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IEEE Transactions on Circuits and Systems I Regular Papers

Sub-Nanoampere One-Shot Single Electron Transistor Readout Electrometry Below 10 Kelvin

Kushal Das, Torsten Lehmann, Andrew S. Dzurak

Published Sep 18, 2014• 16 citations
Publisher

Abstract

The Single Electron Transistor holds the potential to be a suitable readout device for future solid-state quantum computers. The low temperature measurement results of a 0.5 μm Silicon-On-Sapphire CMOS circuit designed to interface with a Single Electron Transistor are presented. Careful design of the experimental set-up is critical for conducting the circuit test and performance measurements at cryogenic temperatures. The circuit operates at 4 K and achieves single-shot readout with a resolution in the order of one nanoampere. A detection delay as low as 1.5 μs is recorded while dissipating only 20-30 μW power.

DOI
10.1109/tcsi.2014.2321196

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Scientific Reports•Nov 18, 2019•27 citations
The Single Electron Transistor holds the potential to be a suitable readout device for future solid-state quantum computers. The low temperature measurement results of a 0.5 μm Silicon-On-Sapphire CMOS circuit designed to interface with a Single Electron Transistor are presented. Careful design of the experimental set-up is critical for conducting the circuit test and performance measurements at cryogenic temperatures. The circuit operates at 4 K and achieves single-shot readout with a resolution in the order of one nanoampere. A detection delay as low as 1.5 μs is recorded while dissipating only 20-30 μW power.
Novel single electron transistor (SET) read-out circuit designs are described. The circuits use a silicon SET interfaced to a CMOS voltage mode or current mode comparator to obtain a digital read-out of the state of the qubit. The design assumes standard submicron (0.35 um) CMOS SOI technology using room temperature SPICE models. Implications and uncertainties related to the temperature scaling of these models to 100mK operation are discussed. Using this technology, the simulations predict a read-out operation speed of approximately Ins and a power dissipation per cell as low as 2nW for single-shot read-out, which is a significant advantage over currently used radio frequency SET (RF-SET) approaches.
We use a cryogenic high-electron-mobility transistor circuit to amplify the current from a single electron transistor, allowing for demonstration of single shot readout of an electron spin on a single P donor in Si with 100 kHz bandwidth and a signal to noise ratio of ∼9. In order to reduce the impact of cable capacitance, the amplifier is located adjacent to the Si sample, at the mixing chamber stage of a dilution refrigerator. For a current gain of ∼2.7×103, the power dissipation of the amplifier is 13 μW, the bandwidth is ∼1.3 MHz, and for frequencies above 300 kHz the current noise referred to input is ≤70 fA/Hz. With this amplification scheme, we are able to observe coherent oscillations of a P donor electron spin in isotopically enriched 28Si with 96% visibility.
A major problem of usual current measurement setup is the severe limitations on the bandwidth due to room temperature electronics. This restricts the practical measurement rate to below 10 Hz and makes impossible to observe the evolution of a quantum state in real time. Here we describe a measurement on a silicon single electron transistor (SET) carried out using a custom CMOS measurement circuit in close proximity to the device under test. Both the device and the CMOS circuit are maintained in the same cryogenic environment. Quantum mechanical states in the single electron transistor (SET) were mapped by continuous microwave spectroscopy. The real time evolution of a particularly long lived quantum mechanical state was observed in a single shot measurement, made possible by the much faster measurement rate. This technique will shortly be applied to the measurement of coherent states in a charge qubit device made of a silicon double dot.
We have fabricated a custom cryogenic complementary metal-oxide-semiconductor integrated circuit that has a higher measurement bandwidth compared to conventional room temperature electronics. This allowed implementing single shot operations and observe the real-time evolution of the current of a phosphorus-doped silicon single electron transistor that was irradiated with a microwave pulse. Relaxation times up to 90μs are observed, suggesting the presence of well isolated electron excitations within the device. It is expected that these are associated with long decoherence time and the device may be suitable for quantum information processing.
