Effect of thermal insulation on the electrical characteristics of NbO_x threshold switches

Niobium oxide (NbO_x) based two terminal threshold switches have recently been considered for applications such as bidirectional selector devices in crossbar memory arrays^1–9 and building blocks for neuromorphic computing.^10–14 For selector applications, NbO_x threshold switches have the advantage of good cycle-to-cycle stability^1,9 and demonstrated potential to work as selector elements in hybrid selector-memory cells without the need for an intermediate electrode.^1–3,6,9 Historically, threshold switching in NbO_x has been mainly attributed to a thermally driven insulator-metal transition of NbO₂.^{2,5,8,9,11,15–18} Recent reports provide strong evidence for alternative thermal feedback models based on Poole-Frenkel conduction.^14,19–25 In either case, however, the threshold switching in NbO_x is highly dependent on the Joule heating, indicating the possibility to tune the electrical characteristics of NbO_x threshold switches by engineering thermal design of the device and its surroundings.

Here, it is experimentally demonstrated that the electrical characteristics of NbO_x threshold switches can be tuned by engineering the thermal insulation between the device and the ambient. We aim at separating the effect of thermal insulation from the effect of other parameter changes by fabricating NbO_x threshold switches with identical process conditions, but on two kinds of substrates with different thermal properties. Figure 1 shows the two cases that are used for comparison. Conceptually, in the non-suspended device, the bulk Si substrate underneath the crosspoint device acts as an effective heat sink, resulting in poor thermal insulation. On the other hand, in the suspended device, the absence of the bulk substrate underneath the crosspoint device leads to good thermal insulation.

The non-suspended device was fabricated on a Si substrate covered with 1 μm thick thermally grown SiO₂. The suspended device was fabricated on a Si substrate with freely suspended LPCVD Si₃N₄ membrane windows, which are 150 nm thick and 45 μm*45 μm large. In both cases, 15 nm Pt was e-beam evaporated and patterned by liftoff to form the bottom electrode (BE). 15 nm Nb₂O₅ was then deposited using radio frequency magnetron sputtering from an Nb₂O₅ target. After that, 2 nm Ti and 25 nm Pt were e-beam evaporated and patterned by liftoff to form the top electrode (TE). Finally, the devices were annealed in N₂ at 400 °$C$ for 5 min. The size of the NbO_x device at the crosspoint of the electrode bars is 2 μm × 2 μm. Electrical measurements were performed using Agilent 4156C. In all cases, the electrical signal was applied to the top electrode, with the bottom electrode grounded.

Here, the role of Ti in TE is to getter oxygen from Nb₂O₅, reducing it into niobium suboxides (NbO_x). According to XPS analysis (supplementary material Figs. S1 and S2), in as-fabricated devices, about half of the Nb is in the +4 state (NbO₂), while the other half is in the +5 state (Nb₂O₅). Therefore, the overall “x” in NbO_x in as-fabricated devices is estimated to be around 2.2–2.3. The NbO_x in as-fabricated devices can undergo further reduction when the devices are electrically operated at large currents or voltages, which is referred to as the forming process (supplementary material Figs. S4 and S5). However, it is found that the forming process can change the non-suspended device and the suspended device in different ways even when electrical operation conditions used for forming are identical [supplementary material Fig. S5(c)]. In other words, for “formed” devices, we can no longer attribute the difference in electrical characteristics between the non-suspended device and the suspended device entirely to the effect of different thermal insulation. Therefore, throughout the main body of this manuscript, we have used electrical operation conditions under which permanent material change (the forming process) does not happen. By the way, some reports have achieved reduction of Nb₂O₅ into NbO_x through a dielectric breakdown process.^11,15,20 In those cases, the reduced NbO_x region is usually highly localized (filamentary), which leads to filamentary electrical conduction. In our as-fabricated devices, however, since there is no dielectric breakdown process, the electrical conduction is likely to be non-filamentary.²⁵ 

