A method for predicting temperature characteristics of a resistive switching device based on a physical model

Abstract

The application discloses a method for predicting temperature characteristics of a resistive switching device based on a physical model. Firstly, according to temperature test curves of different resistance states of the resistive switching device, a relationship among temperature characteristics, a device conductance and a conductive filament morphology is constructed in combination with multiple physical mechanisms. Then, a general physical model expression is proposed according to the relationship. The model can well predict the conductance change of the device for all storage states in a given temperature interval in a large range, thereby providing guidance for subsequent simulation or correction work.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of semiconductor devices and integrated circuits, and particularly relates to a method for predicting temperature characteristics of a resistive switching device based on a physical model. BACKGROUND

[0002] Under the background of the vigorous development of big data and artificial intelligence, as an important member of new memory, resistive random access memory (RRAM) is widely used in high-density storage, computing and storage integration, etc. due to its high response speed, low power consumption, good non-volatile characteristics and excellent multi-value storage characteristics. At present, most of the mature resistive random access memory adopts the 1T1R scheme, that is, the basic unit is composed of a transistor and a resistive switching device in series, and the transistor is responsible for the selection of the unit, while the conductance (or resistance) of the resistive switching device represents the current storage value of the unit. The resistive switching device is generally a three-layer or four-layer structure, and the three-layer structure is composed of a top electrode, a dielectric layer and a bottom electrode from top to bottom, and the four-layer structure adds a thermal enhancement layer on the basis of the former. The basic principle is to adjust the morphology of the conductive filament in the dielectric layer by an external voltage to obtain the corresponding conductance. In the aspect of multi-value storage application, most of them currently adopt the single device 2-bit and 4-bit scheme, and the specific operation is to uniformly divide 4 or 16 states as different storage values in the conductance range that the device can reach. Under the trend of the development of memory to larger integration density and three-dimensional stacking, the problem of power consumption and heating in the chip is increasingly prominent. Under this background, resistive random access memory also faces corresponding problems. Firstly, the reliability of resistive random access memory is challenged due to the high sensitivity of resistive switching devices to temperature. Further, the conduction mechanism of resistive switching devices is complex, and current research work has revealed the possibility of Nanowire transport, Hopping conduction, Poole-Frankel emission, Schottky emission, Quantum Point Contact, etc. in the conductive filament, which leads to different temperature characteristics of different storage states. At present, the systematic modeling of the same is still less, and it is difficult to completely express all the temperature characteristics of the resistive switching device, thus leading to limited effect of related simulation evaluation work. SUMMARY

[0003] In view of the problems that resistive random access memory has multiple temperature characteristics and its internal mechanism is complex, the present application proposes a physical model of a resistive switching device for predicting temperature characteristics. The model can better predict the conductance change of the device for all storage states within a given temperature range, which can provide guidance for subsequent simulation or correction work.

[0004] The resistive switching device can be divided into oxygen vacancy type and metal ion type, and the principle of the present application is discussed below by taking the oxygen vacancy type resistive switching device as an example. The resistance of the device is determined by the conductive filament in the dielectric layer, and in the oxygen vacancy type resistive switching device, the conductive filament is composed of a plurality of oxygen vacancies.

[0005] The relationship between the conductance of the device and the morphology of the conductive filament is discussed: the higher the density of oxygen vacancies in the region, the stronger the conductive ability, so that when the device is in a high conductance state, it corresponds to a conductive filament with a larger cross-sectional area and a more dense arrangement of oxygen vacancies, and when the device is in a low conductance state, it corresponds to a conductive filament with a smaller cross-sectional area and a more sparse arrangement of oxygen vacancies, or even a partial disappearance of the conductive filament.

[0006] The relationship between the morphology of the conductive filament and the temperature characteristics is discussed: in the region with a high density of oxygen vacancies, the spacing between oxygen vacancies is small and the arrangement is tight, forming a nanowire structure, and the transmission mode is nanowire conduction, and the temperature characteristics are that the conductance is negatively correlated with the temperature (metallic temperature characteristics); in the region with a low density of oxygen vacancies, the spacing between oxygen vacancies is large and the arrangement is sparse, and at this time, oxygen vacancies capture and release electrons as traps, and the transmission mode is Poole-Frankel emission, and the temperature characteristics are that the conductance is positively correlated with the temperature (semiconductor temperature characteristics).

