INTRODUCTION
The development of silicon-based integrated circuits (Si-ICs) has revolutionized information technology worldwide over the last 60 years. Si-based complementary metal oxide semiconductor (Si-CMOS) circuits, as the core of Si-ICs, have doubled their integration density every 18 months according to Moore's Law1. However, with the exponentially increasing complexity of processing technology, the scaling down process has begun to decelerate, and the increased integration has also been experiencing clock frequency bottlenecks, power walls and memory walls of the von Neumann architecture. While Si-CMOS technology is approaching its performance limits1,2, the demand for more advanced computing performance is still rising in several fields, such as the Internet of Things, big data, artificial intelligence and materials science. Therefore, researchers in science and industry have been exploring new avenues for improving computing capabilities to perpetuate and extend Moore's Law. One promising strategy is cryogenic electronics, which is also demonstrated in the International Roadmap for Devices and Systems (IRDSTM) 2022 Edition, including superconductor electronics, cryogenic semiconductor electronics and quantum information processing3.
The main operating temperature region of modern Si-ICs has been focused in the ambient temperature range. Compared with the performance of ambient-temperature Si-CMOS, that of Si-CMOS below liquid-nitrogen temperature is enhanced, which yields increasing efficiency and computational performance of digital logic computing at cryogenic temperatures, as is schematically shown in Fig. 1a4-6. The reason accounting for the phenomenon above is that, at low temperatures, the increased mobility of the devices results in higher operating speeds7, increased on/off ratios, improved subthreshold characteristics8,9 and lower operating voltages for lower power consumption. Furthermore, the reduced resistance of metal interconnections accelerates signal transmission, and the low-temperature environment moderates the heat dissipation issues of devices, which permits a higher density of integration. On the other hand, the emergence of quantum mechanical effects at low temperatures facilitates the design of innovative quantum electronic devices. For example, highly anticipated quantum computing systems, which operate at millikelvin temperatures, have exhibited supremacy over conventional computing architectures, with multiqubit coherent operations and the successful demonstration of quantum algorithms10,11. However, in order to operate a quantum computer system, some interfaces with the nonquantum world are needed. This means that many bulky backend electronics sit at ambient temperature, as the total number of interfaces in a fridge is capped, which limits the scaling up of quantum computing5,12,12,12,13. To solve this “wiring bottleneck”14-18 researchers at Interuniversity Microelectronics Centre (IMEC) developed an radio-frequency multiplexer19o extract some of those cables and join the qubits in the fridge; this circuit can control the signals to and from multiple qubits. The placement of the control circuit for qubits into a fridge6,15,16,18,20, close to a qubit array, or even the integration of the circuit into a quantum chip17 can circumvent wiring bottlenecks and improve the efficiency of manipulation and error correction on qubits due to the closer signal transmission distance21,22. Moreover, a reduction in thermal noise at low temperatures can improve the accuracy and signal-to-noise ratio of the detecting systems, enabling superior quantum sensing with quantum effects. Precise and localized detection of electromagnetic fields and temperatures in cryogenic environments is also required for maintaining the proper operation of cryogenic electronics. Electronic devices for cryogenic temperatures, such as low-noise amplifiers (LNAs)6,23, can also be applied in the fields of deep space, astronomy and biology, as well as industrial and scientific researches at cryogenic temperatures. A typical architecture of quantum computing in a refrigerator is shown in Fig. 1b5,15,15,15,24, where cryogenic amplifiers, cryogenic sensors and cryogenic circuits are equipped at different temperature stages. Therefore, driven by the above demands, the exploration of modern electronics for use in the cryogenic regime has continued to increase (summarized in Fig. 2).
Fig. 1. a, Schematic illustration of the transfer characteristics of a field-effect transistor (FET) at ambient and cryogenic temperatures. b, A typical architecture in a dilution fridge for quantum computing. |
Fig. 2. Application of cryoelectronics. |
Despite improved performance of semiconductor devices is achieved at low temperatures, efforts are still needed to sustain the proper operation of electronics and their potential release in such regimes. Firstly, due to the temperature-dependent characteristics of materials and devices, the relative characteristics of individual devices change dramatically when Si-CMOS circuits operate at low temperatures, and thus, substantial reengineering is required for the models of devices that make up the control circuitry25. Secondly, the variations and other deterioration effects resulted from the incomplete dopant ionization, carrier freezing and undesirable kink effects at low temperatures mainly caused by injection doping in Si-CMOS, will lead to circuit failure26,27. In addition, there also exist other problems at low temperatures, such as the increase in band gap of the semiconductor material due to the significant disappearance of thermal spreading, the appearance of quantum effects7,28, the deterioration of impedance matching resulting from the increase in the quality factor of passive devices as well as the decrease in thermal noise which results in a higher requirement of noise management for more prevalent 1/f noise6,18,28,29. The special mechanism of quantum computing requires the prevention of charged defects, which can lead to the failure of the dynamic and static properties of qubits, so higher material purity and interface quality are demanded30-32. On the other hand, the cooling power for every temperature stage in the fridge is finite. Commonly, the control chip is placed in the 3 to 4 K temperature regime for obtaining a higher power budget, which sets the upper limit of power consumption of the chip33. In particular, the dynamic power consumption of devices is required, as the leakage current of static power consumption is significantly suppressed at low temperatures7. Therefore, in order to reduce dynamic power consumption, ultralow operating voltage (dynamic power consumption is proportional to the third power of the voltage) or adjustable threshold voltage characteristic is needed by cryogenic electronic devices. The thermal dissipation of resistive elements also needs to be limited to attenuate the phonon-heat flow interference from the electronics to qubits. Moreover, for achieving efficient design of future large-scale quantum computing architectures, three-dimensional (3D) integrated control modules are required by two-dimensional (2D) arrays of qubit cells to improve system efficiency and integration5.
As a result, the materials and devices for cryogenic electronics are required to be featured with precisely predictable temperature-dependent properties, low dynamic power consumption, fast response time, high interface quality and 3D-integratable design. Although bulk Si-CMOS at cryogenic temperature experiences increased threshold voltages and kink effects due to the carrier freeze-out, it is either reduced or absent in more mature and advanced CMOS technologies34,35. Low-temperature quantum control chips and integration with qubit in advanced Si-CMOS technology have been successfully demonstrated at 4 K5,15,16,36. In addition to bulk Si-CMOS, the fully-depleted silicon on insulator (FDSOI) transistor with an external back gate provides an additional knob for adjusting the threshold voltage, to compensate for the increased threshold voltage at cryogenic temperature, and can be switched between low power and high performance, which is a potential candidate for cryogenic electronics37. An integrated quantum chip based on 22 nm FDSOI technology has been reported38, but extensive data analysis and compact model are still in progress to design reliable and optimized cryo-FDSOI-based circuits39-42. High-electron-mobility transistor (HEMT), which is realized in two-dimensional electron gas (2DEG)-based heterojunctions with high-quality material interfaces, could achieve high electron mobility at 4 K without the freezing out of carrier due to the low effective mass of electrons, and have been widely investigated for quantum transport. GaAs-based HEMT preamplifier grown by molecular beam epitaxy is commercially available with the power consumption as low as 0.3 mW at 4.2 K43. However, the self-heating of the InGaAs channel limits the noise reduction at cryogenic temperature44. LNA based on InP HEMT dominates the application at 1 to 200 GHz and 5 to 15 K, which is superior to other transistor technology, such as Si-CMOS, SiGe heterojunction bipolar transistor, GaAs or GaN HEMT45. However, HEMT technology does not meet the requirement for temperature below 4 K due to the excess power budget.
