A method for evaluating nbti aging effect

Abstract

The application discloses an evaluation method of NBTI aging effect, comprising the following steps: using a recovery time kinetics model to evaluate the NBTI aging effect of a MOS device in a first preset time period, and obtaining threshold voltage drift of a recovery stage at each unit time in the first preset time period; using a recoverable defect degradation model and a quasi-permanent defect degradation model to evaluate the effect of the device in a second preset time period, and obtaining threshold voltage drift of a stress stage at each unit time in the second preset time period; obtaining an evaluation result according to the threshold voltage drift; the above models are obtained according to first threshold voltage measurement results and second threshold voltage measurement results; the first threshold voltage measurement results are threshold voltages measured when different gate voltages are applied to a first MOS device at a first preset temperature; and the second threshold voltage measurement results are threshold voltages measured when different gate voltages are applied to a second MOS device at a second preset temperature.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor technology, specifically relating to a method for evaluating the NBTI aging effect. Background Technology

[0002] Most existing research on NBTI focuses on the physics of reliability, but the increasingly complex physical mechanisms make NBTI modeling and prediction more difficult. Industry companies typically model NBTI for specific processes based on a large amount of DC stress measurement data, requiring a considerable amount of experimental procedures and data. Therefore, it is particularly important to accurately evaluate NBTI with lower experimental costs and faster efficiency.

[0003] Traditional power-law model In the formula, Vth is the threshold voltage, K is the Boltzmann constant, T is the temperature, and a, Ea, β, and n are the parameters to be extracted. Each data point required by the model needs to be tested, including stress degradation and recovery curves under different voltages and temperatures. When extracting parameters based on test data, the voltage parameter β is extracted first. Under the same temperature and stress time conditions, three degradation data points under different voltage and stress conditions are measured to extract the voltage parameter β. Then, the temperature factor Ea is extracted. Under the same voltage and stress time conditions, three degradation data points at different temperatures are measured to extract the temperature factor Ea. Based on the above six data curves, parameters a and time factor n are extracted and optimized. Parameter a is process-related. After obtaining the degradation under DC conditions, an AC term (ΔV) is added to the DC degradation model. thAC =ΔV thDC *exp(R*DF), where R is the parameter to be fitted and DF is the recovery duty cycle under AC signal, and extrapolates to evaluate the impact of NBTI on the circuit several years later. Extract the parameters related to the AC term, i.e., the degradation data curves under different duty cycles.

[0004] Clearly, traditional evaluation models require experimental design for different stress condition factors, resulting in a large amount of data and numerous test conditions, thus making the evaluation cycle for NBTI relatively long. Furthermore, traditional evaluation models introduce the influence of AC signals on NBTI by fitting a degradation AC term, while a suitable model should predict degradation under AC signals using degradation data under DC signals, rather than by fitting. This makes the evaluation results inaccurate. Summary of the Invention

[0005] To address the aforementioned problems in related technologies, this invention provides a method for evaluating the NBTI aging effect. The technical problem to be solved by this invention is achieved through the following technical solution:

[0006] This invention provides a method for evaluating the NBTI aging effect, comprising:

[0007] The recovery time dynamics model is used to evaluate the NBTI aging effect of the MOS device under evaluation within the first preset time period, and the threshold voltage drift of the recovery stage at each unit time within the first preset time period is obtained.

[0008] Within a second preset time period, a recoverable defect degradation model and a quasi-permanent defect degradation model are used respectively to evaluate the NBTI aging effect of the MOS device to be evaluated, and the threshold voltage drift of the stress stage at each unit time within the second preset time period is obtained.

[0009] The evaluation result of the MOS device to be evaluated is obtained based on the threshold voltage drift. The recovery time dynamics model, the recoverable defect degradation model, and the quasi-permanent defect degradation model are models obtained based on the first threshold voltage measurement result of the first MOS device and the second threshold voltage measurement result of the second MOS device. The first threshold voltage measurement result is the threshold voltage of the first MOS device measured during a first time period when different gate voltages are applied to the first MOS device at a first preset temperature. The second threshold voltage measurement result is the threshold voltage of the second MOS device measured during a second time period when different gate voltages are applied to the second MOS device at a second preset temperature.

[0010] The present invention has the following beneficial technical effects:

[0011] Since the model used to evaluate the NBTI aging effect of a device is determined using data from two sets of test conditions for two different devices, this invention can obtain a model for evaluating the NBTI aging effect of a device with very little test data, thereby reducing the model establishment time and improving the efficiency of NBTI evaluation in the circuit. Furthermore, since the model of this invention does not introduce fitted degradation AC terms, the evaluation results obtained using the model provided by this invention are accurate.

[0012] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0013] Figure 1 A flowchart of an NBTI aging effect assessment method provided in an embodiment of the present invention;

[0014] Figure 2 A schematic diagram illustrating different gate voltages applied to a first device during a first time period, provided as an embodiment of the present invention;

[0015] Figure 3A schematic diagram illustrating different gate voltages applied to a second device during a second time period, provided as an embodiment of the present invention;

[0016] Figure 4 An exemplary comparison chart provided for embodiments of the present invention shows the comparison between the measured values ​​and evaluation results of device 1 within a time period consisting of multiple first preset time periods and multiple second preset time periods. Detailed Implementation

[0017] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0018] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" or "several" means two or more, unless otherwise explicitly specified.