Figure 2 shows the thermal simulation results of the non-suspended device and the suspended device using COMSOL Multiphysics^®.²⁶ Details about the simulation can be found in the supplementary material. Briefly, a spatially uniform heat generation rate is defined within the NbO_x at the crosspoint of BE and TE bars (the “active NbO_x region”), and the resulting steady state temperature profile is simulated. As is shown in Figs. 2(a)–2(d), while the heat generation rate is kept identical in the two cases, the average temperature rise $(ΔTaverage)$ within the active NbO_x region for the suspended device is ∼10× larger compared to the non-suspended device. Note that the temperature variation within the active NbO_x region is small compared to the temperature difference between the active NbO_x region and the ambient heat sink. Therefore, a lumped thermal model can be used as a good approximation, where the thermal insulation between the active NbO_x region and the ambient heat sink can be represented by an effective thermal resistance (⁠$Rth$⁠). $Rth$ can be calculated from $ΔTaverage=Rth·P$⁠, where $P$ is the input power to the active NbO_x region. Therefore, the calculated $Rth$ for the suspended device (6.07 × 10⁵ K/W) is ∼10× larger than that for the non-suspended device (6.42 × 10⁴ K/W).

Figure 3(a) shows experimental quasi-static IV characteristics of the NbO_x threshold switches along with the definition of threshold current (⁠$Ith)$⁠, threshold voltage $(Vth)$⁠, and half-selection leakage $(I1/2)$⁠. Compared with the non-suspended devices, the suspended devices show ∼7× reduction in threshold current and ∼45% reduction in threshold voltage. The reduced threshold voltage leads to reduced read voltage $(Vread)$⁠, which results in ∼5× reduction in half-selection leakage at $12Vread$⁠, highlighting the effectiveness of reducing half-selection leakage of NbO_x selectors by engineering the thermal insulation. Note that for both the non-suspended and the suspended devices, the data in Fig. 3(a) come from 5 nominally identically devices, with 5 positive polarity sweeps plus 5 negative polarity sweeps per device. Clearly, both device-to-device variation and cycle-to-cycle variation are negligible compared to the difference between the non-suspended devices and the suspended devices. The 500 $μA$ compliance current for the non-suspended devices is chosen so that it is large enough for the threshold switching to show up but small enough to avoid permanent material change during electrical operation. On the other hand, operating the suspended devices at 500 $μA$ compliance current causes them to undergo permanent material change [supplementary material Fig. S4(a)]; therefore, a smaller compliance current (100 $μA$⁠) is used.

Figure 3(b) shows equivalency of a current sweep and a voltage sweep for both the non-suspended device and the suspended device, where the current controlled negative differential resistance (CC-NDR) shows up as hysteretic threshold switching when the device is operated using a voltage sweep. While a voltage sweep is more straightforward for the evaluation of selector properties, a current sweep provides more information within the hysteresis window. Therefore, we will use the current sweep IV curves for comparison with simulation results.

To understand how the difference in thermal insulation results in different electrical characteristics of NbO_x threshold switches, we adopted the thermal feedback model recently developed by Gibson et al.,²¹ where the electrical conductivity in NbO_x is described by a modified 3D Poole-Frenkel conduction

where $β=(q3πε0εi)12$⁠, $εi$ is the high frequency dielectric constant, $F$ is the electric field, $Ea$ is the activation energy, and $σp$ is the prefactor. Using a lumped thermal model, the heat transfer during quasi-static IV sweep is described by

where $Tamb$ is the ambient temperature and $Vdev$ is the voltage drop on the NbO_x as opposed to the applied voltage $(Vapp)$⁠, which are related through

Also, we have

Here, $A=4 μm2$ is the active device area, $d=15 nm$ is the NbO_x thickness, and $Rseries$ is the parasitic resistance in series with the NbO_x and is measured to be 304 $Ω$ for our device using a test structure where the TE bar contacts the BE bar directly without any NbO_x in between. While $Rseries$ could change due to heating of the electrode bars, here it is assumed to be constant for simplicity. Note that we have assumed the overall electrical conduction to be limited by the bulk Poole-Frenkel conduction instead of interfacial barriers, which is supported by the fact that the IV characteristics are quite symmetric despite the different metal contacts (Pt and Ti) on two sides of the NbO_x. Also note that (5) implicitly assumes a spatially uniform electrical conduction within the active NbO_x region, which should be a reasonable approximation for our devices due to their non-filamentary nature of electrical conduction.