In addition to driving ambient-temperature Si-CMOS to low-temperature applications, another way is to find new electronics materials, especially low-dimensional materials that are already of interest in the field of ambient-temperature electronics. Among the promising candidates, carbon-based materials, including carbon nanotubes (CNTs) and graphene, are well suited for the development and application of cryogenic electronics due to their excellent electrical, thermal and mechanical properties, low dimension, ultralight mass and ultraclean surface.
In the current work, the criteria used for materials and devices were analyzed, and the research progress of CNTs and graphene for cryogenic electronics was discussed, excluding optoelectronic devices and the construction of qubits. Several sections are included in this review. The first section is the introduction, which presents the background of cryogenic electronics development and the problems associated with Si-CMOS at low temperatures. The second section describes carbon-based materials, including CNTs and graphene, and their material properties and compatibility for cryogenic temperature applications. The third section summarizes the recent progress of carbon-based cryogenic electronics, including logic devices at low temperature, quantum dot devices, temperature sensors, nanoelectromechanical devices, Hall devices and superconducting Josephson junction devices. In the final section, the summary and outlook are presented. It is expected that this review will shed new light on the development of carbon-based cryogenic electronics.
Carbon-based nanomaterials
Low-dimensional carbon-based materials consist of pure carbon atoms, mainly including fullerenes, CNTs and graphene; the latter two materials have received considerable attention in the post-Moore era for their electrical development. The primary advantages of low-dimensional carbon-based materials for cryogenic electronics are discussed in the current work. A brief description of the electronic structure is given below, while the detailed properties of graphene46-48 and CNTs49,50 can be found in the relevant reviews.
Graphene
Graphene is a 2D material consisting of sp2-bonded carbon atoms in a honeycomb arrangement. The energy band structure shown in Fig. 3a is known as the Dirac cone. In k-space, the conduction and valence bands of graphene are in contact at six points, i.e., the Dirac points, and thus, graphene is a semimetal with a zero-band gap. Unlike the parabolic dispersion relation in conventional 3D bulk materials, the linear dispersion relation of graphene around the low-energy region of the Dirac point contributes to electron motion with novel relativistic quantum phenomena described by the Dirac equation. Therefore, the electrons in graphene are theoretically Dirac fermions with an effective mass of zero, which can induce many exotic properties, such as the half-integer quantum Hall effect and Klein tunneling. However, the zero-band gap of graphene limits its electronics applications. There are some approaches to open the band gap of graphene, such as “shearing” the material into a narrow ribbon (0.1 to 3 eV) and breaking the spatial symmetry by a strong electric field in multilayer stacks. The electronic properties of a graphene narrow ribbon (GNR) depend highly on its width and edge structure. Two methods are generally adopted to fabricate GNRs, top-down “cutting” and bottom-up assembly, the latter of which permits atomically precise growth control by welding different precursors51,52. However, the scalable synthesis and fabrication of narrow GNR devices still remains a challenge, and GNRs with nonideal edges induce severe scattering and thus drastically degrade the carrier mobility and saturation velocity. Although edge passivation techniques can be adopted to suppress scattering, such as the use of h-BN, further improvement in the performance of GNR-based devices is still needed.
Fig. 3. Electronic structure of graphene (a) and carbon nanotubes (b). Reprinted with permission from ref.50. © 2015 American Physical Society. |
Carbon nanotubes
CNTs are considered to be quasi-1D hollow cylindrical structures which are formed by wrapping a single graphene sheet into a cylinder. The band structure of a CNT is defined by a series of k⊥ lines cut on the graphene Dirac cone due to the radial periodic quantization condition and determined by chiral indices (n, m) during convolution, as shown in Fig. 3b. The band gap of a CNT is zero without other secondary effects and exhibits metallic properties when the quantized line passes through the Dirac point (n − m = 3a, a is an integer); otherwise, it has a finite band gap of approximately 0.7 (eV)/D (nm) and exhibits semiconducting properties, where, D is the diameter of the CNT. Thus, the ratio of metallic to semiconducting CNTs is 1 : 2 in the natural case. The electronic structure of CNTs can be adjusted by multiple dimensionalities, such as electric fields, magnetic fields and stress, for novel applications. Semiconducting CNTs are mainly used as channel materials and widely applied in the field of electronics, while metallic CNTs are more suitable for the study of quantum transport. Customized chiral growth of CNTs, even on a single tube, can be employed to optimize the performance of target functional devices. Moreover, network and parallel arrays of purified semiconducting CNTs have shown great potential in large-scale ICs.
Carbon-based materials exhibit the advantages of higher mobility, thermal conductivity, current density and saturation velocity, as are summarized in Table 1. For cryogenic electronics, its is necessary to understand the temperature-dependent properties of materials, such as carrier density, scattering mechanisms, noise, and thermal expansion. Carbon-based materials not only demonstrate the potential to outperform Si-CMOS in ambient-temperature electronics, but also provide unique advantages in cryogenic electronics:
Table 1. Comparison of electronical parameters of Si-based and carbon-based materials. |
| Empty Cell | Si | CNT49,50 | Graphene46,49 |
|---|---|---|---|
| Mobility (cm2 V−1 s−1) | 1600 (electron) 500 (hole) | 106 | 106 |
| Thermal conductivity (W m−1 K−1) | 230 | 3500 | 5000 |
| Band gap (eV) | 1.12 | 0-2 | 0 |
| Current density (A cm−2) | 120 | 109 | 108 |
| Saturation velocity (cm s−1) | 107 | 4 × 107 | 4 × 107 |
1.Weak temperature-dependent material properties and doping-free technology enable carbon-based electronics to operate properly at cryogenic temperatures, moreover lower power consumption is achieved compared with Si-CMOS;
2.Low-temperature process technology allows for monolithic 3D integrated chips, and the higher thermal conductivity mitigates heat dissipation issues, thereby facilitating an increase in device density;
3.Nanometer-scale carbon-based materials are convenient for the design of quantum dot (QD) devices and single-electron transistors (SETs)53 for sensitive electric field, magnetic field and temperature detection;
4.Carbon-based quantum devices are featured with higher coherence times and additional interference with qubits is avoided due to their high stability with strong carbon‒carbon bonds, moreover lower defect density is realized due to ultraclean and nonsuspended bond surfaces;
5.Suspended carbon-based materials facilitate the fabrication of excellent electromechanical sensors, which benefit from ultralight mass and is conductive to detect the effect of small forces or individual charges reaching the quantum limit;
6.Based on their strong interactions with substrates, carbon-based low-dimensional materials can be functionalized with a variety of substrates to customize device characteristics at variable temperatures and cryogenic temperatures.
TRANSISTORS
Field-effect transistors (FETs) are the core components of modern logic computing circuits, where carbon-based nanomaterials have demonstrated great potential at ambient temperature from individual devices to circuits and chips64-72. Recent research studies have focused on individual devices and simple circuits, moreover the characteristics of carbon-based FETs at cryogenic temperatures are discussed below.