[0019] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0020] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, disclosure, and appended claims in carrying out the claimed invention. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. A single processor or other unit can implement several functions listed in the claims. While different dependent claims may recite certain measures, this does not mean that these measures cannot be combined to produce good results.

[0021] Figure 1 This is a flowchart of a method for evaluating the NBTI aging effect provided in an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes the following steps:

[0022] S101. During the first preset time period, the recovery time dynamics model is used to evaluate the NBTI aging effect of the MOS device to be evaluated, and the threshold voltage drift of the recovery stage at each unit time during the first preset time period is obtained.

[0023] Here, the MOS device to be evaluated can be a CMOS device or a PMOS device, without limitation.

[0024] Here, the first preset time period can be any preset time period; there can be one or more first preset time periods.

[0025] In some embodiments, the recovery time dynamics model is as follows:

[0026]

[0027] Where c1, c2, c3, and c4 are time factors of recoverable defects determined based on preset results from the first threshold voltage measurement; t1 represents each unit time within the first preset time period, ΔV threc ΔV represents the threshold voltage drift during the recovery phase at time t1, and ts0 is the preset equivalent pressure application time; where ΔV th rec =ΔV th / ΔV th0 ΔV th ΔV represents the remaining degradation of a recoverable defect during the recovery phase. th0 This represents the net amount of recoverable defects accumulated at the previous moment.

[0028] Here, each unit of time can be set arbitrarily according to actual needs. For example, when the first preset time period is 1 minute, the unit of time can be every 2 seconds, or every second, and so on.

[0029] S102. During the second preset time period, the NBTI aging effect of the MOS device to be evaluated is assessed using a recoverable defect degradation model and a quasi-permanent defect degradation model, respectively, to obtain the threshold voltage drift of the stress stage at each unit time during the second preset time period.

[0030] Here, the second preset time period can be any preset time period, and it is a time period preceding the first preset time period. Furthermore, there can be one or more second time periods. For example, when there are two first preset time periods, minute 2 and minute 4, the two second time periods could be minute 1 and minute 3.

[0031] Here, the traps in the NBTI of a MOS transistor consist of two parts. The first part is a recoverable trap, meaning that the threshold voltage shift caused by this component can recover after the voltage stress is removed within the observable experimental window. The second part is a quasi-permanent trap, meaning that the threshold voltage shift caused by this component will not recover within the experimental window, and is therefore called a quasi-permanent trap.

[0032] In some embodiments, the recoverability defect degradation model is as follows: (2)

[0033]

[0034] Where K represents the Boltzmann constant, T represents the preset temperature, t2 represents each unit time within the second preset time period, and V g ΔV represents the gate stress voltage applied at time t2. th1 The threshold voltage drift at stress stage t2 represents the voltage drift at stress stage t2. a1, a2, a3 and a4 are the process parameters, temperature factor, voltage parameter and time factor of recoverable defects determined based on the first threshold voltage measurement results and the second threshold voltage measurement results, respectively. exp(.) represents an exponential function with the natural constant e as the base.

[0035] In some embodiments, the quasi-permanent defect degradation model is as follows: (3)

[0036]

[0037] Where K represents the Boltzmann constant, T represents the preset temperature, t3 represents each unit time within the second preset time period, and V g ΔV represents the gate stress voltage applied at time t3. th2 The threshold voltage drift at stress stage t3 is represented by b1, b2, b3 and b4, which are the process parameters, temperature factor, voltage parameter and time factor of quasi-permanent defects determined based on the first threshold voltage measurement results and the second threshold voltage measurement results. exp(.) represents an exponential function with the natural constant e as the base.

[0038] S103. Based on the threshold voltage drift, the evaluation result of the MOS device to be evaluated is obtained; the recovery time dynamics model, the recoverable defect degradation model, and the quasi-permanent defect degradation model are models obtained based on the first threshold voltage measurement result of the first MOS device and the second threshold voltage measurement result of the second MOS device; the first threshold voltage measurement result is the threshold voltage of the first MOS device measured during a first time period when different gate voltages are applied to the first MOS device at a first preset temperature; the second threshold voltage measurement result is the threshold voltage of the second MOS device measured during a second time period when different gate voltages are applied to the second MOS device at a second preset temperature.

[0039] Here, the first MOS device, the second MOS device, and the MOS device to be evaluated are of the same type; the first preset temperature and the second preset temperature are different.

[0040] Here, the threshold voltage drift of the stress stage at each unit time within the second preset time period includes: the threshold voltage drift obtained from the recoverable defect degradation model at each unit time within the second preset time period, and the threshold voltage drift obtained from the quasi-permanent defect degradation model at each unit time within the second preset time period. Specifically, the threshold voltage drifts obtained from the recoverable defect degradation model and the quasi-permanent defect degradation model at each unit time within the second preset time period can be summed to obtain a first summation value; the threshold voltage drift of the recovery stage at each unit time within the first preset time period can be summed with the threshold voltage drift obtained from the quasi-permanent defect degradation model at the last unit time within the second preset time period to obtain a second summation value; based on the first summation value and the second summation value, the evaluation results for each unit time within the prediction time period composed of the first preset time period and the second preset time period are obtained.

