Switching Current Distribution Research Articles

Study of Phase Dynamics in Moderately Damped Josephson Junctions

The moderately damped regime (MDR) in a Josephson junction (JJ) is quite distinct from the well-known case of underdamped systems and quite common in devices characterized by low critical currents. Measurements of switching current distribution (SCD) are a direct way of discriminating the phase dynamics and the transport also in nontrivial cases of moderate damping. MDR is going to be more and more common with advances in nanopatterning superconductors and in materials science finalized to build hybrid devices. We report on measurements of SCDs, both in the thermal and quantum regime, on moderately damped NbN/MgO/NbN JJs. A transition from the Thermal Activation (TA) regime to Macroscopic Quantum Tunnelling (MQT) occurs at about 90 mK, while above 1.6 K a phase diffusive dynamics is clearly observed. The combined analysis of these regimes through numerical simulations allowed us to extract the fundamental parameters, which completely characterize the phase dynamics of such moderately damped JJs.

A two-step transition description of underdamped phase diffusion

A two-step transition model describing phase diffusion and switching process in underdamped Josephson junctions is discussed. The model takes into account the phase particle's escape rate out of the potential well and transition rate from phase diffusion to the running state. Using as examples the experimental switching current distributions of two Nb/AlOx/Nb junctions of different sizes fabricated on the same chip, we extract the transition rate, which turns out to follow the predicted Arrhenius law in the thermal regime but is greatly enhanced when macroscopic quantum tunneling becomes the dominant escape mechanism. Our results show the validity of applying the model to obtain the transition rate out of the phase diffusion state into the running state from measured switching current distribution of underdamped Josephson junctions. The temperature and bias-current dependent data provide strong evidence for phase diffusion in both thermal and quantum regimes.

Progress and Prospects of Spin Transfer Torque Random Access Memory

We report our progress on material improvement, device design, wafer processing, integration with CMOS, and testing of STT-RAM memory chips at 54 nm node with cell sizes of 14 and 28 F2 (F=54 nm). A dual tunnel barrier MTJ structure was found to have lower and more symmetric median spin transfer torque writing switching currents, and much tighter parallel to antiparallel switching current distribution. In-plane MTJ devices write endurance data, read and write soft error rates data and simulation fits, and solutions to the long write error rate tail at fast write speeds are discussed.

Macroscopic quantum tunneling and phase diffusion in a La2−xSrxCuO4intrinsic Josephson junction stack

We performed measurements of switching current distribution in a submicron La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) intrinsic Josephson junction (IJJ) stack in a wide temperature range. The escape rate saturates below approximately 2\,K, indicating that the escape event is dominated by a macroscopic quantum tunneling (MQT) process with a crossover temperature $T^{*}\approx2\,$K. We applied the theory of MQT for IJJ stacks, taking into account dissipation and the phase re-trapping effect in the LSCO IJJ stack. The theory is in good agreement with the experiment both in the MQT and in the thermal activation regimes.

Stochastic and deterministic phase slippage in quasi-one-dimensional superconducting nanowires exposed to microwaves

We study current–voltage (V–I) characteristics of short superconducting nanowires of length ∼100 nm exposed to microwave (MW) radiation of frequencies between 2 and 15 GHz. The radiation causes a decrease of the average switching current of the wire. This suppression of the switching current is modeled assuming that there is one-to-one correspondence between Little's phase slips, which are microscopic stochastic events induced by thermal and quantum fluctuations, and the experimentally observed switching events. We also find that at some critical power P* of the radiation a dissipative dynamic superconducting state occurs as an extra step on the V–I curve. It is identified as a phase slip center (PSC), which is essentially a deterministic and periodic in-time phase rotation. With the dependence of the switching currents and the standard deviations observed at the transitions: (i) from the supercurrent state to the normal state and (ii) from the supercurrent state to the PSC regime, we conclude that both of the two types of switching events are triggered by the same microscopic event, namely a single-phase slip. We show that the Skocpol–Beasley–Tinkham model is not applicable to our MW-driven PSCs, probably due to the tendency of the PSC to synchronize with the MW. Through the analysis of the switching current distributions at a sufficiently low temperature, we also present evidence that quantum phase slips play a role in switching events even under MWs.

