A method for determining the number of traps in a multi-trap RTN signal

Abstract

The present invention discloses a method for judging the number of traps in a multi-trap RTN signal. First, HMM extraction is performed on the value within the range of the number of traps; then, wavelet transformation is performed on the measured RTN signal after subtracting the HMM extraction, the distribution of wavelet coefficients is statistically calculated using a histogram, the kurtosis and skewness of the wavelet coefficient distribution are extracted using the kurtosis and skewness formula, and a threshold is set for Gaussian discrimination; if the absolute values ​​of the kurtosis and skewness of the measured data simultaneously meet the condition of being less than the threshold, it is a Gaussian signal, and its quantization value is recorded; the Gaussian quantization values ​​under different values ​​are sorted and compared to obtain the number of traps corresponding to the minimum value. The present invention accurately fits the HMM model of the RTN signal under the premise of ensuring the coverage rate through wavelet decomposition and Gaussian judgment, and then analyzes the degree of fit between the residual signal obtained by subtracting before and after the extraction and the Gaussian signal, so as to judge the appropriate number of traps. The accuracy of the present invention in judging the number of traps is higher than that of the previously known methods, and can cover most of the measured RTN signals.

Description

Technical Field

[0001] The present invention relates to the field of electronic information technology, and in particular to a method for determining the number of traps in a multi-trap RTN signal. Background Art

[0002] In recent years, integrated circuits have developed into the nanometer era. As device size continues to decrease, reliability issues caused by traps have become more prominent. Currently, random telegraph noise (RTN) accounts for more than 60% of the measurable noise in MOS transistors, and RTN is particularly prominent in short-channel devices.

[0003] The RTN of MOS devices is caused by the continuous capture / release of carriers by a single trap in the gate oxide layer over time, which forms the movement of carriers in the channel, causing the threshold voltage and drain current of the tube to fluctuate greatly over time, which is directly manifested as the random distribution of high and low states. It is one of the important sources of dynamic changes in MOSFET. RTN is the main component of low-frequency noise. In the early days, it was believed that it mainly affected analog and radio frequency circuits. However, as the feature size of devices continues to shrink, RTN and the threshold drift fluctuations caused by it have intensified, and its impact on digital circuits has become increasingly important, especially in advanced logic devices and emerging memory devices. RTN makes the probability of fluctuations in the number of carriers in the device channel increasingly large, which greatly reduces the reliability of components and limits the development of integrated circuits in the direction of miniaturization.

[0004] When there are multiple traps in the device that are involved in capturing / releasing carriers, the measured RTN will show more than 2 states. When analyzing multi-trap RTN, it is very necessary to determine the number of traps in order to accurately extract the RTN and its parameters.

[0005] When the existing technical criteria are applied to HMM extraction to determine the appropriate number of traps, they cannot distinguish some complex multi-trap situations well. For a relatively typical RTN, the number of traps can be roughly inferred based on the number of states. However, when there is trap coupling, the criterion from the number of states to the number of traps is no longer accurate. For some complex and atypical RTNs, the BIC criterion can accurately select the most appropriate trap number model to a certain extent, but the BIC criterion cannot accurately determine the number of traps with full coverage. In some cases, the trap number model selected by the BIC criterion will contradict the actual situation (for example, the simulated two-trap normalized RTN Figure 1 The trend of BIC value with the number of traps is shown in Figure 2 shown).

[0006] Therefore, it is necessary for us to improve the existing methods to overcome the above defects. Summary of the invention

[0007] The purpose of the present invention is to provide a method for determining the number of traps in a multi-trap RTN signal. Through wavelet decomposition and Gaussian judgment, the HMM model of the RTN signal is accurately fitted under the premise of ensuring coverage, and then the fitting degree between the residual signal obtained by subtracting before and after extraction and the Gaussian signal is analyzed to determine the appropriate number of traps. The accuracy of the present invention in determining the number of traps is higher than that of the previously known methods, and can cover most of the measured RTN signals.

