Low-temperature CMOS carrier MFP and microscopic parameter extraction method and system

Abstract

The invention discloses a low-temperature CMOS carrier MFP and microscopic parameter extraction method and system, which are corresponding schemes, in the scheme, a carrier MFP extraction model for eliminating a microscopic unknown quantity is constructed by utilizing a geometric scaling rule of quasi-ballistic transport and an existing effective mobility extraction technology, and an MFP extraction model for eliminating the microscopic unknown quantity is constructed by utilizing the geometric scaling rule of quasi-ballistic transport and the existing effective mobility extraction technology; the MFP extracted by the carrier MFP extraction model is ensured to be a pure experiment observation value on the basis that effective quality, Fermi velocity and scattering time do not need to be predicted based on the self-consistency of macroscopic current and voltage data along with the change of channel length; meanwhile, on the basis, the microcosmic parameters are decoupled, so that the decoupled microcosmic parameters are extracted one by one; compared with an existing scheme, the method can be directly applied to a standard wafer-level test board in the industry, MFP distribution of hundreds of devices can be rapidly counted, and a feasible engineering scheme is provided for low-temperature process monitoring.

Description

Technical Field

[0001] This invention relates to the field of low-temperature CMOS (Complementary Metal-Oxide-Semiconductor) carrier MFP and micro-parameter extraction technology, and particularly to a method and system for low-temperature CMOS carrier MFP and micro-parameter extraction. Background Technology

[0002] With the rapid development of quantum computing, deep space exploration, and high-sensitivity sensor technologies, low-temperature CMOS (Cryo-CMOS) circuits operating in the liquid helium temperature range (e.g., 4K, where K is Kelvin) have become the core interface technology for realizing quantum bit control and readout. As semiconductor process nodes advance to the deep sub-micron and even nanoscale, the channel length L of transistors continues to shrink, gradually approaching or even becoming smaller than the mean free path of charge carriers. (Mean Free Path, MFP). At this scale, the carrier transport mechanism undergoes a fundamental shift, moving from the traditional drift-diffusion mode to the quasi-ballistic transport region. In this region, mean free path and ballistic efficiency replace the traditional mobility, becoming the core physical quantities that determine the limiting performance of devices (such as limiting transconductance and injection velocity) and circuit design.

[0003] At the industrial application level, as cryogenic electronics moves from the laboratory to large-scale applications, new challenges are posed to device characterization: (1) The need for wafer-level process monitoring (WAT): Wafer foundries urgently need a method to quickly monitor interface quality and process fluctuations at low temperatures. However, traditional micro-parameter measurements (such as SdH oscillations and Hall effect) rely on expensive superconducting magnets and special Hall bar structures, with long testing cycles, and cannot be deployed on automated probe stations on the production line.

[0004] (2) The need for accurate PDK modeling: Existing industry standard compact models (such as BSIM) are mostly developed based on room temperature physics. When directly extrapolated to low temperature (such as 4K), the inability to accurately describe ballistic transport and quantum effects often leads to huge errors in current and timing predictions.

[0005] However, accurately extracting carrier MFP and related microphysical parameters (such as effective mass) at low temperatures is crucial. Heat injection speed (etc.) faces enormous challenges. Currently, the mainstream extraction methods mainly include the following three, but they all have significant shortcomings in practical engineering applications.

[0006] (1) Magnetic transport measurement: This is the gold standard in fundamental physics research. By measuring the oscillation of conductivity (SdH effect) or the Hall effect under a strong magnetic field, researchers can accurately separate the quantum lifetime and transport lifetime of charge carriers. However, its drawback is that this method has extremely high requirements for the test environment, usually requiring extremely low temperatures at the milliKelvin (mK) level and strong magnetic fields at several Tesla (Tesla). More importantly, it requires the device under test to have a special Hall bar geometry, which cannot be directly applied to standard MOSFET (metal-oxide-semiconductor transistor) transistors in large-scale integrated circuits. Therefore, this method is limited to basic materials research in the laboratory and cannot meet the needs of industry for rapid screening, process monitoring, and modeling of wafer-level devices.

[0007] For example, magnetic transport measurement can be found in reference 1: Ben Shalom M et al. Shubnikov–De HaasOscillations in SrTiO3 / LaAlO3 Interface. Phys Rev Lett, 2010, 105(20): 206401.

