Multi-channel Precision Voltage Source for Experiments on Quantum dots

: To realize precise control of single quantum dots (Qdots) device, the high-performance bias source play the key role. In this paper, the 16-channel high precision voltage bias source prototype for Qdots device with 18-bit resolution was designed. The prototype was made and its performance was tested. The short time fluctuations can reach 50μV. The up -step and the down- step response time can achieve less than 3μ s. The stability, linearity and setting time of the bias source exhibits good performance. What's more, the voltage bias source can be controlled by local and online. The results show that it is one effective and feasible topology for the high precision voltage bias source in Qdots device application.

In general, it is necessary to apply bias voltage on the gate of quantum dots to empty the two-dimensional electron gas below them and form quantum dots or quantum dot contact channels [17]. The Qdots device is mostly general driven by electric including current and voltage bias [18,19]. The stability, linearity and setting time of bias source are key factors to affect the Qdots device performance [20][21][22][23]. In order to realize precise control of single quantum dots and quantum channels, it is meaningful to investigate on the high precision and quality bias source for Qdots device.
To our knowledge, the existing instruments are large volume with few channels or with limited accuracy [24,25], meanwhile multi-channel and high precision bias voltage source is rarely reported in the literature. ADI recommends to use high resolution DAC chip to design the bias voltage source [26,27].
Although precision DAC components are already on the market, building a multi-channel high-resolution system is not easy and cannot be treated hastily. The sources of error must be fully considered, which occur at this level of accuracy. In high-resolution circuits, the main error sources are noise, temperature drift, thermoelectric voltage, and physical stress. The construction technology of precision circuits should be followed to minimize the coupling and propagation effects of such errors in the entire circuit and avoid external interference. To further complicate the issue, mixed-signal ICs have both analog and digital ports, and because of this, much confusion has resulted with respect to proper grounding techniques. In addition, some mixed-signal ICs have relatively low digital currents, while others have high digital currents. In many cases, these two types must be treated differently with respect to optimum grounding[28]. design and analysis: The key point of the circuit design is to completely separate the digital circuit and the analog circuit, and use independent power and ground processing, and the signal transmission between the two is isolated from each other through the optocoupler, so as to ensure that the digital circuit noise does not enter the analog circuit.

1)system design
where: Vrefn provides a negative reference voltage for the DAC; Vrefp provides a positive reference voltage for the DAC; D is an 18-bit binary programming value. Regardless of the influence of the op amp bias current, assuming that the op amp offset voltage is Vos1, let Vr'=Vr+Vos1, according to the "virtual disconnection" principle, the following formula：

2) Output voltage accuracy and temperature drift analysis
So that, As shown in Fig 3(b), assuming that the op amp offset voltage is Vos2, let Vr''=Vr+Vos2, and the same can be obtained: Where : Vrefn provides a negative reference voltage for the DAC; Vrefp provides a positive reference voltage for the DAC.
It can be seen from the above formula that the bias output voltage will be affected by the drift of the DAC, resistance, reference voltage, and operational amplifier.
The reference voltage source adopts ADR445BRZ to output 5V, and the temperature drift is about 2ppm/℃, which is 10 uV/℃.
The temperature drift of the voltage divider resistance is about 2ppm, and the temperature drift of the voltage divider resistance is required to be consistent, and the tracking temperature coefficient is less than 5 uV/℃.
The offset drift of AD8676 is about 0.6 μV/°C. AD5781 has a very low temperature coefficient of about 0.05ppm/°C, which is much lower than the drift of the reference voltage source.
Ignoring the temperature drift of the op amp and DAC, it is mainly affected by the reference voltage source, and the drift is about 20 uV/°C.
Generally speaking, for a 20V voltage range, 18-bit system, the temperature drift is required to be controlled within 80uV, and the temperature cannot change more than 4 degrees.   The phase delay caused by CL is compensated by the advanced correction, which is equivalent to adding a buffer at DAC output stage, and responding in time to the first stage operational amplifier response.

Results and discussion:
The multi-channel precision voltage source (MPVS-X) prototype was shown in Fig.5.The LCD screen and controller were distributed in the front panel layout. The Input-Power, power controller, muti-output, RS232 output interface and network interface were distributed in the rear panel layout. The size of prototype is 437mm*420mm*133mm (3U chassis size).

2)Short time fluctuations
Set different voltage output in the program, wait for 0.5s after setting the voltage value each time, and then read the actual output voltage value with an 8.5-digit digital multi-meter (Agilent 3458A), continuously measure 100 s, and count the peak-to-peak voltage jitter. The whole process is repeated 5 times. The voltage output range of this system is -10V~10V. For 18-bit system, 1 LSB is 76μV, and the maximum voltage jitter does not exceed 50μV in the full voltage range.

3) Uniformity between two channels
As shown in Fig.7, the two channels have the same set voltage of -5.5V and -1V respectively, and read the actual output voltage value with an 8.5-digit digital multi-meter (Agilent 3458A)，continuously measure for a long time. Fig.7 the uniformity between different channels

4) Step response
As shown in Fig.8，The step is set from -5V to +5V. According to the test results of the oscilloscope, the 10V step has a settling time of about 2.4~2.7us. Turn on the output of 16 test channels at the same time and set their voltage output to 10 V at the same time, test the voltage value of random channels among them, read it every 10s, and the test duration is 24 hours. The output voltage change curve with time is as follows: Fig. 9 the output voltage stability test The output stability of the system was show in the Fig.9. After starting up and running for about 2 hours, the internal temperature of the instrument gradually rises, and the output voltage will drift by 160μV, and then the internal environment of the instrument gradually stabilizes. When multiple channels work at the same time, the system has excellent long-term stability of voltage output and maximum fluctuation. The range is less than 20 μV.

Conclusion:
Multi-channel bias voltage source technology is a typical technology of low noise circuit design, involving resolution, noise, accuracy, linearity, temperature, channel consistency, bias, long-term stability, low complexity and other aspects. The project research focuses on these problems closely, and achieves 4ppm conversion accuracy by designing high-resolution digital to analog conversion circuit; Through scientific exploration, a series of low noise circuit design problems such as power supply, grounding processing and signal isolation are solved; Through closed-loop measurement and digital correction, accurate voltage output is obtained; The problem of capacitive load and linearity is solved by two-stage op amp output; Through careful heat dissipation, the whole machine controls the temperature change on the one hand; On the other hand, the temperature drift of components is very low, which minimizes the temperature drift coefficient of the system and improves the working temperature range through temperature compensation; Through careful structure design of the whole machine, the complexity of the system is reduced, and the humanized manmachine interface is realized. The results show that it is one effective and feasible topology for the high precision voltage bias source in Qdots device application.