Methods, systems, equipment and storage media for mobility extraction in low-temperature CMOS

Abstract

This invention discloses a method, system, device, and storage medium for extracting mobility in low-temperature CMOS. These are corresponding solutions. The solution can accurately extract effective carrier mobility from standard I-V data without requiring a pre-set mobility model, avoiding errors caused by model dependence. Furthermore, it can effectively distinguish and quantify the different contributions of strong and weak fields to mobility, thereby decoupling the physical mechanism of mobility. Simultaneously, it extracts drain-source parasitic resistance to avoid interference with mobility errors, enhancing the consistency and physical integrity of modeling. Moreover, it has good robustness and versatility, applicable to different process nodes and device sizes, and is easy to integrate into automated modeling and evaluation processes. Finally, the extracted mobility has clear physical parameter interpretation and can be directly used for tasks such as low-temperature circuit simulation, process analysis, and device reliability assessment, possessing significant engineering practical value.

Description

Technical Field

[0001] This invention relates to the field of mobility extraction technology for low-temperature CMOS, and more particularly to a method, system, device, and storage medium for mobility extraction in low-temperature CMOS. Background Technology

[0002] With the development of technologies such as quantum computing and cryogenic sensing, the application of cryogenic CMOS (complementary metal-oxide-semiconductor) devices in the 4K (4 Kelvin) temperature range is becoming increasingly widespread, and their electrical modeling has become a research hotspot. In this type of modeling, effective carrier mobility... Effective carrier mobility is a key parameter that determines device performance and circuit design, directly affecting drive current, transconductance, and overall circuit performance. Therefore, accurately extracting effective carrier mobility is crucial. It not only helps to gain a deeper understanding of the physical behavior of devices, but also forms the basis for low-temperature CMOS circuit simulation and design, which is especially important at the deep submicron technology node.

[0003] Traditionally, Can be determined by the linear region of the device Feature extraction, the formula is:

[0004] ;

[0005] in, For the inversion layer charge density, Gate-source voltage, drain-source voltage The influence of drain-source parasitic resistance has been taken into account. This is the applied drain-source voltage (excluding contact resistance). The drain-source current is represented by L and W, which correspond to the device channel length and width, respectively.

[0006] Those skilled in the art will understand that "gate-source" and "drain-source" are commonly used abbreviations in the industry. "Gate" refers to the gate electrode, "source" refers to the source electrode, and "drain" refers to the drain electrode. Similar abbreviations will be used in the following text, so they will not be elaborated further.

[0007] Inversion layer charge density Low-frequency split capacitance-voltage (Split C-V) measurement is possible, but this method requires expensive equipment and suffers from bias mismatch between C-V and I-V (current-voltage) measurements. While the S-parameter method can improve accuracy, it relies on radio frequency instruments. A more practical method depends solely on I-V measurement, using approximations... ,Will The calculation is converted to threshold voltage. and drain-source parasitic resistance Accurate extraction is required, but this remains extremely challenging in low-temperature environments.

[0008] To address this, researchers have proposed several methods for extracting low-temperature mobility. The Y-function method (Reference 1: A. Emrani, F. Balestra, and G. Ghibaudo, “Generalized mobility law for drain current modeling in sim mus transistors from liquid helium to room temperatures,” IEEE Transactions on Electron Devices, vol. 40, no. 3, pp. 564–569, 1993.) can be used regardless of the temperature. Extraction under influence However, it is not possible to obtain Based on the linear fitting of channel resistance and channel length (Reference 2: G. Niu, J. Cressler, S. Mathew, and S. Subbanna, “A total resistance slope-based effective channel mobility extraction method for deep submicrometer cmostechnology,” IEEE Transactions on Electron Devices, vol. 46, no. 9, pp. 1912–1914, 1999.), it is possible to extract... However, the assumption that mobility is independent of channel length often does not hold true in submicron CMOS; based on small-signal output conductivity method (Literature 3: F. Kong, Y. Yeow, and Z. Yao, "Extraction of mosfet threshold voltage, series resistance, effective channel length, and inversion layer mobility from small-signal channel conductance measurement," IEEE Transactions on Electron Devices, vol. 48, no. 12, pp. 2870–2874, 2001.; Document 4: F. Jazaeri, A. Pezzotta, and C. Enz, “Free carrier mobility extraction in fets,” IEEE Transactions on Electron Devices, vol. 64, no. 12, pp. 5279–5283, 2017.) or based on low The multi-point measurement method (Reference 5: JP Campbell, KP Cheung, JS Suehle, and A. Oates, “A simple series resistance extraction methodology for advanced cmos devices,” IEEE Electron Device Letters, vol. 32, no. 8, pp.1047–1049, 2011.) is extremely sensitive to noise.

[0009] These methods are acceptable at room temperature or under long-channel conditions, but accurate extraction is not feasible in 4K and submicron devices. This makes the situation even more challenging. This is not only due to the size effect brought about by the device structure, but also because at extremely low temperatures, thermal excitation is significantly weakened, and carrier transport is mainly controlled by mechanisms such as interface roughness, Coulomb scattering, and long-range impurity scattering. Its behavior is different from that at room temperature, and traditional empirical models often fail.

[0010] It is worth noting that, in addition to extraction The numerical values ​​themselves are also important for decoupling the physical mechanisms by which they affect the system. Different scattering processes (such as surface roughness and Coulomb scattering) play a dominant role in different bias regions. Separating their relative contributions helps to establish a mobility model based on physical mechanisms, thereby improving the simulation accuracy of cryogenic devices and providing guidance for process optimization and circuit design. For example, power-law behavior can be used to identify the dominance of Coulomb scattering, while linear behavior is common in surface scattering in strong field regions.