[0008] (2) Theoretical derivation based on microscopic physical parameters: A common approach is based on physical constitutive relations. The derivation is performed; among which, Let represent the macroscopic mobility and q represent the charge. However, its drawback is that although the above physical constitutive relations are rigorous, their application in practical nanodevices is extremely difficult. This is because, under extremely low temperatures and confined nanoscale spaces, the effective mass of charge carriers is limited. and heat injection rate It is no longer a bulk material constant, but is strongly modulated by quantum confinement, mechanical stress engineering, and a non-ideal Fermi-Dirac distribution. Experimentally, it is almost impossible to accurately measure these microscopic quantities in specific devices. Researchers are often forced to use theoretical values ​​of room temperature or bulk materials in their calculations. This misapplication introduces huge systematic errors, resulting in a significant reduction in the reliability of the extracted MFP values.

[0009] (3) Traditional IV (current-voltage) characteristic extraction method: This type of method attempts to rely only on the linear region Extracting features is the lowest-cost method, among which... This is the drain-source current. The gate-source voltage is used, but existing technologies often have serious model defects: (3.1) Incomplete de-embedding of parasitic resistance: At low temperatures, due to the incomplete ionization of impurities in the drain-source region (Freeze-out), the drain-source parasitic resistance... A sharp increase, if not accurately eliminated The voltage drop will be incorrectly attributed to channel scattering, resulting in a serious underestimation of MFP; (3.2) Extraction algorithm failure: The existing Y function method (Reference 2: Ghibaudo G, Balestra F. A method for MOSFET parameter extraction at very low temperature. Solid-State Electronics, 1989, 32(3): 221-223) relies on the assumption that mobility changes in a bell shape with gate voltage, but this often does not hold true in low-temperature short-channel devices; The method based on linear regression of channel resistance and length (Reference 3: Niu G, Cressler JD, Mathew SJ, Subbanna S. A total resistance slope-based effective channel mobility extraction method for deep submicrometer CMOS technology. IEEE Transactions on Electron Devices, 1999, 46(9): 1912-1914.) assumes that mobility is independent of length and ignores the ballistic enhancement effect under short channels; while the method based on small signal output conductivity (Reference 4: Jazaeri F, Pezzotta A, Enz C.) (3.2) Confusion of physical mechanisms: Traditional methods cannot distinguish the contributions of different scattering mechanisms (such as Coulomb scattering and surface rough scattering), resulting in the extraction result being a mixed average of multiple mechanisms, and the physical image is blurred.

[0010] In summary, there is an urgent need for a low-temperature MFP and micro-parameter extraction method that does not require special test structures, does not rely on preset micro-parameters, and can accurately eliminate the influence of parasitic resistance, in order to support the process optimization and accurate modeling of low-temperature chips. Summary of the Invention

[0011] The purpose of this invention is to provide a method and system for extracting microscopic parameters of low-temperature CMOS carrier MFPs. This method and system do not require special test structures, do not rely on preset microscopic parameters, and can accurately eliminate the influence of parasitic resistance. The entire scheme constructs a complete physical logic chain from microscopic constitutive relations to macroscopic transport models. By establishing a strict mapping between macroscopic observations and microscopic physical quantities, self-consistent parameter extraction is achieved, which can support the process optimization and accurate modeling of low-temperature chips.

[0012] The objective of this invention is achieved through the following technical solution: A method for low-temperature CMOS carrier MFP and micro-parameter extraction includes: Based on the quasi-ballistic transport model and effective mobility extraction technology, a carrier MFP extraction model that eliminates microscopic unknowns is constructed, expressed as: Among them, strong-field scattering and weak-field scattering terms are obtained based on the effective mobility extraction technique. This is a strong-field scattering term; Base value coefficient, B is the length modulation coefficient, and B is the power exponent. , B and B are the fitting parameters in the carrier MFP extraction model, and they are all obtained using the weak field scattering term. This is the effective gate overdrive voltage; For carrier MFP, MFP is the mean free path; In a temperature range below a set temperature, a group of CMOS devices with different channel lengths are measured, and the effective gate overdrive voltage is extracted from the measured current and voltage data; wherein, CMOS is complementary metal-oxide semiconductor. Based on the effective gate overdrive voltage, a resistance model is constructed to decouple the effective mobility, and the fitting parameters in the carrier MFP extraction model are solved. The solved fitting parameters and the effective gate overdrive voltage are substituted into the carrier MFP extraction model to obtain the carrier MFP that varies with the effective gate overdrive voltage. The micro-parameters are decoupled based on the carrier MFP that varies with the effective gate over-drive voltage and the measured current data, and the decoupled micro-parameters are extracted one by one.

