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参考文献

1 Introduction▲
2 Layout design and simulation result▲
3 Fabrication and characterization▲
4 Conclusion▲
图表▲

Rare Metals2019年第10期

Fabrication and characterization of superconducting RSFQ circuits

Gang Li Hao Li Jian-She Liu Wei Chen

Tsinghua National Laboratory for Information Science and Technology,Institute of Microelectronics,Department of Microelectronics and Nanoelectronics,Tsinghua University

作者简介：*Wei Chen e-mail:weichen@tsinghua.edu.cn;

收稿日期：25 April 2018

基金：financially supported by the Natural Science Foundation of China (No.60836001);the State Key Program for Basic Research of China (No.2011CBA00304);the Tsinghua University Initiative Scientific Research Program (No. 20131089314);

Fabrication and characterization of superconducting RSFQ circuits

Gang Li Hao Li Jian-She Liu Wei Chen

Tsinghua National Laboratory for Information Science and Technology,Institute of Microelectronics,Department of Microelectronics and Nanoelectronics,Tsinghua University

Abstract：

To meet the specification of the qubits in our laboratory,a 0.4 kA·cm^-2 superconducting rapid single flux quantum(RSFQ) circuit was designed and successfully fabricated with an improved Nb-based self-aligned lift-off process.This circuit consists of a single-fluxquantum(SFQ) pulse generator,a Josephson transmission line(JTL) and a T-flip flop(TFF),and it acts as a frequency pider.The values of the inductors in this circuit were extracted using InductEX and the basic function of this circuit was confirmed using the simulation software WRspice before fabrication.After fabrication,the basic parameters of this circuit were measured at ～2.5 K in a Janis He-3 cryostat.This work laid the theoretical and experimental basis for the future research on the RSFQqubit control circuits.

Keyword：

Rapid single flux quantum; Frequency pider; WRspice; InductEX;

Received： 25 April 2018

1 Introduction

The quantum computation using superconducting circuits [ 1, 2, 3] has been rapidly evolving in the past few decades.At present,this field has advanced from the operation of a single qubit to the demonstration of quantum algorithm with a multi-qubit system [ 3, 4, 5] but there is still a long way to go to achieve a scalable quantum computer.Currently,traditional circuitry was used for the control and readout of multi-qubit,which unfortunately introduces a significant amount of noise from room temperature and needs a powerful data processor to process the measurement data in real-time.

In the superconducting rapid single flux quantum(RSFQ) [ 6] logic circuitry,the information is stored in the form of magnetic flux quanta and transferred in the form of single flux quantum (SFQ) voltage pulses.Because of its high speed,low power consumption and compatible process with superconducting qubits,the superconducting RSFQ circuitry provided a potential candidate for a low temperature real-time processing to achieve quantum control and readout.So far,the accurate control of flux qubits has been successfully realized in many basic cells including Josephson transmission line (JTL) [ 7] ,DC to SFQ (DC/SFQ) converter and SFQ to DC (SFQ/DC) converter [ 8] ,T-flip flop (TFF) [ 9] ,etc.In addition,some researchers designed a microwave source [ 10] ,or an SFQ microwave chopper [ 11, 12] to control the microwave signal applied from room temperature to realize the control of the qubits.Instead of controlling the qubits,some groups used JTL [ 13, 14, 15, 16] or SFQ comparator [ 17, 18, 19, 20, 21] as readout circuits to determine the fluxoid in the qubits.

However,standard RSFQ technology aimed for maximizing the clock speed,simple circuits have been demonstrated with speeds around 770 GHz [ 22] ,and complex RSFQ processors 20-33 GHz [ 23, 24, 25, 26] .However,they used large critical current density (5.0-25.0 and4.5-20.0 kA·cm^-2,respectively),which was not optimal for qubit control and readout.In our laboratory,a low current density (～0.4 kA·cm^-2) self-aligned lift-off process [ 27] for fabricating Nb-based Josephson junction circuits was implemented.Based on this process,rf-SQUID qubit [ 28] and current-driven n-SQUID [ 29] have already been characterized.

Fig.1 a Layout of basic RSFQ circuit containing a DC/SFQ converter,a JTL and b TFF,schematic of b DC/SFQ converter and c TFF used in layout

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Table 1 Inductance extraction result for DC/SFQ converter generated by InductEX

In this paper,the results for a basic RSFQ circuit,containing a DC/SFQ converter,JTL and TFF will be shown.This circuit was designed and successfully fabricated based on the low current density (～0.4 kA·cm^-2) self-aligned lift-off process,which is optimal for the rf-SQUID qubits.Furthermore,the design of RSFQ-Qubit chip,which can realize accurate control of qubits by adjusting its magnetic field using RSFQ circuits,is under development.This paper gives the main numerical results for the basic RSFQ circuit,and the fabrication process and some low temperature measurement results of the successful fabricated chip.

2 Layout design and simulation result

To design RSFQ circuits,three functional elements need to be determined:the critical current of junction (I_c),the bias current (I_b) and inductance (L).In addition,RSFQ circuits require nonhysteretic or overdamped Josephson junctions;shunted resistances are used to achieveβ_c<1,whereβ_c is the Stewart-McCumber parameters of junction.