CNT-FETs
CNTs are potential candidates for extending Si-CMOS and have demonstrated the potential to surpass the performance of Si-CMOS of the same size73ue to their excellent electrical properties. Benefitting from the 1D geometry of CNTs, the Fermi pinning effect is moderated74,75. The polarity of CNT-FETs can be defined by the different contact metals, which determine the type of carriers that can be injected more easily into the CNT channel, instead of the injection doping in conventional Si-CMOS. Thus, contact metals with appropriate work functions can be used for the fabrication of p-FETs (Pd76,77) and n-FETs (Sc78,79, Y80, Hf81) while maintaining a high quality of ohmic contact down to 4.3 K76,78,80. The technology circumvents the performance loss and strong temperature-dependent electrical characteristics caused by dopant freeze-out and incomplete ionization at cryogenic temperatures. The transport properties of devices with ideal ohmic contact are dominated by the scattering mechanism arising from the dielectric environment of CNTs, such as lattices, carriers, gate stacks and substrates. The electron mean free path, LMFP, of CNTs can exceed microns at room temperature due to the ultraclean and robust carbon‒carbon bonds, and metallic CNTs exhibit a longer LMFP82,83. Therefore, CNT-FETs can work near the ballistic transport regime with the ideal performance at room temperature as long as the channel length L < LMFP76-84. When phonon scattering dominates the temperature-dependent characteristics of devices, the inelastic scattering between electrons and acoustic phonons is suppressed inducing an increase in current; however, temperature-independent Coulomb scattering and roughness scattering dominate at cryogenic temperatures7. As a result, the LMFP of a device tend to increase with decreasing temperature and subsequently saturates due to freezing out of the phonons and temperature-independent elastic scattering85, which extends the parameter space of the low-temperature ballistic device based on CNTs.
Lower power consumption is another important requirement for cryogenic electronics. The finite cooling power of a fridge limits the power ceiling of circuits, and higher design flexibility can be achieved by low-power electronics within the power budget at cryogenic temperatures. The operating voltage of CNT-FETs can be reduced to less than 0.6 V, which significantly reduces the dynamic power consumption63. The energy gap and effective mass of CNTs used for the FET channel (∼0.5 eV of 1.5 nm diameter; 0.01 to 0.1 m0) are smaller than those of Si (1.12 eV; > 0.15 m0), and hence demonstrating higher static power consumption owing to the higher leakage current at room temperature86,87. However, cooling compensates for this drawback since the thermal excitation current is suppressed in the off state, which directly results in a significant increase in the on/off ratio from 105 (300 K) to 109 (4.3 K), as shown in Fig. 4a88. Moreover, the subthreshold swing (SS) is simultaneously reduced from 100 mV/dec (300 K) to 30 mV/dec (4.3 K) in Fig. 4b with a standard linear dependent-scaling law, which demonstrates an increase in the switching speed and a reduction in the power consumption of CNT-FETs at cryogenic temperatures. Therefore, CNT-FETs are advantageous for cryogenic applications with improved performance and the avoidance of negative effects from dopants. There can be further optimization of device structure and processing due to temperature-dependent movable charge traps in the gate stacks, and the effect of a substrate can lead to variations in threshold voltage and performance.
Fig. 4. Carbon nanotube-based FET at cryogenic temperatures. a, Temperature-dependent ON- and OFF-state currents. The inset is a schematic diagram of the CNT FET device with a self-aligned top gate structure. b, Transfer characteristics of the CNT FET measured at 300 K and 4.3 K88. c, Photo of the CNT FET embedded in RF pads. d, fT versus gate voltage Vgs at several temperatures90. e, Schematic energy band diagram for the CNT FET at different bias voltages. f, Schematic diagram of the CNT film-based FET device with a self-aligned top gate structure. g, SEM image of CNT five-stage ring oscillators (ROs) based on the self-aligned FET. h, Comparison of temperature stability between different devices. i, The relative temperature coefficient of the oscillation frequency (f0) in five-stage ROs101. Reprinted with permission from refs.88,90,101. © 2011, 2012, 2021 Wiley-VCH GmbH. |
The 1D geometry of CNTs theoretically and experimentally yields a very low intrinsic (quantum) capacitance per tube of 60 aF/µm, and the transit frequency (fT) of CNT-FETs exceeds 110 GHz/µm in the ballistic limit89, which is an attractive device for analog high-frequency applications. Multiple CNTs without semiconducting purification can also be used for radio frequency (RF) applications as long as the intrinsic voltage gain is above unity89. The RF performance is characterized in Fig. 4d at cryogenic temperature in a fork-finger FET structure (Fig. 4c) with thousands of single-wall CNTs90. The weak temperature dependence of fT (8 GHz at 300 K; 9 GHz at 77 K) is associated with the temperature dependence of the gate/source capacitance Cgs. The maximum intrinsic voltage gain increases (gm/gds) with decreasing temperature (1.53 at 300 K; 2.34 at 10 K), which demonstrates the potential for analog power applications operating at cryogenic temperatures. The noise factor is improved by the reduction in thermal noise in the gate and source resistance at 10 K90. However, in terms of direct current (DC) characteristics, the on-state current does not behave like the ohmic behavior in a single CNT due to the presence of a Schottky barrier (SB) between the semiconducting CNT and the metallic CNT.
For large-scale ICs, the development of CNT electronics requires that materials be featured with high semiconducting purity and wafer-level homogeneity. Currently, solution-derived randomly oriented CNT films with the purity of 99.9999% and large area uniformity91re proved to be the most mature CNT materials for electronics. Network-CNT film-based large-scale ICs have also been reported92-94. The transport mechanism in the network-CNT film becomes complex compared with that in the single CNT. In network-CNT films, carriers are not only transported in individual CNTs but also hop across the junction between individual CNTs, which tends to be more complicated considering from the aspects of the angle, chirality, disorder and field screening of CNTs. The films can be viewed as a disordered semiconductor whose macroscopic conductivity is limited by carrier hopping between the conducting elements95. In addition, the semiconducting purification process of network CNT films requires a polymer to be wrapped around CNTs to distinguish between metallic and semiconducting CNTs. This also leads to changes in the electrical characteristics of network CNT-based devices. Both the on-state current and carrier mobility in the network-CNT film decrease with decreasing temperature, as does the hysteresis96. The fluctuation-induced tunneling97,98 model can describe the transport behavior instead of the variable-range hopping (VRH)99,100 model in a pure-network-CNT film (without semiconducting purification). Transport barriers are formed between polymer-wrapped CNTs to block inter-tube charge transport, leading to the domination of thermal excitation at high temperature, while the domination of temperature-independent tunneling at low temperature. The temperature-dependent performance of CNT FETs is also suppressed by the reduction ratio of phonon-assisted tunneling due to narrowed barriers on the contact and inter-tube at large bias voltages, as shown in Fig. 4e. The temperature dependency of the network-CNT-based FET (Fig. 4f) can be weakened by the combination of two temperature-dependent transport mechanisms on the condition that the opposite temperature-dependent effect of phonon scattering is taken into account. Consequently, the network-CNT-based FET exhibits higher temperature stability than the single CNT-based FET and Si-based FET, as shown in Fig. 4h101. The maximum oscillation frequency (fo) of five-stage ring oscillators (ROs) constructed by the above temperature-stable FETs (Fig. 4g) can reach 1.5 GHz, which could meet the requirement of amplification or detection of spin qubits. Benefited from the improvements in materials and processes, a higher oscillation frequency of 5.54 GHz at room temperature based on network-CNT film has been achieved94, which can cover the frequency of superconducting qubit (typically between 4 ro 6 GHz). The oscillation frequency varies within 0.5% in the temperature range of 300 to 80 K, as shown in Fig. 4i101. Although the network-CNT film electronics at cryogenic temperature mainly focus on an individual device and are still in progress, the weak-temperature dependence of network-CNT film electronics allows us to give qualitative predictions for the electronical performance101: the logic circuits at terahertz frequencies94,102, the RF amplifiers with high gain and good linearity in the terahertz band103,104, and the more highly integrated cryogenic chips68,92,93.
