A model of temperature effect on square resistance and a modeling method thereof

Abstract

The application discloses a square resistance temperature effect model and a modeling method thereof, and the method comprises the following steps: step S1, establishing a normal-temperature square resistance model based on WAT actual test data; step S2, obtaining a global model of resistance temperature effect based on an existing temperature effect formula; and step S3, introducing a size parameter into the global model of resistance temperature effect, and adjusting the size parameter to make the resistance temperature effect of square resistances with different sizes all accurately fitted, so that the square resistance temperature effect model is obtained.

Description

Technical Field

[0001] This invention relates to the field of device modeling technology, and in particular to a sheet resistance temperature effect model and its modeling method. Background Technology

[0002] Currently, the modeling method for the temperature effect of sheet resistance typically employs the following approach:

[0003] First, the sheet resistance values ​​of different sizes at different temperatures are compiled into a table, as shown in Table 1 below:

[0004] Table 1. List of sheet resistance temperature test data

[0005]

[0006] To facilitate data processing, the resistance data were normalized to the sheet resistance at room temperature, resulting in the following table:

[0007] Table 2 Normalized list of sheet resistance temperature test data

[0008]

[0009] Then, the calculation formula is based on the following existing resistance temperature effect model:

[0010] RSH_T N = 1 + TC1R*(T-25) + TC2R*(T-25) 2

[0011] Among them, RSH_T N Here, T is the normalized sheet resistance value, T is the corresponding temperature, and TC1R and TC2R are the first and second temperature effect parameters.

[0012] By adjusting the first temperature effect parameter TC1R and the second temperature effect parameter TC2R, a global model of the temperature effect is obtained. The approximate trend curve of the temperature effect and the fitting curve corresponding to a single dimension are shown below. Figure 1 and Figures 2a-2e As shown, Figures 2a-2eThe comparisons are shown for the following data sets: RKV_SPI003A_LVNWAA (10_10, N=10, Width=10), RKV_SPI003B_LVNWAA (6_15, Width=6, N=15), RKV_SPI003C_LVNWAA (4_15, Width=4, N=15), RKV_SPI003D_LVNWAA (2_15, Width=2, N=15), and RKV_SPI003E_LVNWAA (1d5_15, Width=1.5, N=15). Figure 1 As can be seen, existing temperature effect models can accurately fit the trend of temperature effect. However, global models of temperature effect cannot account for resistors of all sizes. Measured data are distributed on both sides of the fitted line, meaning that TC1R and TC2R are different for each size, with typical values ​​of TC1R = 2.8523E-3 and TC2R = 1.0485E-5. Therefore, regardless of the values ​​of TC1R and TC2R, for a single size resistor, the measured data and the model still cannot fit accurately.

[0013] It is evident that existing formulas for the temperature effect of resistance can only establish a global model, that is, fit the general trend of the temperature effect of resistance. The global model cannot accurately take into account resistors of different sizes. Summary of the Invention

[0014] To overcome the shortcomings of the existing technology, the purpose of this invention is to provide a sheet resistance temperature effect model and its modeling method, so as to solve the problem that the existing resistance temperature effect model cannot take into account resistors of different sizes, realize the adjustable temperature effect model of sheet resistors of different sizes, and establish a more accurate resistance model.

[0015] To achieve the above and other objectives, this invention proposes a sheet resistance temperature effect model. The sheet resistance temperature effect model is based on an existing resistance temperature effect model, with the addition of size-related dimensional parameters. By adjusting the dimensional parameters, the resistance temperature effect models of different sizes are accurately fitted, thereby obtaining the sheet resistance temperature effect model.

[0016] Optionally, the sheet resistance temperature effect model establishes a global model of the resistance temperature effect based on existing temperature effect formulas, and introduces size parameters into the global model of the resistance temperature effect. By adjusting the size parameters, the temperature effect of sheet resistance of each size can be accurately extracted, thereby obtaining the final model.

[0017] Optionally, a first dimension parameter and a second dimension parameter related to the size are introduced into the global model of the resistance temperature effect.