[0013] A low-temperature CMOS carrier MFP and micro-parameter extraction system, used to implement the aforementioned method, includes: The carrier MFP extraction model building unit is used to construct a carrier MFP extraction model that eliminates microscopic unknowns based on the quasi-ballistic transport model and effective mobility extraction technology, and is represented as follows: Among them, strong-field scattering and weak-field scattering terms are obtained based on the effective mobility extraction technique. This is a strong-field scattering term; Base value coefficient, B is the length modulation coefficient, and B is the power exponent. , B and B are the fitting parameters in the carrier MFP extraction model, and they are all obtained using the weak field scattering term. This is the effective gate overdrive voltage; For carrier MFP, MFP is the mean free path; The current and voltage data acquisition and preprocessing unit is used to measure a group of CMOS devices with different channel lengths in a temperature range below a set temperature, and extract the effective gate over-drive voltage from the measured current and voltage data; wherein, CMOS is complementary metal-oxide semiconductor. The effective mobility decoupling and fitting parameter solving unit is used to decouple the effective mobility based on the effective gate over-drive voltage by constructing a resistance model and solving for the fitting parameters in the carrier MFP extraction model. The carrier MFP extraction unit is used to input the solved fitting parameters and the effective gate over-drive voltage into the carrier MFP extraction model to obtain the carrier MFP that varies with the effective gate over-drive voltage. The micro-parameter decoupling and extraction unit is used to decouple the micro-parameters based on the carrier MFP that varies with the effective gate over-drive voltage and the measured current data, and extract the decoupled micro-parameters one by one.

[0014] As can be seen from the technical solution provided by the present invention, by utilizing the geometric scaling law of quasi-ballistic transport and existing effective mobility extraction technology, a carrier MFP extraction model that eliminates microscopic unknowns is constructed. Furthermore, based on the self-consistency of macroscopic current and voltage data as a function of channel length, it is not necessary to know the effective mass, Fermi velocity, or scattering time, ensuring that the MFP extracted by the carrier MFP extraction model is a pure experimental observation value. At the same time, on this basis, the microscopic parameters are decoupled, thereby extracting the decoupled microscopic parameters one by one. Compared with existing solutions, the present invention can be directly applied to industrial standard wafer-level test benches, and can quickly statistically analyze the MFP distribution of hundreds or thousands of devices, providing a feasible engineering solution for low-temperature process monitoring. Attached Figure Description

[0015] 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.

[0016] Figure 1This is a flowchart of a low-temperature CMOS carrier MFP and micro-parameter extraction method provided in an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of a low-temperature CMOS carrier MFP and micro-parameter extraction system provided in an embodiment of the present invention. Detailed Implementation

[0018] 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.

[0019] First, the following explanations are provided for the terms that may be used in this article: 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.

[0020] 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.

[0021] The following provides a detailed description of the low-temperature CMOS carrier MFP and micro-parameter extraction method and system 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. Where specific conditions are not specified in the embodiments of this invention, they should be performed according to conventional conditions in the art or conditions recommended by the manufacturer. Instruments used in the embodiments of this invention, unless otherwise specified by the manufacturer, are all commercially available conventional products.

[0022] Example 1 This invention provides a method for low-temperature CMOS carrier MFP and micro-parameter extraction, such as... Figure 1 As shown, it mainly includes the following steps: Step 1: Based on the quasi-ballistic transport model and effective mobility extraction technology, construct a carrier MFP extraction model to eliminate microscopic unknowns.

[0023] The preferred implementation method for this step is as follows:

[0024] (1) Quasi-ballistic transport model refers to the device channel conductance G DS From the ballistic limiting conductivity G bal and transmission probability A joint decision, expressed as: ; Among them, transmission probability The transport probability represents the probability that a charge carrier successfully crosses the channel without being scattered back to the source. Depending on the ratio of channel length L to MFP, it is expressed as: .

[0025] (2) In the traditional drift-diffusion model, the device channel conductance in the linear region With effective migration rate The relationship between the channel length L and the channel length L is as follows: ; in, Carrier concentration, Let q represent the channel width and q represent the charge. In the diffusion-limited case ( In this case, transmission probability Combining the two, we can obtain: ; .

