Integrated resistance model construction method based on self-heating effect
Patent Information
- Application Number
- CN202611015956.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-08
- Publication Date
- 2026-10-20
AI Technical Summary
[0006]本发明的目的在于提供一种基于自热效应的集成电阻模型构建方法，以解决现有电阻模型未从能量与热效应角度进行系统建模，也未考虑器件几何尺寸对热阻的放大作用，从而导致电阻模型一致性较差、拟合稳定性较差的问题
[0025]本申请提供的所述基于自热效应的集成电阻模型构建方法中，先利用基础的电阻模型获取基准电阻值R0，然后在外加扫描电压的作用下，根据基准电阻值R0，获取电阻器件的瞬时功耗，接着根据电阻器件的几何尺寸，引入等效热阻模型，根据等效热阻模型和当前瞬时功耗，获取电阻器件内部因自热引起的温度增量ΔT，随后，根据环境温度和温度增量ΔT，获取电阻器件的等效工作温度，接着利用引入温度系数的电阻模型，对基准电阻值R0进行温度修正，得到考虑自热效应的修正电阻值R1，随后在外加扫描电压的作用下，重新获取通过电阻器件的瞬时电流和瞬时功耗，最后循环执行获取功耗—获取热阻—获取温度增量—电阻修正的步骤，以形成闭环求解过程，直至所述电阻器件的修正电阻值R1、瞬时电流以及所述电阻器件内部因自热引起的温度增量ΔT达到稳定状态。本申请从能量与热效应角度进行系统建模，并且充分考虑器件几何尺寸对热阻的放大作用，引入尺寸相关的等效热阻模型和引入温度系数的电阻模型，通过获取功耗—获取热阻—获取温度增量—电阻修正的闭环过程，实现不同几何尺寸器件之间的统一描述，提高了不同尺寸的电阻器件电压非线性特性的建模一致性和模型拟合稳定性。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of semiconductor integrated circuit technology, and in particular to a method for constructing an integrated resistor model based on the self-heating effect. Background Technology
[0002] As integrated circuit technology continues to shrink, on-chip resistors are increasingly used in analog, power management, and precision circuits. Ideally, the resistance value of a resistor is independent of the port voltage and can be considered a linear element. However, in practical testing, it has been found that as the size of the resistor decreases, especially under short channel length or narrow width conditions, even in the lower port voltage range, the resistance value exhibits significant voltage-dependent nonlinear characteristics, manifesting as "warping" or abnormal curvature of the resistance in the high-voltage region. This phenomenon is particularly pronounced under high-temperature conditions and varies significantly between devices of different sizes.
[0003] Existing resistance models often fit this nonlinear behavior by introducing simple voltage correction terms or volume bias factors. They typically directly superimpose voltage and volume bias effects, but do not model the system from the perspective of energy and thermal effects. That is, they do not explicitly introduce the relationship between electrical power and temperature rise, nor do they consider the amplification effect of device geometry on thermal resistance. This makes it impossible to simultaneously consider the modeling consistency and model fitting stability of voltage nonlinear characteristics of devices of different sizes, resulting in poor consistency and poor fitting stability of resistance models.
[0004] From a device physics perspective, a resistive device generates current when a voltage is applied to its port, inevitably producing Joule heat power internally. When the device size is large, the heat can be effectively dissipated through the surrounding silicon substrate and metal interconnects, having little impact on the device temperature. However, when the device has a short channel or narrow width, the current density per unit area increases significantly, the heat diffusion path is restricted, and the local temperature rise effect is significantly enhanced.
[0005] Under the aforementioned short-channel or narrow-width conditions, the power consumption and resistance of the resistive device form the following positive feedback loop: Increased applied voltage → increased power consumption → increased device temperature → increased resistance → further increased power consumption. As the temperature rise continues to increase, the temperature coefficient of resistance causes the resistance value to continuously increase, thus exhibiting a "warping" phenomenon where the resistance increases with voltage. Therefore, this "warping" is essentially a result of the voltage-driven self-heating effect being fed back to the resistance value through the temperature coefficient. Summary of the Invention
[0006] The purpose of this invention is to provide a method for constructing an integrated resistance model based on the self-heating effect, so as to solve the problems of poor consistency and poor fitting stability of existing resistance models, which do not model the system from the perspective of energy and thermal effects, nor do they consider the amplification effect of device geometry on thermal resistance.
