Electro-Thermal Model of Threshold Switching in TaOx-Based Devices

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Electro-Thermal Model of Threshold Switching in TaOx‑Based Devices Jonathan M. Goodwill,*,† Abhishek A. Sharma,‡ Dasheng Li,† James A. Bain,‡ and Marek Skowronski*,† †

Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States Department of Electrical and Computer Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States

‡

S Supporting Information *

ABSTRACT: Pulsed and quasi-static current−voltage (I−V) characteristics of threshold switching in TiN/TaOx/TiN crossbar devices were measured as a function of stage temperature (200−495 K) and oxygen flow during the deposition of TaOx. A comparison of the pulsed and quasistatic characteristics in the high resistance part of the I−V revealed that Joule self-heating significantly affected the current and was a likely source of negative differential resistance (NDR) and thermal runaway. The experimental quasi-static I−V’s were simulated using a finite element electro-thermal model that coupled current and heat flow and incorporated an external circuit with an appropriate load resistor. The simulation reproduced the experimental I−V including the OFF-state at low currents and the volatile NDR region. In the NDR region, the simulation predicted spontaneous current constriction forming a small-diameter hot conducting filament with a radius of 250 nm in a 6 μm diameter device. KEYWORDS: tantalum oxide, Poole−Frenkel conduction, threshold switch, negative differential resistance, thermal runaway

1. INTRODUCTION The ever-increasing need for faster and more energy- and space-efficient ways to store data has driven the interest in passive crossbar memory arrays. This design offers excellent scalability with the smallest possible cell size of 4F2, where F is the minimum feature size, but suffers from the so-called sneak path problem where all cells along the word and bit lines corresponding to the selected cell are half-selected. The parasitic current flowing through these cells can cause read errors and severely limits the array size. One way to reduce the sneak path problem is to incorporate a highly nonlinear selection device in series with the memory element.1−3 Threshold switching devices are one of the candidates for this application.4,5 This report is focused on one class of such devices, namely, structures based on transition metal oxides with highly temperature dependent conductivity, and the underlying mechanism of their operation. The current−voltage (I−V) characteristics of a threshold switch resemble the letter “S” and consist of three branches. The branch with the lowest current is referred to as the high resistance OFF-state, which continues until the slope of the I− V becomes infinite at the threshold voltage (VTH). At higher currents, the slope of the I−V becomes negative, giving rise to the intermediate branch known as the negative differential resistance (NDR) region. The last region, the low resistance ON-state, is defined as the high-current region above the NDR region where the slope of the I−V becomes positive once again. © XXXX American Chemical Society

While the conductivity in OFF- and ON-states is thought to be mostly uniform, the NDR region exhibits formation of high current density filaments.6 A number of mechanisms have been suggested to give rise to NDR in different materials/devices. For example, in amorphous chalcogenides, the proposed mechanisms include double injection,7 field-induced filling of traps,8 energy gain by electrons hopping between defect sites,9 electric field-induced secondary phase nucleation,10 and even thermal runaway,11,12 among others. In addition to amorphous chalcogenides, threshold switching has been extensively studied in VO2 and NbO2 where it was generally interpreted as due to a field- or Joule heating-induced insulator-to-metal transition.13−18 There are only a few reports of threshold switching in dielectric oxides such as TiOx, TaOx, or HfOx, and the mechanism behind this phenomenon is not well established.19−21 Three recent reports on NbOx offer some insight into the proposed mechanism of threshold switching in dielectric oxides, namely, thermal runaway.22−24 The three publications report the quasi-static I−V’s of NbOx-based devices and fit the data with a Poole−Frenkel-type formula to obtain conductivity as a function of temperature and electric field. Simulations including self-heating showed that, at a certain voltage, the Received: December 23, 2016 Accepted: March 15, 2017 Published: March 15, 2017 A

DOI: 10.1021/acsami.6b16559 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces

Figure 1. (a) Quasi-static I−V measured at 300 K for a device with a 7.5% O2 flow TaOx film. The inset shows the low voltage characteristics. (b) Low field conductivities of devices fabricated with three different flow rates of oxygen during sputtering. (c) A comparison between the pulsed I−V (triangles) and quasi-static I−V (continuous lines) at different stage temperatures for a 7.5% oxygen film and (d) pulsed I−V for the same film (triangles) versus the fit of the Poole−Frenkel formula (lines) at different stage temperatures. fraction is not the same as the percentage of oxygen in the TaOx layer, nor are these two proportional. The devices fabricated with these films will be referred to by the respective O2 percentages of the ambient in which they were sputtered. The lateral size of the devices was 5 × 5 μm, and they were patterned in a ground-signal-ground configuration allowing for short pulse measurements. The quasi-static I−V’s were obtained using a circuit consisting of the source and load resistor along with the device under test connected in series. The transient data were obtained using Time Domain Transmissometry.27 The details of the fabrication, device layout, and experimental setups can be found in our earlier publications.21,28−30 All data are plotted versus the voltage across the device rather than source voltage.

devices undergo thermal runaway. The estimated functional layer temperature increase right before the threshold was estimated to be 35 K24 and 150 K22 above the stage temperature of 300 K. Both of these are far below the insulator-to-metal transition in NbO2 at 1081 K.25,26 The devices discussed in these publications needed to be electroformed, a procedure that leads to the formation of a smalldiameter permanent filament consisting of a conductive reduced oxide. Neither the size nor the composition of the filament is known. Moreover, the inhomogeneous material does not allow for observation and/or simulation of the salient feature of a threshold switch, specifically, the spontaneous current constriction in a structurally uniform device. In this work, we present experimental data on I−V characteristics of TiN/TaOx/TiN devices as a function of stage temperature and deposition conditions of the TaOx film. These were simulated using a finite element model incorporating coupled heat and current flow. The model correctly describes the S-NDR characteristics and predicts the spontaneous current constriction to a small-diameter filament of elevated current density and temperature. These insights reveal some of the limitations of TaOx-based threshold switches as selectors.

3. RESULTS A typical experimental quasi-static I−V of a tantalum oxide device structure is shown in Figure 1a. These data were obtained at a stage temperature of 300 K on a 7.5% oxygen device with a series load resistor of 26.7 kΩ. The devices were not electroformed, and the current and dissipated power were intentionally limited to 1 mA and 3 mW to prevent permanent changes to the device. The initial characteristics remained unchanged throughout the entire series of experiments, which was confirmed by measuring the high resistance state characteristics before and after the transition to the NDR region. The I−V shows the OFF-state at low voltages/currents with gradually increasing slope until eventually becoming vertical at 10 V. The functional I(V) dependence in the OFFstate is discussed in detail below. At higher current, the slope of the I−V becomes negative as the device enters the NDR region. Between 9.5 and 3.5 V, the I−V shows a straight line corresponding to a transition between two points in the NDR region along the load line. Above the transition, the device current increases rapidly with small changes in voltage. The inset in Figure 1a shows the I−V at low voltages where the initial current dependence is linear. This slope was used to determine the low field conductivity for the simulations discussed in the section below. The slope of the linear part of the I−V as a function of the stage temperature and oxygen fraction is shown in Figure 1b.

2. MATERIALS AND METHODS Devices with a TiN/TaOx/TiN structure were fabricated on a silicon wafer with 1 μm of thermal oxide. The metal−insulator−metal structure consisted of 30 nm thick sputtered TiN electrodes and 150 nm of functional reactively sputtered TaOx layer. Since the functional layer was deposited on a nonplanar surface with a patterned bottom electrode, the relative variations in film thickness over the edges of the electrode are expected to be large. In order to minimize the effect of such variations, a relatively large thickness of the functional layer was chosen. The TiN electrodes were sputtered at room temperature with an argon flow rate of 60 sccm and a chamber pressure of 3 mTorr. The TaOx films were sputtered at room temperature with a chamber pressure of 3 mTorr, an oxygen flow of 3, 4.5, and 6 sccm, and a constant total flow of Ar and O2 at 60 sccm. This corresponds to 5, 7.5, and 10% of oxygen fraction in the sputtering ambient. This B


