. With the MFLI you can measure up to 3 higher harmonics and fundamental at the same time.
How to set filter bandwidth at 500 Hz or low frequencies say 17 Hz. In any case use the Oscilloscope and Plotter together with Spectrum tool in order to see what is the SNR and how is your filter setting affecting it. There are several concerns here:
- Surrounding noise – how close is the dominant noise peak?
If the dominant peak is nearby at ΔF, you need to reduce the filter BW to about ΔF/10 – rule of thumb.
- 2ω component i.e signal at double the frequency that naturally comes from demodulation (see this white paper)
Here Δf=f, so go for BW= f/10; notch the 2ω component using the sinc filter.
- What is the signal-to-noise (SNR) ratio? What do you need to do to increase it?
In this case, maybe you need to go with BW=f/100 if the noise floor is too large or your signal too small. YOu can try the cross correlation measurements described in this application note, and watch the video on how to do this in more detail here.
Quantum-dot characterization using the lock-in amplifier is a standard technique where you move the dot energy levels using the back-gate voltage and align the source and drain chemical potentials using the source-drain voltage Vsd. The ac lock-in voltage signal is superimposed on the Vsd. During the measurement, both Vg and Vsd are swept and the differential conductance G is measured using the lock-in. This is done by choosing a small voltage excitation that is on the order of 10s of μV and the current is measured using the lock-n current port at the same reference frequency. The reference is typically below 100 Hz which makes the measurements quite slow. See about adding the analog bias to the MFLI that improves the measurement quality in this blog post.
How is the μV signal level provided by the lock-in? As lock-ins can’t provide a good quality signal at that level, for example lowest output range of MFLI is 10 mV (16 bit) and you can nominally choose 100 μV for example however it is better to go with 1 mV signal amplitude and proceed with voltage division of both ac and dc signals. Choosing the correct ac signal amplitude is crucial for the measurement as too large of an amplitude can smear out the energy levels and reduce the resolution.
Figure 5: Slide from the webinar showing the quantum-dot characterization idea and measurement results.
Coulomb diamond peaks are a typical signature of the QD measurements and they also serve as a thermometer in a measurement setup. The Coulomb diamond peaks with is temperature dependent so by fitting the peak to a Lorentzian we can determine the temperature. We can expend this topic further, let me know what are the quantum dot structures you are characterizing. The final topic of the webinar was RF reflectometry. To speed up the quantum dot characterization a resonant circuit can be attached to either source or drain electrode or a side gate.
Figure 6: a) RF reflectometry setup for a double quantum dot system. b) Amplitude and phase of the resonating circuit. c) Colored scale plot of RF conductance as a function of source-drain and back-gate voltage bias.
The resonant and measurement frequencies can be on the order of several 100 MHz. This allows us to increase the measurement BW according to the concerns above regarding the measurement setting and that’s where we need faster lock-ins such as UHFLI. In this case we also need to think about the high data transfer rate, which is addressed here. The example I have shown is from the UCL Lab of Mark Buitelaar and we also have a blog post on the topic here.
In some instances, such as FMR measurements where the measurement frequency needs to be several 10s of GHz, it is sufficient to use a microwave source to up and down convert the local oscillator frequency and the measurement can be done using an MFLI with a measurement bandwidth up to 200 kHz. That said, you don’t always need a higher frequency lock-in amplifier even if measurements require higher carrier frequencies.
With this post I covered most of the concepts you asked about, but some details might still be missing. If you don’t find your answer here or would like to discuss further, drop me a line at firstname.lastname@example.org.
Thank you so much again for your interest!