[0018] To achieve the above objectives, the present invention also provides a modeling method for a sheet resistance temperature effect model, comprising the following steps:

[0019] Step S1: Based on actual WAT test data, establish a room temperature sheet resistance model;

[0020] Step S2: Based on the existing temperature effect formula, obtain a global model of the resistance temperature effect;

[0021] Step S3: Introduce size parameters into the global model of the resistance temperature effect, and adjust the size parameters so that the resistance temperature effect of sheet resistors of different sizes is accurately fitted, thereby obtaining the sheet resistor temperature effect model.

[0022] Optionally, in step S1, based on actual WAT test data, sheet resistance data of different sizes at different temperatures are obtained, and the room temperature sheet resistance model is extracted by adjusting relevant parameters.

[0023] Optionally, the relevant parameters include sheet resistivity (RSH), effective resistor length (DL), and effective resistor width (DW).

[0024] Optionally, in step S2, the temperature effect parameters are adjusted according to the existing normalized resistance temperature effect model to fit the general trend of the resistance temperature effect and obtain a global model of the temperature effect.

[0025] Optionally, in step S3, a first size parameter and a second size parameter related to the size are introduced into the global model of the resistance temperature effect.

[0026] Optionally, in step S3, the sheet resistance temperature effect model is as follows:

[0027]

[0028] Among them, RSH_T NW Here, T represents the sheet resistance value, TC1R and TC2R represent the first and second temperature effect parameters, and TC1_W and TC2_W represent the first and second size parameters related to the dimensions.

[0029] Optionally, after step S3, the method may further include:

[0030] Step S4: Denormalize the sheet resistance temperature effect model obtained in step S3 to obtain the denormalized sheet resistance temperature size model.

[0031] Compared with existing technologies, the present invention provides a sheet resistance temperature effect model and its modeling method by adding size-related dimensional parameters to the classic resistance temperature effect model. By adjusting the dimensional parameters, the resistance temperature effect model of different sizes can be accurately fitted, thereby solving the problem that existing resistance temperature effect models cannot take into account resistors of different sizes. This achieves the goal of making the sheet resistance temperature effect model of different sizes adjustable and establishing a more accurate resistance model. Attached Figure Description

[0032] Figure 1 The temperature effect model curve is from the existing technology;

[0033] Figures 2a-2e The model curves for sheet resistors of different sizes in the prior art before introducing size parameters are shown.

[0034] Figure 3 This is a flowchart illustrating the steps of a modeling method for a sheet resistance temperature effect model according to the present invention.

[0035] Figures 4a-4e These are model curves corresponding to blocks of different sizes after introducing size parameters in embodiments of the present invention. Detailed Implementation

[0036] The following describes the embodiments of the present invention through specific examples and in conjunction with the accompanying drawings. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific examples, and various details in this specification can also be modified and changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0037] This invention provides a sheet resistance temperature effect model by adding size-related dimensional parameters to existing resistance temperature effect models. By adjusting these dimensional parameters, the model accurately fits resistance temperature effect models of different sizes, thus obtaining the final sheet resistance temperature effect model. It should be noted that this invention's model only considers the temperature effect; therefore, it does not consider the basic resistance model or voltage effect model. The modeling process of this invention's sheet resistance temperature effect model is described in detail below:

[0038] Figure 3 This is a flowchart illustrating the steps of a modeling method for a sheet resistance temperature effect model according to the present invention. Figure 3 As shown, the modeling method for the temperature effect model of sheet resistance according to the present invention includes the following steps:

[0039] Step S1: Based on actual WAT test data, establish a room temperature sheet resistance model.

[0040] In this embodiment of the invention, based on actual WAT (Wafer Acceptance Test) test data, sheet resistance data of different sizes at different temperatures are obtained, and a room temperature sheet resistance model is extracted by adjusting the sheet resistance coefficient (RSH), effective resistance length (DL), and effective resistance width (DW).

[0041] In a specific embodiment of the present invention, taking the LVNWAA resistor model under the 55norflash platform as an example, firstly, based on the WAT room temperature test results, the sheet resistance values ​​of different sizes at room temperature are compiled into a table. By adjusting the sheet resistance coefficient (RSH), effective resistance length (DL), and effective resistance width (DW), the basic room temperature resistor model is extracted. Specifically, taking a room temperature of 25 degrees Celsius as an example, the room temperature test data and fitting results of the sheet resistance are shown in Table 3.

