Method for predicting temperature characteristics of resistive device based on physical model

Abstract

The invention discloses a method for predicting temperature characteristics of a resistive device based on a physical model. The method comprises the following steps: firstly, according to temperature test curves of different resistance states of the resistive random access device, combining a plurality of physical mechanisms to construct a relationship among temperature characteristics, device conductivity and conductive filament morphology; then, a universal physical model expression is provided according to the relation. The model can better predict the conductivity change of the device for all storage states in a given temperature interval in a larger range, and provides guidance for subsequent simulation or correction work.

Description

Technical Field

[0001] The present invention belongs to the field of semiconductor devices and integrated circuits, and in particular relates to a method for predicting temperature characteristics of a resistive switching device based on a physical model. Background Art

[0002] In the context of the booming development of big data and artificial intelligence, as an important member of the new memory, resistive random access memory (RRAM) has been widely used in high-density storage, storage and computing integration and other fields with its high response speed, low power consumption, good non-volatile characteristics and excellent multi-value storage characteristics. At present, most of the more mature RRAMs adopt the 1T1R scheme, that is, the basic unit is composed of a transistor and a resistive device in series, in which the transistor is responsible for the gating of the unit, and the conductivity (or resistance) of the resistive device represents the storage value of the current unit. Resistive devices are generally three-layer or four-layer structures. The three-layer structure is the top electrode, the dielectric layer, and the bottom electrode from top to bottom. 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 filaments in the dielectric layer by an external voltage to obtain the corresponding conductivity. In terms of multi-value storage applications, most of them currently use single-device 2-bit and 4-bit schemes. The specific operation is to evenly divide 4 or 16 states with the same conductivity interval within the conductivity range that the device can achieve, and use them as different storage values. As memories are generally developing towards higher integration density and three-dimensional stacking, the power consumption and heat generation issues inside the chip are becoming increasingly prominent. In this context, RRAM is also facing corresponding problems. First, due to the high sensitivity of RRAM devices to temperature, the reliability of RRAM is challenged. Furthermore, the conductive mechanism of RRAM itself is complex. Current research has revealed the possibility of mechanisms such as nanowire transport, hopping conduction, Poole-Frankel emission, Schottky emission, and quantum point contact tunneling in conductive filaments, which leads to different temperature characteristics of different storage states. However, there are still few systematic modelings, making it difficult to fully describe all temperature characteristics of RRAM devices, which results in limited results of related simulation evaluation work. Summary of the invention

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

[0004] Resistive switching devices can be divided into oxygen vacancy type and metal ion type. The following uses oxygen vacancy type resistive switching devices as an example to discuss the principle of the present invention. The resistance of the device is determined by the conductive filaments in its dielectric layer. In oxygen vacancy type resistive switching devices, the conductive filaments are composed of a plurality of oxygen vacancies arranged.

[0005] The relationship between device conductivity and the morphology of conductive filaments is discussed: the higher the density of oxygen vacancies in the region, the stronger its conductivity. Therefore, when the device is in a high conductivity state, it corresponds to conductive filaments with larger cross-sectional areas and denser arrangement of oxygen vacancies. When the device is in a low conductivity state, it corresponds to conductive filaments with smaller cross-sectional areas and sparse or even partially disappeared oxygen vacancies.

[0006] The relationship between the morphology of conductive filaments and the temperature characteristics is discussed: in areas with higher oxygen vacancy density, the oxygen vacancies are closely spaced and closely arranged, forming a nanowire structure. The transmission mode is nanowire conduction, and its temperature characteristic is that the conductivity is negatively correlated with temperature (temperature characteristics of metals); in areas with lower oxygen vacancy density, the oxygen vacancies are widely spaced and sparsely arranged. At this time, oxygen vacancies act as traps to capture and release electrons. The transmission mode is Poole-Frankel emission, and its temperature characteristic is that the conductivity is positively correlated with temperature (temperature characteristics of semiconductors).

[0007] In summary, the higher the conductance of the resistive switching device, the greater the proportion of the high-density oxygen vacancy area inside it, the more the conduction mode is biased towards nanowire conduction, and thus the temperature characteristics are more biased towards the behavior of metals. On the contrary, the lower the conductance of the resistive switching device, the greater the proportion of the low-density oxygen vacancy area inside it, the more the conduction mode is biased towards Poole-Frankel emission, and thus the temperature characteristics are closer to the behavior of semiconductors.