[0007] To address the aforementioned technical problems, this invention provides a method for constructing an integrated resistance model based on the self-heating effect, comprising:
[0008] First step: Based on the geometric dimensions of the resistive device, use the basic resistance model to obtain the reference resistance value R0 of the resistive device without considering the self-heating effect.
[0009] The second step: Under the action of the applied scanning voltage, the instantaneous power consumption generated inside the resistive device is obtained according to the reference resistance value R0;
[0010] The third step: Based on the geometric dimensions of the resistor device, an equivalent thermal resistance model is introduced, wherein the equivalent thermal resistance model is used to characterize the ability of the resistor device to dissipate heat to the substrate and the surrounding medium.
[0011] Fourth step: Based on the equivalent thermal resistance model and the current instantaneous power consumption generated inside the resistive device, obtain the temperature increment ΔT caused by self-heating inside the resistive device;
[0012] Fifth step: Obtain the equivalent operating temperature of the resistor based on the ambient temperature and the temperature increment ΔT caused by self-heating inside the resistor;
[0013] Step 6: Using a resistance model that incorporates a temperature coefficient, the reference resistance value R0 of the resistive device is corrected for temperature to obtain a corrected resistance value R1 that takes into account the self-heating effect.
[0014] Step 7: Under the action of the applied scanning voltage, the instantaneous current through the resistor and the instantaneous power consumption of the resistor are reacquired using the correction resistor value R1.
[0015] Step 8: Return to step 4 and repeat step 4 to step 7 until the corrected resistance value R1 of the resistor, the instantaneous current, and the temperature increment ΔT caused by self-heating inside the resistor reach a stable state.
[0016] Optionally, in the method for constructing an integrated resistor model based on self-heating effect, in the first step, the basic resistor model is: R0 = Rsh × L_eff / W_eff, where R0 is the reference resistance value of the resistor device without considering self-heating effect; Rsh is the sheet resistance; W_eff is the effective heating width of the current resistor device; and L_eff is the effective heating length of the current resistor device.
[0017] Optionally, in the method for constructing an integrated resistor model based on self-heating effect, in the second step, the formula for calculating the instantaneous power consumption generated inside the resistor device is: P0=ksh×V^2 / R0, where P0 is the basic instantaneous power consumption generated inside the resistor device; ksh is the self-heating coupling coefficient; V is the voltage value of the applied scanning voltage; and R0 is the reference resistance value of the resistor device without considering the self-heating effect.
[0018] Optionally, in the method for constructing an integrated resistance model based on the self-heating effect, in the third step, the equivalent thermal resistance model is: R_th1 = R_th0 × (W_ref / W_eff)^a_w × (L_ref / L_eff)^a_l, where R_th1 is the equivalent thermal resistance of the current resistor device under test; R_th0 is the thermal resistance of the reference device; W_ref is the reference reference width of the calibration thermal resistance model; L_ref is the reference reference length of the calibration thermal resistance model; W_eff is the effective heating width of the current resistor device; L_eff is the effective heating length of the current resistor device; a_w is the width thermal resistance scaling index; and a_l is the length thermal resistance scaling index.
[0019] Optionally, in the integrated resistor model construction method based on self-heating effect, in the fourth step, the formula for calculating the temperature increment ΔT caused by self-heating inside the resistor device is: ΔT = R_th1×P0, where ΔT is the temperature increment caused by self-heating inside the resistor device; R_th1 is the equivalent thermal resistance of the resistor device under test; and P0 is the basic instantaneous power consumption generated inside the resistor device.
[0020] Optionally, in the method for constructing an integrated resistor model based on self-heating effect, in the fifth step, the formula for calculating the equivalent operating temperature of the resistor device is: T_eff=(T_ambient−25)+ΔT, where T_eff is the actual equivalent operating temperature of the resistor device; T_ambient is the reference temperature of the environment and / or substrate; and ΔT is the temperature increment inside the resistor device caused by self-heating.