[0011] Therefore, there is an urgent need for a new solution that has the following characteristics: (1) based solely on I-V data, without the need for expensive or complex equipment; (2) applicable to 4K and submicron CMOS devices; (3) independent of a preset mobility model; (4) able to distinguish and quantify the contribution of different scattering mechanisms to mobility; and (5) possessing strong versatility and automation potential.

[0012] In view of this, the present invention is hereby proposed. Summary of the Invention

[0013] The purpose of this invention is to provide a method, system, device, and storage medium for extracting mobility in low-temperature CMOS. It relies only on conventional I-V data acquisition, without the need for split C-V or RF measurement, and has good feasibility and data universality. The final output effective carrier mobility not only has a clear functional form as it changes with the bias, but can also be clearly decomposed into the physical contributions of multiple scattering mechanisms, thereby forming a low-temperature mobility model with explanatory power and scalability.

[0014] The objective of this invention is achieved through the following technical solution:

[0015] A method for extracting mobility in low-temperature CMOS, comprising:

[0016] Based on the carrier transport mechanism, the reciprocal of the effective carrier mobility is decomposed into a strong-field scattering term and a weak-field scattering term;

[0017] By combining strong-field scattering terms and weak-field scattering terms, a linear region resistance model is constructed.

[0018] An enhanced resistance model is obtained by combining the linear region resistance model and derivative processing techniques, and the threshold voltage of the device under test is extracted by utilizing the threshold voltage offset between the device under test and the selected reference device.

[0019] The weak-field scattering term was quantitatively modeled and fitted using an enhanced resistance model to obtain the power-law model parameters.

[0020] The parameters of the strong field scattering term and the drain-source parasitic resistance of the reference device are extracted by combining the parameters of the power-law model;

[0021] By utilizing the drain-source parasitic resistance of the reference device and combining it with the current and voltage measurement data of the device under test, the effective carrier mobility of the device under test is calculated. The effective carrier mobility model is then reconstructed through mathematical analysis, and the contributions of the strong-field scattering field and the weak-field scattering term are quantified by combining the power-law model parameters and the strong-field scattering term parameters.

[0022] A low-temperature CMOS mobility extraction system for implementing the aforementioned method includes:

[0023] The mobility model decomposition unit is used to decompose the inverse of the effective carrier mobility into strong field scattering and weak field scattering terms based on the carrier transport mechanism.

[0024] The linear region resistance modeling unit is used to combine strong field scattering terms and weak field scattering terms to construct a linear region resistance model;

[0025] The threshold voltage extraction unit is used to obtain the enhanced resistance model by combining the linear region resistance model and derivative processing technology, and to extract the threshold voltage of the device under test by utilizing the threshold voltage offset between the device under test and the selected reference device.

[0026] The weak-field scattering term physical parameter fitting unit is used to quantitatively model and power-law fit the weak-field scattering term using the enhanced resistance model, and obtain the power-law model parameters.

[0027] The strong field scattering term parameter and drain-source parasitic resistance extraction unit is used to extract the strong field scattering term parameters and the drain-source parasitic resistance of the reference device by combining the power law model parameters.

[0028] The effective carrier mobility calculation and contribution quantization unit is used to calculate the effective carrier mobility of the device under test by using the drain-source parasitic resistance of the reference device and combining the current and voltage measurement data of the device under test. It also reconstructs the effective carrier mobility model through mathematical analysis and quantifies the contribution of the strong field scattering term and the weak field scattering term by combining the parameters of the strong field scattering term.

[0029] A processing device includes: one or more processors; and a memory for storing one or more programs;

[0030] When the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned method.

[0031] A readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method.

[0032] As can be seen from the technical solutions provided by the present invention: (1) Without the need for a preset mobility model, the effective carrier mobility can be accurately extracted from the standard I-V data, avoiding errors caused by model dependence; (2) It can effectively distinguish and quantify the different contributions of strong fields (such as surface rough scattering) and weak fields (such as Coulomb scattering) to mobility, thereby achieving decoupling of the physical mechanism of mobility; (3) Drain-source parasitic resistance is extracted simultaneously to avoid its interference with mobility error, enhancing the consistency and physical integrity of modeling; (4) It has good robustness and versatility, is applicable to different process nodes and different size devices, and only requires conventional linear region I-V data, which is easy to integrate into the automated modeling and evaluation process; (5) The extracted mobility model has clear physical parameter interpretation and can be directly used for tasks such as low temperature circuit simulation, process analysis and device reliability evaluation, which has important engineering practical value. Attached Figure Description

[0033] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0034] Figure 1 This is a flowchart of a low-temperature CMOS mobility extraction method provided in an embodiment of the present invention.

[0035] Figure 2 This is a schematic diagram of a low-temperature CMOS mobility extraction system provided in an embodiment of the present invention.

[0036] Figure 3 This is a schematic diagram of a processing device provided in an embodiment of the present invention. Detailed Implementation

[0037] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of the present invention.

[0038] First, the following explanations are provided for the terms that may be used in this article:

[0039] The terms "comprising," "including," "containing," "having," or other similar semantic descriptions should be interpreted as non-exclusive inclusion. For example, including a technical feature element (such as raw material, component, ingredient, carrier, dosage form, material, size, part, component, mechanism, device, step, process, method, reaction conditions, processing conditions, parameter, algorithm, signal, data, product or article of manufacture, etc.) should be interpreted as including not only the expressly listed technical feature element, but also other technical feature elements that are not expressly listed and are well-known in the art.

[0040] The term "composed of" excludes any technical features not expressly listed. When used in a claim, it closes the claim to exclude all technical features other than those expressly listed, except for associated conventional impurities. If the term appears only in a clause of a claim, it limits the claim to the elements expressly listed in that clause; elements recited in other clauses are not excluded from the overall claim.