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

[0009] First, the conductive filaments are divided into different regions according to the conductive mechanism. Based on the discussion of the distribution of oxygen vacancies in conductive filaments in existing studies, the present invention divides the conductive filaments into three regions. The first region exists in the head region of the conductive filament, where 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. Its internal electrical characteristics are expressed as follows:

[0010]

[0011] Among them, R bulk is the resistance of the first region, ρ bulk is the resistivity of the first region, t CF Height of the conductive filament head, 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 central part of the tail region of the conductive filament, where the oxygen vacancy density is high and the conduction mode is nanowire conduction. The electrical characteristics inside are as follows:

[0013]

[0014] Among them, R nano is the resistance of the second region, ρ nano is the resistivity of the second region, t gap is the height of the tail of the conductive filament, 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 outer part of the tail region of the conductive filament, where the oxygen vacancy density is low and the conduction mode is Poole-Frankel emission. The electrical characteristics inside are as follows:

[0016]

[0017] Among them, G PF is the conductivity of the third region, σ0 and β0 are physical constants, V is the external reading 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 device conductance and the size of each region is established. Many studies have shown that when the resistive switching device switches state, the volume of the bulk region changes very little. Considering the second and third regions as a whole, when the conductance increases, it reflects the increase in the cross-sectional area of ​​the whole. This relationship can be approximately expressed as follows:

[0019] S eff =α(G0-ε)

[0020] Among them, S eff is the overall equivalent cross-sectional area (the sum of S1 and S2), G0 is the conductivity at temperature T0, α is the proportionality coefficient, and ε is set to take into account other regions or mechanisms that contribute to the conductivity.

[0021] Furthermore, when the conductivity increases, at the tail of the conductive filament, the proportion of the second region increases, and the proportion of the corresponding third region decreases. This relationship can be approximately expressed as follows:

[0022] p=γG0

[0023] S2=pS 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 second region resistor and the third region resistor in parallel, and then connected in series with the first region resistor, so 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, in order to correctly apply the model expression, all parameters need to be determined. They can be divided into three categories, and the following will explain how to obtain their values.

[0030] The first category is known parameters, including ρ bulk , 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 , nano is the resistivity of the region, the former is between 10 -6 ~10 -5 In the range of Ω·m, the latter is between 10 -4 ~10 -3 In the range of Ω·m. CF ,t gap , S CF It 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. It can be calculated by the formula, where 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, α, ε, γ, these parameters are extracted from the measured temperature characteristic curve, and remain constant in products with the same production process, without the need for repeated extraction. The extraction method of A is to program the resistive switching device to the highest conductivity that can be achieved, test the change relationship of its conductivity G with temperature T, and make G~(kT+b) -1 Fitting, at this time the value of S1 is S CF, S2 takes the value of 0, and the value of A can be obtained by solving the simultaneous equations. σ0, The extraction method is: program the resistive switching device to the lowest conductivity that can be obtained, test the relationship between its conductivity G and temperature T, and make G~λ·T -1 ·exp(μ / T) fitting, λ, μ are fitting parameters, the conductivity is determined by the conductivity of the third region, S2 takes S CF The solution of the simultaneous equations can be between 1 / 4 and 1 / 2 of σ0, The extraction method of α, ε, and γ is: select several conductances evenly between the highest and lowest conductances, and test the response of the conductance G of the resistive switching device programmed at these conductances to the temperature T, and fit the complete model expression to obtain α, ε, and γ.

[0032] The third category is the parameters used for prediction, including conductivity G0 and temperature T. If the parameters of the first two categories have been set, the user only needs to set the corresponding G0 and T according to their needs to obtain the conductivity prediction value under this condition.

[0033] Therefore, the present invention proposes a method for predicting the temperature characteristics of a resistive switching device based on a physical model, and its main contributions include: (1) According to the temperature test curves of the resistive switching device in different resistance states, combined with multiple physical mechanisms, the relationship between the temperature characteristics, the device conductivity and the morphology of the conductive filaments is constructed; (2) Based on the above relationship, a universal physical model expression is proposed, which can better predict the temperature characteristics of the device at various temperatures and conductivity states. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 4 is a retention characteristic curve of each storage state of the resistive random access memory using a 4-bit multi-value storage scheme in the embodiment.