Magnetic tunneling junction with Fe/NiFeB free layer for magnetic logic circuits

We have developed a shape varying magnetic tunneling junction (SVM) with a Fe/NiFeB free layer for use in magnetic logic circuits. Inserting the thin Fe film between an NiFeB free layer and MgO tunneling barrier improved the magnetoresistance (MR) ratio: it increased up to 130%, as the thickness of the Fe film increased. In addition, the switching current distribution of the SVM was reduced to 8%. By using NiFeB as a free layer, the roughness under the MgO was reduced and the crystallization of the MgO was enhanced. This led to both the high MR ratio and the low switching current distribution. Our developed Fe (0.4 nm)/NiFeB free layer satisfies the requirement of the MTJ’s characteristics that the magnetic logic circuits operate with a high bit yield.

A cryogen-free dilution refrigerator based Josephson qubit measurement system

We develop a small-signal measurement system on cryogen-free dilution refrigerator which is suitable for superconducting qubit studies. Cryogen-free refrigerators have several advantages such as less manpower for system operation and large sample space for experiment, but concern remains about whether the noise introduced by the coldhead can be made sufficiently low. In this work, we demonstrate some effective approaches of acoustic isolation to reduce the noise impact. The electronic circuit that includes the current, voltage, and microwave lines for qubit coherent state measurement is described. For the current and voltage lines designed to have a low pass of dc-100 kHz, we show that the measurements of Josephson junction's switching current distribution with a width down to 1 nA, and quantum coherent Rabi oscillation and Ramsey interference of the superconducting qubit can be successfully performed.

Distribution of Supercurrent Switching in Graphene under the Proximity Effect

We study the stochastic nature of switching current in hysteretic current-voltage characteristics of superconductor-graphene-superconductor junctions. We find that the dispersion of the switching current distribution scales with temperature as σ(I) proportional to T(α(G)) with α(G) as low as 1/3. This observation is in sharp contrast to the known Josephson junction behavior where σ(I) proportional to T(α(J)) with α(J)=2/3. We propose an explanation using a generalized version of Kurkijärvi's theory for the flux stability in rf-SQUID and attribute this anomalous effect to the temperature dependence of the critical current which persists down to low temperatures.

Magnetic Nanoparticle Characterization Using Nano-SQUID based on Niobium Dayem Bridges

Abstract Magnetic nano-sensors based on niobium dc SQUID (Superconducting Quantum Interference Device) for nanoparticle characterization are presented. The SQUIDs consists of two Dayem bridges of 90 nm x 250 nm and loop area of 4, 1 and 0.55 μm2. The SQUIDs were designed to have a hysteretic current-voltage characteristic in order to work as a magnetic flux-current transducer. Current-voltage characteristics, critical current as a function of the external magnetic field and switching current distributions were performed at liquid helium temperature. A critical current modulation of about 20% and a current-magnetic flux transfer coefficient (responsivity) of 30 μA/Φ0 have been obtained, resulting in a magnetic flux resolution better than 1 mΦ0. In order to show the effectiveness of sensor for nanomagnetism applications, we performed measurements with and without magnetic nanoparticles on the SQUID loop applying a magnetic field parallel to the SQUID plane. In this configuration the magnetic flux coupled to the SQUID is mainly due to the presence of magnetic nanoparticles. The magnetic nanoparticles can be easily detected and their response to magnetic field studied. Measurements has been performed on Fe3O4 nanoparticles prepared by thermal decomposition method with a nominal particle size of 8 nm. Some examples of magnetization measurements were recorded at low temperature after Zero Field Cooling.

Spin-Transfer Torque Switching Above Ambient Temperature

We report the temperature dependences of tunneling magnetoresistance ratio, coercivity, thermal stability, and switching current distribution of magnetic tunnel junctions (MTJs) in the temperature range 25-80°C, the most probable working environment for spin-transfer torque random access memory (STT-RAM). Two distinct temperature dependence of the switching current density are apparent due to two switching mechanisms: a switching current density decrease with increasing temperature in the long-pulse ( >; 1 μs) regime, a result of thermally activated switching, but no decrease in the short-pulse (>;10 ns) regime, as a result of precessional switching. In the temperature range studied, the switching current density variation is less sensitive to environmental temperature than it is to switching time. Thus, switching time is the more important factor to consider in STT-RAM design.

Thermal hopping and retrapping of a Brownian particle in the tilted periodic potential of a NbN/MgO/NbN Josephson junction

We report on the occurrence of multiple hopping and retrapping of a Brownian particle in a tilted washboard potential. The escape dynamic has been studied experimentally by measuring the switching current distributions as a function of temperature in a moderately damped NbN/MgO/NbN Josephson junction. At low temperatures the second moment of the distribution increases in agreement with calculations based on Kramers thermal activation regime. After a turnover temperature ${T}^{*}$, the shape of the distributions starts changing and width decreases with temperature. We analyze the data through fit of the switching probability and Monte Carlo simulations and we find a good agreement with a model based on a multiple retrapping process.

