Threshold Switching by Bipolar Avalanche Multiplication in Ovonic Chalcogenide Glasses

An ovonic threshold switch (OTS) based on chalcogenide glasses finds application as a selecting device in storage class memory (SCM) arrays. The OTS operation relies on the threshold switching, where the device switches from the off to the on state without phase transition, then the device turns off almost immediately as the voltage is reduced below a certain holding value. The physics behind the switching phenomenon has attracted wide interest due to the complicated interplay between electronic transport, joule heating and phase transition. In this work, it is shown that the current‐voltage characteristic close to the switching point carries the fingerprint of carrier multiplication. The physical mechanism of threshold switching is then explained by bipolar impact ionization leading to avalanche multiplication, which in turn gives rise to the typical S‐shaped characteristic. Numerical simulations by this physics‐based model account for the measured switching properties, namely threshold voltage and current, at various chalcogenide thicknesses and compositions. These results provide the theoretical framework for future design and optimization of OTS in memory and computing applications.

An ovonic threshold switch (OTS) based on chalcogenide glasses finds application as a selecting device in storage class memory (SCM) arrays. The OTS operation relies on the threshold switching, where the device switches from the off to the on state without phase transition, then the device turns off almost immediately as the voltage is reduced below a certain holding value. The physics behind the switching phenomenon has attracted wide interest due to the complicated interplay between electronic transport, joule heating and phase transition. In this work, it is shown that the currentvoltage characteristic close to the switching point carries the fingerprint of carrier multiplication. The physical mechanism of threshold switching is then explained by bipolar impact ionization leading to avalanche multiplication, which in turn gives rise to the typical S-shaped characteristic. Numerical simulations by this physics-based model account for the measured switching properties, namely threshold voltage and current, at various chalcogenide thicknesses and compositions. These results provide the theoretical framework for future design and optimization of OTS in memory and computing applications.

Introduction
The ovonic threshold switch (OTS) is an emerging device based on chalcogenide glasses such as sulfides, selenides, and tellurides. First discovered in the 1960s, the OTS is capable of threshold switching, where the current characteristics exhibit an abrupt transition from the off state to the on state at a characteristic threshold voltage V T . [1] In general, the OTS is uncapable of memory switching, namely the device always returns to the off state as the supplied voltage is reduced below a certain minimum level, known as the holding voltage V H . This is Figure 1a shows a sketch of the 1S1R structure where the OTS serves as the selector element, while the memory element consists of a Phase Change Memory (PCM) device. The 1S1R structure is connected to perpendicular top and bottom electrode lines within a cross-point array. Such a cross-point structure of the memory array receives strong interest in view of the extremely small cell size and the ability to process the materials and structures in the back end of the process, which allows for 3D stacking of several memory arrays. [27][28][29] The storage mechanism of the 1S1R structure consists of the different V T in the S-shaped I-V characteristic. This is shown in Figure 1b, where the I-V curves for the "1" and "0" states have different V T due to the memory element being in the amorphous (high V T ) or crystalline state (no V T due to the lack of S-shape NDR). The V T difference between the two states yields the memory window ΔV T , where the device can be probed for measuring the read current. [8] Stable, controllable V T with tight statistical distribution is therefore mandatory for accurate, reliable readout of the memory cell.