In this paper,the overdamped junctions were designed based on the critical current density of 0.4 kA·cm^-2 and sheet resistances of 0.7Ω-square^-1;the bias current around0.7I_c was chosen;as for the most important parameter,the inductance of different components,InductEX [ 30] ,was used for inductance extraction.A final layout of a basic RSFQ circuit containing a DC/SFQ converter,JTL and TFF is shown in Fig.1a;the schematic of the DC/SFQ converter is shown in Fig.1b,where L0-L5 are inductances,J1,J2,J3,R1,R2,R3 are junctions and their shunted resistances,R4,R5 are line resistances for bias currents.The schematic of the TFF is shown in Fig.1c,where L_TFF is the most important inductance,the J1-J4 are the core shunted junctions and all the shunted resistances are not drawn.

Fig.2 WRspice results of frequency pider:a input current to DC/SFQ converter,b SFQ-pulses generated by DC/SFQ converter,c SFQ-pulses after passing through JTL,d current flowing through L_TFF and e SFQ-pulses at output of TFF

Fig.3 a Cross-section of fabrication process,b schematic diagram of cross-section represents and c optical micrograph of frequency pider

With the help of InductEX,the inductance of the layout was extracted.Table 1 shows the extracted inductance for the DC/SFQ converter,whose layout and schematic are shown in Fig.1a,b.These results are obtained after several adjustments on the layout to make sure that the inductance values are within a margin of±5%.All values are in pH.

Fig.4 Experimental results of junctions and dc-SQUID:a I-V curve of a 10μm×10μm junction,b I-V curve of a 20μm×20μm junction,cI-V curve of an overdamped dc-SQUID composed of two 10μm×10μm junctions and d dc-SQUID voltage versus flux bias current for constant bias current (～0.666 mA)

After the extraction of all the parameters,WRspice [ 11] was used to simulate the behavior of the basic RSFQ circuit before fabricating a real chip.Figure 2 shows the basic function of this circuit.Figure 2a shows the input current(IIN) before the DC/SFQ converter;Fig.2b-e shows the simulation results of different points named in Fig.1a,where V_A,V_B and V_C are the output voltage after DC/SFQ converter,JTL and TFF,respectively;I_TFF is the current flowing through L_TFF,which will be used to manipulate the magnetic field of qubit in RSFQ-Qubit chip.From the simulation result,our circuits can act as a frequency pider,and output a square wave,which will be easily control by RSFQ circuits.

3 Fabrication and characterization

To implement Josephson junction,resistance and inductance in the same chip,the fabrication process in Ref. [ 28] was improved by adding a ground layer and a resistance layer.In this new process,a 2-inch (1 in.=2.54 cm)<100>crystalline N-type single-sided polished wafer,which has a 400-nm-thick SiO₂ on its surface,was used.Before in situ deposition of an Nb/Al-AlO_x/Nb trilayer,a100-nm-thick Nb ground layer and a 120-nm-thick SiO₂insulator layer were deposited and patterned by lift-off.Then,the following step was defined the shape of Josephson junction (also,protected the Nb Via) by etching the top Nb films of the trilayer with SF_6.Afterwards,200-nm-thick SiO₂ was used to isolate the Josephson junction bottom electrode;an Nb Via was defined by etching the top Nb films with SF₆ and wet-etching the AlO_xfilm with phosphoric acid to connect the bottom electrode.Then,before the deposition of Pt resistance,a 10-nm-thick Ti layer was sputtered to improve adhesion;here,100-nmthick Pt was used to obtain a sheet resistance of 0.7Ω·square^-1.For the last step,a 250-nm-Nb wiring layer was deposited and patterned to define the connection of resistors and Josephson junctions.A cross section of the fabrication process is illustrated in Fig.3a with thickness values in parentheses and its schematic diagram in Fig.3b.An optical micrograph of the RSFQ chip is shown in Fig.3c.

Based on Janis He-3 cryostat,a low temperature weak signal measurement system was built.As mentioned in Sect.2,I_c,I_b and L are the functional elements of RSFQ circuits and overdamped junctions are required to build an RSFQ circuit.To calibrate the critical current density,fourterminal method was used and the results are shown in Fig.4a,b shows I-V curve of a 10μm×10μm junction and a 20μm×20μm junction,respectively.Obtained from these curves,the critical current density is about 0.32kA·cm^-2,which is a little smaller than our design.To check the resistance and inductance,an overdamped dcSQUID was used and the results are shown in Fig.4c,d.Figure 4c shows I-V curve of the overdamped dc-SQUID,which is composed of two overdamped 10μm×10μm junctions;Fig.4d shows the voltage variations of the dcSQUID when it is biased at 0.666 mA and modulated by an external magnetic flux via current along an inductively coupled flux bias line.Calculated from these curves,the sheet resistance is 0.8Ω·square^-1 and the mutual inductance between the on-chip flux bias line and dc-SQUID is3.517 pH,compared with the extracted value of 3.69 pH from InductEX.

4 Conclusion

In summary,a low critical current density RSFQ circuit,containing a DC/SFQ converter,JTL and TFF,was implemented.The basic function of the circuit was simulated by WRspice and was shown to be a frequency pider.After inductance extraction and layout adjustment using InductEX,a chip containing this circuit was designed and successfully fabricated using an improved Nb-based lift-off process.The chip was tested at low temperature.Parameters including critical current density,sheet resistance and mutual inductance were measured.The critical current density is about 0.32 kA·cm^-2 and the sheet resistance is about 0.8Ω·square^-1 calculated from the I-V curves of a few junctions and a shunted dc-SQUID,the mutual inductance is obtained from the modulation curve of dc-SQUID,which is matched with the simulation result.The next crucial step is the on-chip testing of the circuit.