[0041] In some embodiments, the first time period includes: M first pressure application cycles and M first recovery cycles alternating with the M first pressure application cycles; the gate stress voltage corresponding to a preset sub-cycle of the i-th first pressure application cycle is greater than the gate stress voltage corresponding to a preset sub-cycle of the (i+1)-th first pressure application cycle; the gate stress voltage corresponding to the i-th second recovery cycle is the same as the gate stress voltage corresponding to the (i+1)-th second recovery cycle; M is an integer greater than or equal to 2, and i is an integer from 1 to M; the second time period includes: N second pressure application cycles and N second recovery cycles alternating with the N second pressure application cycles; the gate stress voltage corresponding to a preset sub-cycle of the j-th second pressure application cycle is greater than the gate stress voltage corresponding to a preset sub-cycle of the (j+1)-th second pressure application cycle; the gate stress voltage corresponding to the j-th second recovery cycle is the same as the gate stress voltage corresponding to the (j+1)-th second recovery cycle; N is an integer greater than or equal to 2, and j is an integer from 1 to N.

[0042] Specifically, each first pressure application cycle or each second pressure application cycle includes: m gate stress time periods and m measurement time points for measuring threshold voltages; for each first pressure application cycle or each second pressure application cycle, the gate stress voltage corresponding to each gate stress time period is the same, the gate measurement voltage corresponding to each measurement time point is the same, and the gate measurement voltage corresponding to the measurement time point is less than the gate stress voltage corresponding to the gate stress time period. Each first recovery cycle or each second recovery cycle includes: n recovery time periods and n measurement time points; the gate measurement voltage corresponding to each measurement time point is the same; for each first recovery cycle or each second recovery cycle, the gate stress voltage corresponding to the recovery time period is the same, and the gate measurement voltage corresponding to the measurement time point is greater than the gate stress voltage corresponding to the recovery time period. Compared to the gate stress time periods or recovery time periods, the measurement time points are very short, for example, they can be a few microseconds.

[0043] For example, the waveforms of different gate voltages applied to the first MOS device under temperature T1 are shown below. Figure 2 As shown. In Figure 2 In the first time period, there are four first pressure application cycles ts and four first recovery cycles tr. Within each first pressure application cycle ts, several (e.g., Figure 2 There are 3 measurement time points used to measure the threshold voltage, and the corresponding gate measurement voltage is Vmeasure. These are the stress time periods within the first first pressure application cycle ts (e.g., Figure 2 There are 3 of them) corresponding to the gate stress voltage Vstress1, and the stress time periods (e.g., within the second first stress application cycle ts) are... Figure 2 The gate stress voltage corresponding to the three (there are three) is Vstress2, and the stress time periods (e.g., within the third first stress application cycle ts) are... Figure 2 The gate stress voltage corresponding to 3 of them is Vstress3, and the stress time periods (e.g., within the 4th first stress application cycle ts) are... Figure 2 There are 3 of them) whose corresponding gate stress voltage is Vstress4, and Vstress1 > Vstress2 > Vstress3 > Vstress4. Several (e.g.,) are inserted within each first recovery cycle tr. Figure 2 There are 3 points in the time frame used for measurement, the corresponding gate measurement voltage is Vmeasure, and the gate stress voltage corresponding to the recovery time period within the 4 first recovery cycles tr is 0V.

[0044] For example, under temperature T2, the waveforms of different gate voltages applied to the second MOS device are as follows: Figure 3 As shown. In Figure 3In the second time period, there are three second stress periods ts and three second recovery periods tr, wherein several (e.g.,) are inserted within each second stress period ts. Figure 3 There are 3 measurement time points used to measure the threshold voltage, and the corresponding gate measurement voltage is Vmeasure. These are the stress time periods within the first second pressure application cycle ts (e.g., Figure 3 The gate stress voltages corresponding to the three stress periods in the second second pressure application cycle ts are Vstress1, Vstress2, and Vstress3, respectively, with Vstress1 > Vstress2 > Vstress3. Several stress periods are inserted within each second recovery cycle tr (e.g., ...). Figure 3 There are 3 measurement time points used to measure the threshold voltage, and the corresponding gate measurement voltage is Vmeasure. In addition, the gate stress voltage within the 3 second recovery cycles tr is 0V, and the corresponding gate measurement voltage within the 3 second recovery cycles tr is Vmeasure. Figure 3 Vstress1, Vstress2, and Vstress3 in the code can be used with... Figure 2 Vstress1, Vstress2, and Vstress3 in the formula are all the same, or at least one of them can be the same, or they can be completely different; there are no restrictions on this.