[0042] Table 3. List of sheet resistance test data and model values ​​at room temperature

[0043]

[0044] Where N is the number of resistor blocks to be measured, Width (um) is the width of the resistor block, T is the temperature, map_data (rsh) is the measured resistor block resistance value at room temperature, and fit_data (rsh) is the fitted result of the resistor block resistance at room temperature. The model parameter values ​​are shown in Table 4 below:

[0045] Table 4. List of basic model parameters for sheet resistance

[0046]

[0047] By adjusting the model parameters RSH (sheet resistivity), DL (effective resistance length), and DW (effective resistance width), the following room-temperature sheet resistance RSH was obtained. 25 Model:

[0048]

[0049] Where L and W are the length and width of the sheet resistor, and L = N * W.

[0050] Meanwhile, the sheet resistance values ​​of different sizes at different temperatures were compiled into a table, as shown in Table 1. For ease of data processing, the resistance data were normalized, as shown in Table 2.

[0051] Step S2: Fit the general trend of the resistance temperature effect based on the existing temperature effect formula to obtain a global model of the resistance temperature effect.

[0052] In this embodiment of the invention, the existing temperature effect formula adopts a normalized resistance temperature effect model, as follows;

[0053] RSH_T N = 1 + TC1R*(T-25) + TC2R*(T-25) 2

[0054] Among them, RSH_T N Here, T represents the sheet resistance value, T represents the corresponding temperature, and TC1R and TC2R are temperature effect parameters.

[0055] In this embodiment of the invention, the temperature effect parameters TC1R and TC2R are adjusted according to the normalized resistance temperature effect model described above to fit the general trend of the resistance temperature effect and obtain a global model of the temperature effect.

[0056] In a specific embodiment of the present invention, the fitted general trend curve of the temperature effect and the fitted curve corresponding to a single dimension are respectively as follows: Figure 1 and Figures 2a-2e As shown, existing temperature effect models can accurately fit the trend of temperature effect, but global models of temperature effect cannot take into account resistors of all sizes. For resistors of a single size, the data and models still cannot fit accurately.

[0057] Step S3: Introduce size parameters into the global model of the temperature effect, and adjust the size parameters so that the temperature effect of resistors of different sizes can be accurately fitted, thereby obtaining the sheet resistance temperature effect model.

[0058] As mentioned above, since the global model of the resistance temperature effect obtained in step S2 still cannot accurately fit the data and model for resistors of a single size, this invention introduces two size parameters, TC1_W and TC2_W, based on the global model of the resistance temperature effect to obtain a size-dependent sheet resistance temperature effect model:

[0059]

[0060] Among them, RSH_T NW , where T is the sheet resistance value, T is the corresponding temperature, TC1R and TC2R are the first and second temperature effect parameters, and TC1_W and TC2_W are the first and second size parameters related to the size.

[0061] Then, TC1_W and TC2_W are adjusted to accurately fit the temperature effect of resistors of different sizes, thereby obtaining the final sheet resistance temperature effect model. In this embodiment of the invention, the values ​​of the first and second size parameters TC1_W and TC2_W are -2.00E-10(-2*10) respectively.-10 ) and -5.00E-13 (-5*10 -13 When this is the case, the temperature effect curves of resistance for different sizes can be accurately fitted, such as... Figures 4a-4e As shown.

[0062] It is evident that this invention can solve the problem that existing resistance temperature effect models cannot take into account resistors of different sizes, enabling adjustable temperature effect models for sheet resistors of different sizes and establishing more accurate sheet resistor temperature effect models.

[0063] Optionally, in this embodiment of the invention, since the obtained sheet resistance temperature effect model is a normalized resistance temperature effect model, after step S3, the invention may further include:

[0064] Step S4: Denormalize the sheet resistance temperature effect model obtained in step S3 to obtain the denormalized sheet resistance temperature size model.