[0041] The following provides a detailed description of a low-temperature CMOS mobility extraction method, system, device, and storage medium provided by this invention. Contents not described in detail in the embodiments of this invention are prior art known to those skilled in the art. Unless otherwise specified in the embodiments of this invention, conditions are performed according to conventional conditions or manufacturer recommendations. Instruments used in the embodiments of this invention, unless otherwise specified, are all commercially available products.

[0042] Example 1

[0043] like Figure 1 As shown in the figure, the mobility extraction method for low-temperature CMOS provided by this embodiment of the invention mainly includes the following steps:

[0044] Step 1: Based on the carrier transport mechanism, the inverse of the effective carrier mobility is decomposed into a strong-field scattering term and a weak-field scattering term (based on the gate overdrive voltage). (For bias variables).

[0045] The preferred implementation method for this step is as follows:

[0046] Based on the carrier transport mechanism, the effective carrier mobility The reciprocal form of is decomposed into strong-field scattering and weak-field scattering terms according to Mathiessen's rule, and is expressed as:

[0047] ;

[0048] Among them, Mathiessen's rule is Mathiessen's rule. Indicates the given gate overdrive voltage Effective carrier mobility with channel length L of the device For strong field scattering, This is a weak field scattering term.

[0049] For the i-th group of devices, the channel length is Strong field scattering term With weak field scattering term They are represented as follows:

[0050] ;

[0051] ;

[0052] in, The channel length with respect to the i-th group of devices under test The relevant strong-field scattering fitting parameters, where M+1 is the cutoff order, m is the order index, and the superscript m+1 indicates the m+1 power. For the bias-dependent weak-field scattering term function, The channel length with respect to the i-th group of devices under test Related geometric scaling factors.

[0053] In the linear region ( In this context, the determination of a strong or weak field is still based on the longitudinal electric field within the channel. With critical field The size relationship shall be used as the standard, among which This is the carrier saturation velocity. Its mobility: If If , then it is a weak field region (weak field linear region); if This is the strong field region (strong field linear region).

[0054] Those skilled in the art will understand that when modeling the carrier transport characteristics in semiconductor devices, scattering mechanisms are typically distinguished into weak-field scattering and strong-field scattering, and represented in the model by corresponding functions. It is important to clarify that the weak-field and strong-field scattering mechanisms coexist and interact across the entire bias operating range of the device, and their relative contributions to the total mobility continuously change with bias conditions and device characteristics. Therefore, the corresponding functions are named "weak-field scattering term" and "strong-field scattering term" based on their respective dominance within specific electric field intensity ranges: the weak-field scattering term plays a dominant role in mobility in the weak-field region, while the strong-field scattering term becomes the dominant factor in the strong-field region. The term "dominant role" here is a relative concept, intended to indicate the physical mechanism that has a decisive influence within this range, without requiring that the absolute contribution of one scattering term must be less than that of the other. Therefore, the division between strong and weak electric fields is essentially a functional theoretical definition that serves to explain physical mechanisms and construct mathematical models. It does not constitute a strict physical boundary or specific threshold for the range of scattering mechanism.

[0055] Step 2: Combine the strong field scattering term and the weak field scattering term to construct a linear region resistance model.

[0056] The preferred implementation method for this step is as follows:

[0057] For the i-th group of devices under test, the corresponding linear region resistance model is expressed as:

[0058] ;

[0059] in, Let be the total source-drain resistance of the i-th group of devices under test. Let be the drain-source parasitic resistance of the i-th group of devices under test, connected in series in the linear region resistance model described above. Hereinafter referred to as drain-source parasitic resistance, unless otherwise specified; Let be the channel length of the i-th group of devices under test. Let be the channel width of the i-th group of devices under test. The capacitance per unit area of ​​the gate oxide layer. Indicates the given gate overdrive voltage With device channel length Effective carrier mobility at that time.

[0060] To simplify the formula writing, the strong field scattering term is separated from... The weak field scattering terms are divided by respectively , represented as:

[0061] ;

[0062] ;

[0063] in, This represents the strong-field scattering component in the linear resistivity model. Indicates the discrete geometric scaling factor in the linear region resistance model. The weak-field scattering component afterwards.

[0064] The reconstructed linear region resistance model is expressed as:

[0065] .

[0066] Step 3: Combine the linear region resistance model with derivative processing techniques to obtain the enhanced resistance model, and use the threshold voltage offset between the device under test and the selected reference device to extract the threshold voltage of the device under test.

[0067] The preferred implementation method for this step is as follows:

[0068] Using nth-order derivative processing techniques (satisfying) The enhanced resistance model is obtained, which is expressed as:

[0069] ;

[0070] in, The sign of the nth-order partial derivative. is the symbol for the nth-order total derivative, and d is the symbol for the total derivative. The gate-source voltage is used in the linear region test. , Gate voltage, The gate voltage is the same as the source voltage. Let be the enhanced resistance model for the i-th group of devices under test.

[0071] Choose a reference device whose enhancement resistance model is denoted as . Using the proportional method for the i-th group of devices Gate-source voltage of the function Perform a horizontal offset operation so that the proportional function is at the optimal voltage offset. The proportional function converges to a constant. Represented as:

[0072] ;

[0073] in, For the i-th group of devices under test, at voltage Horizontal offset is The resistance nth-order derivative at time n.

[0074] The objective function to be optimized is:

[0075] ;

[0076] in, The gate voltage of the kth sample. For a given gate voltage With voltage offset The proportional function of time, The mean of the scaling function for N samples.

[0077] Optimal voltage offset The threshold voltage of the i-th group of devices relative to the reference device The offset is combined with the threshold voltage of the reference device to extract the threshold voltage of the i-th group of devices. :

[0078] .