[0026] Returning to the general formula for the transmission coefficient across the entire trajectory and propagation range: ; in, For effective migration rate, For diffusion mobility, The sign is much larger than the symbol.

[0027] (3) By simplifying the above general formula and taking its reciprocal, we obtain: .

[0028] Based on the effective mobility extraction technique, the reciprocal of the effective mobility is decomposed into a strong-field scattering term and a weak-field scattering term, expressed as: ; in, For strong field scattering, This is a weak-field scattering term. This is the effective gate drive voltage.

[0029] Weak field scattering term Represented as: ; in, For the bias-dependent weak-field scattering term function, A is a geometric scaling factor related to the device channel length L. The amplitude parameter introduced during modeling, The coefficients of the weak-field scattering term related to the channel length L are expressed as: , Base value coefficient, B is the length modulation coefficient; B is the power exponent. , B and B are the fitting parameters in the carrier MFP extraction model, both obtained through the weak field scattering term.

[0030] Will Combining the expression with the inverse decomposition expression of the effective mobility, we obtain the following relationship: .

[0031] For example, the effective mobility extraction technology can refer to existing solutions, such as the Chinese invention patent "Method, System, Device and Storage Medium for Mobility Extraction of Low Temperature CMOS" with authorization announcement number CN120688425B.

[0032] (4) General formula based on effective mobility and The expression establishes a physical mapping, and the above relationship is modified to obtain the carrier MFP extraction model that eliminates microscopic unknowns, expressed as: .

[0033] Preferably, the general formula based on effective mobility is... The expression establishes a physical mapping and modifies the above relation, including: Establish the following physical mapping: , ;in, It is the reciprocal of the diffusion mobility. This is a ballistic correction item.

[0034] Based on the above physical mapping, the ratio of the ballistic correction term to the reciprocal of the diffusion mobility is calculated, excluding the microscopic unknowns, i.e., the diffusion mobility. ,get: .

[0035] Simplifying the above equation yields the carrier MFP extraction model that eliminates microscopic unknowns.

[0036] Step 2: In the low-temperature region, measure a group of CMOS devices with different channel lengths, and extract the effective gate over-drive voltage from the measured current and voltage data. ).

[0037] The preferred implementation method for this step is as follows: (1) In a temperature range below the set temperature (referred to as the low temperature range), a group of CMOS devices with different channel lengths were subjected to linear region testing and saturation region testing respectively, and the corresponding current and voltage data were obtained respectively; wherein, the current and voltage data corresponding to the linear region test is the drain-source current of the linear region. With gate-source voltage The data, including the current and voltage data corresponding to the saturation region test, represents the drain-source current in the saturation region. With gate-source voltage data.

[0038] In this embodiment of the invention, the set temperature can be set according to the actual situation. For example, it can be between 70K and 30K. Taking 70K and 30K as examples, the corresponding low temperature range can be 1K~70K or 1K~30K.

[0039] (2) For linear region testing, the gate-source voltage is used. Calculate the threshold voltage in the linear region And from this, the effective gate overdrive voltage in the linear region can be calculated. .

[0040] (3) For saturation region testing, combine the drain-source current in the linear region. and saturation region drain-source current In the subthreshold region, an objective function is constructed to find the optimal voltage shift, and the threshold voltage in the linear region is utilized. The threshold voltage of the saturation region is calculated using the optimal voltage shift. And from this, the effective gate overdrive voltage in the saturation region can be calculated. .

[0041] Preferably, the objective function is constructed in the subthreshold region to find the optimal voltage shift, and the threshold voltage in the linear region is used. The threshold voltage of the saturation region is calculated using the optimal voltage shift. include: Selecting the drain-source current in the linear region and the drain-source current in the saturation region of the same CMOS device, in the subthreshold region Construct the following objective function to find the optimal voltage shift: ; in, This represents the optimal voltage shift. To represent any voltage shift, the function This indicates the minimum value of the subsequent modulo. As the optimal voltage shift;

[0042] Using the threshold voltage of the linear region The threshold voltage of the saturation region is calculated using the optimal voltage shift. , represented as: .

[0043] Step 3: Based on the effective gate over-drive voltage, construct a resistance model to decouple the effective mobility and solve for the fitting parameters in the carrier MFP extraction model.