Electrically Tunable Macroscopic Quantum Tunneling in a Graphene-Based Josephson Junction

Stochastic switching-current distribution in a graphene-based Josephson junction exhibits a crossover from the classical to quantum regime, revealing the macroscopic quantum tunneling of a Josephson phase particle at low temperatures. Microwave spectroscopy measurements indicate a multiphoton absorption process occurring via discrete energy levels in washboard potential well. The crossover temperature for macroscopic quantum tunneling and the quantized level spacing are controlled with the gate voltage, implying its potential application to gate-tunable superconducting quantum bits.

Switching current modulations induced by vortices rearrangement in mesoscopic superconducting loops

Periodic modulations in the switching current of niobium mesoscopic thin loops have been observed as a function of a perpendicular magnetic field. These modulations reflect the formation of specific vortices configurations in the arms and in the contacts of the loops. The voltage measured just before the current-driven transition to the normal state takes either zero or nonzero values depending on whether the vortices are efficiently pinned or move under the action of the applied current. This switching voltage varies sharply in the vicinity of the regularly spaced matching fields at which the switching current is minimum. This reflects the rearrangement of the vortices pattern from an unstable configuration into a more stable one. In addition, multimodal switching current distributions obtained at a constant field highlight that the few vortices involved in the field-cooling process freeze into a limited number of configurations. Finally, the spacing between the matching fields allows us to extract the critical field for complete vortex expulsion of the samples. Electrical transport measurements appear to be an efficient tool to determine the superheating field of submicrometer-wide structures, which is not obvious when measured by scanning probe microscopy.

Quantum Phase Diffusion in a Small Underdamped Josephson Junction

Quantum phase diffusion in a small underdamped Nb/AlO(x)/Nb junction (∼0.4 μm(2)) is demonstrated in a wide temperature range of 25-140 mK where macroscopic quantum tunneling (MQT) is the dominant escape mechanism. We propose a two-step transition model to describe the switching process in which the escape rate out of the potential well and the transition rate from phase diffusion to the running state are considered. The transition rate extracted from the experimental switching current distribution follows the predicted Arrhenius law in the thermal regime but is greatly enhanced when MQT becomes dominant.

Phase-Diffusion in Switching Process of Underdamped Josephson Junctions

We measured the switching from a superconducting state to a finite voltage state in a dc SQUID, which is equivalent to a single Josephson junction with tunable critical current Ic. The width and the mean of the switching current distribution depend on the effective temperature Teff and Ic. The phase-diffusion was observed by investigating the switching current distribution as a function of Teff. It is found that the crossover from the thermal activation to the phase-diffusion scaling with the ratio of Ic and Teff, clarifying the physical picture of the phase-diffusion. We developed an analytical multi-retrapping model which can address the experimental results very well.

짧은 전류 펄스를 이용한 전류 유도 자화 반전에서 에너지 장벽 분포의 효과

본 논문에서는 짧은 전류 펄스를 이용한 미소자기 소자에서의 전류 유도 자화 반전에 대한 매크로 스핀 시뮬레이션 연구를 수행하였다. 자화 반전 전류 분포에 있어서 에너지 장벽이 미치는 효과에 특별히 주목하였다. 자화 반전 전류의 크기 및 분포는 전류 펄스 폭의 감소에 따라 증가했다. 여기서 긴 전류 펄스 폭 영역에서는 에너지 장벽과 자화 반전 전류 분포 사이의 관계가 아레니우스-닐 법칙에 의해 서술된다. 하지만 짧은 전류 펄스 폭의 영역에서는 이 관계가 풀리지 않은 채로 남아있다. 이는 짧은 전류 펄스로 인한 자화 반전이 열적 활성화에 의해서가 아닌 세차 운동에 의해 좌우되기 때문이며, 이를 해결하는 데에 있어서 어려움이 발생한다. 그러므로 포커-플랑크 방정식을 풀어서 짧은 전류 펄스 영역에서의 자화 반전에 대한 정확한 공식을 얻어내는 것이 필요하며 이를 통해 짧은 전류 펄스 영역에서의 자화 반전 양상을 이해 할 수 있을 것으로 본다. We performed macro-spin simulation studies of the current-induced magnetization reversal of nanomagnetic elements with short current pulses. A special attention was paid to the effect of the energy barrier on the switching current distribution. The switching current and its distribution increase with decreasing the current pulse-width. The relationship between the energy barrier and switching current distribution is described by the Arrhenius-N<TEX>$\'{e}$</TEX>el law at a long pulse-width regime. At a regime of short pulse-width, however, the relationship is left unaddressed. The difficulty to address this issue arises because the magnetization switching with a short current pulse is governed not by the thermal activation but by the precession motion. Therefore, an exact formulation for the short pulse regime by solving the Fokker-Plank equation is needed to understand the result.

