A method for lifetime prediction of time-dependent breakdown of ultrathin high-k dielectric layers

Abstract

The disclosure provides a life prediction method for time breakdown of ultrathin high-k dielectric layer, which adopts an improved ramp voltage test method, specifically: for any to be predicted device, after applying a starting voltage, step-by-step voltage is increased at a set voltage increasing rate and rise time, and each voltage step is kept for a preset time; after increasing voltage n times, the voltage is decreased to the rated voltage, and the increasing-decreasing process is repeated until the voltage applied to the to-be-predicted device after the last increasing reaches 5 times of the rated voltage; after each increasing, decreasing and exceeding 5 times of the rated voltage, the leakage current of the to-be-predicted device is detected and recorded, so as to obtain the ramp voltage test result. The leakage current data obtained by the method is subjected to multiple stress tests, and is more consistent with the long-term aging trend of the device than single direct high voltage or long-time standing test. The step rhythm balances the test efficiency and accuracy, so that the life prediction is stable in the reliable interval.

Description

Technical Field

[0001] This disclosure relates to the field of semiconductor device process reliability testing technology, and in particular to a lifetime prediction method for ultrathin high-k dielectric layers after time-induced breakdown. Background Technology

[0002] Ultrathin high-k dielectric layers (such as HfO2 and Al2O3) are insulating materials with dielectric constants (k values) much higher than those of traditional SiO2. They are primarily used as gate dielectric layers in advanced MOSFETs and other devices, suppressing leakage current at ultrathin thicknesses and supporting device miniaturization. They are widely used in FinFETs, GAAFETs, and third-generation semiconductor devices. However, they face challenges such as breakdown voltage dispersion due to dielectric thickness and microstructure inhomogeneity, interface defects affecting carrier mobility, and decreased reliability under high temperature and high field conditions, posing stringent challenges to testing and process control.

[0003] Ramp voltage testing is widely used in the testing of ultra-thin high-k dielectrics. However, existing ramp voltage testing methods have significant limitations: the standard linear voltage application method is prone to premature breakdown due to charge accumulation; the adaptive ramp rate method relies on a preset leakage current threshold, making it difficult to adapt to dielectric inhomogeneities; the pulsed stepped stress method suffers from low testing efficiency due to relaxation periods; and the improved Vdd readback method suffers from low efficiency due to frequent readbacks and lacks a clearly defined current change threshold. These shortcomings are particularly pronounced in advanced processes, where the breakdown voltage distribution varies significantly due to the inhomogeneity of dielectric thickness and microstructure. Existing methods struggle to balance testing efficiency, accuracy, and reliability, failing to meet the evaluation requirements of advanced semiconductor devices. Summary of the Invention

[0004] The purpose of this disclosure is to solve the problem that the breakdown location is significantly random and the test results drift is large due to the high degree of non-uniformity of the microstructure of ultrathin high-k dielectric layers.

[0005] To address the aforementioned problems, this application provides a method for predicting the lifetime of ultrathin high-k dielectric layers after a period of time, comprising:

[0006] Obtain ramp voltage test information for the device group to be predicted, wherein the ramp voltage test information includes the ramp voltage test results of each device to be predicted in the device group to be predicted; Based on the slope voltage test information and the nominal insulating dielectric layer thickness, the TDDB lifetime of the ultrathin high-k dielectric layer of each device to be predicted is obtained using the E electric field acceleration model corresponding to TDDB. The methods for obtaining the slope voltage test results include: After applying an initial voltage to any device to be predicted, a stepped voltage increase is performed with a set boost rate and rise time, and the voltage is held at each voltage step for a preset time. After every n voltage increases, the voltage is reduced back to the rated voltage, and the boost-reset process is repeated until the voltage applied to the device to be predicted after the last boost reaches 5 times the rated voltage. After each boost, reset, and exceeding 5 times the rated voltage, the leakage current of the device to be predicted is detected and recorded, thereby obtaining the ramp voltage test results.

[0007] As a further improvement to this application, n is 2 or 3.

[0008] As a further improvement to this application, the E-electric field acceleration model is as follows: , in, TTF For expiration time, To accelerate the time to dielectric breakdown of 63.2% of the test samples under stress conditions (corresponding to the characteristic lifetime under the Weibull distribution). γ The electric field acceleration factor, Vstress Let be the stress voltage of any device to be predicted. Vuse Let be the rated voltage of any device to be predicted. E a To activate energy, k Boltzmann's constant, Stress Let be the stress temperature of any device to be predicted. Showers is the actual operating temperature of any device to be predicted.

[0009] As a further improvement to this application, the activation energy E a The methods for obtaining the electric field acceleration factor γ include: Acquire three-temperature, three-pressure accelerated life test data, and based on the three-temperature, three-pressure accelerated life test data, determine the activation energy in the electric field acceleration model using the Weibull cumulative distribution function and the Arrhenius equation. E a And the electric field acceleration factor γ.