Thousands to millions of sensitive signals will need to be conveyed through all the temperature stages of a dilution fridge to operate future large-scale quantum processors made of many quantum bits. The exploding number of heat-conductive coaxial cables will overwhelm the fridge cooling capabilities, detrimental to the quantum core. Moving the control electronics down to cryogenic temperatures allows the use of already-available superconducting cables, alleviating heat conduction between low-temperature stages, and appears as a clear path towards scalability in the number of operating qubits.This Ph.D. work aimed to explore the use of the industrial CMOS 28nm Fully-Depleted Silicon-On-Insulator (FD-SOI) technology at cryogenic temperatures for quantum computing applications. Our first objective is to extend the sparse existing knowledge about the FD-SOI 28nm transistors at cryogenic temperatures for practical aspects of circuit design and later for developments of compact models.To speed-up the characterization of single devices with the inherent hour-long cooling cycles, we designed an integrated circuit multiplexing a thousand of transistors for different geometries and gate-stack flavors for low-frequency measurement of the current-voltage characteristics and pair-matching analysis from 300 down to 0.1K. We discuss and analyze the evolution trends with varying geometry at different temperatures for important quantities in circuit design, such as the transconductance, the conductance, and the transconductance over drain current ratio of individual transistors.Secondly, we explore the low-temperature co-integration and the full on-chip integration of semiconductor quantum devices with classical electronics aimed at specific measurements down to the millikelvin range.We first focus on the sub-nanoampere current measurement of quantum dot devices by designing and characterizing a low-power transimpedance amplifier (TIA). The high-gain amplifier is successfully applied to measure the current across single- and double quantum-dot devices, respectively wire-bonded a few mm away or on-chip integrated a few micrometers-away. To further leverage the integration into the same substrate, we connected GHz-range voltage-controlled oscillators to one of the gates of the double dot in an attempt to observe discrete charge pumping in a fully-integrated device.Lastly, we tackled the measurement of the gate capacitance of single quantum devices by proposing a new measurement scheme making use of the cryogenic electronics capabilities as an alternative to the well-known reflectometry. By integrating a voltage-controlled current excitation and a voltage-sensing amplifier in the 200 MHz range, both in close proximity to the quantum device connected to an LC tank, the read-out circuitry of a variation in the device capacitance becomes a purely lumped-element system with impedance measurement of the resonant circuit without any wave propagation like in reflectometry. This approach increases simplicity and compactness of the measurement set-up. We even replace the bulky passive inductor used in reflectometry by an active inductor made of transistors and capacitors, offering improved scalability with a 3-orders of magnitude lower area for the same inductance. The resulting circuit successfully measured aF-capacitance variations of nanometric transistors at 4.2K revealing oscillatory quantum effects in the gate capacitance as a function of the gate and back-gate voltages.At the end of this dissertation, a picture is given with the challenges laying ahead related to circuit architecture and design for the ultimate goal of entering into the era of large-scale quantum processing.
Abstract High-fidelity single-shot readout of spin qubits requires distinguishing states much faster than the T 1 time of the spin state. One approach to improving readout fidelity and bandwidth (BW) is cryogenic amplification, where the signal from the qubit is amplified before noise sources are introduced and room-temperature amplifiers can operate at lower gain and higher BW. We compare the performance of two cryogenic amplification circuits: a current-biased heterojunction bipolar transistor circuit (CB-HBT), and an AC-coupled HBT circuit (AC-HBT). Both circuits are mounted on the mixing-chamber stage of a dilution refrigerator and are connected to silicon metal oxide semiconductor (Si-MOS) quantum dot devices on a printed circuit board (PCB). The power dissipated by the CB-HBT ranges from 0.1 to 1 μ W whereas the power of the AC-HBT ranges from 1 to 20 μ W. Referred to the input, the noise spectral density is low for both circuits, in the 15 to 30 fA/ Hz\sqrt{{\bf{Hz}}}Hz​ Hz range. The charge sensitivity for the CB-HBT and AC-HBT is 330 μ e/ Hz\sqrt{{\bf{Hz}}}Hz​ Hz and 400 μ e/ Hz\sqrt{{\bf{Hz}}}Hz​ Hz , respectively. For the single-shot readout performed, less than 10 μ s is required for both circuits to achieve bit error rates below 10 −3 , which is a putative threshold for quantum error correction.