Sub-Threshold Characteristics
To better understand the threshold switching phenomenon and its characteristic V T , the sub-threshold current plays a fundamental role. [22,23] Figure 2a shows the measured I-V curves of the OTS device with Te-based chalcogenide glass with a standard Ovshinsky composition Te 5 As 3 GeSi [1] with increasing thickness u a from 15 to 35 nm. To measure the conduction and switching characteristics, the OTS device was connected in series with an integrated transistor, to form a one-transistor/ one-resistor (1T1R) structure, allowing a tight control of the maximum compliance current I C = 100 µA after threshold switching (see Figure S1, Supporting Information). Note the turn-off behavior of the current in correspondence of the holding voltage V H as the voltage is reduced back to zero.
Adv. Electron. Mater. 2023, 9,2300037   The threshold voltage exhibits a monotonic increase with thickness u a , while the subthreshold slope STS = dlogI/dV decreases at increasing u a . These results are in line with the PF model with the current given by: where I 0 an area-dependent pre-exponential factor, E A0 the energy barrier at zero electric field (associated with the half of the band gap value E G of the chalcogenide glass [22,23] ) for the charge carriers (generally holes in chalcogenide glasses [30] ), k is the Boltzmann constant, T is the temperature and Δφ PF is the field-dependent barrier lowering given by: where q is the electron charge, ε is the electronic component of the dielectric constant, and V is the applied voltage. The PF model of Equation (2) predicts an exponential increase of the current with the square root of the electric field F = V/u a . [31][32][33] This is confirmed by the results in Figure 2b, showing the measured current as a function of the square root of F. All data overlap below about 1 nA, while the current exhibits a superexponential increase at higher field and current.

Avalanche Multiplication
The super-exponential transport phenomenon can be ascribed to avalanche multiplication due to impact ionization (II) at high electric field. To better support this interpretation, Figure 3a shows the extracted multiplication factor M, given by: where I is the measured current and I PF is the current of primary carriers, estimated by extrapolating the low-voltage PF characteristic as a function of F 1/2 in Figure 2b. The multiplication factor steeply increases with the electric field, showing larger values for increasing thickness u a . This is consistent with avalanche multiplication, where a thicker amorphous layer results in more generated pairs at a given field, as illustrated in Figure 3b. Note also that M reaches relatively large values despite the relatively low voltage (below 3.5 V in Figure 2a). Such a large value of M would not be possible for conventional band-to-band II, as the typical band gap of chalcogenide glasses is between 1 and 2 Ev. [34] The large M can be understood by the lucky-drift II model, where II can take place at sub-band gap energies, for example, requiring an ionization energy E I of the primary carriers much lower than the band gap E G . [35] The large multiplication factor M is also consistent with bipolar II, where the primary holes generate secondary electrons which in turn generate tertiary carriers in a positive feedback process. [36] From the multiplication factor, one can extract the II coefficient α, which is linked to M by the formula e ua = α M , assuming single-particle II. [37] Figure 3c shows the II coefficient α as a function of 1/F, indicating an exponential dependence given by: where A is a pre-exponential factor, q is the electron charge, λ is the mean free path for II and E I is the threshold energy for impact ionization to generate an electron-hole pair. [35] Data are in line with previous results showing comparable value of α for chalcogenide glasses. [35] To provide a wider support for the observed field-dependent α, a detailed electrical characterization of OTS devices was conducted for several chalcogenide glasses with various compositions obtained by the gradual substitution of Te with Se in our Te-based chalcogenide glass. The change in the composition of the chalcogenide glass allows to gradually modulate the energy gap in a range between 0.8 and 1.8 eV, as extracted from optical absorption measurements by the Tauc plot (see Figure S2, Supporting Information). Figure 4a shows the extracted M at varying E G for a thickness u a = 35 nm. As E G increases, M decreases as a result of the higher ionization energy required for II. Figure 4b shows the extracted α as a function of 1/F, which confirms the agreement with Equation (4) where the slope in the exponential plot increases with E G (see Figure S3, Supporting Information). In addition to DC measurements, the power spectral density (PSD) of 1/f current noise, already observed in amorphous chalcogenide glasses. [37,38] was also  characterized in our OTS devices (see Figure S4, Supporting Information). Figure 4c reports the measured excess 1/f noise factor in the pre-switching region as a function of the multiplication factor M. The almost linear increase of the excess noise with M is a strong indication supporting bipolar II in the OTS device, whereas simulation results for unipolar avalanche predicts an almost constant excess noise with M, asymptotically approaching 2. [39] The slope of the excess noise as a function of M is in line with previous analytical models of II. [40]