[0010] As a further improvement to this application, the method for obtaining the three-temperature and three-pressure accelerated life test data includes: The average breakdown voltage of the device group to be predicted is determined based on the ramp voltage test information. The time required for the ultrathin high-k dielectric layer in the device to be predicted to break down under a preset temperature-voltage combination is obtained and used as the data of the three-temperature and three-pressure accelerated life test. The preset temperature-voltage combination is determined as follows: First, within a temperature range of 25℃-200℃, three different temperature values ​​are selected as experimental temperature parameters; second, within a range of 0.7 times-0.9 times the average breakdown voltage, three different voltage values ​​are selected as experimental voltage parameters; finally, the three selected temperature values ​​and three voltage values ​​are paired and combined to form multiple sets of experimental parameter combinations, and each set of experimental parameter combinations serves as the preset temperature-voltage combination.

[0011] As a further improvement to this application, the specific steps for recording the slope voltage test results are as follows: If the leakage current is observed to be greater than the maximum leakage current under the safe voltage after step-up voltage, the leakage current of the device to be predicted is observed again under the rated voltage. If the leakage current is greater than the maximum leakage current under the safe voltage or 10 times the initial leakage current judgment threshold, the device to be predicted is marked as the first failure mode, the breakdown voltage of the device to be predicted is recorded, and the test of the device to be predicted is terminated. If, after N consecutive step-up voltage increases, the leakage current is observed to be less than the maximum leakage current under safe voltage, and at the same time, after returning to the rated voltage, the leakage current is observed to be greater than 10 times the initial leakage current judgment threshold, then the device to be predicted is marked as the second failure mode, the breakdown voltage of the device to be predicted is recorded, and the test on the device to be predicted is terminated. If the voltage applied to the device under test after the step-up voltage boost is greater than 5 times the rated voltage, it is applied for 10 seconds. If the leakage current is observed to be greater than the maximum leakage current under the safe voltage within 10 seconds, the device under test is marked as the third failure mode, and the breakdown voltage of the device under test is recorded. The test on the device under test is then terminated. If the leakage current is not observed to be greater than the maximum leakage current under the safe voltage within 10 seconds, the device under test is marked as a normal sample that has not failed, and the breakdown voltage value of the device under test is recorded as 1. The test on the device under test is then terminated.

[0012] As a further improvement of this application, the rule for applying a starting voltage to any device to be predicted is as follows: the starting voltage of the first device to be predicted is set to the rated voltage; the starting voltage of the m-th device to be predicted is the maximum of the rated voltage and 0.9 times the average of the breakdown voltages of the adjacent 1-3 devices to be predicted; where m is the number of devices to be predicted in the group of devices to be predicted.

[0013] As a further improvement to this application, the method further includes: Before applying the starting voltage to any device to be predicted, the device to be predicted is first monitored for its initial state: the rated voltage is applied to the device to be predicted, and the leakage current of the device to be predicted is observed. If the leakage current is greater than the initial leakage current judgment threshold, the device to be predicted is marked as premature failure mode, and the breakdown voltage of the device to be predicted is recorded as 0. The test of the device to be predicted is terminated. Otherwise, the starting voltage is applied to the device to be predicted and a step-by-step boost action is performed.

[0014] As a further improvement to this application, the method for obtaining the ramp voltage test results also includes: Before applying the starting voltage to any device to be predicted, pre-stabilize it by continuously applying 50% of the starting voltage to the device to be predicted for 10 seconds.

[0015] As a further improvement to this application, the nominal insulating dielectric layer thickness is the design value of the insulating dielectric layer when the device to be predicted is designed in the process.

[0016] The beneficial effects of this application are as follows: It provides an improved ramp voltage testing method, employing a stepped boost-drop cycle for any device to be predicted. The drop-off after each boost stage prevents continuous charge accumulation in high-field regions, achieving a phased reset of the system; the drop-off to the rated voltage eliminates localized damage interference, ensuring subsequent tests start from zero and avoiding error accumulation. Real-time monitoring of leakage current during the brief dwell time at each step accurately captures the device state at that voltage. After this cycle, even if the voltage far exceeds the normal operating range, the device does not break down, indicating that the true weak point has been verified multiple times, ruling out occasional failures. The leakage current data obtained by this method has undergone multiple stress tests, and compared to a single high-voltage boost or long-term static test, it better reflects the long-term aging trend of the device. The stepped rhythm balances testing efficiency and accuracy, ensuring that the lifetime prediction remains within a reliable range. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the ramp voltage time-voltage detection mechanism for any device to be predicted in this application. Detailed Implementation

[0018] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0019] Numerous specific details are set forth in the following description to provide a thorough understanding of the invention. However, the invention may be practiced in other ways than those described herein, and therefore is not limited to the specific embodiments disclosed below. As indicated in this application and the claims, unless the context clearly indicates otherwise, the words "a," "an," "an," and / or "the" are not specifically singular and may include the plural. Generally, the terms "comprising" and "including" only indicate the inclusion of explicitly identified steps and elements, which do not constitute an exclusive list, and the method or apparatus may also include other steps or elements.