[0035] Figure 2 1 is a temperature characteristic curve of each state of the resistive random access memory in the embodiment, wherein the upper figure shows the test results of the part where the conductivity is positively correlated with the temperature, and the lower figure shows the test results of the part where the conductivity is negatively correlated with the temperature.

[0036] Figure 3 A schematic diagram of a method for establishing a physical model of a resistive random access memory of the present invention.

[0037] Figure 4 The comparison and verification of the model prediction value and the measured value of the conductivity of the resistive random access memory in different storage states and at different temperatures in the embodiment is shown.

[0038] Figure 5 This is a further verification result of the model prediction ability at various temperatures and conditions in the examples. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical scheme and advantages of the present invention clearer, the scheme for predicting temperature characteristics based on the physical model of the resistive switching device of the present invention is clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] For a resistive random access memory using a 4-bit multi-value storage solution, in order to fully study all temperature characteristics of the device, this embodiment selects a larger conductivity range as the 4-bit multi-value storage interval. Figure 1 As shown in the figure, 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, so it is suitable for multi-value storage. For example, in Figure 1 In the figure, for all storage states, 10 devices are selected and programmed to the state, and the conductance of the device is repeatedly read within 100 seconds. The thin line segment represents the conductance fluctuation of a single device within the time, and the thick line segment represents the average conductance of all devices in the state. The results show that the multi-value storage characteristics of this embodiment are good and suitable for testing temperature characteristics and verifying model predictions.

[0041] Figure 2 The test results of the temperature characteristics of each state are shown in the temperature range of 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 different states have different correlations with temperature. 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 a method for establishing a physical model of a resistive random access memory. Figure 3The left side is a longitudinal cross-sectional view of the device, showing the morphological changes of the conductive filaments under different conductance states. The difference in conductivity mainly comes from the tail of the conductive filament. Under low conductance, no area with high oxygen vacancy density is formed at the tail of the conductive filament, and only sporadic areas with low oxygen vacancy density are responsible for conducting current; as the conductance gradually increases, the oxygen vacancies at the tail begin to gather, and the area with oxygen vacancies begins to expand. In addition, the central part gradually forms an area with high oxygen vacancy density; as the conductance further increases, the area with oxygen vacancies gradually approaches the area occupied by the entire Bulk, and the change at this time mainly comes from the expansion of the high oxygen vacancy area in the central part. 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 of 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 content, for the first type of parameters, T0 is set to 25°C, V is set to 0.2V, 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, select state "0" as the state with the lowest conductance, and plot the temperature characteristic curve obtained in state "16" as G~(kT+b) -1 Fitting, extraction and solution give A as 3.354×10 -3 K -1 , and the temperature characteristic curve obtained in state "0" is G~λ·T -1·Exp(μ / T) fitting, solving for σ0 is 2.566×10 5 S / m, The temperature characteristic curves of the remaining states ("1" to "15") were obtained by testing, and the optimal fit was obtained by substituting the model expression into the optimal fit to obtain α of 2.723×10 -14 m 2 / S, ε is 3.516×10 -5 S,γ is 3.274×10 3 S -1 The parameters required for the model are shown in the following table:

[0044] Table 1. Summary of model parameters of the embodiment

[0045]

[0046] Figure 4 The comparison between the model prediction and the measured values ​​is verified. The verification covers all storage states ("1" to "16") and the complete temperature range of the test. The results show that at all data points, the measured values ​​fluctuate within a small range above and below the predicted values, demonstrating good consistency between the model and the actual device.

[0047] Figure 5 The results are further validation results of the model prediction capability at various temperatures and states. In order to exclude the influence of natural fluctuations (such as the increase in device noise at high temperatures), the evaluation index is defined as the root mean square error minus the standard deviation (RMSE-SD). Figure 5 The closer the square is to blue, the higher the prediction accuracy under this condition. The results show that the prediction ability of the model remains relatively stable in most cases, and only declines in a small number of cases, but is still within a relatively accurate range (<2μS).