Bipolar II-Based Threshold Switching Model
The experimental findings in the previous section allow to develop a novel interpretation of threshold switching in the OTS device based on bipolar II. Previous interpretations of threshold switching revolved around two main concepts, namely: a) purely electronic models of threshold switching based on high-field PF or II [18,22] and, b) thermal models where joule heating causes a change in the number or mobility of the conduction carriers giving rise to a positive thermal feedback on conductivity. [26] The thermal model is in contrast with recent data of optical experiments, indicating that threshold switching can take place within the electric pulse on sub-picosecond time scales, which is apparently too short to enable joule heating. [41] Moreover, such mechanism could not be uniquely ascribed to chalcogenide alloys since thermal run-away is a well-known effect in silicon and other non-chalcogenide devices which in general do not show the S-type NDR. On the other hand, our data evidencing II in the pre-switching regime provides substantial support to an interpretation of threshold switching as an electronic switching phenomenon. Note that, although joule heating can be ruled out as the root cause of threshold switching, significant thermal effects can indeed take place after threshold switching, as the conductivity increases to the ON state.
We carried out device simulations based on the Boltzmann's equation solved in its energy-balance (EB) formulation with the average carrier energies W n for electrons and W p for holes given by [40] : where S is the carrier energy flux, that is the current multiplied by the carrier temperature, J n and J p are the electron current densities, respectively, and E C and E V are the conduction and valence band energies, respectively. In Equation (5), the righthand side contains the carrier energy gain by the electric field and its loss for the carrier relaxation time τ en,p via lattice phonons. The time derivative term in the left-hand side can be dropped for steady-state conditions. To reproduce the S-type NDR in the I-V characteristic as a solution of the EB transport in Equation (5), we implemented the PF transport for the primary carrier describing the low field current and the bipolar II coefficient α as in Figure 3, where the secondary-generated electrons also contribute to the avalanche multiplication mechanism, thus leading to a positive feedback. The resulting concentration of holes at the cathode side enhances the electric field, thus sustaining an even higher II rate. The S-type NDR can be explained by the decrease of the voltage drop between the top and bottom electrodes at increasing currents, due to the high mobility of the secondary electrons. Figure 5 shows a sketch of the proposed mechanism for switching phenomenon including the simulation of the I-V characteristic and the band diagram for three device conditions, namely deep subthreshold regime, preswitching regime and ON-state. Simulations of the I-V curve by assuming equal mobilities of electron and holes did not show any NDR characteristic (see Figure S5, Supporting Information), thus supporting the essential role of bipolar II in the presence of a large unbalance between the hole and electron mobilities.
The heuristic idea behind the switching mechanism is that the electric field becomes non-uniform in the ON-state as a result of the energy balance equation including the large bipolar multiplication factor at high electric fields and the higher mobility of electrons. In particular, the field decreases close to the anode since the large current of the ON-state can be sustained by the large concentration of secondary electrons combined with their high mobility without requiring the presence of a high electric field. The voltage decrease for increasing current above the threshold current I T gives rise to the S-shaped NDR at the basis of the threshold switching process. Note that the threshold switching phenomenon in chalcogenide glasses as manifestation of the cooperation of holes and electrons was originally foreseen by Sir Nevil Mott and the bipolar avalanche effectively fits in this physical picture. [43] Moreover,  Simulation results for unipolar avalanche multiplication according to the noise model in [41] indicate an almost constant excess noise factor. the larger mobility of electrons compared to holes in chalcogenide materials is supported by the carrier effective mass in cubic Ge 2 Sb 2 Te 5 (GST) extracted from the density of states (DoS), being 3 to 4 times larger for electrons than for holes. [44] We can expect a similar unbalance between electron and hole mobilities in the OTS chalcogenide glass, where, similar to GST, states at the top of the valence band are due to p-orbitals of chalcogen atoms, mainly originating from lone pairs, while states at the bottom of the conduction band are due to the antibonding p-type states with mainly cation character. [45] Data on electron and hole mobility in Ge x Se 1-x glass measured by the time-of-flight technique reveal that the µ n >> µ p . [46]