[0044] The preferred implementation method for this step is as follows: (1) Utilizing the effective gate overdrive voltage in the linear region Construct a system that includes drain-source parasitic resistance resistance model : ; Where W is the channel width and L is the channel length. The capacitance per unit area of ​​the gate oxide layer; For strong field scattering, For weak-field scattering terms, these two terms are derived by decomposing the reciprocal of the effective mobility using an effective mobility extraction technique and incorporating it into the effective gate overdrive voltage in the linear region. get.

[0045] (2) By using derivative-enhanced fitting and based on effective mobility extraction technology, drain-source parasitic resistance can be eliminated. And physically separate the strong field scattering term With weak field scattering term , where parameters and This can be derived based on the effective mobility extraction technique. Specifically, referring to the example of the effective mobility extraction technique provided above, it can be obtained using the enhanced resistance model. right The intercept and slope of the linear fit are derived here. The sign of the partial derivative. This is the nth-order partial derivative. Considering that the principle of the enhanced resistance model involved here can also be found in the example of effective mobility extraction technology provided earlier, it will not be elaborated upon further. Then, for... about Perform linear fitting This allows us to obtain the fitting parameters in the carrier MFP extraction model. .

[0046] Step 4: Substitute the solved fitting parameters and the effective gate overdrive voltage into the carrier MFP extraction model to obtain the carrier MFP that varies with the effective gate overdrive voltage.

[0047] In this embodiment of the invention, the solved fitting parameters and the effective gate over-drive voltage of the linear region are... By substituting the carrier MFP extraction model, the carrier MFP that varies with the effective gate over-drive voltage can be calculated.

[0048] Step 5: Decouple the micro parameters based on the carrier MFP that varies with the effective gate over-drive voltage and the measured current data, and extract the decoupled micro parameters one by one.

[0049] In this embodiment of the invention, the linear region ballistic rate is calculated using the carrier MFP, which varies with the effective gate overdrive voltage. Combined with the drain-source current in the saturation region The micro-parameters are decoupled, and each decoupled micro-parameter is calculated individually, including: effective mass, theoretical thermal injection rate, and ballistic rate in the saturation region. .

[0050] Preferred methods for calculating effective mass include:

[0051] Based on the ballistic injection model in the saturation region, we obtain: ; Where W is the channel width, The capacitance per unit area of ​​the gate oxide layer. BE is the heat injection velocity; BE is the ballistic rate, which is the ballistic rate in the linear region. Then the preliminary calculated heat injection rate is obtained. : .

[0052] According to semiconductor carrier statistics, the thermal injection rate and effective mass satisfy the following Fermi-Dirac statistical relationship: ; in, Boltzmann's constant, Absolute temperature Let π be the mathematical constant, e be the natural constant, and ln be the natural logarithm. For the Fermi-Dirac integral, To reduce the Fermi level.

[0053] When the charge carriers are in a strongly degenerate state, the above equation can be rewritten to obtain the following analytical relation: ; in, To reduce Planck's constant, The capacitance per unit area of ​​the gate oxide layer. Let q be the Fermi velocity and q be the charge.

[0054] Select a preset field strength inversion region as the extraction window, and extract the effective gate overdrive voltage within the extraction window. Substituting the analytical relationship into the effective gate overdrive voltage The initially calculated heat injection rate Substituting the analytical relation as Calculate the effective mass .

[0055] Preferably, the theoretical thermal injection velocity and the ballistic rate in the saturation zone are calculated. The method is as follows: Combined with effective quality and the effective gate overdrive voltage in the saturation region The theoretical heat injection rate was calculated using the analytical relationship between heat injection rate and effective mass. ; Combined with the theoretical heat injection rate Drain-source current in saturation region With the effective gate overdrive voltage in the saturation region Calculate the ballistic rate in the saturation region .

[0056] 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.

[0057] I. Overall Description of the Plan

[0058] The solution provided in this invention constructs a complete physical logic chain from microscopic constitutive relations to macroscopic transport models. By establishing a rigorous mapping between macroscopic observables (i.e., macroscopic mobility) and microscopic physical quantities (i.e., microscopic parameters), it achieves self-consistent parameter extraction. The main principles of each part are introduced below.

[0059] 1. Derivation of the constitutive relationship between microscopic parameters and macroscopic mobility.