[0007] In summary, the higher the conductance of the resistive switching device, the greater the proportion of the region with a high density of oxygen vacancies inside the device, and the more the conductive mode is biased towards nanowire conduction, so the temperature characteristics are more biased towards the behavior of a metal. Conversely, the lower the conductance of the resistive switching device, the greater the proportion of the region with a low density of oxygen vacancies inside the device, and the more the conductive mode is biased towards Poole-Frankel emission, so the temperature characteristics are more close to the behavior of a semiconductor.

[0008] Based on the above principle, the resistive switching device model expression can be further derived.

[0009] Firstly, the conductive filament is divided into different regions according to the conduction mechanism. Based on the discussion of the distribution of oxygen vacancies in the conductive filament in existing research, the conductive filament is divided into three regions in the present application. The first region exists in the head region of the conductive filament, the oxygen vacancy density is the highest, the resistivity is extremely low, and it contributes a very small part of the device resistance, which is called the Bulk region. The internal electrical characteristics are as follows:

[0010]

[0011] wherein R bulk is the resistance of the first region, p bulk is the resistivity of the first region, t CF is the height of the head of the conductive filament, S CF is the equivalent cross-sectional area of the region, A is the temperature coefficient of resistivity, T is the current temperature, and T0 is the reference temperature.

[0012] The second region exists in the center part of the conductive filament tail region, with a high oxygen vacancy density and a nanowire conduction mode. The electrical characteristics of the second region are as follows:

[0013]

[0014] wherein R nano is the resistance of the second region, p nano is the resistivity of the second region, t gap is the height of the conductive filament tail, S1 is the equivalent cross-sectional area of the region. A is the temperature coefficient of resistivity, T is the current temperature, and T0 is the reference temperature.

[0015] The third region exists in the peripheral part of the conductive filament tail region, with a low oxygen vacancy density and a Poole-Frankel emission mode. The electrical characteristics of the third region are as follows:

[0016]

[0017] wherein G PF is the conductance of the third region, s0 and b0 are physical constants, V is the applied read voltage, is the barrier height, S2 is the equivalent cross-sectional area of the region, k is the Boltzmann constant, and T is the current temperature.

[0018] Next, the relationship between the device conductance and the size of each region is established. Numerous studies have shown that the volume of the bulk region changes little when the resistance switching device switches states. When the conductance increases, it is the cross-sectional area of the whole that increases, which can be approximately expressed as follows:

[0019] S eff = a (G0 - e)

[0020] wherein S eff is the equivalent cross-sectional area of the whole (the sum of S1 and S2), G0 is the conductance at temperature T0, a is the proportional coefficient, and e is set to consider other regions or mechanisms that contribute to the conductance.

[0021] Furthermore, when the conductance increases, the proportion of the second region in the conductive filament tail region increases, and the proportion of the third region decreases, which can be approximately expressed as follows:

[0022] p = y G0

[0023] S2 = p S eff

[0024] S1 = (1 - p) S eff

[0025] Among them, γ is the proportional coefficient, and p represents the proportion of the third area.

[0026] The equivalent circuit of the resistive switching device can be expressed as the resistance of the second region connected in parallel with the resistance of the third region, and then connected in series with the resistance of the first region. Therefore, its conductance can be written as:

[0027]

[0028] in, is the predicted conductivity at temperature T, G0 is the conductivity at temperature T0, and this formula is the final model expression.

[0029] Based on the above physical model, a method for predicting the temperature characteristics of resistive switching devices can be constructed. First, to correctly apply the model expression, all parameters must be determined. These parameters can be divided into three categories, and the following describes how to obtain their values.

[0030] The first category is known parameters, including ρ bulk , ρ nano , t CF , t gap 、S CF , T0, k, V, β0, these parameters can be obtained from existing knowledge, remain constant and do not require additional acquisition costs. k is the Boltzmann parameter, which can be obtained by looking up the table. T0 is the reference temperature, which can be set to room temperature. V is the read voltage, which is a pre-set quantity. ρ bulk , ρ nano is the resistivity of the region, the former is between 10 -6 ~10 -5 In the range of Ω·m, the latter is within 10 -4 ~10 -3 In the range of Ω·m. CF , t gap 、S CF β0 is a parameter related to the conductive filament and is related to the material and process of the resistive switching device. There are several research works for reference. The calculation is as follows: q is the charge constant, ε0 is the vacuum dielectric constant, and ε r is the relative dielectric constant of the dielectric layer material.