[0020] It should be understood that when a unit or module is described as "connecting" to other units, modules, or blocks, it may refer to a direct connection, communication with other units, modules, or blocks, or the presence of intermediate units, modules, or blocks, unless the context explicitly indicates otherwise. The term "and / or" as used herein may include any and all combinations of one or more of the related listed items.

[0021] The embodiments of this invention mainly describe a reliability testing method for semiconductor devices, such as ultrathin high-k dielectric layers, and particularly a TDDB testing method for ultrathin high-k dielectric layers. The TDDB test is based on a Vramp test. The TDDB testing method involves applying a TDDB test voltage to the ultrathin high-k dielectric layer to be tested in the semiconductor device test structure. After a time t, the ultrathin high-k dielectric layer breaks down. The breakdown time of the ultrathin high-k dielectric layer is calculated using the corresponding equivalent lifetime calculation formula and the area-dependent lifetime scaling formula.

[0022] The significant randomness of breakdown locations and large drift in test results due to the highly non-uniform microstructure of ultrathin high-k dielectric layers pose a key challenge in achieving rapid and stable characterization of their true lifetime limits. Traditional testing methods have obvious limitations: First, when using a continuous linear voltage ramp mode, charge continuously accumulates within the dielectric layer, which is equivalent to applying continuous stress to a system already in a critical state, easily leading to premature breakdown in the weakest area, and the measured data is actually early failure data rather than the inherent lifetime; Second, although a pulsed pause strategy can reduce the accumulation effect through charge relaxation, it significantly increases the test time, resulting in insufficient statistical sample size and thus artificially stretching the lifetime distribution.

[0023] To address the aforementioned problems, this disclosure provides a method for predicting the lifetime of ultrathin high-k dielectric layers after a period of time, comprising: Obtain ramp voltage test information for the device group to be predicted, wherein the ramp voltage test information includes the ramp voltage test results of each device to be predicted in the device group to be predicted; Based on the slope voltage test information and the nominal insulating dielectric layer thickness, the TDDB lifetime of the ultrathin high-k dielectric layer of each device to be predicted is obtained using the E electric field acceleration model corresponding to TDDB. The methods for obtaining the slope voltage test results include: After applying an initial voltage to any device to be predicted, a stepped voltage increase is performed with a set boost rate and rise time, and the voltage is held at each voltage step for a preset time. After every n voltage increases, the voltage is reduced back to the rated voltage, and the boost-reset process is repeated until the voltage applied to the device to be predicted after the last boost reaches 5 times the rated voltage. After each boost, reset, and exceeding 5 times the rated voltage, the leakage current of the device to be predicted is detected and recorded, thereby obtaining the ramp voltage test results.

[0024] Based on the above technical solution, this application proposes a ramp voltage test method that monitors leakage current by returning to the rated voltage after each voltage boost. The ramp-down process after each voltage boost avoids the continuous accumulation of charge in the high-field region, similar to resetting the system after a phased test. The ramp-down operation restores the device to a safe operating state, eliminating interference from potential localized damage and ensuring subsequent tests are performed in the initial state, avoiding error accumulation. Simultaneously, during the brief dwell time at each step, leakage current can be monitored in real time, accurately capturing the device state at that voltage level. Through this cyclic process, even at voltages far exceeding the normal operating range, if the device does not break down, it indicates that its true weakness has been repeatedly verified, rather than an isolated failure event. Ultimately, the leakage current data obtained through this method, after multiple stress tests, more accurately reflects the aging trend of the device during long-term use compared to the results of a single high-voltage surge or long-term static test. The dynamic test rhythm of the ramp-down step-up method cleverly balances the contradiction between test efficiency and result accuracy, ensuring that the lifetime prediction results stably fall within a reliable range.

[0025] In an optional implementation, n is 2 or 3. In the stepped boost-reset cycle test, setting "actively returning to the rated voltage after every two or three steps" as the test cycle can achieve accurate characterization of the breakdown characteristics of ultrathin high-k dielectric layers. Selecting a step interval of n=2 or 3 can avoid disrupting the continuity of electric field accumulation due to excessively frequent resetting, and can effectively prevent the continuous capture and retention of charge at defects. When n is 2 or 3, each resetting operation can quickly eliminate local overheating and charge accumulation, and promptly reset potential false breakdown signals, preventing such interference from being amplified in subsequent step tests; at the same time, the voltage span of 2 to 3 steps precisely matches the spatial distribution scale of typical defects in the dielectric, so that each resetting process can sequentially verify the stress of weak points at different locations, and the overall test cycle will not be prolonged due to excessively high resetting frequency. Through this continuous and efficient "boost-drop" cycle, the device is repeatedly characterized under graded voltage stress, and the real weak points are continuously triggered without false breakdown. Thus, in the test sequence of "two-stage drop-off" or "three-stage drop-off", the test efficiency and defect discrimination accuracy are optimized and balanced at the same time, and the true breakdown threshold and lifetime limit of the dielectric layer can be accurately captured.