[0021] Optionally, in the method for constructing an integrated resistance model based on the self-heating effect, in the sixth step, the resistance model with a temperature coefficient is: R1=R0×(1+ tc1×T_eff+tc2×T_eff^2), where R1 is the corrected resistance value of the resistance device considering the self-heating effect; R0 is the reference resistance value of the resistance device; tc1 is the first-order resistance temperature coefficient; tc2 is the second-order resistance temperature coefficient; and T_eff is the actual equivalent operating temperature of the resistance device.
[0022] Optionally, in the integrated resistor model construction method based on self-heating effect, in the seventh step, the formula for calculating the instantaneous current through the resistor device when considering the self-heating effect is: I=V / R1, where I is the instantaneous current through the resistor device when considering the self-heating effect; V is the voltage value of the applied scanning voltage; and R1 is the corrected resistance value of the resistor device considering the self-heating effect.
[0023] Optionally, in the integrated resistor model construction method based on self-heating effect, in the seventh step, the formula for calculating the instantaneous power consumption of the resistor device when considering the self-heating effect is: P1=ksh×V^2 / R1, where P1 is the current instantaneous power consumption generated inside the resistor device when considering the self-heating effect; ksh is the self-heating coupling coefficient; V is the voltage value of the applied scanning voltage; and R1 is the corrected resistance value of the resistor device considering the self-heating effect.
[0024] Optionally, in the integrated resistance model construction method based on self-heating effect, in the eighth step, when the change in the corrected resistance value R1 of the resistor device, the change in the instantaneous current through the resistor device, and the change in the temperature increment ΔT caused by self-heating inside the resistor device in two adjacent iterations are all less than their respective pre-set convergence thresholds, it is determined that the corrected resistance value R1 of the resistor device, the instantaneous current, and the temperature increment ΔT caused by self-heating inside the resistor device have reached a stable state.
[0025] In the integrated resistor model construction method based on self-heating effect provided in this application, a reference resistance value R0 is first obtained using a basic resistor model. Then, under the action of an applied scanning voltage, the instantaneous power consumption of the resistor device is obtained based on the reference resistance value R0. Next, based on the geometric dimensions of the resistor device, an equivalent thermal resistance model is introduced. Based on the equivalent thermal resistance model and the current instantaneous power consumption, the temperature increment ΔT caused by self-heating inside the resistor device is obtained. Subsequently, based on the ambient temperature and the temperature increment ΔT, the equivalent operating temperature of the resistor device is obtained. Then, using a resistor model with an introduced temperature coefficient, the reference resistance value R0 is temperature-corrected to obtain a corrected resistance value R1 considering the self-heating effect. Subsequently, under the action of an applied scanning voltage, the instantaneous current and instantaneous power consumption through the resistor device are re-obtained. Finally, the steps of obtaining power consumption, obtaining thermal resistance, obtaining temperature increment, and resistance correction are executed cyclically to form a closed-loop solution process until the corrected resistance value R1, instantaneous current, and temperature increment ΔT caused by self-heating inside the resistor device reach a stable state. This application performs system modeling from the perspective of energy and thermal effects, and fully considers the amplification effect of device geometry on thermal resistance. It introduces a size-dependent equivalent thermal resistance model and a resistance model with a temperature coefficient. Through a closed-loop process of obtaining power consumption, obtaining thermal resistance, obtaining temperature increment, and resistance correction, it achieves a unified description between devices with different geometric sizes, thereby improving the modeling consistency and model fitting stability of voltage nonlinear characteristics of resistive devices of different sizes.
[0026] Furthermore, this application achieves a unified description of devices with different geometric dimensions through a closed-loop process of obtaining power consumption, obtaining thermal resistance, obtaining temperature increment, and resistance correction. It does not rely on empirical high-order voltage correction terms and can naturally generate voltage-related nonlinear behavior.