[0031] The second category is the parameters extracted from the test curve, including A, σ0, Parameters α, ε, and γ are extracted from the measured temperature characteristic curve. They remain constant for products in the same production process and do not need to be extracted repeatedly. The extraction method for A is to program the resistive switching device to the highest conductance it can achieve, test the change in its conductance G with temperature T, and calculate G~(kT+b). -1 Fitting, at this time the value of S1 is S CF, S2 takes 0, and the value of A can be obtained by solving the equations simultaneously. The extraction method of the resistance change device is as follows: the resistance change device is programmed to the lowest obtainable conductance, the change relationship of the conductance G with respect to the temperature T is tested, and G~lambda*T -1 exp(mu / T) fitting is performed, and lambda and mu are fitting parameters, at this time, the conductance is determined by the conductance of the third region, S2 takes S CF between 1 / 4 and 1 / 2 of the conductance of the first region, and the value of sigma0 The extraction method of alpha, epsilon and gamma is as follows: a plurality of conductances are uniformly selected between the highest and lowest conductances, and the response of the conductance G of the resistance change device programmed at the conductances to the temperature T is tested, and alpha, epsilon and gamma can be obtained by fitting the complete model expression.

[0032] The third type is the parameter used for prediction, including the conductance G0 and the temperature T. If the parameters of the first two types are set, the user only needs to set the corresponding G0 and T according to the own demand, and the conductance prediction value under the condition can be obtained

[0033] Therefore, the present application proposes a method for predicting the temperature characteristics of a resistance change device based on a physical model, and the main contributions include: (1) according to the temperature test curve of the resistance change device in different resistance states, a relationship among the temperature characteristics, the conductance of the device and the morphology of the conductive filament is constructed by combining a plurality of physical mechanisms; (2) according to the above relationship, a general physical model expression is proposed, which can better predict the temperature characteristics of the device under each temperature and each conductance state. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 The retention characteristic curves of each storage state of the resistance change random memory adopting the 4-bit multi-value storage scheme in the embodiment are shown.

[0035] Figure 2 The temperature characteristic curves of each state of the resistance change random memory in the embodiment are shown, wherein the upper graph shows the test results of the positive correlation part of the conductance and the temperature, and the lower graph shows the test results of the negative correlation part of the conductance and the temperature.

[0036] Figure 3 The schematic diagram of the physical model establishment method of the resistance change random memory of the present application is shown.

[0037] Figure 4 The comparison and verification of the model prediction value and the actual measurement value of the conductance of the resistance change random memory in different storage states and at different temperatures in the embodiment are shown.

[0038] Figure 5 The further verification results of the model prediction ability at each temperature and state in the embodiment are shown. DETAILED DESCRIPTION

[0039] To further clarify the objectives, technical solutions, and advantages of the present invention, the following, in conjunction with the accompanying drawings, provides a clear and complete description of a method for predicting temperature characteristics of a resistive switching device based on the physical model of the present invention. It should be understood that the described embodiments are only a portion of the embodiments of the present invention, not all of them. All other embodiments derived by persons of ordinary skill in the art based on the embodiments of the present invention without inventive effort are intended to fall within the scope of protection of the present invention.

[0040] For a resistive random access memory using a 4-bit multi-value storage scheme, this embodiment uses a larger conductivity range as the 4-bit multi-value storage interval in order to fully study all temperature characteristics of the device. Figure 1 As shown, the conductance of state "1" is 5μS, the conductance of state "16" is 245μS, and the intermediate conductances are separated by 16μS in sequence, for a total of 16 storage states. Each storage state can be maintained for a long time within a conductance range, making it suitable for multi-value storage. For example, Figure 1 In the figure, 10 devices were selected for each storage state and programmed into that state. The device conductance was read repeatedly over 100 seconds. The thin line segments represent the conductance fluctuation of a single device during that time, while the thick line segments represent the average conductance of all devices in that state. The results demonstrate that this embodiment exhibits excellent multi-value storage characteristics, making it suitable for testing temperature characteristics and validating model predictions.