Graphene-FETs
There is a finite residual conductance even at the Dirac point where the density of states (DOS) is zero105, which limits the on/off ratio of graphene FETs to approximately 2-20 at room temperature. Therefore, it is of great challenges for graphene to be used as a channel material in digital FETs. However, graphene-based devices are excellent candidates in high-frequency areas, such as amplifiers, mixers and high-performance RF FETs, owing to their ultrahigh carrier mobility and saturation current71,72. In addition, graphene can also be used as an interconnection material106r an antenna (>3.5 GHz)107. As a 2D material, all charge transport occurs at the graphene surface, which leads to high sensitivity to the environment through metal contacts, gate stacks and substrates, leading to a dramatic effect on transport behavior. The characteristics of a graphene-FET with a Pd contact in the temperature range of 300 to 6 K are shown in Fig. 5a. Here, the current increases with decreasing temperature, and the inset demonstrates the enhanced carrier mobility at low temperature. The contact resistance (Rc) extracted in the graphene-FET exhibits anomalous temperature-dependent behavior that increases with increasing temperature, as shown in Fig. 5b108. While, Rc decreases with increasing temperature in conventional metal-semiconductor junctions due to the reduction in the effective SB height and the enhancement of thermionic carrier emission. The anomalous behavior of Rc arises from the competition of characteristic lengths between the ballistic and diffusive transport at the contact of metal electrodes and graphene. The ratio of two characteristic lengths (λ: mean free path; λm: metal-graphene coupling length) varies with temperature, leading to a variation in metal-graphene transmission, TMG, shown in Fig. 5c. The lower Rc at low temperature is attributed to the domination of ballistic transport, where, TMG = 75%108. Meanwhile, the suppressed phonon scattering increases the carrier mobility with ohmic contact at low temperature48.
Fig. 5. Graphene-based FET at cryogenic temperatures. a, Temperature-dependent transfer characteristics of a graphene-FET. The inset is the measured electron and hole mobilities as a function of temperature at a carrier density. b, Measurement of the Pd-graphene contact resistance as a function of temperature at different gate voltage values. c, Calculated transmission efficiency TMG, determined using Matthiessen's rule, as a function of the ratio of the mean free path (λ) and metal-graphene coupling length (λm). The inset is the Pd-graphene contact, showing the transfer length LT. Reprinted with permission from ref.108. © 2011 Nature Publishing Group. d, Temperature dependence of the carrier mobility in the graphene FET fabricated on NFC polymer substrates. Reprinted with permission from ref.110. © 2009 American Chemical Society. e, Schematic diagram of a top-gated graphene r.f. transistor on the DLC substrate. f, Cross-sectional TEM image of a graphene transistor with a gate length of 40 nm. g, Current gain as a function of frequency for three channel lengths at 4.3 K. The values of fT are 28 GHz, 70 GHz and 140 GHz. h, Summary plot of the temperature dependence of fT for three different devices; little temperature dependence was found. Reprinted with permission from ref.115. © 2011 Nature Publishing Group. |
The discrepancy in temperature-dependent mobility can also be induced by the different substrates of graphene devices due to differences in scattering intensity109. For example, the Coulomb scattering-dominated mechanism leads to a weak temperature dependence on a silicon substrate. However, on a polyhydroxystyrene-based polymer (NFC) substrate, phonon-dominated scattering contributes to strong temperature-dependent behavior, and the substantially reduced Coulomb scattering leads to higher mobility, as shown in Fig. 5d71,110. Minimal scattering can also be obtained with cleaner substrates, such as h-BN or suspended graphene, resulting in higher mobility and higher RF performance, as well as weaker temperature-dependent devices109,111. Such ultraclean substrates can also greatly suppress noise in graphene-based devices for low-noise measurements and attenuate interference with qubits112-114. A graphene-based RF FET on a diamond-like carbon film grown on SiO2 (Fig. 5e and 5f) with a channel length of 40 nm exhibits an fT of 155 GHz, as shown in Fig. 5g115. There is no significant variation in fT from 300 to 4.3 K in Fig. 5h, which demonstrates the potential of graphene with gigahertz capabilities over a large temperature range. Although the low on/off ratio does not affect the use of RF FETs, the performance can be limited by the high leakage current72. In addition to traditional FETs and RF FETs, graphene can also be utilized to tunnel FETs for steeper SS.
Table 2. Comparison of electronical metrics of Si-based and carbon-based devices at cryogenic temperature. |
| Empty Cell | Si-based34,40,116 | CNT-based88,90,101 | Graphene-based115 |
|---|---|---|---|
| Mobility (cm2 V−1 s−1) | 200-300 (5 K)a | 5500 (4.3 K)d | 4000 (6 K) |
| SS (mV dev−1) | 20 (5 K)a | 30 (4.3 K)d | |
| fT (GHz) | 494/337 (n/p 5.5 K)b | 9 (77 K) 8 (10 K)e | 155 (4.3 K) |
| fmax (GHz) | 497/372 (n/p 5.5 K)b | 9 (77 K) 8 (10 K)e | |
| gm/gds | 20.1/12.4 (n/p 70 K) 19.3/12.4 (n/p 5.5 K)b | 9 (77 K) 2.3 (10 K)e | |
| τP (ps) | 10 (4.3 K 101-stage)c | 90 (80 K 5-stage)e | |
| fO shift | ∼7% (300-40 K)c | ∼0.5% (300-80 K)e |
fmax: power gain cut-off frequency; τP: stage delay; fO shift: temperature dependence of oscillation frequency. a: 14 nm FinFET; b: 22 nm FDSOI; c: 28 nm FDSOI; d: single CNT; e: network-CNT film; |
QUANTUM DOT DEVICES
One of the main advantages of carbon-based nanomaterials is their low-dimensional geometry, which allows for the scaling down of Si-ICs while maintaining high electrical performance. Alternatively, the electrical performance of conventional bulk Si at thicknesses less than 3 nm is greatly degraded by strong surface scattering. Furthermore, novel quantum-mechanical electronic devices can be developed, where quantum effects arise from the reduced dimensionality, especially at low temperatures. In a low-dimensional structure, a zero-dimensional QD combined with the long quantum coherence time (spin, valley and Kramers) of carbon-based materials50,117, facilitates the studying of electronic states, quantum transport and coherent qubits. SET based on QDs can be developed as a sensitive sensor to detect charge states, the external electromagnetic environment and temperature, etc. CNTs and graphene, by restricting the electron transport in only one or two dimensions, are convenient for building QDs with high quality and small size; this structure is much smaller than that of bulk Si or 2DEG. Moreover, carbon-based low-dimensional materials can provide defect-free lattices at the microscopic scale, and replaceable substrates offer a wider selection of dielectric environments, so these materials are ideal platforms for fabricating QD devices. The approaches of limiting electron transport in micro- and nanoprocessing technologies usually induce potential barriers to form a longitudinal constraint, which can be established by electrostatic potential on gate voltages or a SB at contact. Detailed information on the classical application of a SET as an electrostatic detector can be seen in other reviews50,118,119. The following section focuses on the latest applications of QD-based SET structures.