[0027] Furthermore, the equivalent thermal resistance model and the resistance model with temperature coefficient introduced in this application are engineering controllable. According to the test requirements, the self-heating coupling coefficient ksh can be set to 0 and / or the equivalent thermal resistance R_th1 of the current resistor device under test can be set to 0 to turn off the self-heating effect of the model. Attached Figure Description
[0028] Those skilled in the art will understand that the accompanying drawings are provided to better understand the invention and do not constitute any limitation on the scope of the invention.
[0029] Figure 1 This is a flowchart of the method for constructing an integrated resistance model based on the self-heating effect according to an embodiment of the present invention. Detailed Implementation
[0030] To make the objectives, advantages, and features of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the drawings are all in a very simplified form and are not drawn to scale, and are only used to facilitate and clearly illustrate the objectives of the embodiments of the present invention. Furthermore, the structures shown in the drawings are often part of the actual structures. In particular, different figures may emphasize different aspects and sometimes use different scales. It should also be understood that, unless specifically stated or indicated, the terms "first," "second," "third," etc., in the specification are only used to distinguish the various components, elements, steps, etc., in the specification, and are not used to indicate the logical or sequential relationships between the various components, elements, steps, etc.
[0031] The inventors discovered that the intensity of the self-heating effect on resistive characteristics is closely related to the geometric dimensions of the resistive device (length and width). For resistive devices with narrow widths and short lengths, under the same voltage conditions, their equivalent thermal resistance is smaller, the current density flowing through the resistive device is larger, and the power consumption per unit volume increases significantly. Simultaneously, small-sized resistive devices have limited effective heat dissipation area, resulting in larger equivalent thermal resistance and thus higher temperature rise under the same power consumption conditions. Therefore, small-sized resistive devices are more likely to enter the nonlinear operating range dominated by the self-heating effect, and the "warping" phenomenon is more pronounced. Furthermore, under the same resistive device geometric dimensions and the same scanning voltage, at higher ambient temperatures, the initial operating temperature of the resistive device increases, the resistance change caused by the temperature coefficient is more significant, and the additional temperature rise generated by self-heating is more likely to trigger a rapid increase in resistance value, thus causing the "warping" phenomenon to appear and be significantly enhanced in lower voltage ranges.
[0032] To address the aforementioned problems, this invention provides a method for constructing an integrated resistance model based on the self-heating effect, referencing... Figure 1 , Figure 1 This is a flowchart of an integrated resistance model construction method based on the self-heating effect according to an embodiment of the present invention. The integrated resistance model construction method based on the self-heating effect includes:
[0033] First, perform the first step: based on the geometric parameters of the resistive device, use the basic resistance model to obtain the reference resistance value R0 of the resistive device without considering the self-heating effect.
[0034] In the first step, the basic resistance model is: R0 = Rsh × L_eff / W_eff, where R0 is the reference resistance value of the resistor without considering the self-heating effect; Rsh is the sheet resistance; W_eff is the effective heating width of the resistor; and L_eff is the effective heating length of the resistor.
[0035] Then, the second step is performed: under the action of an external scanning voltage, the instantaneous power consumption generated inside the resistive device is obtained according to the reference resistance value R0.
[0036] In the second step, the formula for calculating the instantaneous power consumption generated inside the resistive device is: P0=ksh×V^2 / R0, where P0 is the basic instantaneous power consumption generated inside the resistive device; ksh is the self-heating coupling coefficient; V is the voltage value of the applied scanning voltage; and R0 is the reference resistance value of the resistive device without considering the self-heating effect.
[0037] Next, the third step is performed: based on the geometry of the resistive device, an equivalent thermal resistance model is introduced, wherein the equivalent thermal resistance model is used to characterize the ability of the resistive device to dissipate heat to the substrate and the surrounding medium.