[0045] Here, the first threshold voltage measurement results include 2M groups of threshold voltages with a measurement time sequence; the second threshold voltage measurement results include 2N groups of threshold voltages with a measurement time sequence. In the 2M groups of threshold voltages, the x-th group includes the threshold voltage of the first MOS device measured at each measurement time point (Vmeasure) within the i-th first pressure application cycle; the (x+1)-th group includes the threshold voltage of the first MOS device measured at each measurement time point within the i-th first recovery cycle; x is an integer from 1 to 2M. In the 2N groups of threshold voltages, the y-th group includes the threshold voltage of the second MOS device measured at each measurement time point within the j-th second pressure application cycle; the (y+1)-th group includes the threshold voltage of the second MOS device measured at each measurement time point within the j-th second recovery cycle; y is an integer from 1 to 2N. For example, when different gate voltages are applied to the first MOS device, the waveforms are as follows: Figure 2As shown, when Vmeasure is applied, the threshold voltage of the first MOS device is measured, thus obtaining eight sets of threshold voltages for the first MOS device. The first set of threshold voltages consists of several gate voltages within the first ts, measured at Vmeasure. For example, the waveforms of different gate voltages applied to the second MOS device are shown below. Figure 3 As shown, when Vmeasure is applied, the threshold voltage of the second MOS device is measured, thus obtaining 6 sets of threshold voltages for the second MOS device. The first set of threshold voltages consists of several voltages within the first ts, which are the threshold voltages measured within Vmeasure. tr and ts can be the same or different.

[0046] In some embodiments, the preset result in the first threshold voltage measurement result can be the M threshold voltages corresponding one-to-one with the M first recovery cycles in the 2M sets of threshold voltages (i.e., the p-th threshold voltage in the 2M sets of threshold voltages, where p is an even number from 1 to 2M). For example, when the first time period is... Figure 2 When the time period shown includes 4 ts and 4 tr, the preset result in the first threshold voltage measurement result can be 4 sets of measurement results corresponding to 4 tr.

[0047] In some embodiments, the recovery time dynamics model includes multiple numerically known first time factors (the numerically known c1, c2, c3, and c4 mentioned above); based on this, before S101 and S102, S201 to S205 are also included:

[0048] S201. Obtain 2M sets of threshold voltages and 2N sets of threshold voltages; M and N are both integers greater than or equal to 2.

[0049] Here, the 2M group threshold voltage is the threshold voltage of the first MOS device measured during a first time period when different gate voltages are applied to the first MOS device at a first preset temperature; the 2N group threshold voltage is the threshold voltage of the second MOS device measured during a second time period when different gate voltages are applied to the second MOS device at a second preset temperature.

[0050] S202. The p-th threshold voltage in the 2M groups of threshold voltages is restored and normalized to obtain the recovery time dynamic model.

[0051] S203. Obtain an initial recoverable defect degradation model and an initial quasi-permanent defect degradation model; the initial recoverable defect degradation model includes: a first process parameter, a first temperature factor, a first voltage parameter, and a second time factor; the initial quasi-permanent defect degradation model includes: a second process parameter, a second temperature factor, a second voltage parameter, and a third time factor.

[0052] Here, in the initial recoverable defect degradation model, the first process parameter, the first temperature factor, the first voltage parameter, and the second time factor are a1, a2, a3, and a4, respectively, with unknown values. In the initial quasi-permanent defect degradation model, the second process parameter, the second temperature factor, the second voltage parameter, and the third time factor are b1, b2, b3, and b4, respectively, with unknown values.

[0053] S204. Based on the threshold voltages of the 2M groups and the threshold voltages of the 2N groups, determine the optimization values ​​of the first voltage parameter, the second time factor, the second voltage parameter, and the third time factor, as well as the optimization values ​​of the first process parameter, the second process parameter, the first temperature factor, and the second temperature factor.

[0054] Here, the initial value of the second time factor a4 can be determined based on at least one set of threshold voltages from the 2M-3 group and the 2M-1 group; the initial values ​​of the first voltage parameter a3, the second voltage parameter b3, and the third time factor b4 can be determined based on the 2M group threshold voltages; using an optimization algorithm, the optimal values ​​of a4, a3, b3, and b4 are obtained based on the initial values ​​of these four factors, and are used as their respective values ​​to be optimized; based on these four values ​​to be optimized, and the threshold voltages from the 2M group and the 2N group, the values ​​to be optimized for the first process parameter a1, the second temperature factor a2, the second process parameter b1, and the second temperature factor b2 are determined. For example, when the first time period is... Figure 2 The threshold voltages shown are for the 2M-3 group and the 2M-1 group, which are the threshold voltages measured in the 3rd ts and the 4th ts, respectively.

[0055] Specifically, the threshold voltages of group 2M-3 and group 2M-1 can be substituted into the initial recoverable defect degradation model to obtain the initial value of the second time factor a4. Then, the threshold voltages of group 2M can be substituted into the comprehensive evaluation process of the initial recoverable defect degradation model, the quasi-permanent degradation model and the recoverable defect recovery model to obtain the initial value of the first voltage parameter a3, the initial value of the second voltage parameter b3 and the initial value of the third time factor b4.