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ACS Applied Materials & Interfaces The three functional layers spanned a conductivity range of over 2 orders of magnitude at room temperature. The conductivity of each device shows thermally activated behavior with activation energies ranging from 0.26 ± 0.01 eV at low oxygen content to 0.44 ± 0.005 eV at high oxygen content. This suggests that the Fermi level in TaOx layers, which is located close to the middle of the band gap in a stoichiometric material, moves closer to the conduction band with decreasing oxygen content. The change is likely due to creation of traps associated with oxygen deficiency. The presence of traps in TaOx with energies of 0.2, 0.3, and 0.6 eV below the conduction band edge has been reported in thermally stimulated current measurements.31 Similar energies of traps have been extracted from fitting the leakage current in TaOxbased structures with the Poole−Frenkel formula.32,33 The effect of Joule self-heating on the I−V characteristics of a typical device can be assessed based on data shown in Figure 1c. All data in this figure have been obtained on the same 7.5% O2 device at three different stage temperatures. The continuous lines represent experimental quasi-static voltage sweeps at a ramp rate of 0.4 V/s, while the triangles denote pulsed I−V characteristics. The dwell time for each voltage step was orders of magnitude longer than the device thermal time constant τo (estimated in our earlier publication to be 3 μs),28 and the device was able to reach a steady state temperature at every point on the curve. In contrast, the pulsed I−V’s were measured with 30 ns long rectangular pulses with the readings taken at 10 ns. A single pulse was applied every few seconds. The RC time constant determined by the device capacitance and its resistance was about 3 ns, much shorter than the length of the pulse. The short pulse length Δt ≪ τo ensured the device did not heat up during the pulse as attested by current and voltage remaining constant during the pulse for most data points. Only at large applied voltages did the current increase slightly with a temperature rise calculated to be less than 10 K. As seen in Figure 1c, the quasi-static curves follow the pulsed ones at low voltages but then increase faster with voltage. The divergence is due to Joule heating and the conductivity increasing with temperature. Additionally, by overlaying pulsed I−V characteristics obtained at different stage temperatures onto a single quasi-static I−V curve, it is possible to estimate the increase of device temperature; the method was outlined by Gala et al.34 As an example, the quasi-static I−V curve at the stage temperature of 400 K diverges from the pulsed I−V at approximately 2.5 V. By the end of the quasi-static curve at 4 V, the current coincides with that obtained in a pulsed I−V corresponding to a stage temperature of 435 K (not shown). Thus, we can infer that the device temperature increased by 35 K due to Joule heating before the device reached VTH. It is also apparent that, even in the absence of Joule heating, the current increases superlinearly with voltage. The I(V) dependence of metal/TaOx/metal structures is typically interpreted as due to either a Schottky effect in thin interfacial barriers,35,36 field-enhanced emission from traps (Poole−Frenkel model),23,37−40 or polaronic conductivity.24,41 Most of the work to date indicates the Poole−Frenkel model as best describing the observations. We adopt this model here, taking the functional dependence of conductivity on field and temperature as23,42

σPF(F ,T ) =

σo(T ) 2 +

2 ⎛β F ⎞ ⎛ β F ⎞⎫ σo(T ) ⎛ kBT ⎞ ⎧ − 1⎟exp⎜ ⎟⎬ ⎟ ⎨1 + ⎜ ⎜ F ⎝ β ⎠⎩ ⎝ kBT ⎠ ⎝ kBT ⎠⎭ ⎪

⎪

⎪

⎪

(1)

where ⎛ Nd ⎞2 ⎛ Ed + Et ⎞ σo(T ) = qμNc ⎜ ⎟ exp⎜ − ⎟ ⎝ 2kBT ⎠ ⎝ Nt ⎠

⎛ q3 ⎞1/2 ⎟ β=⎜ ⎝ πεoεi ⎠ (2)