[0060] In semiconductor physics, mean free path Compared with macroscopic migration rate Relationship This derivation is based on the classical Drude model (a theory of electron transport in metals) and the kinematic definition. This invention uses this as a bridge connecting the macroscopic and microscopic worlds; the detailed derivation is as follows: (A1) Definition of migration rate based on the Drude model: Macro-migration rate This describes the average drift velocity of charge carriers under a unit electric field. At the microscopic level, according to the momentum balance equation, it consists of the charge q, effective mass, and other parameters. And momentum relaxation time (i.e., mean scattering time) Decide: .

[0061] (A2) Kinematic definition of mean free path: mean free path Defined as the average distance a charge carrier travels between two consecutive scattering events. Within the quasi-ballistic transport framework, this distance is determined by the characteristic thermal injection velocity of the charge carrier. and mean scattering time Decide: .

[0062] (A3) Statistical relationship between thermal injection velocity and Fermi velocity: For the low-temperature (e.g., 4K) strong inversion region of interest in this invention, the two-dimensional electron gas in the channel is in a strongly degenerate state. At this time, the carriers in the velocity space obey the Fermi-Dirac statistical step approximation, and the radius of the fill is the Fermi velocity. Fermi circle. Heat injection rate. Defined as the carriers injected into the channel at the source end within half the Fermi circle ( The average unidirectional velocity within ) This refers to the statistical average of the velocity components of the charge carriers injected into the channel from the source (from the source to the drain) along the channel direction. It can be obtained by performing a velocity-weighted integral over a semi-circular region, and its value is related to the Fermi velocity. The following specific geometric statistical relationship exists: ; The coefficients mentioned above It is the key theoretical basis for connecting experimental observations (thermal injection rate) with material band parameters (Fermi velocity and effective mass).

[0063] (A4) Simultaneous elimination to derive the constitutive equation: The average scattering time in (A1) above... Substituting the expression into (A2) above, the average scattering time, which is difficult to measure directly, is eliminated. That is, to obtain the macroscopic mobility of the connection. Constitutive equations with microscopic parameters: .

[0064] 2. Derivation of the mapping between the quasi-ballistic transport model and the IV decoupling parameters.

[0065] In order to achieve effective quality without prior knowledge and heat injection rate Directly extract the mean free path in the case of This invention introduces a quasi-ballistic transport model and establishes a mathematical mapping between it and experimental decoupling parameters.

[0066] (B1) Quasi-ballistic conductance: Device channel conductance G DS From the ballistic limiting conductivity G bal and transmission probability A joint decision, expressed as: ; Among them, transmission probability This represents the probability that a charge carrier successfully crosses the channel without being scattered back to the source. According to the quasi-ballistic transport model, the transport probability is... Depending on the ratio of channel length L to MFP, it is expressed as: .

[0067] (B2) Compare the above quasi-ballistic conductance with the traditional expression for diffusion transport conductance. Jointly established, among which, This represents the inversion layer charge density. When... At the long channel limit, transport degenerates into diffusion dominance, and the mobility approaches the diffusion mobility. Therefore, by calibrating the model, the general formula for effective mobility is obtained: ; in, For effective migration rate, For diffusion mobility, The sign is much larger than the symbol.

[0068] (B3) Linearization of the reciprocal form and physical mapping: Taking the reciprocal of the above general formula yields: .

[0069] Meanwhile, based on the effective mobility extraction technique, the reciprocal of the effective mobility is decomposed into a strong-field scattering term and a weak-field scattering term, expressed as: ; in, For strong field scattering, This is a weak-field scattering term. This is the effective gate drive voltage.

[0070] Weak field scattering term Represented as: .

[0071] Extracted from CMOS devices with different communication lengths L Data analysis confirmed this. As it changes linearly with 1 / L, a linear fit is performed to obtain: ; in, The coefficients of the weak-field scattering term are related to the channel length L. Base value coefficient, is the length modulation coefficient.

[0072] Will The expression is combined with the inverse factorization expression of the effective mobility to obtain the effective mobility. The reciprocal of the product and 1 / L are related as follows: .

[0073] General formula based on effective mobility and Expressions establish physical mappings: ,in, As the reciprocal of the diffusion mobility, the above physical mapping confirms the strong field scattering term and the basic coefficients. It is independent of the channel length L and corresponds to the diffusion limit under long channels.