[0038] In the third step, the equivalent thermal resistance model is: R_th1 = R_th0 × (W_ref / W_eff)^a_w × (L_ref / L_eff)^a_l. This equivalent thermal resistance model is established based on the law of thermal diffusion path of resistive device changing with geometric size, and uses a power function to describe the scaling relationship of the geometric size of resistive device with thermal resistance. Here, R_th1 is the equivalent thermal resistance of the current resistive device under test; R_th0 is the thermal resistance of the reference device; W_ref is the reference reference width of the calibration thermal resistance model; L_ref is the reference reference length of the calibration thermal resistance model; W_eff is the effective heating width of the current resistive device; L_eff is the effective heating length of the current resistive device; a_w is the width thermal resistance scaling exponent; and a_l is the length thermal resistance scaling exponent.
[0039] Furthermore, the fourth step is performed: based on the equivalent thermal resistance model and the current instantaneous power consumption generated inside the resistive device, the temperature increment ΔT caused by self-heating inside the resistive device is obtained.
[0040] In the fourth step, the formula for calculating the temperature increment ΔT caused by self-heating inside the resistive device is: ΔT = R_th1×P0, where ΔT is the temperature increment caused by self-heating inside the resistive device; R_th1 is the equivalent thermal resistance of the current resistive device under test; and P0 is the basic instantaneous power consumption generated inside the resistive device.
[0041] Specifically, by substituting the specific calculation formulas of the first to third steps into the calculation formula of the temperature increment ΔT caused by self-heating inside the resistor device in the fourth step, we can obtain: ΔT=R_th0×(W_ref / W_eff)^a_w×(L_ref / L_eff)^a_l×ksh×V^2 / (Rsh×L_eff / W_eff).
[0042] Next, the fifth step is performed: based on the ambient temperature and the temperature increment ΔT caused by self-heating inside the resistor, the equivalent operating temperature of the resistor is obtained.
[0043] In the fifth step, the formula for calculating the equivalent operating temperature of the resistive device is: T_eff = (T_ambient − 25) + ΔT, where T_eff is the actual equivalent operating temperature of the resistive device; T_ambient is the reference temperature of the environment and / or substrate; and ΔT is the temperature increment caused by self-heating within the resistive device. In this embodiment, 25°C is the reference temperature.
[0044] Furthermore, the formula for calculating T_eff is: T_eff = (T_ambient−25)+R_th0×(W_ref / W_eff)^a_w×(L_ref / L_eff)^a_l×ksh×V^2 / (Rsh×L_eff / W_eff).
[0045] Further, the sixth step is performed: using a resistance model with an introduced temperature coefficient, the reference resistance value R0 of the resistive device is temperature-corrected to obtain a corrected resistance value R1 that takes into account the self-heating effect.
[0046] In the sixth step, the resistance model with temperature coefficient is introduced as: R1 = R0 × (1 + tc1 × T_eff + tc2 × T_eff^2), where R1 is the corrected resistance value of the resistive device considering self-heating effect; R0 is the reference resistance value of the resistive device; tc1 is the first-order resistance temperature coefficient; tc2 is the second-order resistance temperature coefficient; and T_eff is the actual equivalent operating temperature of the resistive device.
[0047] Next, the seventh step is performed: under the action of the applied scanning voltage, the instantaneous current through the resistor and the instantaneous power consumption of the resistor are reacquired using the correction resistor value R1.
[0048] In the seventh step, the formula for calculating the instantaneous current through the resistive device when considering the self-heating effect is: I=V / R1, where I is the instantaneous current through the resistive device when considering the self-heating effect; V is the voltage value of the applied scanning voltage; and R1 is the corrected resistance value of the resistive device considering the self-heating effect.
[0049] Furthermore, in the seventh step, the formula for calculating the instantaneous power consumption of the resistive device when considering the self-heating effect is: P1=ksh×V^2 / R1, where P1 is the current instantaneous power consumption generated inside the resistive device when considering the self-heating effect; ksh is the self-heating coupling coefficient; V is the voltage value of the applied scanning voltage; and R1 is the corrected resistance value of the resistive device considering the self-heating effect.
[0050] In this application, the equivalent thermal resistance model and the resistance model with the temperature coefficient are engineering controllable and highly flexible. According to the test requirements, the self-heating coupling coefficient ksh can be set to 0 and / or the equivalent thermal resistance R_th1 of the current resistor device under test can be set to 0. That is, the self-heating effect of the resistance model can be turned off according to the actual test requirements.