SET imaging
If the operating point of a QD is placed on the slope of the Coulomb blockade peak (maximum transconductance), then a weak change in potential and capacitance will induce a sensitive variation in the charge of the QD, which contributes to drastic changes in the current through the QD, as shown in Fig. 6a. The effect can be employed to detect any external changes in potential and capacitance, such as electronic and mechanical effects. The charge sensitivity of a graphene-SET can reach approximately 10−3 e/Hz0.5 at cryogenic temperatures120,121, and an RF-SET based on a CNT with a high operating frequency of 754.2 MHz could achieve a charge sensitivity of 2.3 × 10−6 e/Hz0.5 over a bandwidth of 85 MHz at 4.2 K by reducing the low-frequency flicker noise, as shown in Fig. 6b122. Moreover, it can act as a noninvasive local detector due to the detection process without charge transfer or mechanical contact on the sample123. However, the cost of ultrasensitive detection is that any nonideal interference, such as photoresist residues and defects in the dielectric environment, can lead to electronic disorder in the quantum system of a detector and detector failure. To avoid chemical contamination, researchers have developed a dry transfer process for CNTs124-130 to obtain ultraclean intrinsic devices. The SET made by this method can circumvent external interferences to become an ultrasensitive sensor. S. Ilani and coworkers developed a locally tunable ultralow disordered electron system based on a CNT SET with the adoption of a customized low-temperature (4 K) scanning probe microscope. These researchers precisely transferred CNTs in situ to a gated array, as schematically shown in Fig. 6c127. A CNT SET on a movable probe cantilever allows for the noninvasive detection of fragile electronic states and then maps the charge states with spatial locations. Thus, an imaging technique, capable of real-time and real-space visualization, is realized for electronics, such as electronic Winger crystals and interacting hydrodynamic electron flow54,55,123,131,132, as shown in Fig. 6d-f. In addition to imaging the above equilibrium mechanism, the voltage drop and current density distribution of flowing electrons in 2D can also be imaged simultaneously (in Fig. 6g) with nanoscale spatial resolution (∼100 nm) and microvolt voltage sensitivity. The technology can work from ambient to cryogenic temperature, tolerating strong magnetic fields due to the SET being strongly thermally coupled to the helium bath. The SET probe induces a local carrier density fluctuation at 109 cm−2, which is smaller than the disorder fluctuation and can be negligible133. This technique allows imaging of nondiffusive flow buried in nanostructures and a full investigation of the transport mechanism caused by disorder, electron-electron interactions and scattering mechanisms, where localized electron flow mapping can reveal critical information beyond conventional methods. The sensitivity of the voltage and current density are 2 µV/Hz0.5 and 10 nA/(µm/Hz0.5) for typical carrier densities in semimetals of n = 1011 cm−2 133.
Fig. 6. CNT-based SET for noninvasive imaging. a, Mechanism of the SET detector. Reprinted with permission from ref.123. © 2013 Nature Publishing Group. b, Charge sensitivity of a CNT-based RF-SET at 4.2 K. Reprinted with permission from ref.122. © 2008 AIP Publishing. c, Schematic diagram of a nanoassembly technique for creating clean and complex CNT-based devices127. d, Schematic diagram of a visualization probe based on CNTs. e, Imaging ballistic and hydrodynamic electron flow profiles54. f, Hydrodynamic electrons flowing in a Corbino disk without Landauer-Sharvin resistance55. g, Imaged current streamlines (black isocontours) superimposed on the zero-field voltage contours (color)133. Reprinted with permission from refs.54,55,127,133. © 2013, 2019, 2022 Nature Publishing Group. |
Electromagnetic field sensors
The same geometry of CNT QDs can work not only in SET mode but also in the charge qubit mode for ultrasensitive detection of electric and magnetic fields134. The construction of a two-level charge qubit based on the lifted degeneracy of the spin and valley in a finite parallel magnetic field is shown in Fig. 7a. The detection signal of the electromagnetic field can be read with the adoption of the simple approach of a conductivity measurement. The sharper coherence-limited transition of qubits significantly improves the potential sensitivity compared with the thermally broadened Coulomb blocking of the SET, as shown in Fig. 7b. The potential sensitivity of ∼600 nV/Hz0.5 is beyond the SET mode133, and the magnetic sensitivity of ∼39 µT/Hz0.5 can operate at 3-8 T, the magnetic sensitivity of which is close to a nitrogen-vacancy (NV) centre magnetic sensors with the sensitivity of 3 µT/Hz0.5 at 6 K and the same nanometer-scale spatial resolution135. The detection performance can be further enhanced by optimizing the contact quality and fluctuation of the magnet. Moreover, the back-action interference of qubit sensor on the sample is also less than that of the SET sensor.
Fig. 7. CNT-based qubit for ultrasensitive electromagnetic sensing. a, Charge stability diagram. The coherence-limited transition of qubits between |B>, |D> and |N> is used for electromagnetic sensing. b, Comparing SET and qubit performance in sensing DC electric potential and DC magnetic field. Reprinted with permission from ref.134. © 2020 Nature Publishing Group. |
TEMPERATURE SENSORS
Highly sensitive temperature-detecting technology can be adopted not only to monitor the temperature in a cryogenic system but also to understand the thermal transport of complex devices to address the heat-dissipation bottleneck caused by increased integration and clock frequency136. The excellent thermal properties and stability of carbon-based materials are beneficial for temperature sensors, especially at extreme temperatures. Moreover, the nanometer sacle of carbon-based materials could provide the advantages of local accurate sensing at the nanoscale, reducing the proximal disturbance to the environment, and low power consumption, which is essential in a sophisticated thermal flow system at cryogenic temperatures137. Therefore, mesoscopic temperature sensors based on carbon-based materials are featured with remarkable advantages in cryogenic temperature. The main mesoscopic experimental techniques for thermometry include resistance, normal-insulator-superconductor transition, Coulomb blockade, noise and Josephson junctions (JJs)136. It has been reported that temperature sensors based on the temperature-dependent resistance of CNT films are endowed with stability and functionality over a wide temperature range and down to 2 K138-143. For precise measurements in cryogenic thermometry, the magnetic sensitivity of a sensor, as one of the most important measurement uncertainties, needs to be quantified, and then the temperature sensor can be calibrated at a finite magnetic field. The magnetic dependence of CNT films can be approximated by the Mott law for three-dimensional variable range hopping (3D-VRH) and correlated with the chirality of CNTs142. Graphene-based resistive temperature sensors, operating from 295 to 20 K, are far more sensitive than resistive (metal) temperature sensors below 50 K144.
Another calorimetry method is based on Johnson-Nyquist noise (thermal noise), which is an excellent and nearly noninvasive probe of electron temperature for nanoscale devices with minimal backaction heating. Noise thermometry can reach the thermodynamic limit, which is preferable for operating at cryogenic temperatures145. The electron gas in graphene is expected to exhibit extreme thermal isolation owing to the ultrahigh phonon thermal conductivity, single-atom thickness, low electron density, linear dispersion and weak electron-phonon coupling146-148. The weak thermal coupling and small electronic heat capacity (rapid thermalization), resulting from a vanishing DOS at the charge-neutrality point, leads to a high sensitivity of the graphene-based bolometer and calorimeter. Ultrasensitive measurements at cryogenic temperatures could be achieved by two-terminal-noise thermometers based on graphene with a thermal noise mechanism145,149-151. Microwave-frequency noise thermometry with a sensitivity of 2 mK/Hz0.5 and a bandwidth of 80 MHz based on graphene at 2 K has been reported, as shown in Fig. 8a145. However, the above mechanisms, in which the device under test is also used as the thermometer, are limited to diffusive conducting states with low energy loss to phonons and low contact resistance, which restricts the applications of graphene152. Thermal transport measurements are beneficial for clarifying the nature of strong electron-electron interaction effects in low-dimensional systems, such as electron Wigner, strongly correlated insulators and 2D magnets. This measurement requires accessing the dissipative properties of electrons separated from the prevailing phonon contribution in thermal transport, which is especially challenging in low-dimensional systems. To measure other materials and the nondiffusive regime, a nonlocal measurement method on a multiterminal device is applied to independently measure the electron-thermal transport behavior in multidimensional systems, such as graphene, CNTs and the microscale bulk electrical insulator RuCl3, with a precision of approximately 1% of the thermal conductance quantum at 5 K, as shown in Fig. 8b152. Moreover, a superconductor-graphene-superconductor Josephson junction bolometer embedded in a microwave resonator shows the energy resolution of a single 32-GHz photon and a short thermal time constant, reaching the fundamental limit imposed by intrinsic thermal fluctuation at 0.19 K153. Contrastively, NV centre-based thermal sensors achieve 97% temperature accuracy from 300 to 80 K154nd an ultra-high temperature sensitivity near ambient temperature of and 2 mK/Hz0.5 155,156.