[0041] Figure 2 The test results of the temperature characteristics of each state are shown in FIG. 1 , and the test temperature range is 25°C to 145°C. Figure 2 The figure above shows the test results of the part where conductivity is positively correlated with temperature. The states that meet this characteristic are "1" to "12", and the correlation between different states and temperature is different. Figure 2 The figure below shows the test results for the part where conductivity is negatively correlated with temperature. The states that meet this characteristic are "13" to "16".

[0042] Figure 3 Schematic diagram of the method for establishing a physical model of resistive random access memory. Figure 3The left side of the figure shows a longitudinal cross-section of the device, illustrating the morphological changes of the conductive filaments under different conductance states. The difference in conductivity primarily originates from the tail of the conductive filament. At low conductance, no high oxygen vacancy density region forms at the tail of the conductive filament; only scattered regions of low oxygen vacancy density conduct current. As conductance gradually increases, oxygen vacancies begin to aggregate at the tail, expanding the region of oxygen vacancies and forming a high oxygen vacancy density region in the center. As conductance further increases, the region of oxygen vacancies approaches the area occupied by the entire bulk, with the primary change now due to the expansion of the high oxygen vacancy region in the center. Figure 3 The upper right part shows the cross-section of the tail conductive filament and a schematic diagram of the corresponding physical mechanism. The conduction mechanism of the low oxygen vacancy region (S1) is Poole-Frankel emission, and the oxygen vacancies act as traps to capture and release charges; the conduction mechanism of the high oxygen vacancy region (S2) is nanowire conduction, and the charges are directly conducted through the oxygen vacancies. Figure 3 The lower right part lists the relevant formulas of the model.

[0043] according to Figure 3 The model shown predicts the change in the conductivity of the resistive random access memory in different storage states and at different temperatures. First, all parameters except G0 and T need to be determined. Under the conditions of this embodiment, according to the requirements of the invention summary, for the first type of parameters, T0 is set to 25°C, V is set to 0.2V, and ρ bulk Take 10 -6 Ω·m,ρ nano Take 6×10 -3 Ω·m,t CF , t gap 、S CF The selection reference is TaO at 40nm process node x Simulation work related to resistive switching devices, CF Take 17nm, t gap Take 3nm, S CF Take 43.19nm 2 For the calculation of β0, the relative dielectric constant is taken as 30, and the calculated result is 4.046×10 -20 C.V. 1 / 2 For the second type of parameters, select state "16" as the state with the highest conductance and state "0" as the state with the lowest conductance. The temperature characteristic curve obtained in state "16" is G~(kT+b) -1 Fitting, extraction and solution give A as 3.354×10 -3 K -1 , the temperature characteristic curve obtained in state "0" is plotted as G~λ·T -1• exp(μ / T) fit, yielding σ0= 2.566 x 10 5 S / m, = 0.347 eV. Temperature dependence curves of the remaining states ("1" to "15") were measured and fitted to the model expression, yielding a = 2.723 x 10 -14 m 2 S / m, ε = 3.516 x 10 -5 S / m, γ = 3.274 x 10 3 S -1 The model parameters are summarized in the following table:

[0044] Table 1. Summary of model parameters for Example

[0045]

[0046] Figure 4 The model prediction is compared to the measured values in the following table. The verification covers all storage states ("1" to "16") and the complete temperature range of the measurements. The results show that the measured values fluctuate within a small range around the predicted values at all data points, demonstrating good agreement between the model and the actual device.

[0047] Figure 5 The further verification of the model prediction capability at different temperatures and states is shown in the following table. To exclude the influence of natural fluctuations (e.g. increased noise of the device at high temperatures), the evaluation criterion is defined as the root mean square error minus the standard deviation (RMSE-SD). Figure 5 The closer the blocks in the table are to blue, the higher the accuracy of the prediction under that condition. The results show that the prediction capability of the model remains relatively stable in most cases, with only a small decline in some cases, but still within a relatively accurate range (< 2 μS).