[0008] The above technical objectives of the present invention are achieved through the following technical solutions:

[0009] A method for determining the number of traps in a multi-trap RTN signal comprises the following steps:

[0010] S1. Perform HMM extraction on the value u within the trap number range [m,n] (n>m);

[0011] S2. The RTN signal extracted under different trap numbers is Y u (k), k = 1, 2, 3…;

[0012] S3. Subtract HMM extraction from the measured RTN signal, ie Z(k) = X(k) - Y u (k), k=1,2,3…; perform wavelet transform, use histogram to count the distribution of wavelet coefficients, use kurtosis formula and skewness formula to extract kurtosis k and skewness s of wavelet coefficient distribution, and set threshold to perform Gaussian discrimination; if the absolute value of kurtosis and skewness of the measured data satisfies the condition of being less than the threshold at the same time, it is a Gaussian signal, and record its quantized value |k|+|s|, otherwise it is a non-Gaussian signal;

[0013] S4. Sort and compare the Gaussian quantization values ​​under different u to obtain the number of traps p corresponding to the minimum value |k|+|s|.

[0014] Furthermore, the kurtosis formula and skewness formula in step S3 are respectively and

[0015] Furthermore, draw a histogram of the measured time series and observe the number of states. k-1 , 2 k ], the number of traps is k, and the range of traps is [m,n]=[k-2,k+2](n>m and m>1);

[0016] The method to search for the trap number range is as follows:

[0017] Input: measured time series X(k), k=1,2,3…

[0018] Output: histogram distribution of measured time series, number of states, and number of traps range [m,n].

[0019] Furthermore, after finding the range of trap numbers, HMM extraction is performed under the set number of traps, and then Gaussian judgment is performed on the measured time series minus the proposed pure RTN. If it is a Gaussian signal, its Gaussian quantization value is recorded, and the number of traps is moved within the range to enter the next extraction; if it is not a Gaussian signal, it directly enters the next extraction. After all extractions within the range of trap numbers are completed, the quantization values ​​are sorted, and the number of traps corresponding to the minimum Gaussian quantization value is the most suitable HMM model;

[0020] The algorithm for determining the number of traps is as follows:

[0021] Input: measured time series X(k), k=1,2,3… and trap number range [m,n] (n>m)

[0022] Output: The most appropriate number of traps p.

[0023] In summary, the present invention has the following beneficial effects:

[0024] The present invention uses wavelet decomposition and Gaussian judgment to accurately fit the HMM model of the RTN signal while ensuring coverage, and then analyzes the degree of fit between the residual signal obtained by subtracting the residual signal before and after extraction and the Gaussian signal to determine the appropriate number of traps. The accuracy of the present invention in determining the number of traps is higher than that of the previously known methods, and can cover most of the measured RTNs. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is the simulated two-trap band noise-normalized RTN1 signal.

[0026] Figure 2 It is a trend diagram of the BIC value of the simulated two-trap noisy RTN1 signal changing with the number of traps.

[0027] Figure 3 It is a flowchart of the trap number determination method based on Gaussian determination provided by the present invention.

[0028] Figure 4 is the normalized RTN2 signal with noise for the simulated two-trap.

[0029] Figure 5 It is the BIC value of the simulated two-trap RTN2 signal with noise and the trend of Gaussian quantization value changing with the number of traps.

[0030] Figure 6 is the normalized RTN3 signal with noise for the simulated two-trap.

[0031] Figure 7It is the BIC value of the simulated two-trap RTN3 signal with noise and the trend of Gaussian quantization value changing with the number of traps.

[0032] Figure 8 is the measured noisy leakage current sequence.

[0033] Fig. 9 is the histogram of the measured noisy leakage current series.

[0034] Fig.10 It is a trend graph of the measured Gaussian quantization value of the noisy leakage current sequence changing with the number of traps. DETAILED DESCRIPTION

[0035] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further described below in conjunction with illustrations and specific embodiments.