[0026] In an optional implementation, the E-electric field acceleration model is: , in, TTF For expiration time, To accelerate the time to dielectric breakdown of 63.2% of the test samples under stress conditions (corresponding to the characteristic lifetime under the Weibull distribution). γ The electric field acceleration factor, Let be the stress voltage of any device to be predicted. Let be the rated voltage of any device to be predicted. E a To activate energy, k Boltzmann's constant, Stress Let be the stress temperature of any device to be predicted. Showers The actual operating temperature of any device to be predicted is given. The E-field acceleration model in this application incorporates both the electric field acceleration factor (γ) and temperature-related acceleration parameters (activation energy). E a The system incorporates Boltzmann constant k, etc., to achieve a quantitative description of the dual acceleration effect of electric field stress and temperature stress. It can accurately extrapolate failure data under accelerated testing conditions to the actual operating conditions of the device (rated voltage Vuse, actual operating temperature Tuse), providing a scientific mathematical characterization basis for TDDB lifetime prediction of ultrathin high-k dielectric layers, and significantly improving the theoretical rigor and accuracy of lifetime prediction results.

[0027] In an optional implementation, the activation energy E a The methods for obtaining the electric field acceleration factor γ include: Acquire three-temperature, three-pressure accelerated life test data, and based on the three-temperature, three-pressure accelerated life test data, determine the activation energy in the electric field acceleration model using the Weibull cumulative distribution function and the Arrhenius equation. E a And the electric field acceleration factor γ. By using three-temperature and three-pressure accelerated life test data, combined with the Weibull cumulative distribution function (adapting the statistical characteristics of failure data) and the Arrhenius equation (quantifying the effect of temperature on aging rate) for parameter fitting, it can be ensured that the values ​​of key acceleration parameters are based on experimental data rather than empirical assumptions, reducing the subjective error of model parameters, making the physical meaning of the E-electric field acceleration model clearer and the prediction accuracy more reliable, and providing a robust parameter basis for life extrapolation.

[0028] In an optional implementation, the methods for obtaining the three-temperature, three-pressure accelerated life test data include: The average breakdown voltage of the device group to be predicted is determined based on the ramp voltage test information. The time required for the ultrathin high-k dielectric layer in the device to be predicted to break down under a preset temperature-voltage combination is obtained and used as the data of the three-temperature and three-pressure accelerated life test. The predetermined temperature-voltage combination is determined as follows: First, within a temperature range of 25℃-200℃, three different temperature values ​​are selected as experimental temperature parameters; second, within a range of 0.7 times-0.9 times the average breakdown voltage, three different voltage values ​​are selected as experimental voltage parameters; finally, the three selected temperature values ​​and three voltage values ​​are paired to form multiple sets of experimental parameter combinations, each set of experimental parameter combinations serving as the predetermined temperature-voltage combination. This application further clarifies the data acquisition scheme for three-temperature, three-pressure accelerated life testing. Selecting a typical accelerated temperature can cover the commonly used temperature range for semiconductor device reliability testing, effectively reflecting the temperature acceleration effect. Combined with a stress voltage of 0.7 times-0.9 times the average breakdown voltage (close to the breakdown threshold, which shortens the test cycle and ensures the failure mechanism is consistent with actual aging), obtaining sufficient sample size of failure time data through multiple temperature-voltage combinations can reduce the impact of test errors under single conditions on parameter fitting and improve... E a The statistical significance of the calculated γ values ​​ensures the robustness of the accelerated model. For example, 100℃, 125℃, and 150℃ can be selected as typical experimental temperature parameters, and stress voltages of 0.8, 0.85, and 0.9 times the average breakdown voltage can be selected as experimental voltage parameters.

[0029] In an optional implementation, the specific steps for recording the ramp voltage test results are as follows: If the leakage current is observed to be greater than the maximum leakage current under safe voltage after step-up voltage, the leakage current of the device under test is observed again under rated voltage. If the leakage current is greater than the maximum leakage current under safe voltage or 10 times the initial leakage current judgment threshold, the device under test is marked as the first failure mode, the breakdown voltage of the device under test is recorded, and the test of the device under test is terminated. The first failure mode refers to "step voltage leakage current exceeding the standard". If, after N consecutive step-up voltage increases, the leakage current is observed to be less than the maximum leakage current under safe voltage, and at the same time, after returning to the rated voltage, the leakage current is observed to be greater than 10 times the initial leakage current judgment threshold, then the device to be predicted is marked as the second failure mode, the breakdown voltage of the device to be predicted is recorded, and the test on the device to be predicted is terminated; where: the second failure mode refers to "leakage current exceeding the standard when returning to the rated voltage". If the voltage applied to the device under test after the step-up voltage boost is greater than 5 times the rated voltage, it will be applied for 10 seconds. If the leakage current is observed to be greater than the maximum leakage current under the safe voltage within 10 seconds, the device under test will be marked as the third failure mode, and the breakdown voltage of the device under test will be recorded. The test on the device under test will then be terminated. If the leakage current is not observed to be greater than the maximum leakage current under the safe voltage within 10 seconds, the device under test will be marked as a normal sample that has not failed, and the breakdown voltage value of the device under test will be recorded as 1. The test on the device under test will then be terminated. Here, the third failure mode refers to "normal sample leakage current exceeds the standard", and "normal sample not failed" refers to "normal sample reaches the test limit".