[0056] Here, the optimization algorithm can be a particle swarm optimization algorithm. First, the initial values ​​of a4, a3, b3, and b4 can be increased or decreased by a preset ratio (e.g., 20%) to obtain the upper and lower search boundaries of a4, a3, b3, and b4 respectively. Then, using the particle swarm optimization algorithm, based on the upper and lower search boundaries of a4, a3, b3, and b4 respectively, the set of a4, a3, b3, and b4 with the highest goodness of fit is searched. In this way, the optimization values ​​of a4, a3, b3, and b4 are obtained.

[0057] Here, after obtaining the four values ​​to be optimized, a4, a3, b3, and b4, the values ​​to be optimized, a4, a3, 2M sets of threshold voltages, and 2N sets of threshold voltages can be substituted into the initial recoverable defect degradation model, the recovery model, and the quasi-permanent defect degradation model to solve for the values ​​of a1 and a2, b1 and b2, and thus obtain the values ​​to be optimized for a1 and a2, b1 and b2.

[0058] S205. Using optimization algorithms and values ​​to be optimized, determine the optimal values ​​of the eight parameters: first temperature factor, first process parameter, second time factor, first voltage parameter, second temperature factor, second process parameter, third time factor, and second voltage parameter, to obtain a recoverable defect degradation model and a quasi-permanent defect degradation model.

[0059] Here, the four values ​​to be optimized—first temperature factor a2, first voltage parameter a3, second temperature factor b2, and second voltage parameter b3—can each be directly taken as their optimal values. Using an optimization algorithm, based on the four values ​​to be optimized—first process parameter a1, second time factor a4, second process parameter b1, and third time factor b4—the optimal values ​​of a1, a4, b1, and b4 are determined, resulting in a recoverable defect degradation model and a quasi-permanent defect degradation model.

[0060] Specifically, the optimization algorithm can be particle swarm optimization. First, the four values ​​to be optimized, a1, a4, b1, and b4, can be increased or decreased by a preset ratio (e.g., 20%) to obtain the upper and lower search boundaries for a1, a4, b1, and b4 respectively. Then, using particle swarm optimization, based on the upper and lower search boundaries of a1, a4, b1, and b4, the set of a1, a4, b1, and b4 with the highest goodness of fit is searched, thus obtaining the optimal values ​​for a1, a4, b1, and b4 respectively.

[0061] Specifically, since a1, a2, a3, and a4 in the initial recoverable defect degradation model are all unknown, and b1, b2, b3, and b4 in the initial quasi-permanent defect degradation model are also unknown, once the optimal values ​​of a1, a2, a3, a4, b1, b2, b3, and b4 are obtained through the above steps, the recoverable defect degradation model and the initial quasi-permanent defect degradation model for prediction can be obtained.

[0062] For example, the steps to obtain the recovery time dynamics model, the known parameters c1, c2, c3, and c4 in the recovery time dynamics model, and the optimal values ​​of a1, a2, a3, a4, b1, b2, b3, and b4 are as follows:

[0063] (1) The recovery model of recoverable defects is established. Recoverable defects originate from gate oxide traps. Since only recoverable defects can cause recovery, while quasi-permanent traps cannot, the recovery characteristics of the four recovery stages (i.e., the four tr stages) of device 1 (the first MOS) and the three recovery stages (i.e., the three tr stages) of device 2 (the first MOS) are caused only by recoverable defects. In the first two stress stages (i.e., the first two ts of the four ts), the voltage applied to device 1 is higher, while the voltage stress applied in the last two stress stages (i.e., the last two ts of the four ts) is lower. Therefore, it can be considered that all recovery stages of devices 1 and 2 (i.e., all tr ​​stages of each device) are basically caused and recovered by only recoverable defects. The threshold voltages measured after the four recovery stages of device 1 are normalized to obtain the recovery kinetic model of recoverable traps, as shown in the above formula (1), where c1, c2, c3, and c4 are fitting parameters and are all unknown. This model represents the result after normalizing the amount of degradation caused by the accumulated recoverable defects at the previous time point. Then, based on the normalized recovery kinetics, c1, c2, c3, and c4 can be obtained.

[0064] (2) Due to the saturation and voltage dependence of degradation, device 1 applies a higher voltage in the Vstress1-2 stages (i.e., the first two ts out of four ts), while the voltage stress applied in the Vstress3-4 stages (i.e., the last two ts out of four ts) is lower. Therefore, it can be considered that only recoverable defects are generated and recovered in the Vstress3-4 stages (i.e., the last two ts out of four ts). Therefore, based on the measurement results of device 1 in the Vstress3-4 stages (i.e., the last two ts out of four ts), the degradation model of recoverable defects can be obtained as shown in the above formula (2), where a1, a2, a3, and a4 are fitting parameters. Based on the measurement results of device 1 in the Vstress3-4 stages, the fitting parameter a4 can be obtained.

[0065] (3) Establishment of the degradation model for quasi-permanent defects and extraction of voltage parameters. The degradation model for quasi-permanent defects is shown in formula (3) above, where b1, b2, b3, and b4 are fitting parameters and are unknown. Based on the measurement results of Vstress 1 to 4 stages (i.e., 4 ts stages) of device 1, some parameters of the quasi-permanent defect model are determined. The historical time effect is considered in the determination, which can accurately separate quasi-permanent defects from recoverable defects. Based on the measurement results of Vstress 1 to 4 stages of device 1, the fitting parameters a3, b3, and b4 can be obtained.