[0036] 1. Overall algorithm

[0037] See also Figure 3 The present invention proposes a method for determining the number of traps in a multi-trap RTN signal, comprising the following steps:

[0038] S1. Perform HMM extraction on the value u within the trap number range [m,n] (n>m)

[0039] S2. The RTN extracted under different trap numbers is Yu(k), k=1,2,3…

[0040] S3. Preprocess Z(k)=X(k)-Yu(k), k=1,2,3… with 3σ criterion to remove local useless values, decompose into 5 layers with db3 wavelet, take the wavelet coefficients of the middle 2 layers for statistical analysis, and use the kurtosis formula and skewness formula to calculate the kurtosis k and skewness s of the distribution of wavelet coefficients. If |k|<0.5 and |s|>0.25, it is a Gaussian signal, and record its quantized value |k|+|s|.

[0041] S4. Sort and compare the Gaussian quantization values ​​under different u to obtain the number of traps p corresponding to the minimum value |k|+|s|.

[0042] 2. Gaussian judgment

[0043] The characteristics of a standard Gaussian signal are that the skewness and kurtosis are close to 0.

[0044] Perform wavelet transform on the measured RTN signal after deducting HMM extraction, use histogram to count the distribution of wavelet coefficients, use the following kurtosis and skewness formula to extract the characteristics of wavelet coefficient distribution, set thresholds for Gaussian discrimination (for example, the kurtosis threshold is 0.5, and the skewness threshold is 0.25). When the absolute values ​​of the kurtosis and skewness of the measured data meet the conditions of being less than the threshold at the same time, it is a Gaussian signal, otherwise it is a non-Gaussian signal.

[0045] If the extraction fit of the measured time series is good under different trap numbers, the measured time series minus the proposed pure RTN should be a Gaussian signal, and the Gaussian quantization value with the best fit is the smallest under different trap numbers.

[0046] Kurtosis formula:

[0047] Skewness formula:

[0048] 3. Determine the search range for the number of traps

[0049] Draw a histogram of the measured time series and observe the number of states. When the number of states is within the range (2 k-1 , 2 k ], the number of traps is k, and the range of trap numbers is [m,n]=[k-2,k+2](n>m and m>1).

[0050] The method to search for the trap number range is as follows:

[0051] Input: measured time series X(k), k=1,2,3…

[0052] Output: measured time series histogram distribution, state number, trap number range [m,n]

[0053] 4. Comparison of Gaussian discrimination and Gaussian quantization values ​​under different numbers of traps

[0054] After finding the trap number range, HMM extraction can be performed under the set trap number, and then Gaussian judgment is performed on the measured time series minus the proposed pure RTN. If it is a Gaussian signal, its Gaussian quantization value is recorded, and the number of traps is moved within the range to enter the next extraction; if it is not a Gaussian signal, it directly enters the next extraction. After all extractions within the trap number range are completed, the quantization values ​​are sorted, and the number of traps corresponding to the minimum Gaussian quantization value is the most suitable HMM model.

[0055] The algorithm for determining the number of traps is as follows:

[0056] Input: measured time series X(k), k=1,2,3… and trap number range [m,n] (n>m)

[0057] Output: The most appropriate number of traps p

[0058] Example

[0059] (1) Take the measured current sequence containing RTN as an example ( Figure 8 As shown), draw its histogram ( Fig. 9 shown).

[0060] (2) The number of states of the sequence is 4, and the number of traps is inferred to be 2. The search range of the number of traps is [1,4]. Set the number of traps u = 1, perform HMM extraction on x(k) to obtain yu(k), and use the 3 criteria to preprocess x(k)-yu(k) to remove local useless values. Then use the db3 wavelet basis to decompose 5 layers, take the low-frequency coefficients of the middle 2 layers of wavelets for statistical analysis, and use the kurtosis formula and skewness formula to calculate the distribution of wavelet coefficients. The kurtosis k = -1.572286 and skewness s = 0.347720 do not meet the threshold requirements k| < 0.5 and |s| > 0.25, indicating that the residual signal after extraction is not a Gaussian signal. Perform HMM extraction when u = 2, and obtain its kurtosis k = 0.003728 and skewness s = 0.199980, which meet the Gaussian threshold requirements, and record the Gaussian quantization value 0.203708. When u=3, the HMM extraction is performed, and the kurtosis k=0.112080 and the skewness s=0.114071 are obtained, which meet the Gaussian threshold requirements, and the Gaussian quantization value is recorded as 0.226151. When u=4, the HMM extraction is performed, and the kurtosis k=-1.194817 and the skewness s=0.269338 are obtained, which do not meet the threshold requirements, indicating that the residual signal after extraction is not a Gaussian signal. (The trend of the Gaussian quantization value with the number of traps is shown in Fig.10 (shown)