and constants Nd, Ed and Nt, Et correspond to the densities and ionization energies of donors and traps, respectively, Nc is the effective density of states in the conduction band, σo(T) is the low field conductivity, μ is the electron mobility, kB is the Boltzmann constant, q is the elementary charge, εo is the permittivity of free space, εi is the relative dielectric constant of the material, F is the electric field, and T is the stage temperature. The σo(T) in the formula was determined from the experimental data in Figure 1b (energies (Ed + Et)/2 in each sample are equal to the activation energies). An additional parameter, the dielectric constant, was used as an adjustable parameter, and the best fit was obtained for its value of 22. This corresponds to the value of the low frequency constant, in agreement with other reports.32,33,43,44 It should be noted, however, that many publications argue for use of the high frequency constant.35,38,39,45 The experimental data and fitting results are shown in Figure 1d for the 7.5% O2 TaOx film at three different stage temperatures. The fits are in good agreement with experiment for all three types of functional layers (not shown), stage temperatures, and fields. The finite element simulation assumed a 6 μm diameter cylindrical device as part of the circuit consisting of the voltage source and load resistor with the coupled current and heat flow. For electrical conductivity, we have used σPF(F,T) obtained from fitting pulsed I−V’s and extrapolated the experimental data range to higher temperatures as needed. The details of the simulation are given in the Supporting Information. The procedure generated I−V curves that reproduce the experimental quasi-static I−V, including the superlinear behavior in the OFF-state and the NDR region. The results are plotted in Figure 2 for three different stage temperatures and the devices with the functional layer deposited with 7.5% O2. The blue, red, and green lines represent the experimental data, while the black dotted lines correspond to the simulation. The same data are plotted in the inset on a logarithmic scale to show the I−V’s at low current values. The simulation reproduced the exper-

Figure 2. Experimental I−V characteristics of TaOx based devices with a film deposited with 7.5% O2 in the chamber (thick color lines) and finite element simulation of the same device (dotted lines) as a function of voltage and stage temperature. C


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resistance to 0.5 K/μW. Also worth noticing is that the current density at the lateral edge is an order of magnitude lower compared to the current density at the same location at VTH. This drop is due to the lower voltage across the device at point “2” than at VTH (as apparent in Figure 2). The temperature at the center of the filament at this point is 1200 K. With a further increase of total current, the calculated temperature is increasing linearly with current with the fwhm increasing only slightly. The simulation is not reliable much beyond point “2”. The temperature is over 700 K past the highest stage temperature used in the calibration shown in Figure 1, and the Poole−Frenkel formula likely deviates from the real values of electrical conductivity. Also, the thermal properties, which are assumed independent of temperature, could have changed significantly. At this point, we would like to stress that the observed current constriction to form the conducting filament is purely caused by local Joule heating of the functional layer. The device characteristics have not changed as the result of testing, indicating that no physical changes occurred in the structure. If changes such as crystallization of the initially amorphous material have occurred,46 they have not affected the electrical characteristics. This is different than in similar memory-type cells which undergo ion redistribution.47,48 Permanent physical changes do occur in these structures at current densities and time-at-voltage just slightly above those used in this work. These were intentionally avoided during testing.

imental data quite well: the curve in the OFF-state at all temperatures overlaps with and/or is parallel to the experimental curve, the threshold voltage is within 5% of the experimental value, and the NDR regions coincide. Similar agreement was obtained for devices with different oxygen flow rates. More insight into the characteristics of threshold switching can be obtained from evolution of temperature and current density with voltage. The 3-D temperature distribution maps for the two points marked “1” and “2” in Figure 2 for a device with a 7.5% O2 layer at a stage temperature of 300 K are shown in Figure 3a. Figure 3b shows the corresponding line profiles of

4. DISCUSSION For all biasing conditions and stage temperatures, the electrical conductivity of the functional layer is much lower than the conductivity of the metallic electrodes, resulting in a laterally uniform voltage across the electrodes. This results in a uniform current flow and uniform heating at low dissipated power. Upon approaching VTH, the temperature in the center of the device increases and the functional layer becomes a little warmer and more conductive than the lateral boundaries of the device. The current and temperature form a positive feedback loop where increases in current cause increases in temperature, and this, in turn, increases current further. The conditions for the runaway can be estimated in a simple model in which the electrical resistivity as a function of temperature is approximated by the linear term in the Taylor series

Figure 3. (a) Temperature and (b) current density distribution in the 7.5% O2 device corresponding to points “1” (at VTH, continuous blue line) and “2” (within NDR region, dotted red line) in Figure 2.