In the low field limit, (1) can be approximated as $σlow≈58σpe−EakBT.$²¹ Therefore, by plotting the natural logarithm of the measured low field conductivity as a function of $1/T$⁠, $Ea$ and $σp$ can be estimated from the slope and intercept of the linear fit, as is shown in Fig. 4(a). Note that material property parameters (such as $Ea$ and $σp$⁠) of the non-suspended and the suspended device are intended to be identical, in order to separate the effect of thermal insulation from the effect of other parameter changes. The slight difference between the two devices in Fig. 4(a) is likely due to wafer-to-wafer variation during fabrication. Figure 4(b) shows comparison of experimental IV curves and the Poole-Frenkel based simulation results [solving (1)–(5) self-consistently using MATLAB^®]. The experimental results in Fig. 4(b) are from the same two devices used in Fig. 4(a). The solid curves in Fig. 4(b) are simulated IV curves as a function of $Rth$⁠, with all the other parameters kept the same for the two devices. Among these parameters, $Ea=0.396 eV$ and $σp=1.44×104 S/m$ come from the average values of the suspended device and the non-suspended device in Fig. 4(a). $εi=7.2$ is a fitting parameter whose value is close to reported values of the high frequency dielectric constant of NbO₂.²⁷ As we can see, the Poole-Frenkel based simulation shows excellent agreement with experimental results. The $Rth$ values extracted from IV fitting are ∼5.8 × 10⁴ K/W for the non-suspended device and ∼5.3 × 10⁵ K/W for the suspended device. These are in good agreement with the COMSOL thermal simulation results [Fig. 4(c)], which further supports the validity of the $Rth$ values.

The grey curve in Fig. 4(b) shows the simulated IV characteristics of a hypothetical device with $Rth=0$ and therefore no temperature rise due to Joule heating. Clearly, this device does not show any threshold switching behavior. While not surprising, this further illustrates the importance of having good thermal insulation in NbO_x threshold switches. Although implementing a suspended structure might be difficult in practice, $Rth$ could also be increased using low thermal conductivity materials/interfaces or device geometries which are optimized for heat confinement, as has been well demonstrated for other kinds of thermally activated devices such as phase change memory.^28–30 Some of these thermal engineering approaches are currently being investigated for NbO_x threshold switches and may be addressed in future publications.

In summary, we have studied the effect of thermal insulation on the electrical characteristics of NbO_x threshold switches and shown that increasing the thermal insulation by ∼10× can lead to ∼7× reduction in threshold current and ∼45% reduction in threshold voltage. The reduced threshold voltage results in ∼5× reduction in half-selection leakage, which highlights the effectiveness of reducing half-selection leakage of NbO_x selectors by engineering the thermal insulation. A thermal feedback model based on Poole-Frenkel conduction is shown to explain the experimental results very well, which is also important as a piece of strong evidence supporting the validity of the Poole-Frenkel based mechanism in NbO_x threshold switches.

See supplementary material for details on the XPS analysis, the forming process, and the COMSOL thermal simulation.

This work was supported by the member companies of Stanford Non-Volatile Memory Technology Research Initiative (NMTRI). Z. Wang was additionally supported by the Stanford Graduate Fellowship. Device fabrication was performed at the Stanford Nanofabrication Facility that is supported by National Science Foundation through the NNIN under Grant No. ECS-9731293.