[0051] Finally, execute the eighth step: return to the fourth step and repeat the fourth step to the seventh step until the corrected resistance value R1 of the resistor, the instantaneous current, and the temperature increment ΔT caused by self-heating inside the resistor reach a stable state.
[0052] Preferably, in the eighth step, when the change in the corrected resistance value R1 of the resistor device, the change in the instantaneous current through the resistor device, and the change in the temperature increment ΔT caused by self-heating inside the resistor device in two adjacent iterations are all less than their respective pre-set convergence thresholds, it is determined that the corrected resistance value R1 of the resistor device, the instantaneous current, and the temperature increment ΔT caused by self-heating inside the resistor device have reached a stable state.
[0053] In this embodiment, the convergence threshold for the change in the corrected resistance value R1 of the resistor device in two adjacent iterations can be set to 0.01%; further, the convergence threshold for the change in the temperature increment ΔT caused by self-heating inside the resistor device in two adjacent iterations can be set to 0.01%; in addition, the change in instantaneous power consumption in two adjacent iterations and the change in instantaneous current through the resistor device in two adjacent iterations converge synchronously with the change in the corrected resistance value R1 of the resistor device in two adjacent iterations.
[0054] In this application, system modeling is performed from the perspective of energy and thermal effects. The amplification effect of device geometry on thermal resistance is fully considered, and a size-dependent equivalent thermal resistance model and a resistance model incorporating a temperature coefficient are introduced. Through a closed-loop process of obtaining power consumption, thermal resistance, temperature increment, and resistance correction, a unified description of devices with different geometric sizes is achieved, improving the modeling consistency and model fitting stability of voltage nonlinear characteristics for resistive devices of different sizes. Furthermore, this application achieves a unified description of devices with different geometric sizes through a closed-loop process of obtaining power consumption, thermal resistance, temperature increment, and resistance correction, without relying on empirical high-order voltage correction terms, and can naturally generate voltage-related nonlinear behavior.
[0055] Furthermore, it should be understood that although the present invention has been disclosed above with reference to preferred embodiments, these embodiments are not intended to limit the present invention. For any person skilled in the art, many possible variations and modifications can be made to the technical solutions of the present invention based on the disclosed technical content, or equivalent embodiments can be modified accordingly, without departing from the scope of the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the content of the present invention, shall still fall within the scope of protection of the present invention.
Claims
1. A method for constructing an integrated resistance model based on the self-heating effect, characterized in that, include: First step: Based on the geometric dimensions of the resistive device, use the basic resistance model to obtain the reference resistance value R0 of the resistive device without considering the self-heating effect. The second step: Under the action of the applied scanning voltage, the instantaneous power consumption generated inside the resistive device is obtained according to the reference resistance value R0; The third step: Based on the geometric dimensions of the resistor device, an equivalent thermal resistance model is introduced, wherein the equivalent thermal resistance model is used to characterize the ability of the resistor device to dissipate heat to the substrate and the surrounding medium. Fourth step: Based on the equivalent thermal resistance model and the current instantaneous power consumption generated inside the resistive device, obtain the temperature increment ΔT caused by self-heating inside the resistive device; Fifth step: Obtain the equivalent operating temperature of the resistor based on the ambient temperature and the temperature increment ΔT caused by self-heating inside the resistor; Step 6: Using a resistance model that incorporates a temperature coefficient, the reference resistance value R0 of the resistive device is corrected for temperature to obtain a corrected resistance value R1 that takes into account the self-heating effect. Step 7: Under the action of the applied scanning voltage, the instantaneous current through the resistor and the instantaneous power consumption of the resistor are reacquired using the correction resistor value R1. Step 8: Return to step 4 and repeat step 4 to step 7 until the corrected resistance value R1 of the resistor, the instantaneous current, and the temperature increment ΔT caused by self-heating inside the resistor reach a stable state.
2. The method for constructing an integrated resistance model based on the self-heating effect according to claim 1, characterized in that, In the first step, the basic resistance model is: R0 = Rsh × L_eff / W_eff, where R0 is the reference resistance value of the resistor without considering the self-heating effect; Rsh is the sheet resistance; W_eff is the effective heating width of the resistor; and L_eff is the effective heating length of the resistor.