[0030] Based on the above technical solution, this application refines the recording rules for ramp voltage test results. By distinguishing failure modes such as "step voltage leakage current exceeding the limit", "return to rated voltage leakage current exceeding the limit", and "normal sample leakage current exceeding the limit" and the judgment criteria of "normal sample reaching the test upper limit", it achieves accurate classification of device failure mechanisms: it can identify instantaneous breakdown caused by local defects and capture potential failures caused by cumulative damage, avoiding misjudgments caused by a single failure criterion (such as misjudging reversible leakage current as breakdown), providing real and detailed failure data for subsequent lifetime analysis, and ensuring the accuracy of lifetime statistical distribution.

[0031] In an optional implementation, the rule for applying the starting voltage to any device to be predicted is as follows: the starting voltage of the first device to be predicted is set to the rated voltage; the starting voltage of the m-th device to be predicted is the maximum of its rated voltage and 0.9 times the average breakdown voltage of the adjacent 1-3 devices to be predicted; where m is the number of devices to be predicted in the group of devices to be predicted. This application optimizes the rule for setting the starting voltage. The first device uses the rated voltage to ensure the safety of the initial test. Subsequent devices are dynamically adjusted based on the average breakdown voltage of the previous 1-3 devices, i.e., 0.9 times the rated voltage. This value avoids premature device failure due to excessively high starting voltage, and also reduces the invalid test phase of gradually increasing from low voltage by using a level close to the breakdown voltage range as the starting point, thereby significantly shortening the overall test time. At the same time, it avoids prolonging the test cycle due to excessively low starting voltage, realizing adaptive optimization of the test process. It significantly improves the overall efficiency while ensuring test accuracy, and is especially suitable for life screening of batch devices.

[0032] In an optional implementation, the method further includes: monitoring the initial state of the device to be predicted before applying a starting voltage to any device to be predicted: applying a rated voltage to the device to be predicted, observing the leakage current of the device to be predicted; if the leakage current is greater than the initial leakage current judgment threshold, the device to be predicted is marked as an early failure mode, and the breakdown voltage of the device to be predicted is recorded as 0, terminating the test on the device to be predicted; otherwise, applying a starting voltage to the device to be predicted and performing a stepped voltage boost operation. Wherein: early failure mode refers to "early failure sample - rated voltage leakage current exceeding the standard". This application adds an initial state monitoring step. By detecting the leakage current under the rated voltage before applying the starting voltage, "early failure samples" caused by inherent defects (such as process defects) can be screened in advance, avoiding such devices from interfering with the lifetime statistics results in subsequent tests (the failure of early failure samples does not reflect the inherent aging characteristics of the dielectric layer), ensuring that all samples included in the lifetime analysis are in a normal initial state, and improving the representativeness and reliability of the lifetime prediction results.

[0033] In an optional implementation, the method for obtaining the ramp voltage test results further includes: before applying the initial voltage to any device to be predicted, applying a 50% initial voltage for 10 seconds to perform pre-stabilization. This application, by applying a 50% initial voltage for 10 seconds, can eliminate initial state fluctuations in the device, such as instantaneous changes in interface state charge, allowing key parameters such as leakage current to reach a stable state before formal testing. This reduces measurement errors in the initial stage of testing, improves the repeatability and consistency of leakage current data, and provides a more reliable benchmark for subsequent failure mode determination.

[0034] In an optional implementation, the nominal dielectric layer thickness is the design value of the dielectric layer during the process design of the device to be predicted. This parameter is the core basis for calculating the electric field strength (E = potential difference / thickness), which is a key driving factor for TDDB lifetime prediction (the core variable of the E-field acceleration model). Using the design value ensures the accuracy of the electric field strength calculation (avoiding deviations introduced by measured thickness errors), providing reliable physical parameter input for the application of the E-field acceleration model, and guaranteeing the quality of the basic data for lifetime prediction.