[0066] (4) Initial parameter optimization of a3, a4, b3, and b4. To ensure the speed and quality of parameter convergence during the parameter optimization process, the particle swarm optimization algorithm is used to expand and shrink the parameters a3, a4, b3, and b4 obtained in steps (2) and (3) by 20% as the upper and lower boundaries of the search during the parameter optimization process. Through the search, a set of a3, a4, b3, and b4 with the highest goodness of fit is obtained.

[0067] (5) Extract a1, a2, b1, b2. Using a3, a4, b3, b4 obtained in (4), fix them. At this time, the only unknown parameters remaining for the two models are a1, a2, b1, b2. Based on the measurement results of all stages of device 1 (4 TS and 4 TR stages) and all stages of device 2 (3 TS and 3 TR stages), obtain the values ​​of a1 and a2 respectively; based on the measurement results of all stages of device 1 and all stages of device 2, obtain the values ​​of b1 and b2 respectively.

[0068] (6) Perform a second parameter optimization. For the values ​​of a1, a2, a3, a4, b1, b2, b3, and b4 obtained in (2) to (5), the values ​​of a2, a3, b2, and b3 are taken as their respective optimal values. Then, the parameters a1, a4, b1, and b4 are all increased and decreased by 20%, which are used as the upper and lower boundaries for the search in the parameter optimization process. Using the particle swarm optimization algorithm, a set of a1, a4, b1, and b4 with the highest goodness of fit is obtained through the search based on the upper and lower boundaries, thereby obtaining the optimal values ​​of a1, a4, b1, and b4 respectively.

[0069] The above method is illustrated below with examples.

[0070] Step 1: Obtain test data for device 1. Test device 1 at 25°C using the waveform described above. Figure 2 As shown, Vstress1 to 4 are -2, -1.9, -1.8, and -1.7V, respectively. Vmeasure is less than Vstress. The dynamic stress degradation data of the gate voltage change at a temperature of 25°C are obtained by scanning in the range of 0 to -1V.

[0071] Step 2: Obtain the test data for device 2. Test device 2 at 75°C with the applied waveform as described above. Figure 3 As shown, Vstress1 to Vstress3 are -2, -1.8, and -1.6V respectively, and Vmeasure is scanned in the range of 0 to -1V to obtain dynamic stress degradation data of gate voltage change at a temperature of 75°.

[0072] Step 3: Extract the time factors c1, c2, c3, and c4 of the recovery model for the recoverable trap. Normalize the measurement results of the four recovery stages of device 1 to obtain a normalized recovery curve. Use this normalized recovery curve to extract the time factors c1, c2, c3, and c4 of the recovery model. Based on experimental results, c1 = 1333.836; c2 = 2.29; c3 = 0.253; and c4 = 0.47. For example, where c1 = 1333.836; c2 = 2.29; c3 = 0.253; and c4 = 0.47.

[0073] Step 4: Extract the time factor of recoverable defects based on the measurement results of Vstress 3-4 of device 1. That is, directly use the newly generated defects in Vstress 3-4 of device 1 to obtain the logarithmic time dynamics and obtain the initial time factor a4 = 364521.

[0074] Step 5: Extract the time factors and voltage parameters of the two types of defects based on the measurement results of Vstress stages 1-4 of device 1. Steps 3 and 4 determined the time factors of the recovery model and degradation model for recoverable defects. Based on the measurement results of Vstress stages 1-4 of device 1, determine the time factor b4 and voltage parameter b3 of the degradation model for quasi-permanent defects, and the voltage parameter a3 of the degradation model for recoverable defects. When determining the parameters, the time history effect needs to be considered, and the equivalent stress time of the degradation amount at the end of each recovery stage in the next stress stage needs to be considered. The results are: a3 = 0.09; b3 = 2.41; b4 = 0.165.

[0075] Step 6: Optimize parameters a3, a4, b3, and b4 based on all stage test data of device 1. Using the average value of a3, a4, b2, and b4 as their own values, expand and shrink them by 20% to define the upper and lower boundaries for parameter optimization. That is, the boundary for a4 is [291616, 437425], the boundary for a3 is [0.072, 0.108], the boundary for b3 is [1.928, 2.892], and the boundary for b4 is [0.132, 0.198]. Using these parameter ranges, optimize these four parameters using the particle swarm optimization algorithm, obtaining a3 = 0.074, a4 ​​= 366432, b3 = 2.42, and b4 = 0.16.

[0076] Step 7: Based on the measurement results of all stages of device 1 and all stages of device 2, determine the temperature factor and process parameters a1, a2, b1, and b2. If a3 and a4 are obtained, determine the values ​​of a1 and a2 based on the measurement results of all stages of device 1 and all stages of device 2; if b3 and b4 are obtained, determine the values ​​of b1 and b2 based on the measurement results of all stages of device 1 and all stages of device 2.

[0077] Step 8: Optimize process parameters and time factor to obtain the values ​​of a1, a4, b1, and b4: a1 = 5.68E-5, a2 = 0.0072, a4 = 365381, b4 = 0.16. At this point, all parameters have been extracted.