NanoSQUID as magnetic sensor for magnetic nanoparticles characterization

Integrated magnetic sensors based on niobium dc SQUID (Superconducting Quantum Interference Device) for nanoparticle characterizations are presented. The SQUIDs consists of two Dayem bridges of 90 nm × 250 nm and loop area of 4, 1, and 0.55 μm2. The devices are realized by using an e-beam lithography nano-fabrication process which can directly pattern the devices in an electron-positive resist and then transferred to a 20 nm single niobium layer by a lift-off post-process. The SQUIDs were designed to have a hysteretic current–voltage characteristic in order to work as a magnetic flux-current transducer. The presence of an integrated niobium coil, tightly coupled to the SQUID, allows us to easily excite the SQUID and to flux bias the SQUID at its optimal working point. Current–voltage characteristics, critical current as a function of the external magnetic field and switching current distributions were performed at liquid helium temperature. A critical current modulation of about 20% and a current-magnetic flux transfer coefficient (responsivity) of 30 μA/Φ0 have been obtained, resulting in a magnetic flux resolution better than 1 mΦ0. The authors performed preliminary measurements with and without iron oxide nanoparticles on the SQUID loop in order to show the device sensitivity in view of nano-magnetism applications. It was showed that the presence of magnetic nanoparticles can be easily detected and the magnetic relaxation curve measured.

Advances and Future Prospects of Spin-Transfer Torque Random Access Memory

Spin-transfer torque random access memory (STT-RAM) is a potentially revolutionary universal memory technology that combines the capacity and cost benefits of DRAM, the fast read and write performance of SRAM, the non-volatility of Flash, and essentially unlimited endurance. In order to realize a small cell size, high speed and achieve a fully functional STT-RAM chip, the MgO-barrier magnetic tunnel junctions (MTJ) used as the core storage and readout element must meet a set of performance requirements on switching current density, voltage, magneto-resistance ratio (MR), resistance-area product (RA), thermal stability factor (¿) , switching current distribution, read resistance distribution and reliability. In this paper, we report the progress of our work on device design, material improvement, wafer processing, integration with CMOS, and testing for a demonstration STT-RAM test chip, and projections based on modeling of the future characteristics of STT-RAM.

Phase escape of current-biased Josephson junctions

Switching current distributions of an Nb/Al–AlOx/Nb Josephson junction are measured in a temperature range from 25 mK to 800 mK. We analyse the phase escape properties by using the theory of Larkin and Ovchinnikov (LO) which takes discrete energy levels into account. Our results show that the phase escape can be well described by the LO approach for temperatures near and below the crossover from thermal activation to macroscopic quantum tunneling. These results are helpful for further study of macroscopic quantum phenomena in Josephson junctions where discrete energy levels need to be considered.

Quantum and classical resonant escapes of a strongly driven Josephson junction

The properties of phase escape in a dc superconducting quantum interference device (SQUID) at 25 mK, which is well below quantum-to-classical crossover temperature ${T}_{cr}$, in the presence of strong resonant ac driving have been investigated. The SQUID contains two $\text{Nb}/{\text{Al-AlO}}_{x}/\text{Nb}$ tunnel junctions with Josephson inductance much larger than the loop inductance so it can be viewed as a single junction having adjustable critical current. We find that with increasing microwave power $W$ and at certain frequencies $\ensuremath{\nu}$ and $\ensuremath{\nu}/2$, the single primary peak in the switching current distribution, which is the result of macroscopic quantum tunneling of the phase across the junction, first shifts toward lower bias current $I$ and then a resonant peak develops. These results are explained by quantum resonant phase escape involving single and two photons with microwave-suppressed potential barrier. As $W$ further increases, the primary peak gradually disappears and the resonant peak grows into a single one while shifting further to lower $I$. At certain $W$, a second resonant peak appears, which can locate at very low $I$ depending on the value of $\ensuremath{\nu}$. Analysis based on the classical equation of motion shows that such resonant peak can arise from the resonant escape of the phase particle with extremely large oscillation amplitude resulting from bifurcation of the nonlinear system. Our experimental result and theoretical analysis demonstrate that at $T⪡{T}_{cr}$, escape of the phase particle could be dominated by classical process, such as dynamical bifurcation of nonlinear systems under strong ac driving.