[0035] In a specific example, this application provides a method for predicting the lifetime of ultrathin high-k dielectric layers after time-induced breakdown, comprising: Set the basic parameters, which include sample size (p), rated voltage, initial leakage current threshold (Idstart), maximum leakage current at safe voltage (Id threshold), film thickness, typical boost rate, actual boost rate (different values ​​depending on the nominal insulation dielectric layer thickness), and duration after boosting. Among them, the rated voltage, initial leakage current threshold, maximum leakage current under safe voltage, film thickness, typical boost rate, actual boost rate, and duration are all preset based on the performance of samples prepared by historical processes. For example, if the leakage current of the device to be predicted prepared by historical processes is within the range of 0-100nA, it is considered a normal sample, so the initial leakage current threshold can be set to 5nA or 10nA; the maximum leakage current under safe voltage can be set to 100nA; the typical boost rate of the ramp voltage test of the device to be predicted prepared by historical processes is generally 1.0MV / cm-s, the nominal insulating dielectric layer thickness of the device to be predicted prepared by historical processes is generally 17nm, the actual boost rate is 1.7V / s, the rise time is 0.1s, the step boost is 0.17V, and the dwell time at each voltage step is preset to 0.1s.

[0036] First, the ramp voltage test information of the device group to be predicted (the number of devices to be predicted in the device group to be predicted is p) is obtained. The ramp voltage test information includes the ramp voltage test results of each device to be predicted in the device group to be predicted. The ramp voltage test results are obtained in the following way: S1. Before applying the starting voltage to any device to be predicted, perform initial state monitoring on the device to be predicted: apply the rated voltage to the device to be predicted, observe the leakage current of the device to be predicted, if the leakage current is greater than the initial leakage current judgment threshold, mark the device to be predicted as premature failure mode, record the breakdown voltage of the device to be predicted as 0, and terminate the test on the device to be predicted; otherwise, perform pre-stabilization on the device to be predicted.

[0037] S2. The specific steps for pre-stabilizing the device to be predicted are as follows: First, apply 50% of the initial voltage to the device to be predicted for 10 seconds to perform pre-stabilization.

[0038] S3. After applying the initial voltage to the device to be predicted after pre-stabilization, such as Figure 1 As shown, a stepped voltage ramp is performed with a set boost rate and rise time, and a preset dwell time (e.g., 0.1s) is maintained at each voltage step. After every two voltage ramps, the voltage drops back to the rated voltage, and this ramp-down process is repeated until the voltage applied to the device under test after the last ramp reaches 5 times the rated voltage. After each ramp, down, and exceeding 5 times the rated voltage, the leakage current of the device under test is detected and recorded to obtain the ramp voltage test results. The rules for applying the starting voltage to the device under test are as follows: the starting voltage of the first device under test is set to the rated voltage; the starting voltage of the m-th device under test is the maximum of its rated voltage and 0.9 times the average breakdown voltage of the adjacent 1-3 devices under test; where m is the number of devices under test in the device under test group. Specifically: If the leakage current is observed to be greater than the maximum leakage current under the safe voltage after step-up voltage, the leakage current of the device to be predicted is observed again under the rated voltage. If the leakage current is greater than the maximum leakage current under the safe voltage or 10 times the initial leakage current judgment threshold, the device to be predicted is marked as the first failure mode, the breakdown voltage of the device to be predicted is recorded, and the test of the device to be predicted is terminated. If, after N consecutive step-up voltage increases, the leakage current is observed to be less than the maximum leakage current under safe voltage, and at the same time, after returning to the rated voltage, the leakage current is observed to be greater than 10 times the initial leakage current judgment threshold, then the device to be predicted is marked as the second failure mode, the breakdown voltage of the device to be predicted is recorded, and the test on the device to be predicted is terminated. If the voltage applied to the device under test after the step-up voltage boost is greater than 5 times the rated voltage, it is applied for 10 seconds. If the leakage current is observed to be greater than the maximum leakage current under the safe voltage within 10 seconds, the device under test is marked as the third failure mode, and the breakdown voltage of the device under test is recorded. The test on the device under test is then terminated. If the leakage current is not observed to be greater than the maximum leakage current under the safe voltage within 10 seconds, the device under test is marked as a normal sample that has not failed, and the breakdown voltage value of the device under test is recorded as 1. The test on the device under test is then terminated.

[0039] S4. Based on the ramp voltage test results recorded in steps S1 and S2 above, statistically analyze the valid data, remove sample data with a breakdown voltage value recorded as 0 or 1, and denote the sample size of the valid data as L. Calculate the mean breakdown voltage based on the breakdown voltage values ​​recorded in the sample size of the valid data, using the following formula:

[0040] in, L represents the mean breakdown voltage, and L is the sample size of the effective data. This represents the breakdown voltage value of any device to be predicted in the valid data sample.

[0041] Secondly, based on the average breakdown voltage mentioned above, the three-temperature and three-pressure accelerated life test data were obtained: In the experiment, preset temperature-voltage combinations of 100℃, 125℃ and 150℃ were combined with 0.8 times, 0.85 times and 0.9 times the average breakdown voltage to form multiple sets of experimental parameters. Based on the above three-temperature and three-pressure experimental parameter settings, the time required for the ultrathin high-k dielectric layer in the device to be predicted to break down under the preset temperature-voltage combinations was obtained and used as the three-temperature and three-pressure accelerated lifetime test data.