3. The method for constructing an integrated resistance model based on the self-heating effect according to claim 1, characterized in that, In the second step, the formula for calculating the instantaneous power consumption generated inside the resistive device is: P0=ksh×V^2 / R0, where P0 is the basic instantaneous power consumption generated inside the resistive device; ksh is the self-heating coupling coefficient; V is the voltage value of the applied scanning voltage; and R0 is the reference resistance value of the resistive device without considering the self-heating effect.
4. The method for constructing an integrated resistance model based on the self-heating effect according to claim 1, characterized in that, In the third step, the equivalent thermal resistance model is: R_th1 = R_th0 × (W_ref / W_eff)^a_w × (L_ref / L_eff)^a_l, where R_th1 is the equivalent thermal resistance of the current resistor under test; R_th0 is the thermal resistance of the reference device; W_ref is the reference reference width of the calibration thermal resistance model; L_ref is the reference reference length of the calibration thermal resistance model; W_eff is the effective heating width of the current resistor; L_eff is the effective heating length of the current resistor; a_w is the width thermal resistance scaling index; and a_l is the length thermal resistance scaling index.
5. The method for constructing an integrated resistance model based on self-heating effect according to claim 1, characterized in that, In the fourth step, the formula for calculating the temperature increment ΔT caused by self-heating inside the resistive device is: ΔT = R_th1×P0, where ΔT is the temperature increment caused by self-heating inside the resistive device; R_th1 is the equivalent thermal resistance of the current resistive device under test; and P0 is the basic instantaneous power consumption generated inside the resistive device.
6. The method for constructing an integrated resistance model based on the self-heating effect according to claim 1, characterized in that, In the fifth step, the formula for calculating the equivalent operating temperature of the resistive device is: T_eff=(T_ambient−25)+ΔT, where T_eff is the actual equivalent operating temperature of the resistive device; T_ambient is the reference temperature of the environment and / or substrate; and ΔT is the temperature increment inside the resistive device caused by self-heating.
7. The method for constructing an integrated resistance model based on the self-heating effect according to claim 1, characterized in that, In the sixth step, the resistance model with temperature coefficient is introduced as: R1=R0×(1+ tc1×T_eff+tc2×T_eff^2), where R1 is the corrected resistance value of the resistive device considering self-heating effect; R0 is the reference resistance value of the resistive device; tc1 is the first-order resistance temperature coefficient; tc2 is the second-order resistance temperature coefficient; and T_eff is the actual equivalent operating temperature of the resistive device.
8. The method for constructing an integrated resistance model based on the self-heating effect according to claim 1, characterized in that, In the seventh step, the formula for calculating the instantaneous current through the resistive device when considering the self-heating effect is: I=V / R1, where I is the instantaneous current through the resistive device when considering the self-heating effect; V is the voltage value of the applied scanning voltage; and R1 is the corrected resistance value of the resistive device considering the self-heating effect.
9. The method for constructing an integrated resistance model based on the self-heating effect according to claim 1, characterized in that, In the seventh step, the formula for calculating the instantaneous power consumption of the resistive device when considering the self-heating effect is: P1=ksh×V^2 / R1, where P1 is the current instantaneous power consumption generated inside the resistive device when considering the self-heating effect; ksh is the self-heating coupling coefficient; V is the voltage value of the applied scanning voltage; and R1 is the corrected resistance value of the resistive device considering the self-heating effect.
10. The method for constructing an integrated resistance model based on self-heating effect according to claim 1, characterized in that, In the eighth step, when the changes in the corrected resistance value R1 of the resistor device, the changes in the instantaneous current through the resistor device, and the changes in the temperature increment ΔT caused by self-heating inside the resistor device in two consecutive iterations are all less than their respective pre-set convergence thresholds, it is determined that the corrected resistance value R1 of the resistor device, the instantaneous current, and the temperature increment ΔT caused by self-heating inside the resistor device have reached a stable state.