Fig. 8. Graphene-based noise thermometry. a, The measurement circuit of a two-terminal microwave-frequency noise thermometry. Reprinted with permission from ref.145. © 2012 American Physical Society. b, Circuit and geometry for four-terminal nonlocal noise thermometry152. Reprinted with permission from ref.152. © 2021 Nature Publishing Group. |
NANOMECHANICS
Mechanical resonators are potential candidates for applications in mass sensing, quantum motion detection and RF signal processing, etc. The resonator performance can be improved by increasing the resonant frequency and decreasing the resonator mass. The ultralight mass and excellent mechanical properties of carbon-based materials provide an attractive platform for high-performance electromechanical nanodevices, which also exhibits a smaller encapsulation size compared with conventional mass spectrometers. Moreover, the oscillation of carbon-based nanomechanical resonators can be easily tuned by the gate voltage, which is well suited for voltage-controlled oscillators157. The gate-tunable conductance of carbon-based materials enables a fully electrical readout of mechanical motion, which facilitates their use in RF devices such as filters and oscillators158,159. Based on the gate-tunable resonant frequency, carbon-based nanomechanical resonators can be used to achieve parametric amplification so as to improve the sensitivity by preamplifying the motion amplitude through parametric effects before electrical conversion. Experimentally, a frequency modulation of 4.9 MHz/V and a parametric amplification gain of 18.2 dB are realized by the CNT-based resonator, as shown in Fig. 9a160. Consistent with the requirements of high-quality QD-based devices, carbon-based electromechanical devices are typically fabricated in suspension to avoid interaction with the dielectric environment and to protect the ultraclean material surface. Moreover, mechanical motion can strongly couple with charge transport, especially considered in few-electron tunneling behavior161-166. A SET combined with electromechanics is the most sensitive nanomechanical probe with an accuracy close to the quantum limit. One common strategy to improve the sensitivity is to reduce the thermal noise through cooling, which is accompanied by a reduction in the mechanical damping rate. This promotes the detection of ultraweak interactions (such as the spin of individual electrons167rmolecules168) and the study of fundamental processes in condensed states (such as the interaction of a nanoresonant cavity with a superconducting qubit169), with an optimizing-noise readout. The effective sensitivity of the probe is determined by the quantum uncertainty, which relates the minimum mechanical displacement with the minimum applied force for detection. The key to enhancing performance is dependant on a mechanical quality factor Q, i.e., the ratio between the energy stored in the resonant cavity and the energy lost in a single oscillation cycle. Generally, the factor Q and resonant frequency increase with the temperature decreasing from ambient to cryogenic temperature, which is mainly attributed to the difference in the coefficient of thermal expansion between carbon-based and contact materials. Therefore, for achieving proper operation over a wide temperature range159,170-174 or obtaining the optimal performance at a given low temperature, the temperature dependence of the oscillation also needs to be fully understood. Moreover, the presence of nonlinear damping in nanomechanical resonators, such as CNTs and graphene, unlike macroscopic resonators, can degenerate the Q factor of the resonators. A Q factor of 105 was achieved in graphene resonators at 90 mK after minimizing the nonlinear damping175. Both improved readout and quality factor are of great significant for higher sensitivity to electron charges, mass and force. Due to themechanically induced changes in the transconductance resulting from the strong coupling, the charge sensitivity of a CNT-based RF-SET is enhanced from 6 × 10−6 e/Hz0.5 for the static case to 9.7 × 10−7 e/Hz0.5 with an operating frequency of 1.3 kHz at 50 mK176.
Fig. 9. Carbon-based nanomechanical devices. a, Left: Schematic and SEM image of parametric amplification based on a suspended CNT. Right: Resonance frequency and gain as a function of the amplitude of the gate voltage. Reprinted with permission from ref.160. © 2011 American Chemical Society. b, Left: Schematic and SEM image of a nanomechanical mass sensor based on a suspended CNT (diameter 1.7 nm; suspended length 150 nm). Right: Measuring mass resolution at 5.5 K. The red dashed line corresponds to the mass of one hydrogen atom. Reprinted with permission from ref.177. © 2012 Nature Publishing Group. c, SEM image of large-scale arrays of graphene-based resonators. Reprinted with permission from ref.172. © 2010 American Chemical Society. d, SEM image and schematic of coherent phonon dynamics between three graphene-based resonators. Reprinted with permission from ref.187. © 2020 National Academy of Sciences. |
A mass detector based on a suspended CNT can reach the sensitivity of 1.7 × 10−24 g, as shown in Fig. 9b, which is close to the mass of a proton (1.67 × 10−24 g) at 5.5 K177. The process of high-current annealing of CNTs is adopted to remove contaminating molecules adsorbed on the surface, resulting in more stable and higher quality detection. Meanwhile, the device can be restored to the initial state after current annealing due to its mechanical robustness and chemical stability. In addition, extending the length of the suspended part of the CNT can amplify the weak force into a considerable displacement more effectively. The force sensitivity in a suspended 4 µm device reaches 12 zN/Hz0.5, When calculating based on the relative height of the driven peak and the thermal resonance at 1.2 K178, the force sensitivity in a suspended 4 µm device could reach 12 zN/Hz0.5. A device with a quality factor of 1.5 × 105 is achieved by suppressed dissipation of mechanical energy, which is attributed to phonon-phonon scattering at 20 mK and suppressed electron motion with Coulomb blocking162. The improved readout technology and stabilized oscillation further induce a quality factor on the order of millions179,180. Based on the above optimization, the detector achieves a displacement sensitivity of 0.5 pm/Hz0.5 and a force sensitivity of 4.3 zN/Hz0.5 at 300 mK181. The large surface area of graphene increases the mass capture efficiency, and the graphene-based nanomechanical resonators are compatible with large-scale implementation, as shown in Fig. 9c172, however, the ultimate mass resolution of graphene is not lower than that of CNTs due to the larger mass173. Therefore, there is a trade-off between extreme resolution in CNTs and higher capture efficiency in graphene. The force sensors at cryogenic temperature based on monocrystal Si182, monocrystal diamond183, monocrystal-strained Si184, hierarchical Si3N4185 and Si3N4 nanostring186lso exhibit ultra-high quality factors and force sensitivity, as summarized in Table 3. Owing to the ultra-small nanometer size and excellent mechanical properties181, the most sensitive force sensors are provided by CNT-based resonators although other competitors show higher quality factors. Electrically tunable coherent phonon dynamics were achieved between three spatially separated graphene-based nanomechanical resonators coupled in series with a Q factor of 1.1 × 105 at 10 mK, as shown in Fig. 9d; this demonstrates that information encoded in vibrational modes can be stored, transmitted, and manipulated in separated spaces187.