[0079] Step 4: Quantitatively model and fit the weak field scattering term using the enhanced resistance model to obtain the power law model parameters.

[0080] The preferred implementation method for this step is as follows:

[0081] set up:

[0082] .

[0083] Set the intermediate parameter K:

[0084] ;

[0085] Where A is the amplitude, B is the power exponent, and both are parameters of the power law model; n is the stage in the derivative processing, and j is the order index.

[0086] For the i-th group of devices, obtain the corresponding threshold voltage. Then, the gate overdrive voltage was calculated. Then pass the gate drive voltage Replace gate-source voltage Substituting the values ​​into the enhanced resistor model, we obtain a new enhanced resistor model. Combining the above settings with the intermediate parameter K, we obtain:

[0087] ;

[0088] in, It is the natural logarithm function.

[0089] Through the and Perform linear fitting to extract the power exponent B and the magnitude A.

[0090] Step 5: Extract the parameters of the strong field scattering term and the drain-source parasitic resistance of the reference device by combining the power-law model parameters.

[0091] The preferred implementation method for this step is as follows:

[0092] Define residual function :

[0093] ;

[0094] in, Let be the total source-drain resistance corresponding to the i-th group of devices under test; The drain-source parasitic resistance of the i-th group of devices under test is expressed as: , The channel width of the reference device, The drain-source parasitic resistance of the reference device; For the strong field scattering component in the linear resistivity model, The M-order polynomial; parameters and Through the It is obtained by polynomial fitting.

[0095] For example, taking M=1, it is represented as: .

[0096] Fitting parameters for strong field scattering Approximately Indicates and If it is irrelevant, then:

[0097] ;

[0098] ;

[0099] In fixed Under the given conditions, for a given Fitting residual function and The linear relationship is used to obtain the fitting parameters for strong field scattering. Then obtain Substitute into the residual function minus Term, through fitting function and The linear relationship is extracted. and This part of the fitting obtains the fitting parameters for strong field scattering. as well as All of these are parameters belonging to the strong field scattering term.

[0100] Combining the example above where M=1, we have:

[0101] ;

[0102] In this example, by fitting the residual function and The linear relationship can be used to obtain parameters. Then, by using the same method as described above, it is possible to extract and .

[0103] Step 6: Using the drain-source parasitic resistance of the reference device and the current and voltage measurement data of the device under test, calculate the effective carrier mobility of the device under test, and reconstruct the effective carrier mobility model through mathematical analysis, combining the power-law model parameters (power exponent B and amplitude A) and the strong field scattering term parameters. The contributions of strong-field scattering and weak-field scattering terms are quantified.

[0104] The calculations involved in this step can be expressed as follows:

[0105] ;

[0106] in, Let be the drain-source parasitic resistance of the i-th group of devices under test, using the drain-source parasitic resistance of the reference device. Calculated; This is the drain-source voltage. Let be the drain-source current of the i-th group of devices under test.

[0107] Furthermore, the formula for calculating effective carrier mobility is transformed into an effective carrier mobility model through mathematical analysis, which is expressed as:

[0108] ;

[0109] in, Using the extracted strong field scattering fitting parameters as well as calculate, The calculation is performed using the obtained power-law model parameters.

[0110] The above-mentioned solutions provided by the embodiments of the present invention mainly achieve the following beneficial effects:

[0111] (1) Without the need for a pre-defined mobility model, it can be derived from the standard Accurately extract effective carrier mobility from (I–V) data to avoid errors caused by model dependence.

[0112] (2) It can effectively distinguish and quantify the different contributions of strong fields (such as surface rough scattering) and weak fields (such as Coulomb scattering) to mobility, thereby achieving decoupling of the physical mechanism of mobility.

[0113] (3) Extract the drain-source parasitic resistance simultaneously to avoid its interference with mobility error and enhance the consistency and physical integrity of modeling.

[0114] (4) It has good robustness and versatility, is applicable to different process nodes and different size devices, and only requires conventional linear region I-V data, which is easy to integrate into the automated modeling and evaluation process.

[0115] (5) The extracted mobility model has clear physical parameter interpretation and can be directly used for tasks such as low temperature circuit simulation, process analysis and device reliability assessment, and has important engineering practical value.

[0116] To more clearly demonstrate the technical solution and its effects provided by the present invention, the method provided by the embodiments of the present invention will be described in detail below with reference to specific examples.

[0117] I. Overall Overview.

[0118] This invention provides a mobility extraction method suitable for low-temperature CMOS devices, typically applicable to the 1K-50K temperature range, and also to the 2K-70K range. The temperature range boundaries are related to actual physical characteristics and device fabrication processes; this application does not impose specific temperature limitations. The method takes the linear region I-V data of the device as input and, based on the carrier transport mechanism, decomposes the inverse form of the effective carrier mobility into two types of contributions: strong-field scattering and weak-field scattering, according to Mathiessen's rule. Through series expansion and higher-order derivative operations, the smooth strong-field scattering term is effectively suppressed, while the contrast of the weak-field scattering term is enhanced, achieving isolation and identification of its dominant mechanisms (such as Coulomb scattering).

[0119] Subsequently, by combining the publicly available Shift-and-Ratio method to accurately extract the threshold voltage of different devices, the linear region resistance model was further fitted to extract the drain-source parasitic resistance. Strong field scattering term With weak field scattering term The parameter expression is then derived, and the complete mobility function form is finally reconstructed.

[0120] This method relies solely on conventional I-V data acquisition, eliminating the need for C-V splitting or RF measurements, thus exhibiting good feasibility and data universality. The final output effective carrier mobility model not only possesses a well-defined functional form with respect to bias but can also be explicitly decomposed into the physical contributions of multiple scattering mechanisms, thereby forming a cryogenic mobility model with explanatory power and scalability.