Claims

1. A method for predicting temperature characteristics of a resistive switching device based on a physical model, wherein the physical model of the resistive switching device is to divide a conductive filament in a medium layer of the resistive switching device into three regions: a first region is a head region of the conductive filament, a second region is a central part of a tail region of the conductive filament, and a third region is a peripheral part of the tail region of the conductive filament; an equivalent circuit of the resistive switching device is that a resistance of the second region and a resistance of the third region are connected in parallel, and then the resistance of the first region is connected in series; and a predicted conductance of the resistive switching device is shown as formula (1) : G = G 0 + G 1 + G 2 wherein the resistance of the first region is shown as formula (2) : R 1 = R 0 + R 1 0 wherein the resistance of the second region is shown as formula (3) : R 2 = R 2 0 + R 2 1 wherein a volume of the first region changes little when the resistive switching device is in a state switching; the second region and the third region are regarded as a whole, when a conductance of the device increases, a cross-sectional area of the whole increases, meanwhile, a proportion of the second region increases, and a proportion of the third region decreases, and these relationships are approximately shown as: p = γG 0 wherein α is a proportional coefficient, ε is set by considering other conductive regions or mechanisms; p represents the proportion of the third region, and γ is a proportional coefficient. wherein G0is the conductance of the resistive switching device at a reference temperature T0, R bulk R1is the resistance of the first region, nano R2is the resistance of the second region, PF R3is the resistance of the third region; ​ where p bulk is the resistivity of the first region, t CF is the height of the head of the conductive filament, S CF is the cross-sectional area equivalent to the first region, and A is the temperature coefficient of resistivity. ​ where p nano is the resistivity of the second region, t gap is the height of the tail of the conductive filament, and S1 is the equivalent cross-sectional area of the second region. The resistance R of the third region PF The reciprocal of its conductance G PF PF As shown in the following equation (4):​ wherein σ0, β0 are physical constants, V is an applied read voltage, is the barrier height, S2 is the cross-sectional area of the third region equivalent, k is the Boltzmann constant; ​ S eff = a(G0- e) S2 = pS eff S1 = (1 - p)S eff ​ where S eff is the cross-sectional area of the second and third regions taken as a whole, G0is the conductance of the resistive switching device at a reference temperature To, ​ For the parameters in the above formula, ρ bulk , ρ nano , t CF , t gap , S CF , T0, k, V, β0 are known parameters, A, σ0, α, ε, γ are obtained from the temperature characteristic curve of the experimental test, and the conductance G0 and temperature T are set, so that the conductance prediction value of the resistance variable device under the condition is obtained 2. The method of predicting temperature characteristics of a resistive switching device of claim 1, wherein, ρ bulk values in the range of 10 -6 ~ 10 -5 Ω·m, and the latter ρ nano values in the range of 10 -4 ~ 10 -3 Ω·m.

3. The method of predicting temperature characteristics of a resistive switching device of claim 1, wherein, β0 is calculated by where q is the charge constant, ε0 is the vacuum permittivity, ε r is the relative dielectric constant of the dielectric layer material, t gap The materials and processes related to the resistive switching device can be obtained by referring to the relevant literature.

4. The method of predicting temperature characteristics of a resistive switching device of claim 1, wherein, The extraction method of A is: programming the resistance variable device to the highest conductance that can be reached, testing the change relation of its conductance G with temperature T, and making G~(kT+b) -1 fitting, at this time the value of S1 takes S CF 2 takes value 0, and the value of A is obtained by solving the equations simultaneously.

5. The method of predicting temperature characteristics of a resistive switching device of claim 1, wherein, σ0, The extraction method is: the resistance variable device is programmed to the lowest available conductance, the relationship between the conductance G and the temperature T is tested, and Gρλ·T -1 exp(μ / T) fitting is made, λ and μ are fitting parameters, at this time the conductance is determined by the conductance of the third region, S2 is between 1 / 4 and 1 / 2 of S CF , and the value of σ0、 can be obtained by solving the equations simultaneously.

6. The method of predicting temperature characteristics of a resistive switching device of claim 1, wherein, In extracting parameters A, σ0, Afterwards, the parameters α, ε, and γ are extracted using the following method: Several conductivities are uniformly selected between the highest and lowest conductivities, and the response of the conductance G of the resistive switching devices programmed at these conductivities to temperature T is tested. The model expressions are then fitted to obtain α, ε, and γ.

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