[0074] ;in, As a ballistic correction term, the above physical mapping confirms... The linear variation with 1 / L reflects the quasi-ballistic effect under short channel conditions.

[0075] (B4) Construct a carrier MFP extraction model to eliminate microscopic unknowns.

[0076] Based on the above physical mapping, the ratio of the ballistic correction term to the reciprocal of the diffusion mobility is calculated to eliminate microscopic unknowns, i.e., the diffusion mobility. ,get: .

[0077] Simplifying the above equation, we obtain the carrier MFP extraction model that eliminates microscopic unknowns, expressed as: .

[0078] 2. Physical differences in ballistic rates between the linear and saturation regions and inverse deduction of microscopic parameters.

[0079] In this embodiment of the invention, a set of CMOS devices with different channel lengths L are subjected to linear region testing and saturation region testing respectively. The mean free path is extracted by using the data obtained from the linear region testing and the aforementioned carrier MFP extraction model. Then, the micro parameters are derived by combining the data obtained from the saturation region testing.

[0080] (C1) Regional differences in ballistic rate ( ): In the linear region (low The carrier energy is low and mainly affected by elastic scattering. The extracted ballistic rate is defined as... In the saturation region (high) The charge carriers rapidly gain energy at the source, potentially exciting inelastic scattering mechanisms such as optical phonon emission. The actual ballistic velocity in the saturation region at this point... Often smaller than the derived value in the linear region This difference ( This directly reflects the inhibitory effect of high-energy scattering mechanisms on transport.

[0081] (C2) Self-consistent extraction of micro-parameters: Drain-source current in the saturation region Following the ballistic injection model: ,in, This indicates that it is proportional to. If a forced assumption is made... Substituting into the formula, the solution is obtained by reverse engineering. and This will include biases caused by scattering (e.g.) (Significantly greater than the theoretical value). This invention utilizes this characteristic to obtain effective mass by anchoring and extracting values ​​in the low-field-strength inversion region (a window where high-energy scattering has not yet dominated). Furthermore, it quantifies the high-energy scattering loss in the saturation region.

[0082] II. Detailed introduction of the plan.

[0083] Since the main technical details of constructing the carrier MFP extraction model to eliminate microscopic unknowns have been described in detail in the previous embodiments, they will not be repeated here. The following mainly focuses on the measurement of current and voltage data and preprocessing, as well as the related carrier MFP and microscopic parameter extraction process.

[0084] 1. Measurement and preprocessing of current and voltage data.

[0085] The following steps are taken to measure a group of CMOS devices with different channel lengths L in a low-temperature environment (e.g., 4K): The current and voltage data corresponding to the linear region test are the drain-source current in the linear region. With gate-source voltage data( (Curve); The current and voltage data corresponding to the saturation region test are the drain-source current in the saturation region. With gate-source voltage data( (curve); for example, the linear region test can be performed at low drain-source voltages (e.g., drain-source voltage). Testing under conditions of high drain-source voltage (e.g., saturation region testing) can be performed under high drain-source voltage (e.g.) Tests under )

[0086] For linear region testing, the shift-and-ratio method (proportional method) is used to model the enhancement resistance of the linear region of each CMOS device. The data is processed to eliminate the influence of contact resistance, thereby utilizing the gate-source voltage. Calculate the threshold voltage in the linear region , The sign of the partial derivative. It is the nth-order partial derivative.

[0087] Threshold voltage in the saturation region The present invention utilizes the physical characteristic that the subthreshold current at low temperatures is dominated by a diffusion mechanism. Since the subthreshold swing (SS) is mainly determined by the device capacitance ratio and is insensitive to drain-source voltage, the logarithmic current curves of the same device in the linear and saturation regions are obtained. The system exhibits highly parallel characteristics in the subthreshold region. Based on this, the threshold shift (i.e., the optimal voltage shift) caused by the drain-induced barrier reduction (DIBL) effect is extracted through the following optimization steps.

[0088] Selecting the drain-source current in the linear region and the drain-source current in the saturation region of the same CMOS device, in the subthreshold region Construct an objective function to find the optimal voltage shift that minimizes the sum of squares of the logarithmic current differences between the two sets of data after voltage correction: ; in, This represents the optimal voltage shift. To represent any voltage shift, the function This indicates the minimum value of the subsequent modulo. As the optimal voltage shift, this optimal voltage shift quantifies the change in drain-source voltage of the CMOS device. The decrease in potential barrier value caused by the increase.