[0121] Overall, this method has the following main advantages:

[0122] (1) No need to pre-set a mobility model, avoiding empirical model errors.

[0123] (2) It can effectively separate the contributions of strong field and weak field scattering mechanisms, thus enhancing the physical explanatory power.

[0124] (3) It can accurately extract threshold voltage and drain-source parasitic resistance, improving the accuracy of low temperature modeling.

[0125] (4) The method is based only on I-V data and has good potential for automation and modeling integration.

[0126] (5) It is particularly suitable for the extraction of mobility and analysis of scattering mechanism of submicron CMOS devices in the low temperature region (e.g., 1K-50K, 2K-70K, etc.).

[0127] In summary, this invention provides a solid foundation for low-temperature CMOS modeling, mobility physics analysis and quantification, and subsequent low-temperature circuit design, and has good promotion and engineering application value.

[0128] II. Detailed introduction.

[0129] This invention mainly comprises six parts, each with a clear dependency: from theoretical model setting to parameter separation and extraction, ultimately achieving complete reconstruction and physical decomposition of mobility. Each part's input depends on the results of the preceding parts and serves the achievement of the final goal.

[0130] 1. Setting the mobility model.

[0131] In this embodiment of the invention, a theoretical basis for effective mobility is established, enabling both physical interpretation and computational feasibility. To this end, starting from Mathiessen's rule, the inverse of effective carrier mobility is decomposed into a parallel term of strong-field scattering (e.g., surface roughness scattering) and weak-field scattering (e.g., Coulomb scattering), providing a fundamental model for subsequent parameter identification and fitting, expressed as:

[0132] ;

[0133] in, This is a strong-field scattering term, characterizing strong-field scattering; This is a weak-field scattering term, characterizing the behavior dominated by the weak-field mechanism, and mainly affecting the low gate overdrive voltage. area.

[0134] To provide a mathematically clear and fitable expression for the strong-field scattering and weak-field scattering terms, this invention further introduces the concept of Laurent series, considering the strong-field scattering term as the regular part and the weak-field scattering term as the singular part. For the i-th group of devices, the strong-field scattering term... With weak field scattering term It can be expanded into the following form:

[0135] ;

[0136] ;

[0137] in, The channel length with respect to the i-th group of devices under test (Geometric structure) Related strong field scattering fitting parameters, where M+1 is the cutoff order. For the bias-dependent weak-field scattering term function, The channel length with respect to the i-th group of devices under test The relevant geometric scaling factor. It is worth noting that... It absorbs the influence of geometry on weak-field scattering, reflects the locality of Coulomb scattering, and facilitates... This is set as a unified function that depends only on the bias. This decomposition method, while maintaining the physical interpretability of the model, lays the mathematical foundation for subsequent parameter extraction and mechanism decoupling through derivative enhancement and scaling methods.

[0138] 2. Linear region resistance modeling.

[0139] After obtaining the physical decomposition model of mobility (i.e., strong-field scattering and weak-field scattering terms) based on Part 1 above, this invention substitutes it into the measurable linear region resistance expression. This process establishes a bridge between mobility and device geometric parameters, current and voltage measurement data, preparing for subsequent derivative analysis and parameter extraction.

[0140] Construct the following linear region resistance model:

[0141] ;

[0142] in, Let be the drain-source parasitic resistance of the i-th group of devices under test. Let be the channel width of the i-th group of devices under test. The capacitance per unit area of ​​the gate oxide layer. This is the drain-source voltage. Let be the drain-source current of the i-th group of devices under test. This is the channel resistance.

[0143] Combining the two terms obtained from the decomposition in Part 1 above, we define:

[0144] ;

[0145] ;

[0146] The symbols with asterisks and superscripts in the above formula represent the strong and weak field scattering functions in the drain-source resistance.

[0147] Finally, the linear region resistance model is rewritten as follows:

[0148] .

[0149] 3. Eliminate strong field scattering terms and extract threshold voltage.

[0150] Based on the resistance model constructed in Part 2 above, the strong field scattering term It can be modeled as a polynomial expression with a cutoff order of M+1, based on the total source-drain resistance obtained in the previous step. Expression (i.e., linear region resistance model), right The highest power order is M. To enhance the identification of weak-field scattering terms, this invention improves the identification of weak-field scattering terms by adjusting the total source-drain resistance. right Find the nth derivative Processing is used to suppress the smoothing of strong field scattering terms.

[0151] Let the order be denoted as n, and the enhanced resistance model can be obtained through the following formula, expressed as:

[0152] ;

[0153] in, The sign of the nth-order partial derivative. The symbol for the nth-order total derivative. d is the sign of the total derivative. This is the gate-source voltage; Let be the enhanced resistance model for the i-th group of devices under test.

[0154] When making relative comparisons, a reference device (denoted as device 0) is selected. This device has a larger channel length and width, and its small-size effects (such as short-channel threshold offset) are relatively weak. Therefore, its threshold voltage... Traditional methods that do not rely on drain-source parasitic resistance can be used, such as the method described in reference 6 (M. Tsuno, M. Suga, M. Tanaka, K. Shibahara, M. Miura-Mattausch, and M. Hirose, “Physically-based threshold voltage determination for mosfet's of all gate lengths,” IEEE Trans. ElectronDevices, vol. 46, no. 7, pp. 1429–34, 1999.).

[0155] Subsequently, the Shift-and-Ratio method (Reference 7: Y. Taur, D. Zicherman, D. Lombardi, P. Restle, C. Hsu, H. Nanafi, M. Wordeman, B. Davari, and G. Shahidi, “A new 'shift and ratio' method for MOSFET channel-length extraction,” IEEE Electron Device Letters, vol. 13, no. 5, pp. 267–269, 1992.) was used to shift the voltage of the curves for different devices, so that the proportional function was at the optimal voltage offset. The lower convergence is constant, and the proportional function is expressed as:

[0156] .