[0078] For example, a comparison graph is shown between the measured values ​​obtained from all stages of device 1 and the evaluation results obtained by evaluating device 1 using the above three models. Figure 4 As shown. Figure 4 As shown, each circle represents the measurement value of device 1 at each unit time, and each dot on the thick black line represents the evaluation result at each unit time. Here, t01 represents the second preset time period, and t02 represents the first preset time period. Figure 4 As shown, the measured values ​​obtained from the measurement results of all stages of device 1 are basically consistent with the evaluation results obtained by evaluating device 1 using the above three models. Therefore, the evaluation results predicted by the model of the present invention are accurate.

[0079] This invention proposes a complete NBTI testing scheme and model. Only two sets of test conditions are needed to obtain complete model parameters, significantly improving device utilization and evaluation efficiency. Furthermore, it allows for the prediction of AC degradation from DC signal degradation, improving the accuracy of NBTI characteristic evaluation. This invention achieves excellent NBTI characteristic prediction capabilities with minimal experimental setup, improving the efficiency of NBTI evaluation in circuits. Combining the testing scheme, model building, and parameter optimization methods, it provides a pathway for modeling and predicting the degradation of NBTI effects in digital circuits.

[0080] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for evaluating the NBTI aging effect, characterized in that, include: The recovery time dynamics model is used to evaluate the NBTI aging effect of the MOS device under evaluation within the first preset time period, and the threshold voltage drift of the recovery stage at each unit time within the first preset time period is obtained. Within a second preset time period, a recoverable defect degradation model and a quasi-permanent defect degradation model are used respectively to evaluate the NBTI aging effect of the MOS device to be evaluated, and the threshold voltage drift of the stress stage at each unit time within the second preset time period is obtained. The evaluation result of the MOS device to be evaluated is obtained based on the threshold voltage drift. The recovery time dynamics model, the recoverable defect degradation model, and the quasi-permanent defect degradation model are models obtained based on the first threshold voltage measurement results of the first MOS device and the second threshold voltage measurement results of the second MOS device; The first threshold voltage measurement result is the threshold voltage of the first MOS device measured during a first time period when different gate voltages are applied to the first MOS device at a first preset temperature. The second threshold voltage measurement result is the threshold voltage of the second MOS device measured during a second time period when different gate voltages are applied to the second MOS device at a second preset temperature.

2. The method for evaluating the NBTI aging effect according to claim 1, characterized in that, The step of obtaining the evaluation result of the MOS device to be evaluated based on the threshold voltage drift includes: The threshold voltage drift obtained from the recoverable defect degradation model and the quasi-permanent defect degradation model corresponding to each unit time within the second preset time period is summed to obtain the first summation value; The threshold voltage drift of the recovery phase at each unit time within the first preset time period is summed with the threshold voltage drift obtained from the quasi-permanent defect degradation model at the last unit time within the second preset time period to obtain a second summation value. The evaluation result is obtained based on the first summation value and the second summation value.

3. The method for evaluating the NBTI aging effect according to claim 1, characterized in that, The first time period includes: M first pressure application cycles and M first recovery cycles alternating with the M first pressure application cycles; the gate stress voltage corresponding to the preset sub-cycle of the i-th first pressure application cycle is greater than the gate stress voltage corresponding to the preset sub-cycle of the (i+1)-th first pressure application cycle; the gate stress voltage corresponding to the i-th second recovery cycle is the same as the gate stress voltage corresponding to the (i+1)-th second recovery cycle; M is an integer greater than or equal to 2, and i is an integer from 1 to M; The second time period includes: N second pressure application cycles and N second recovery cycles alternating with the N second pressure application cycles; the gate stress voltage corresponding to the preset sub-cycle of the j-th second pressure application cycle is greater than the gate stress voltage corresponding to the preset sub-cycle of the (j+1)-th second pressure application cycle; the gate stress voltage corresponding to the j-th second recovery cycle is the same as the gate stress voltage corresponding to the (j+1)-th second recovery cycle; N is an integer greater than or equal to 2, and j is an integer from 1 to N.

4. The method for evaluating the NBTI aging effect according to claim 1, characterized in that, The recovery time dynamics model is as follows: Where c1, c2, c3, and c4 are time factors of recoverable defects determined based on preset results from the first threshold voltage measurement results; t1 represents each unit time within the first preset time period, ΔV threc ts0 represents the threshold voltage drift during the recovery phase at time t1, and ts0 is the preset equivalent pressure application time.

5. The method for evaluating the NBTI aging effect according to claim 1, characterized in that, The recoverable defect degradation model is as follows: Where K represents the Boltzmann constant, T represents the preset temperature, t2 represents each unit time within the second preset time period, and V g ΔV represents the gate stress voltage applied at time t2. th1 The threshold voltage drift at stress stage t2 represents the voltage drift at stress stage t2. a1, a2, a3 and a4 are the process parameters, temperature factor, voltage parameter and time factor of recoverable defects determined based on the first threshold voltage measurement result and the second threshold voltage measurement result, respectively. exp(.) represents an exponential function with the natural constant e as the base.