[0061] (3) The number of traps corresponding to the minimum Gaussian quantization value is the trap number model in the RTN signal. In this embodiment, the number of traps = 2.

[0062] The present invention uses wavelet decomposition and Gaussian judgment to accurately fit the HMM model of RTN while ensuring coverage. The present invention verifies the simulated two-trap RTN signal and finds that for a typical RTN ( Figure 4 ), Figure 5 The results of this method are consistent with those of the BIC method, that is, the minimum value is obtained when the number of traps is appropriate. Figure 6 ), the BIC criterion is wrong, but this method can still accurately determine the optimal number of traps. Figure 7 As shown in the figure, it can be seen that the accuracy of this method in determining the number of traps is higher than that of the previously known methods, and it can cover most of the measured RTNs.

[0063] In this document, the directions or positional relationships indicated by terms such as "up", "down", "front", "back", "left", "right", "top", "bottom", "inside", "outside", "vertical", and "horizontal" are based on the directions or positional relationships shown in the accompanying drawings and are only for the clarity of expressing the technical solutions and the convenience of description, and therefore should not be understood as limitations of the present invention.

[0064] In this document, the terms "comprises," "comprising," or any other variations thereof, are intended to cover a non-exclusive inclusion of elements other than those listed and may also include additional elements not expressly listed.

[0065] The above shows and describes the basic principles, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. The present invention may be subject to various changes and improvements without departing from the spirit and scope of the present invention. These changes and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for determining the number of traps in a multi-trap RTN signal, characterized in that: The steps include: S1. Perform HMM extraction on the value u in the trap number range [m,n], n>m, wherein the steps for determining the trap number search range are: Draw a histogram of the measured time series and observe the number of states. When the number of states is within the range (2 k-1 , 2 k ], the number of traps is k, and the range of traps is [m,n]=[k-2,k+2], n>m and m>1; The method to search for the trap number range is as follows: Input: measured time series X(k), k=1,2,3… Output: histogram distribution of measured time series, number of states, and range of number of traps [m,n]; S2. The RTN signal extracted under different trap numbers is Y u (k), k = 1, 2, 3…; S3. Subtract HMM extraction from the measured RTN signal, ie Z(k) = X(k) - Y u (k), k=1,2,3…; perform wavelet transform, use histogram to count the distribution of wavelet coefficients, use kurtosis formula and skewness formula to extract kurtosis k and skewness s of wavelet coefficient distribution, and set threshold to perform Gaussian discrimination; if the absolute value of kurtosis and skewness of the measured data satisfies the condition that it is less than the threshold at the same time, it is a Gaussian signal, and record its quantized value |k|+|s|, otherwise it is a non-Gaussian signal, wherein the kurtosis formula and skewness formula are respectively and S4. Sort and compare the Gaussian quantization values ​​under different u to obtain the number of traps p corresponding to the minimum value |k|+|s|.

2. The method for determining the number of traps in a multi-trap RTN signal according to claim 1, characterized in that: After finding the range of trap numbers, perform HMM extraction under the set number of traps, and then perform Gaussian judgment on the measured time series minus the proposed pure RTN. If it is a Gaussian signal, record its Gaussian quantization value and move the number of traps within the range to enter the next extraction; if it is not a Gaussian signal, directly enter the next extraction. After all extractions within the range of trap numbers are completed, sort the quantization values, and the number of traps corresponding to the minimum Gaussian quantization value is the most suitable HMM model. The algorithm for determining the number of traps is as follows: Input: measured time series X(k), k=1,2,3… and trap number range [m,n], n>m Output: the most appropriate trap number p.

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