[0042] Based on the three-temperature, three-pressure accelerated life test data, the activation energy in the electric field acceleration model was determined using the Weibull cumulative distribution function and the Arrhenius equation. E a And the electric field acceleration factor γ. Preferably, the electric field acceleration factor γ is jointly determined by the lifetime Lnt (x-axis) and the Weilbull function (y-axis), with a linear relationship between x and y. The slope B and intercept k can be obtained, and then t0.1% and the characteristic lifetime t63.2% can be calculated. Through three sets of voltage experiments at constant temperature, three sets of lifetimes can be obtained. Plotting the three sets of lifetime Lnt63.2% data against the corresponding voltages yields a linear graph; the slope is γ. Similarly, the following can be calculated... E a Under constant voltage, in three sets of temperature experiments, the three data points of 1nt63.2% were compared with the corresponding 1 / (T) k Plot a line graph. k Given the Boltzmann constant, the slope E is obtained. a .

[0043] Based on the slope voltage test information and the nominal insulating dielectric layer thickness, the TDDB lifetime of the ultrathin high-k dielectric layer of each device to be predicted is obtained using the E-field acceleration model corresponding to the TDDB; the E-field acceleration model is:

[0044] in, TTF For expiration time, To accelerate the time to dielectric breakdown of 63.2% of the test samples under stress conditions (corresponding to the characteristic lifetime under the Weibull distribution). γ The electric field acceleration factor, Vstress Let be the stress voltage of any device to be predicted. Vuse Let be the rated voltage of any device to be predicted.E a To activate energy, k Boltzmann's constant, Stress Let the stress temperature of any device to be predicted be... Showers is the actual operating temperature of any device to be predicted.

[0045] In addition, this example also provides a method for calculating dielectric film consistency and process stability based on valid data, as follows:

[0046] It is the standard deviation of the effective data sample. L represents the average breakdown voltage, and L is the sample size of the effective data. This represents the breakdown voltage of any device to be predicted in the valid data sample. In this example, a smaller standard deviation indicates better dielectric film consistency.

[0047]

[0048] CV is the coefficient of variation of the effective data sample. It is the standard deviation of the effective data sample. This represents the mean breakdown voltage. The coefficient of variation (CV) is a relative indicator that measures the degree of data dispersion. In this scenario, the standard deviation / mean essentially reflects the degree of dispersion of the breakdown voltage data relative to its mean. The smaller the CV value, the more concentrated the breakdown voltage data of the sample and the better the consistency; conversely, it indicates that the data dispersion is high and the breakdown characteristics of the devices are different.

[0049] Skewness=

[0050] Skewness is the skewness of the valid data samples. It is the standard deviation of the effective data sample. L represents the average breakdown voltage, and L is the sample size of the effective data. Skewness represents the breakdown voltage value of any device to be predicted in the valid data sample. In practical applications, skewness can help determine the shape of the data distribution. For example, in the breakdown voltage test data of this example, skewness can reflect whether the distribution of breakdown voltage values ​​is symmetrical, and whether there are abnormally high or low breakdown voltage samples, providing a reference for analyzing the consistency of device performance. The closer the skewness is to 0, the more symmetrical the data distribution, and the better the consistency of the dielectric film.

[0051] Kurtosis=

[0052] Kurtosis is the kurtosis of the effective data sample. It is the standard deviation of the effective data sample. L represents the average breakdown voltage, and L is the sample size of the effective data. This represents the breakdown voltage value of any device to be predicted in the valid data sample. Kurtosis is mainly used to measure the steepness (peak height) or flatness of the data distribution, as well as the thickness of the tail (the concentration or dispersion of the tail data compared to a normal distribution). When kurtosis = 3, the steepness of the distribution is consistent with the normal distribution, which is called a "mesomorphic distribution". In the example of this application, a "mesomorphic distribution" is used to reflect the difference from the normal distribution.