Table 3. Comparison of quality factor and force sensitivity of various force sensors at cryogenic temperature. |
| Empty Cell | Q | Force sensitivity (N/Hz0.5) | T (K) |
|---|---|---|---|
| Monocrystal Si182 | 1.5 × 105 | 8.2 × 10−19 | 0.11 |
| Monocrystal diamond183 | 6 × 106 | 5 × 10−19 | 0.093 |
| Monocrystal-strained Si184 | 1010 | 5 × 10−20 | 7 |
| Hierarchical Si3N4185 | 1.1 × 109 | 9 × 10−20 | 6 |
| Si3N4 nanostring186 | 2.3 × 109 | 9.6 × 10−21 | 0.046 |
| Single CNT181 | 6 × 106 | 4.3 × 10−21 | 0.3 |
In addition to detecting small forces, the strong electromechanical coupling means that the slightest motion of the CNTs can affect the flow of electron through the device, and thus, a suspended CNT can act as an excellent electromechanical sensor that converts mechanical motion into electron flow, and vice versa. Even the force exerted by a single electron can change the mechanical dynamics, and the displacement can also creat a back-action force, which suppresses and amplifies the thermal vibrational fluctuation, as well as generates self-oscillation, simply by applying a DC current188,189. The suppression of the thermal vibrational fluctuation of the mechanical eigenmode is equivalent to cooling the eigenmode according to the equipartition theorem. Therefore, the delayed back-action force induced by Joule heating from constant current can amplify and attenuate the amplitude of the suspended CNT, the schematic is shown in Fig. 10a. Amplification leads to self-sustaining oscillations, which can “cool” the mechanical mode to only five quanta of vibration energy, as shown in Fig. 10b, and Joule heating is used to cool mechanical vibrations180,190. Forty times higher electron-mediated mechanical cooling is achieved by simply allowing current to flow through the device191. More efficient ground state cooling depends on higher back-action efficiency by a higher transconductance and stronger gate coupling in the devices.
Fig. 10. CNT-based electromechanical resonator. a, Measurement schematic and SEM image of the suspended nanotube. b, Mechanical vibrations are cooled to 4.6 ± 2.0 quanta (n) at Vsd = 0.565 mV. Reprinted with permission from ref.180. © 2019 Nature Publishing Group. |
HALL SENSORS
In the absence of long-range impurity scattering, the mobility of graphene is enhanced at a low carrier density48, which is ideal for Hall magnetic detection, while the mobility of most other semiconductor-based 2D electronic systems is decreased at a low carrier density192. Graphene-based Hall sensors have been extensively studied at ambient temperature193. Other high-performance Hall sensors, such as 2DEGs, exhibit significant nonlinearity and voltage saturation at a high field and 1.5 K194, thus limiting their application at high fields. In addition, conventional Hall sensors are not recommended for low-temperature applications due to dopant freeze-out. In contrast, the magnetic sensitivity of graphene gate control devices can be significantly increased at low temperatures. The charge noise in graphene devices can be minimized by encapsulating ultraclean graphene in h-BN so as to reduce the intrinsic charge inhomogeneity and avoid the carrier density fluctuations induced by charge hopping in the dielectric material of the gate-controlled devices. Subsequently, a high carrier mobility at a low carrier density can be achieved195, resulting in an unusually large Hall coefficient and stable sensitivity196. However, the quantum Hall effect in graphene at low temperature poses great challenges for the cryogenic applications of the graphene-based Hall sensors. There is a constant Hall voltage when the magnetic field or carrier density changes in the quantum Hall regime48. Schaefer et al. modulated the carrier density to a regime where the Hall voltage varies with the magnetic field, shown in Fig. 11b, at 4.2 K. As shown in Fig. 11c, the sensitivity reaches 3 µT/Hz0.5 despite the increased low-frequency noise, which is mainly attributed to charge fluctuations between the local and extended quantum Hall states196. ParagrafTM, a spin-out from Colin Humphreys’ group, developed a large-area and high-quality graphene growth technique to produce a robust, low-noise and high-sensitivity (sub 100 nT) Hall sensor. The Paragraf sensor exhibits a highly linear response at 1.5 K, within 30 T and a lower heat (∼pW), as shown in Fig. 11d197.
Fig. 11. Graphene-based Hall sensor. a, Optical microscope image and schematic diagram of the graphene Hall sensor encapsulated in h-BN. b, Magnetic field dependence of Hall resistance in the quantum Hall regime at 4.2 K. c, Hall coefficient RH and magnetic sensing sensitivity as a function of gate voltage Vg at 3 T. Reprinted with permission from ref.196. © 2020 Nature Publishing Group. d, Hall voltage response at 1.5 K of Paragraf's graphene Hall sensor and a commercially available 2DEG sensor between 0 and 30 T. Reprinted with permission from ref.197. © 2021 Paragraf Limited. e, Quantum Hall resistance standard in graphene-based devices compared with GaAs/AlGaAs devices. f, Examples of convenient combinations of relaxed operational conditions in graphene-based devices. Reprinted with permission from ref.201. © 2015 Nature Publishing Group. |
One application for graphene Hall sensors is to be used as an improved electrical standard198-201. The quantum Hall effect provides a universal and reproducible standard for resistance, which is theoretically based only on Planck's constant h and the electronic charge e. Benefiting from the massless relativistic particles in graphene, the energy spacing between the first two degenerate Landau levels in graphene is larger than that in GaAs/AlGaAs at the same magnetic field48,200. Hall sensors based on high-quality graphene chemical vapor deposition (CVD) grown on SiC can achieve the resistance standard in relaxed experimental conditions compared with that in GaAs/AlGaAs202. The quantum Hall resistance standard in graphene can be accurately quantized to within 1 × 109 over a wide range of magnetic flux densities, down to low magnetic flux density (3.5 T), at a high temperature (10 K) or with a high current (0.5 mA), as shown in Fig. 11e and 11f201. The condition will be further relaxed with further improvements in graphene growth and device technology.