[0065] In this embodiment of the invention, the sheet resistance temperature effect model obtained in step S3 is denormalized to obtain the following denormalized sheet resistance temperature size model:

[0066]

[0067] Among them, RSH = 592, TC1R = 2.8523E-3, TC2R = 1.0485E-5, TC1_W = -2.00E-10, and TC2_W = -5.00E-13.

[0068] After obtaining the temperature dimension model of the sheet resistor, simulation verification is performed using programming.

[0069] As can be seen, the sheet resistance temperature effect model and its modeling method of the present invention add size-related dimensional parameters to the classic resistance temperature effect model. By adjusting the dimensional parameters, the resistance temperature effect model of different sizes can be accurately fitted, thereby solving the problem that the existing resistance temperature effect model cannot take into account resistors of different sizes. This achieves the goal of making the sheet resistance temperature effect model of different sizes adjustable and establishing a more accurate resistance model.

[0070] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can make modifications and changes to the above embodiments without departing from the spirit and scope of the invention. Therefore, the scope of protection of the present invention should be as set forth in the claims.

Claims

1. A sheet resistance temperature effect model, characterized in that: The sheet resistance temperature effect model is obtained by adding size-related dimensional parameters to the existing resistance temperature effect model, and by adjusting the dimensional parameters to accurately fit the resistance temperature effect model for different sizes; the sheet resistance temperature effect model is as follows: Among them, RSH_T NW Here, T is the normalized resistance value, T is the corresponding temperature, TC1R and TC2R are the first and second temperature effect parameters, TC1_W and TC2_W are the first and second size parameters related to the dimensions, W is the width of the sheet resistor, and DW is the effective width of the resistor.

2. The sheet resistance temperature effect model as described in claim 1, characterized in that: The sheet resistance temperature effect model is based on the existing temperature effect formula to establish a global model of the resistance temperature effect. Size parameters are introduced into the global model of the resistance temperature effect. By adjusting the size parameters, the temperature effect of sheet resistors of each size can be accurately extracted, thereby obtaining the final model.

3. The sheet resistance temperature effect model as described in claim 2, characterized in that: A first dimension parameter and a second dimension parameter related to the size are introduced into the global model of the resistance temperature effect.

4. A modeling method for the temperature effect of sheet resistance, comprising the following steps: Step S1: Based on actual WAT test data, establish a room temperature sheet resistance model; Step S2: Based on the existing temperature effect formula, obtain a global model of the resistance temperature effect; Step S3: Introduce size parameters into the global model of the resistance temperature effect, and adjust the size parameters to accurately fit the resistance temperature effect of sheet resistors of different sizes, thus obtaining the sheet resistance temperature effect model; the sheet resistance temperature effect model is as follows: in, RSH_T NW Here, T is the normalized resistance value, T is the corresponding temperature, TC1R and TC2R are the first and second temperature effect parameters, TC1_W and TC2_W are the first and second size parameters related to the dimensions, W is the width of the sheet resistor, and DW is the effective width of the resistor.

5. The modeling method for the sheet resistance temperature effect model as described in claim 4, characterized in that, In step S1, based on actual WAT test data, sheet resistance data of different sizes at different temperatures are obtained, and the room temperature sheet resistance model is extracted by adjusting relevant parameters.

6. The modeling method for the sheet resistance temperature effect model as described in claim 5, characterized in that: The relevant parameters include the sheet resistance coefficient RSH, the effective length of the resistor DL, and the effective width of the resistor DW.

7. The modeling method for the sheet resistance temperature effect model as described in claim 5, characterized in that: In step S2, the temperature effect parameters are adjusted according to the existing normalized resistance temperature effect model to fit the trend of the resistance temperature effect and obtain a global model of the temperature effect.

8. The modeling method for the sheet resistance temperature effect model as described in claim 7, characterized in that: In step S3, a first size parameter and a second size parameter related to the size are introduced into the global model of the resistance temperature effect.

9. The modeling method for a sheet resistance temperature effect model as described in claim 8, characterized in that, After step S3, the method may further include: Step S4: Denormalize the sheet resistance temperature effect model obtained in step S3 to obtain the denormalized sheet resistance temperature size model.

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