[0157] The objective function to be optimized is:

[0158] .

[0159] Let the mean of the proportional function be expressed as:

[0160] ;

[0161] in, The gate voltage of the kth sample. For a given gate voltage With voltage offset The scaling function is given by N, where N is the number of samples.

[0162] Optimal voltage offset The threshold voltage offset of the i-th group of devices relative to the reference device By combining the threshold voltage of the reference device, the threshold voltage of the i-th group of devices can be extracted. :

[0163] .

[0164] This invention transforms the threshold voltage extraction problem of small-sized devices into a relative offset relative to a reference device, thereby indirectly achieving robust and accurate results. extract.

[0165] 4. Fit the physical parameters of the weak field scattering term.

[0166] This section builds upon the enhanced resistance model described in Part 3, quantitatively modeling and fitting the weak-field scattering term to clarify the relationship between the scattering mechanism and the bias voltage. The fitting results will be used to isolate the weak-field component from the total source-drain resistance, preparing for the next step of strong-field analysis.

[0167] Based on the physical assumption that weak-field scattering at low temperatures is dominated by Coulomb scattering, the scattering rate is approximately power-law related to the electric field. Therefore, we set:

[0168] .

[0169] For the i-th group of devices, obtain the corresponding threshold voltage. Then, the gate overdrive voltage was calculated. Then pass the gate drive voltage Replace gate-source voltage Substituting the values ​​into the enhanced resistor model, we obtain a new enhanced resistor model. Based on the above settings, we obtain:

[0170] ;

[0171] Wherein, the intermediate parameter K:

[0172] .

[0173] Through the and By performing linear fitting, the power exponent B and amplitude A are extracted, thereby quantitatively characterizing the Coulomb scattering pair. The impact.

[0174] 5. Extract strong field scattering terms and drain-source parasitic resistance.

[0175] After successfully fitting and removing parameters related to the weak-field scattering term, this section focuses on the total resistance. Subtract the obtained weak field scattering function The remaining resistance residuals were analyzed to extract the drain-source parasitic resistance and strong-field scattering parameters. After this part of the modeling was completed, all components of the mobility expression were fully extracted and reconstructed.

[0176] Define residual function :

[0177] ;

[0178] in, Let be the drain-source parasitic resistance of the i-th group of devices under test. It is usually assumed that it is inversely proportional to the channel width and independent of the channel length, i.e.:

[0179] ;

[0180] in, The channel width of the reference device, The drain-source parasitic resistance of the reference device.

[0181] To model the normalized strong field scattering term The bias dependence, referring to the expansion of the strong-field scattering and weak-field scattering terms in Part 1 above, is approximated using a finite-order power form:

[0182] .

[0183] The adoption of this power law form with M = 1 is reasonable for the following reasons:

[0184] (1) In actual low-temperature experiments, the strong field scattering term affects The dependence is usually relatively smooth, especially in the medium to high bias region, where its growth trend can be well approximated by a low-order power function.

[0185] (2) Higher powers are mathematically feasible, but may lead to overfitting, loss of physical meaning, and sensitivity to measurement errors.

[0186] (3) If the residual function The fitting performance exhibits systematic bias, and higher-order fittings (such as...) can be flexibly introduced based on its specific form. This forms an extensible modeling mechanism.

[0187] It mainly reflects the surface roughness scattering mechanism and is weakly correlated with the channel length, which can be approximated as: , yes First order Dependencies can be used in subsequent model refactoring. The calculation, and Approximately , indicating and It is irrelevant; during subsequent fitting, it can be considered as related to... Irrelevant constants.

[0188] Will Substituting into the aforementioned residual function formula, we obtain:

[0189] ;

[0190] In fixed Under the given conditions, for a given Fitting residual function Follow Changes obtained Then obtain Substitute into the formula and subtract Term, fitted residual function and Relationships, extract and This ultimately provides a foundation for formal modeling and parameter extraction of strong-field scattering terms.

[0191] This example uses M=1. When M is greater than 1, a similar method can be used to obtain the result. ,as well as , m=1,…,M.

[0192] 6. Extract the effective carrier mobility.

[0193] With all the parameters defined above, this section recombines the strong-field scattering and weak-field scattering terms to construct a complete expression for the effective carrier mobility. This expression can be used to analyze mobility behavior under different bias conditions and supports circuit modeling and performance evaluation at low temperatures.

[0194] Based on model reconstruction:

[0195] ;

[0196] The above equation is the analytical calculation form of the effective carrier mobility of the device under test, which decouples the effective carrier mobility into a strong field scattering term. and weak field scattering term It can quantitatively decouple the contributions of strong-field scattering and weak-field scattering terms, as shown in the above equation. The parameters of the strong field scattering term extracted in the previous section , calculate, Then, the power exponent B and amplitude A, which were extracted earlier from the power law model, are used for calculation.

[0197] Based on the definition of linear regions:

[0198] .

[0199] In this embodiment of the invention, the two expressions are essentially the same. The former is the model form, and the latter is the definition of the linear region. The corresponding model form can be obtained by mathematically analyzing the definition of the linear region. In addition, the two correspond to different algorithms for effective carrier mobility, which can be used to verify the self-consistency of the model.

[0200] Based on the above-mentioned solution provided by the present invention, an effective carrier mobility extraction with high robustness, no model dependence, and physical decoupling is finally achieved.