Numerical Simulation Results Versus Experimental Trends
To validate the proposed interpretation of threshold switching, Figure 6 shows a) the measured threshold voltage V T , b) the threshold current I T , and c) the threshold power P T = V T I T (c) as a function of chalcogenide thickness. The figure also shows the calculated threshold values extracted from the simulated I-V curves at the onset of the NDR. We underline the ability of the model to correctly capture the not obvious experimental signatures like the non-zero intercept of the V T projected at zero thickness of the OTS layer and the increasing value of the switching current with chalcogenide layer thinning.
The non-zero intercept of the V T extrapolation in Figure 6a can be used as a further indication of the II phenomenon at the basis of the switching event. In fact, devices with a thinner chalcogenide layer require higher electric field for promoting II in line with the thickness dependence in Figure 2b. On the other hand, other models purely based on field-driven switching generally yield a zero intercept at zero thickness. [22] Similarly, a higher switching current for thinner devices comes in turn from the higher field for switching, since the current is ruled by the electric field.

Figure 7a
shows the measured and calculated V T as a function of the band gap of the chalcogenide glass between ≈0.8 and 1.8 eV. For a given thickness, the V T value results from the optical band gap of the chalcogenide glasses used to build the device in agreement with the model that accounts for the key role of the optical band gap controlling both the low field region through the PF transport model of Equation (1) and the pre-switching region through impact ionization described by Equation (4).
Finally, Figure 7b reports, in semi-log scale, the correlation plot of the measured V T as a function of sub-threshold current I leak collected at V T /2, from chalcogenide-based glasses of various composition, hence E G . Data indicate a clear correlation which is accurately captured by our model, since I leak is exponentially controlled by the band gap according to Equation (1), while V T linearly increases with E G according to Figure 7a. In general, the model accounts well for the measured switching values.
It is useful to view the results in Figure 7 from an application viewpoint, where the trade-off between V T and sub-threshold current represents an important figure of merit for the OTS device. In fact, the OTS requires both a high V T and low subthreshold current to minimize the leakage current from unselected and partially-selected cells in the cross-point array. [7] Further experimental trends that are straightforwardly described by the model are reported in Figure 8, namely, the linear decrease of the V T with increasing temperature (Figure 8a) and the V T drift behavior (Figure 8b). The V_T lowering with temperature increase is coherent with the PF current of primary carriers increase with temperature in addition with a slightly positive temperature dependence of the impact ionization observed in amorphous semiconductors. [47] The V T drift over the waiting time after the programming operation is a natural consequence of the combination between the band gap widening (see Figure S6, Supporting Information) at the basis of the structural relaxation [48] and the V T increase with E G , highlighted in Figure 7a. Note that the results in Figure 7 can also indirectly explain the area dependence of V T , where V T slightly decreases for increasing device area at a given chalcogenide layer thickness. [49] In fact, as the area increases, there is an increasing probability to find a path with relatively low E G , where switching can be initiated at a slightly lower V T .
These results support the improved understanding and modeling of threshold switching for materials-driven engineering and scaling of the OTS technology for storage class memory.

Conclusions
We have carried out a detailed characterization of the subthreshold I-V characteristics for a class of OTS materials at various composition, hence energy gaps. The study of the subthreshold characteristics in the pre-switching region evidences current multiplication at high fields due to II. The improved  understanding of the II effect allows to develop a physics-based model of threshold switching accounting for the S-type NDR behavior by means of these three key ingredients, namely a) PF-like conduction by majority holes at low electric field, b) bipolar avalanche multiplication in the pre-switching regime, and c) threshold switching triggered by the large electron mobility compared to hole mobility. Simulation results well describe the transport and switching parameters as a function of material composition, thickness, temperature, and time. The model paves the way for materials engineering and scaling of the OTS device for a wide portfolio of applications, ranging from memory to in-memory computing.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.