[0053] The detailed descriptions listed above are merely specific descriptions of feasible implementations of this disclosure and are not intended to limit the scope of protection of this disclosure. All equivalent implementations or modifications made without departing from the spirit of the art of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for predicting the lifetime of ultrathin high-k dielectric layers after time-induced breakdown, characterized in that, include: Obtain ramp voltage test information for the device group to be predicted, wherein the ramp voltage test information includes the ramp voltage test results of each device to be predicted in the device group to be predicted; Based on the slope voltage test information and the nominal insulating dielectric layer thickness, the TDDB lifetime of the ultrathin high-k dielectric layer of each device to be predicted is obtained using the E electric field acceleration model corresponding to TDDB. The E-field acceleration model is as follows: ， in, TTF For expiration time, To accelerate the time to dielectric breakdown in 63.2% of the test samples under stress conditions, γ The electric field acceleration factor, Vstress Let be the stress voltage of any device to be predicted. Vuse Let be the rated voltage of any device to be predicted. E a To activate energy, k Boltzmann's constant, Tstress Let the stress temperature of any device to be predicted be... Tuse The actual operating temperature of any device to be predicted; The activation energy E a and the electric field acceleration factor γ The methods of obtaining it include: Acquire three-temperature, three-pressure accelerated life test data, and based on the three-temperature, three-pressure accelerated life test data, determine the activation energy in the electric field acceleration model using the Weibull cumulative distribution function and the Arrhenius equation. E a and the electric field acceleration factor γ ; The methods for obtaining the accelerated life test data under three temperature and three pressure conditions include: The average breakdown voltage of the device group to be predicted is determined based on the ramp voltage test information. The time required for the ultrathin high-k dielectric layer in the device to be predicted to break down under a preset temperature-voltage combination is obtained and used as the data of the three-temperature and three-pressure accelerated life test. The preset temperature-voltage combination is determined as follows: First, within a temperature range of 25℃-200℃, three different temperature values ​​are selected as experimental temperature parameters; second, within a range of 0.7 times-0.9 times the average breakdown voltage, three different voltage values ​​are selected as experimental voltage parameters; finally, the three selected temperature values ​​and three voltage values ​​are paired and combined to form multiple sets of experimental parameter combinations, and each set of experimental parameter combinations serves as the preset temperature-voltage combination. The methods for obtaining the slope voltage test results include: After applying an initial voltage to any device to be predicted, a stepped voltage increase is performed with a set boost rate and rise time, and the voltage is held at each voltage step for a preset time. After every n voltage increases, the voltage is reduced back to the rated voltage, and the boost-reduction process is repeated until the voltage applied to the device to be predicted after the last boost reaches 5 times the rated voltage, where n≥2 and n is a positive integer. After each boost, reduction, and exceeding 5 times the rated voltage, the leakage current of the device to be predicted is detected and recorded, thereby obtaining the ramp voltage test results.

2. The lifetime prediction method according to claim 1, characterized in that, The value of n is 2 or 3.

3. The lifetime prediction method according to claim 1, characterized in that, The specific steps for recording the slope voltage test results are as follows: If the leakage current is observed to be greater than the maximum leakage current under the safe voltage after step-up voltage, the leakage current of the device to be predicted is observed again under the rated voltage. If the leakage current is greater than the maximum leakage current under the safe voltage or 10 times the initial leakage current judgment threshold, the device to be predicted is marked as the first failure mode, the breakdown voltage of the device to be predicted is recorded, and the test of the device to be predicted is terminated. If, after N consecutive step-up voltage increases, the leakage current is observed to be less than the maximum leakage current under safe voltage, and at the same time, after returning to the rated voltage, the leakage current is observed to be greater than 10 times the initial leakage current judgment threshold, then the device to be predicted is marked as the second failure mode, the breakdown voltage of the device to be predicted is recorded, and the test on the device to be predicted is terminated. If the voltage applied to the device under test after the step-up voltage boost is greater than 5 times the rated voltage, it is applied for 10 seconds. If the leakage current is observed to be greater than the maximum leakage current under the safe voltage within 10 seconds, the device under test is marked as the third failure mode, and the breakdown voltage of the device under test is recorded. The test on the device under test is then terminated. If the leakage current is not observed to be greater than the maximum leakage current under the safe voltage within 10 seconds, the device under test is marked as a normal sample that has not failed, and the breakdown voltage value of the device under test is recorded as 1. The test on the device under test is then terminated.

4. The lifetime prediction method according to claim 1, characterized in that, The rules for applying an initial voltage to any device to be predicted are as follows: the initial voltage of the first device to be predicted is set to the rated voltage; the initial voltage of the m-th device to be predicted is the maximum of the rated voltage and 0.9 times the average of the breakdown voltages of the 1-3 adjacent devices to be predicted; where m is the number of devices to be predicted in the group of devices to be predicted.

5. The lifetime prediction method according to claim 1, characterized in that, The method further includes: Before applying the starting voltage to any device to be predicted, the device to be predicted is first monitored for its initial state: the rated voltage is applied to the device to be predicted, and the leakage current of the device to be predicted is observed. If the leakage current is greater than the initial leakage current judgment threshold, the device to be predicted is marked as premature failure mode, and the breakdown voltage of the device to be predicted is recorded as 0. The test of the device to be predicted is terminated. Otherwise, the starting voltage is applied to the device to be predicted and a step-by-step boost action is performed.

6. The lifetime prediction method according to claim 1 or 5, characterized in that, The method for obtaining the ramp voltage test results also includes: Before applying the starting voltage to any device to be predicted, pre-stabilize it by continuously applying 50% of the starting voltage to the device to be predicted for 10 seconds.

7. The lifetime prediction method according to claim 1, characterized in that, The nominal insulating dielectric layer thickness is the design value of the insulating dielectric layer when the device to be predicted is designed.

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