JOSEPHSON PARAMETRIC AMPLIFIERS
In quantum circuits, the power of the probe microwave is required to be small down to the energy of a few photons so as to avoid the incoherent fluctuations in qubit. Then, the low-power microwave carrying information of qubits at cryogenic temperature (usually below 1 K) needs to be amplified with low noise and high signal-to-noise ratio (usually by amplifier chains), followed by demodulation at room temperature. Meanwhile, the position of the first amplifier closest to the qubits (about millikelvin) optimally eliminates losses between the readout circuit and the amplifier, which also limits the use of conventional LNAs and HEMT amplifiers with milliwatt power beyond microwatt cooling power. Therefore, ultra-low power, ultra-low noise and high gain parametric amplifiers are strong contenders which are preferred to be used as amplifiers, while cryogenic HEMT amplifiers are used at 3 K, followed by LNAs near the room temperature, the schematic is shown in Fig. 1b203. Parametric amplification modulates the nonlinear reactance of the system instead of the resistance in other amplification mechanisms for avoiding thermal noise sources204. The earliest parametric amplifiers were based on varactor diodes205,206, and were realized by JJs in superconducting quantum information, namely Josephson parametric amplifier (JPA), moreover, they are often configured in superconducting quantum interference device (SUIQD) topology based on Al-AlOx-Al tunneling junctions207,208. The total critical current of the SQUID is controlled by the magnetic flux through the loop, which provides a knob to modulate the resonant frequency of the SQUID-JPA. However, the global effect of flux has difficulty avoiding crosstalk issues between different parts of the circuit. Due to the nonlinear inductive nature of JJs, superconductor-normal-superconductor (SNS) junctions are potential candidates for gated JPAs, especially those based on 2D materials. Graphene-based JJs, which benefit from the realization of 2D van der Waals geometries209-211 can tune the junction properties (e.g., critical current) with a local gate potential and have been successfully used in quantum electrodynamic circuits62,63,212,213. At the high gain limit, the output signal of any phase-preserving amplifier comes with at least the noise of half a photon, hω/2. The quantum mechanical limit of the additional noise is the standard quantum limit (SQL). Guilliam Butseraen et al. and Joydip Sarkar et al. implemented a quantum noise-limited JPA with the adoption of a graphene JJ214,215. Graphene encapsulated in h-BN contacts superconducting MoRe to form a SNS junction, as is shown in Fig. 12a. The Josephson inductance is adjusted by the gate potential, and the linear resonance frequency is increased from 2 to 5.5 GHz. As a consequence, graphene-based JPA reaches 3.5 GHz linear resonance gate tunability, 24 dB amplification with a 10 MHz bandwidth and an ultralow 130 dBm saturation power, operating in the quantum limit of noise regime, as is shown in Fig. 12b214. Similarly, a graphene-based JPA in contact with Ti/Al achieves 22 dB amplification in Fig. 12c, as well as a resonant frequency of 1 GHz with a gain beyond 15 dB in Fig. 12d, which exceeds 100 times the amplifier bandwidth with a noise level close to the SQL215. The variable frequency amplifier allows a reasonable selection of amplification frequencies according to the operating frequency of the circuit, especially for qubit readout. Careful optimization of device parameters such as stray inductance and capacitance is required for stable operation of JPAs.
Fig. 12. Graphene-based parametric amplifier. a, Schematic diagram of the graphene JJ-based parametric amplifier. b, Parametric amplification and the measured system noise temperature, which is very close to the SQL (green dashed line)214. c, Parametric amplification in the Ti/Al contacted parametric amplifier. d, Gate voltage tuning of the amplifier215. Reprinted with permission from refs.214,215. © 2022 Nature Publishing Group. |
CONCLUSION AND OUTLOOK
Outlook
Disorders and defects in a device greatly affect the transport characteristics since the thermal fluctuations of the environment cool down at cryogenic temperatures, which means higher requirements for both material quality and processing technology. The theoretically calculable material properties and realization of ultraclean material synthesis of carbon-based nanomaterials contribute to the comprehensive investigation of device physics. The excellent properties and doping-free technology of carbon-based nanomaterials are outstanding for applications at low temperature or in a wide temperature range, but an adequate understanding of scattering and noise mechanisms is required first. While verifying the cryogenic-temperature feasibility of fundamental electronic components, the large-area growth of materials needs to be advanced for large-scale integration. The high-purity and chirality-concentrated growth of CNTs216,217 and large-area growth of monocrystalline graphene218,219 can be realized experimentally. High-performance logic electronics based on wafer-level uniformity, high purity and density-controlled aligned-CNT (A-CNT) arrays have demonstrated electrical performance exceeding that of Si-based devices220-222. Moreover, A-CNT-based devices can operate from ambient to cryogenic temperature without apparent degradation, as shown in Fig. 13, which demonstrates the prospect of cryogenic applications. However, due to unremoved polymers from purification, low-quality gate stacks and imperfect contacts, some undesirable temperature-dependent characteristics such as SS and nonohmic contacts appear. The associated optimized process facilitates both enhancement and stability of the performance223,224, as well as systematic analysis at low temperature. Combined with the device characteristics at low temperature, more information can be obtained so as to deepen the understanding of device mechanisms, and then the appropriate material properties for low-temperature applications can be identified, such as the customized density of A-CNTs. Similarly, networks and aligned arrays of GNRs with a finite energy gap have also been studied51,225 The construction of carbon-based compact models based on stable materials and technology is necessary for the design of reliable and optimized large- and ultra-large-scale ICs. 2. The current reports of sensors are mainly based on the demonstration of a few devices and how to achieve stable-scale fabrication is an important goal. 3. Although the demonstration of amplification and noise in graphene-based JPAs has been reported, the practicality compared with SQUID-based JPAs is an important presentation to advance them.
Fig. 13. A-CNT-based FET. a, Schematic diagram of A-CNT-based FET. b, Transfer characteristics of a 400 nm A-CNT-FET measured from 300 K to 1.8 K under various applied bias voltages. c, Output characteristics of a 400 nm A-CNT-FET measured at 300 K and 1.8 K, respectively. |
Owing to low-temperature processing technology228-240 resulting from robust carbon‒carbon bonds, nanoscale cross-sectional area and low atomic number CNTs, allow their application in the space industry and astronomy. Moreover, carbon-based materials have long been of interest in the field of condensed matter physics. A deeper understanding of the physical mechanisms and discovered quantum phenomena facilitates the novel design of electronic and quantum devices. The strong electron-electron interactions in 1D CNTs50, the nontrivial phenomena in the Moire superlattice of twisted graphene241nd the multiple degrees of freedom (charge, spin, valley and orbit) enrich the range of applications in the areas of quantum simulators, spintronics, valleytronics, and topological electronics. Periodic repetition of carbon-based materials, e.g., A-CNT and GNR arrays, may stimulate the researches on coupling interactions and collective transport behavior and thus the design of large-scale quantum device arrays. The composite design between carbon-based materials with different dimensionalities also produces interesting phenomena, such as Dirac-source FETs with SS below 60 mV/dec242,243, 1D waveguides induced in graphene244nd the drag effect245,246. Moreover, based on highly compatible processing, carbon-based devices can not only be compounded with other materials, such as superconductors, magnetic domain materials, topological materials and other low-dimensional materials but also embedded with other architectures for electron (QDs), phonon (mechanical resonant cavities) and photon (microwave optical cavities) coupling. There exists a vast scope for the development of novel cryogenic devices. Several applications of carbon-based cryoelectronics are promising: 1. FETs and circuits based on network-CNT films and aligned-CNT arrays have demonstrated sufficient potential and maturity in room-temperature electronics, which is very promising to promote the cryogenic electronics, after realization of low fluctuations of performance and combination with doping-free technology. 2. Graphene-based cryo-Hall sensors are now commercially available. 3. The graphene-based JPAs with ultra-low power and noise, which also shows intrinsic advantages over the SQUID JPA, offering high development potential and application prospects due to the promotion of quantum technology.
Conclusion
In summary, the excellent properties and processing technology of carbon-based nanomaterials offer great advantages in cryogenic electronics. This paper reviews current developments in carbon-based cryoelectronics, including logic transistors, QD devices, temperature sensors, nanoelectromechanical devices, Hall sensors and parametric amplifiers. The advantages of carbon-based cryoelectronics were discussed compared with those of conventional Si-CMOS. More researches are required for not only achieving higher performance and new mechanisms in functional modules based on the improved purity of materials, but also deeply and systematically investigating the low-temperature transport mechanics of large-scale assembled materials. The realization from individual schematic devices to large-scale functional circuits in the cryogenic regime will greatly promote advances in computing, sensing and communications.
MISCELLANEA
Funding This work is supported by the National Key Research & Develop- ment Program (Grant No. 2022YFB4401601) and Natural Science Foundation of China (62225101, 12374035 and 11974026).
Declaration of Competing Interest The authors declare that there are no competing interests.