6. The method for evaluating the NBTI aging effect according to claim 1, characterized in that, The quasi-permanent defect degradation model is as follows: Where K represents the Boltzmann constant, T represents the preset temperature, t3 represents each unit time within the second preset time period, and V g ΔV represents the gate stress voltage applied at time t3. th2 The threshold voltage drift at stress stage t3 represents the voltage drift at stress stage t3. b1, b2, b3 and b4 are the process parameters, temperature factor, voltage parameter and time factor of quasi-permanent defects determined based on the first threshold voltage measurement result and the second threshold voltage measurement result. exp(.) represents an exponential function with the natural constant e as the base.

7. The method for evaluating the NBTI aging effect according to claim 1, characterized in that, The recovery time dynamics model includes multiple first time factors with known numerical values; The first threshold voltage measurement results include: 2M sets of threshold voltages with a measurement time sequence; the second threshold voltage measurement results include: 2N sets of threshold voltages with a measurement time sequence; before evaluating the NBTI aging effect of the MOS device to be evaluated using a recovery time dynamics model within a first preset time period to obtain the threshold voltage drift of the recovery stage at each unit time within the first preset time period, the method further includes: Obtain the 2M sets of threshold voltages and the 2N sets of threshold voltages; M and N are both integers greater than or equal to 2; The recovery time dynamics model is obtained by restoring and normalizing the p-th group of threshold voltages in the 2M group of threshold voltages; p is an even number from 1 to 2M. An initial recoverable defect degradation model and an initial quasi-permanent defect degradation model are obtained; the initial recoverable defect degradation model includes: a first process parameter, a first temperature factor, a first voltage parameter, and a second time factor; the initial quasi-permanent defect degradation model includes: a second process parameter, a second temperature factor, a second voltage parameter, and a third time factor. Based on the 2M group threshold voltages and the 2N group threshold voltages, the optimization values ​​of the first voltage parameter, the second time factor, the second voltage parameter, and the third time factor, as well as the optimization values ​​of the first process parameter, the second process parameter, the first temperature factor, and the second temperature factor, are determined. Using an optimization algorithm and the values ​​to be optimized, the optimal values ​​of the eight parameters—first temperature factor, first process parameter, second time factor, first voltage parameter, second temperature factor, second process parameter, third time factor, and second voltage parameter—are determined, thereby obtaining the recoverable defect degradation model and the quasi-permanent defect degradation model.

8. The method for evaluating the NBTI aging effect according to claim 7, characterized in that, The process of determining the optimization values ​​of the first voltage parameter, the second time factor, the second voltage parameter, and the third time factor, as well as the optimization values ​​of the first process parameter, the second process parameter, the first temperature factor, and the second temperature factor, based on the 2M sets of threshold voltages and the 2N sets of threshold voltages, includes: The initial value of the second time factor is determined based on the voltages of the 2M-3 group and the 2M-1 group in the 2M group threshold voltages. The initial values ​​of the first voltage parameter, the third time factor, and the second voltage parameter are determined based on the 2M group threshold voltages; q1 is an odd number from 1 to 2M, and q2 is an odd number from 1 to 2N. An optimization algorithm is used to obtain the optimal values ​​of the first voltage parameter, the second time factor, the third time factor, and the second voltage parameter based on their initial values. These optimal values ​​are then used as the values ​​to be optimized. Based on the four values ​​to be optimized—the first voltage parameter, the second time factor, the third time factor, and the second voltage parameter—as well as the 2M sets of threshold voltages and the 2N sets of threshold voltages, the four values ​​to be optimized—the first temperature factor, the first process parameter, the second temperature factor, and the second process parameter—are determined.

9. The method for evaluating the NBTI aging effect according to claim 7, characterized in that, The optimization algorithm and the value to be optimized are used to determine the optimal values ​​of eight parameters: first temperature factor, first process parameter, second time factor, first voltage parameter, second temperature factor, second process parameter, third time factor, and second voltage parameter. This yields the recoverable defect degradation model and the quasi-permanent defect degradation model, including: The four values ​​to be optimized—the first voltage parameter, the first temperature factor, the second voltage parameter, and the second temperature factor—are each taken as their optimal values. An optimization algorithm is used to determine the optimal values ​​of the four parameters to be optimized: the first process parameter, the second time factor, the second process parameter, and the third time factor. This yields the recoverable defect degradation model and the quasi-permanent defect degradation model.

10. The method for evaluating the NBTI aging effect according to claim 3, characterized in that, Each first pressure application cycle or each second pressure application cycle includes: m gate stress time periods and m measurement time points for measuring threshold voltages; for each first pressure application cycle or each second pressure application cycle, the gate stress voltage corresponding to the gate stress time period is the same, the gate measurement voltage corresponding to the measurement time point is the same, and the gate measurement voltage corresponding to the measurement time point is less than the gate stress voltage corresponding to the gate stress time period. Each first recovery cycle or each second recovery cycle includes: n gate recovery time periods and n measurement time points for measuring threshold voltages; the gate stress voltage corresponding to each gate recovery time period is 0V; the gate measurement voltage corresponding to each measurement time point is greater than the gate stress voltage corresponding to the gate recovery time period.

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