[0201] Through the above description of the embodiments, those skilled in the art can clearly understand that the above embodiments can be implemented by software, or by using software plus necessary general-purpose hardware platforms. Based on this understanding, the technical solutions of the above embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, mobile hard drive, etc.), including several instructions to cause a computer device (such as a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0202] Example 2

[0203] This invention also provides a low-temperature CMOS mobility extraction system, which is mainly used to implement the methods provided in the foregoing embodiments, such as... Figure 2 As shown, the system mainly includes:

[0204] The mobility model decomposition unit is used to decompose the inverse of the effective carrier mobility into strong field scattering and weak field scattering terms based on the carrier transport mechanism.

[0205] The linear region resistance modeling unit is used to combine strong field scattering terms and weak field scattering terms to construct a linear region resistance model;

[0206] The threshold voltage extraction unit is used to obtain the enhanced resistance model by combining the linear region resistance model and derivative processing technology, and to extract the threshold voltage of the device under test by utilizing the threshold voltage offset between the device under test and the selected reference device.

[0207] The weak-field scattering term physical parameter fitting unit is used to quantitatively model and power-law fit the weak-field scattering term using the enhanced resistance model, and obtain the power-law model parameters.

[0208] The strong field scattering term parameter and drain-source parasitic resistance extraction unit is used to extract the strong field scattering term parameters and the drain-source parasitic resistance of the reference device by combining the power law model parameters.

[0209] The effective carrier mobility calculation and contribution quantization unit is used to calculate the effective carrier mobility of the device under test (DUT) using the drain-source parasitic resistance of the reference device and the current and voltage measurement data of the DUT. It also reconstructs the effective carrier mobility model mathematically, incorporating power-law model parameters. and strong field scattering parameters The contributions of strong-field scattering and weak-field scattering terms are quantified.

[0210] Those skilled in the art will understand that, for the sake of convenience and brevity, the above-described division of functional modules is used as an example. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the system can be divided into different functional modules to complete all or part of the functions described above.

[0211] Example 3

[0212] The present invention also provides a processing device, such as Figure 3 As shown, it mainly includes: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the method provided in the foregoing embodiments.

[0213] Furthermore, the processing device also includes at least one input device and at least one output device; in the processing device, the processor, memory, input device, and output device are connected via a bus.

[0214] In this embodiment of the invention, the specific types of the memory, input device, and output device are not limited; for example:

[0215] Input devices can be touchscreens, image acquisition devices, physical buttons, or mice, etc.

[0216] The output device can be a display terminal;

[0217] The memory can be random access memory (RAM) or non-volatile memory, such as disk storage.

[0218] Example 4

[0219] The present invention also provides a readable storage medium storing a computer program that, when executed by a processor, implements the method provided in the foregoing embodiments.

[0220] In this embodiment of the invention, the readable storage medium is a computer-readable storage medium and can be disposed in the aforementioned processing device, for example, as a memory in the processing device. Furthermore, the readable storage medium can also be any medium capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory (ROM), magnetic disk, or optical disk.

[0221] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. The information disclosed in the background section is intended only to enhance the understanding of the overall background technology of the present invention and should not be construed as an admission or implication in any way that such information constitutes prior art known to those skilled in the art.

Claims

1. A method for extracting mobility in low-temperature CMOS, characterized in that, include: Based on the carrier transport mechanism, the reciprocal of the effective carrier mobility is decomposed into a strong-field scattering term and a weak-field scattering term; By combining strong-field scattering terms and weak-field scattering terms, a linear region resistance model is constructed. An enhanced resistance model is obtained by combining the linear region resistance model and derivative processing techniques, and the threshold voltage of the device under test is extracted by utilizing the threshold voltage offset between the device under test and the selected reference device. The weak-field scattering term was quantitatively modeled and fitted using an enhanced resistance model to obtain the power-law model parameters. The parameters of the strong field scattering term and the drain-source parasitic resistance of the reference device are extracted by combining the parameters of the power-law model; By utilizing the drain-source parasitic resistance of the reference device and combining it with the current and voltage measurement data of the device under test, the effective carrier mobility of the device under test is calculated. The effective carrier mobility model is then reconstructed through mathematical analysis, and the contributions of the strong-field scattering term and the weak-field scattering term are quantified by combining the power-law model parameters and the strong-field scattering term parameters.

2. The mobility extraction method for low-temperature CMOS according to claim 1, characterized in that, The method of decomposing the inverse of the effective carrier mobility into strong-field scattering and weak-field scattering terms based on the carrier transport mechanism includes: Based on the carrier transport mechanism, the effective carrier mobility The reciprocal form of is decomposed into strong-field scattering and weak-field scattering terms according to Mathiessen's rule, as follows: ； Among them, Mathiessen's rule is Mathiessen's rule. Indicates the given gate overdrive voltage Effective carrier mobility with channel length L of the device For strong field scattering, This is a weak-field scattering term; For the i-th group of devices, the strong field scattering term With weak field scattering term They are represented as follows: ； ； in, The channel length with respect to the i-th group of devices under test The relevant strong-field scattering fitting parameters, where M+1 is the cutoff order, m is the order index, and the superscript m+1 indicates the m+1 power. For the bias-dependent weak-field scattering term function, The channel length with respect to the i-th group of devices under test Related geometric scaling factors.