Claims

1. A method for predicting temperature characteristics of a resistive device based on a physical model. The physical model of the resistive device used is to divide the conductive filament in the dielectric layer of the resistive device into three regions: the first region is the head region of the conductive filament, the second region is the central part of the tail region of the conductive filament, and the third region is the peripheral part of the tail region of the conductive filament; the equivalent circuit of the resistive device is 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, then the predicted conductance of the resistive device is as shown in formula (1): in, is the predicted conductance of the resistive switching device at temperature T, G0 is the conductance of the resistive switching device at reference temperature T0, R bulk is the resistance of the first region, R nano is the resistance of the second region, R PF is the resistance of the third region; The resistance of the first region is expressed as follows: Among them, ρ bulk is the resistivity of the first region, t CF Height of the conductive filament head, S CF is the equivalent cross-sectional area of ​​the first region, A is the temperature coefficient of resistivity; The resistance of the second region is expressed as follows: Among them, ρ nano is the resistivity of the second region, t gap is the height of the tail of the conductive filament, S1 is the equivalent cross-sectional area of ​​the second region; The resistance R of the third region PF Its conductivity G PF The reciprocal of G PF As shown in the following formula (4): Among them, σ0 and β0 are physical constants, V is the external reading voltage, is the potential barrier height, S2 is the equivalent cross-sectional area of ​​the third region, and k is the Boltzmann constant; When the resistive switching device switches state, the volume of the first region changes very little; considering the second and third regions as a whole, when the device conductance increases, it is reflected in the increase of the cross-sectional area of ​​the whole, while the proportion of the second region increases and the proportion of the corresponding third region decreases. These relationships are approximately expressed as follows: S eff =α(G0-ε) S2=pS eff S1=(1-p)S eff p=γG0 Among them, S eff is the equivalent cross-sectional area of ​​the second and third regions as a whole, G0 is the conductivity of the resistive switching device at the reference temperature T0, α is the proportionality coefficient, and ε is set to take into account other regions or mechanisms that contribute to the conductivity; p represents the proportion of the third region, and γ is the proportionality coefficient; For the parameters in the above formula, ρ bulk , nano ,t CF ,t gap , S CF , T0, k, V, β0 are known parameters, A, σ0, α, ε, and γ are extracted from the temperature characteristic curve of the experimental test. By setting the conductance G0 and temperature T, the conductance prediction value of the resistive switching device under this condition can be obtained.

2. The method for predicting the temperature characteristics of a resistor according to claim 1, characterized in that: ρ bulk The value is 10 -6 ~10 -5 In the range of Ω·m, the latter ρ nano The value is 10 -4 ~10 -3 In the range of Ω·m.

3. The method for predicting the temperature characteristics of a resistor according to claim 1, wherein: β0 is It can be calculated by the formula, where q is the charge constant, ε0 is the vacuum dielectric constant, and ε r is the relative dielectric constant of the dielectric layer material, t gap Related to the materials and processes of resistive switching devices, refer to relevant literature.

4. The method for predicting the temperature characteristics of a resistor according to claim 1, wherein: The method of extracting A is to program the resistive switching device to the highest conductivity that can be achieved, test the relationship between its conductivity G and temperature T, and make G~(kT+b) -1 Fitting, at this time the value of S1 is S CF , S2 takes the value of 0, and the simultaneous equations are solved to obtain the value of A.

5. The method for predicting the temperature characteristics of a resistor according to claim 1, wherein: σ0, The extraction method is: program the resistive switching device to the lowest conductivity that can be obtained, test the change relationship of its conductivity G with temperature T, and make Gρλ·T -1 ·exp(μ / T) fitting, λ, μ are fitting parameters, the conductivity is determined by the conductivity of the third region, S2 takes S CF The solution of the simultaneous equations can be between 1 / 4 and 1 / 2 of σ0, The value of .

6. The method for predicting the temperature characteristics of a resistor according to claim 1, characterized in that: In extracting parameters A, σ0, Afterwards, the parameters α, ε, and γ are extracted by the following method: a number of conductances are uniformly selected between the highest and lowest conductances, and the response of the conductance G of the resistive switching device programmed at these conductances to the temperature T is tested, and the model expression is fitted to obtain α, ε, and γ.

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