current density along the radius of the device. Point “1” corresponds to the knee of current at VTH. The average temperature of the functional layer increased by about 50 K above the stage temperature of 300 K with the center of the device being 30 K higher than the lateral edges. The corresponding current density ratio is a factor of 2. The variations across the device at this point are due to lateral heat flow. At point “2” in the NDR region, the current density and temperature distribution are highly nonuniform even though the voltage across the device is the same everywhere. The current density in the center of the device is about 4 orders of magnitude higher than the current density at the lateral edge with the full width at half-maximum (fwhm) of 250 nm. It is interesting to note that the thermal resistances of the OFF-state and NDR regions are different from each other. In the OFFstate, the current and power dissipation is more or less uniform across the diameter of the device, corresponding to a thermal resistance of 0.05 K/μW. In the NDR region, power dissipation is confined to a much smaller area, increasing the thermal

⎛ ⎞ 1 ∂σ V = IRo⎜1 − IVRTH + ···⎟ σ(To) ∂T ⎝ ⎠

(3)

where Ro is the resistance at the stage temperature, σ is the electrical conductivity, and RTH is the thermal resistance between the functional layer and the heat sink. The runaway will occur when ∂V/∂I is zero, leading to IV =

σ(To) ⎛ ∂σ ⎞−1 ⎜ ⎟ 2RTH ⎝ ∂T ⎠

(4)

This gives the value of resistance at runaway R(T) = Ro/2. Thus, runaway will occur when the Joule heating causes the resistance to drop by a factor of 2 and can occur at very different temperatures of the filament depending on the stage temperature. It is easy to notice that the quasi-static current at voltages approaching VTH is, in fact, about twice that of the current in the pulsed I−V’s (Figure 1c). D


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and load resistor, and heat and current flow. The current density as a function of electric field and temperature was obtained from short pulse I−V measurements. It was shown that the threshold switching in TaOx could be well accounted for by a thermal runaway process leading to the formation of a small-diameter hot filament. The thermal runaway is shown to be a direct consequence of the strong dependence of conductivity on temperature.

There are two possible scenarios for the end of a runaway. If the circuit includes a small load resistor, the voltage across the device will remain approximately constant during the runaway. The filament will expand and its temperature will keep increasing until the device is destroyed. On the other hand, if the load resistance is significantly larger than the resistance of the filament, the voltage drop across the device will decrease, limiting the total dissipated power. The device will come to the steady state with a small-diameter hot filament. Figure 4a compares the experimental and simulated values of the threshold voltage for three different functional layers as a

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b16559. Device structure and material parameters and justification used in COMSOL simulation of experimental I−V curves (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (J.M.G.). *E-mail: [email protected] (M.S.). ORCID

Jonathan M. Goodwill: 0000-0002-3466-3350 Marek Skowronski: 0000-0002-2087-0068 Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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Figure 4. Comparison between the experimentally measured (solid lines) and simulated (dashed lines) threshold voltage (a) and threshold power (b) for devices with three different O2 flows.

ACKNOWLEDGMENTS This work was supported in part by FAME, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA and by NSF Grant DMR 1409068.

function of stage temperature. There are two apparent trends: VTH is decreasing with increasing oxygen deficiency and stage temperature. It should be kept in mind that the conductivities of all devices are increasing with stage temperature and the current at VTH is increasing even though VTH is decreasing. The power at the beginning of the runaway (Figure 4b) is increasing with the stage temperature for both experiment and simulation. The decrease of VTH at lower O2 content in the ambient is associated with the decreasing activation energy of the conductivity. It results in a lower ∂σ/∂T, which means that a greater change of temperature is necessary to halve the initial resistance and, hence, higher dissipated power is required for the runaway. At low stage temperatures and oxygen deficiencies, the only way to increase dissipated power is to increase the VTH. A similar decrease of VTH with an increase of stage temperature was reported in our earlier work on TaOx34 and other oxides.22,23,49 Lastly, it is important to notice that the predicted size of the hot filament, while small, is much bigger than the size of the access devices to be used in memory arrays. The 10 nm-size devices retain the general shape of their I−V characteristics (simulated), i.e., exhibit NDR and threshold switching. The scaling behavior is somewhat complex and will be described in a separate publication.

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REFERENCES

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5. CONCLUSIONS The quasi-static I−V characteristics of different compositions of TaOx were experimentally measured and simulated by a finite element model that included power distribution between device E


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