3. The mobility extraction method for low-temperature CMOS according to claim 2, characterized in that, The method of combining strong-field scattering and weak-field scattering terms to construct a linear region resistance model includes: For the i-th group of devices under test, the corresponding linear region resistance model is expressed as: ； in, Let be the total source-drain resistance of the i-th group of devices under test. Let be the drain-source parasitic resistance of the i-th group of devices under test. Let be the channel width of the i-th group of devices under test. The capacitance per unit area of ​​the gate oxide layer. Indicates the given gate overdrive voltage With the length of the channel Effective carrier mobility at that time; strong field scattering term and Divide by respectively , represented as: ； ； in, This represents the strong-field scattering component in the linear resistivity model. Indicates the separation geometry factor in the linear region resistance model The weak-field scattering component afterwards; The reconstructed linear region resistance model is expressed as: 。 4. The mobility extraction method for low-temperature CMOS according to claim 3, characterized in that, The enhanced resistance model is obtained by combining the linear region resistance model and derivative processing techniques, and the threshold voltage of the device under test (DUT) is extracted using the threshold voltage offset between the DUT and a selected reference device. Using the nth-order derivative processing technique, the enhanced resistance model is obtained, expressed as: ； in, The sign of the nth-order partial derivative. The symbol for the nth-order total derivative. d is the sign of the total derivative. This is the gate-source voltage; Let i be the enhanced resistance model for the i-th group of devices under test; Choose a reference device whose enhancement resistance model is denoted as . The enhancement resistance model of the i-th group of devices is modeled using the scaling method. Gate-source voltage Perform a horizontal offset operation so that the proportional function is at the optimal voltage offset. The proportional function converges to a constant. Represented as: ； in, For the i-th group of devices under test, at voltage Horizontal offset is The nth derivative of the resistance at time n; The objective function to be optimized is: ； in, The gate voltage of the kth sample. For a given gate voltage With voltage offset The proportional function of time, The mean of the proportional function; Optimal voltage offset The threshold voltage of the i-th group of devices relative to the reference device The offset is combined with the threshold voltage of the reference device to extract the threshold voltage of the i-th group of devices. : 。 5. The mobility extraction method for low-temperature CMOS according to claim 4, characterized in that, The quantitative modeling and power-law fitting of the weak-field scattering term using the enhanced resistance model, to obtain the power-law model parameters, include: set up: ； Set the intermediate parameter K: ； Where A is the amplitude, B is the power exponent, and both are parameters of the power law model; n is the stage in derivative processing, and j is the order index; For the i-th group of devices, obtain the corresponding threshold voltage. Then, the gate overdrive voltage was calculated. Then pass the gate drive voltage Replace gate-source voltage Substituting the values ​​into the enhanced resistor model, we obtain a new enhanced resistor model. Combining the above settings with the intermediate parameter K, we obtain: ； in, It is the natural logarithm function; Through the and Perform linear fitting to extract the power exponent B and the magnitude A.

6. The mobility extraction method for low-temperature CMOS according to claim 5, characterized in that, The extraction of strong-field scattering parameters by combining power-law model parameters, and the extraction of drain-source parasitic resistance of the device under test thereby, includes: Define residual function : ； in, The total source-drain resistance of the i-th group of devices under test; the drain-source parasitic resistance of the i-th group of devices under test. Represented as: , The channel width of the reference device, The drain-source parasitic resistance of the reference device; For the normalized strong field scattering term, The M-order polynomial; parameters Fitting parameters with strong field scattering Through the Obtained by polynomial fitting; Let the strong field scattering fitting parameters Indicates and If it is irrelevant, then: ； In fixed Under the given conditions, for a given For the residual function and Polynomial fitting is performed to obtain the strong field scattering fitting parameters. , and then obtain Substitute into the residual function minus Term, through fitting function and The linear relationship is extracted. and This part obtains the fitting parameters for strong field scattering. as well as All of these are parameters belonging to the strong field scattering term.

7. The mobility extraction method for low-temperature CMOS according to claim 6, characterized in that, The method of calculating the effective carrier mobility of the device under test (DUT) using the drain-source parasitic resistance of the reference device and combining it with the current and voltage measurement data of the DUT, and reconstructing the effective carrier mobility model through mathematical analysis, and quantifying the contributions of the strong-field scattering term and the weak-field scattering term by combining the power-law model parameters and the strong-field scattering term parameters, includes: The effective carrier mobility of the device under test is calculated using the following formula. : ； Among them, the drain-source parasitic resistance of the i-th group of devices under test Utilizing the drain-source parasitic resistance of the reference device Calculated; This is the drain-source voltage. Let be the drain-source current of the i-th group of devices under test; Furthermore, the formula for calculating effective carrier mobility is transformed into an effective carrier mobility model through mathematical analysis, which is expressed as: ； in, Using the extracted strong field scattering fitting parameters as well as calculate, The calculation is performed using the obtained power-law model parameters.

8. A low-temperature CMOS mobility extraction system, characterized in that, To implement the method according to any one of claims 1 to 7, comprising: The mobility model decomposition unit is used to decompose the inverse of the effective carrier mobility into strong field scattering and weak field scattering terms based on the carrier transport mechanism. The linear region resistance modeling unit is used to combine strong field scattering terms and weak field scattering terms to construct a linear region resistance model; The threshold voltage extraction unit is used to obtain the enhanced resistance model by combining the linear region resistance model and derivative processing technology, and to extract the threshold voltage of the device under test by utilizing the threshold voltage offset between the device under test and the selected reference device. The weak-field scattering term physical parameter fitting unit is used to quantitatively model and power-law fit the weak-field scattering term using the enhanced resistance model, and obtain the power-law model parameters. The strong field scattering term parameter and drain-source parasitic resistance extraction unit is used to extract the strong field scattering term parameters and the drain-source parasitic resistance of the reference device by combining the power law model parameters. The effective carrier mobility calculation and contribution quantization unit is used to calculate the effective carrier mobility of the device under test by using the drain-source parasitic resistance of the reference device and combining the current and voltage measurement data of the device under test. It also reconstructs the effective carrier mobility model through mathematical analysis and quantifies the contribution of the strong field scattering term and the weak field scattering term by combining the parameters of the strong field scattering term.

9. A processing device, characterized in that, include: One or more processors; Memory, used to store one or more programs; Wherein, when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method as described in any one of claims 1 to 7.

10. A readable storage medium storing a computer program, characterized in that, When a computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

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