[0089] Using the threshold voltage of the linear region The threshold voltage of the saturation region is calculated using the optimal voltage shift. , represented as: .

[0090] For the linear and saturation regions, the gate-source voltage is used. The difference between the voltage and the extracted threshold voltage is used to calculate the corresponding effective gate over-drive voltage, providing a unified physical reference for the extraction of subsequent parameters.

[0091] 2. Linear region mobility scattering decoupling.

[0092] Processing linear region data based on effective mobility extraction technology: Construct a system that includes drain-source parasitic resistance Resistance model: ; Where W is the channel width and L is the channel length. The capacitance per unit area of ​​the gate oxide layer; For strong field scattering, These are weak-field scattering terms, and these two terms are obtained by decomposing the inverse of the effective mobility using the effective mobility extraction technique.

[0093] Derivative-enhanced fitting is used to eliminate drain-source parasitic resistance. The strong-field scattering term and the weak-field scattering term were physically separated, and the fitting parameters in the carrier MFP extraction model were solved.

[0094] 3. Extract the mean free path and the ballistic rate in the linear region.

[0095] Based on the fitting parameters obtained from the aforementioned linear region mobility scattering decoupling, and substituted into the carrier MFP extraction model constructed earlier, the carrier MFP varying with the effective gate over-drive voltage is obtained, expressed as: ; in, The MFP represents the carrier that varies with the effective gate over-drive voltage.

[0096] Then, the linear region ballistic rate (characterizing the probability of low-energy carriers successfully crossing the channel) can be calculated using the carrier MFP that varies with the effective gate over-drive voltage, expressed as: ; in, This represents the ballistic rate in the linear region.

[0097] 4. Extraction and analysis of micro-parameters from combined saturation region data.

[0098] Using the linear zone ballistic rate obtained above As a benchmark, combined with the drain-source current in the saturation region Microscopic parameters are decoupled.

[0099] (D1) Extraction of thermal injection rate and analysis of non-idealities.

[0100] Based on the ballistic injection model in the saturation region, we obtain: ; In the above formula, BE represents the ballistic probability, which is substituted into the linear region ballistic probability. Then the preliminary calculated heat injection rate is obtained. : ; in, This represents the preliminary calculated heat injection rate.

[0101] Analyzing the trend of hot injection velocity with effective gate over-drive voltage, if a deviation from the ideal square root law (such as linearity or saturation) occurs under high field strength, it indicates the true ballistic rate in the saturation region. Its ballistic rate is significantly lower than that in the linear region due to high-energy scattering (such as optical phonon emission). .

[0102] (D2) Extract effective quality.

[0103] To obtain accurate microscopic parameters, a low-field-strength inversion region was selected as the extraction window, and the effective gate overdrive voltage within the extraction window was denoted as... For example: Within this extraction window, high-energy scattering is not yet dominant, satisfying the condition... Using this as a known condition, the heat injection rate can be decoupled from the saturation current. .

[0104] According to semiconductor carrier statistics theory, the heat injection rate With effective quality It satisfies the following Fermi-Dirac statistical relationship: ; in, Let π be the mathematical constant, e be the natural constant, and ln be the natural logarithm. For the Fermi-Dirac integral, To reduce the Fermi level.

[0105] Under the specific condition of strong inversion at low temperatures (such as 4K), the charge carriers are in a strongly degenerate state. Based on the aforementioned derivation of the statistical properties of two-dimensional electron gas (i.e., part A3 above), the above relationship is now approximated by a limiting value, and its thermal injection rate is determined by the Fermi velocity. and its coefficients A decision is expressed as: .

[0106] Using the analytical relationships derived above, the heat injection rate initially calculated in the previous section can be recalculated. Perform fitting and calculate effective mass. .

[0107] If the calculated effective mass A value close to the theoretical value (e.g., the lateral mass of silicon electrons is 0.19m0) indicates that the CMOS device is close to ideal ballistic transport. If the calculated effective mass... If the value is significantly greater than the theoretical value (e.g., > 0.3m0), then the increment reflects the additional scattering loss in the saturation region and can be used to quantify the non-equilibrium transport efficiency of the device; where m0 is the inertial mass of the electron.

[0108] (D3) Calculate the theoretical thermal injection velocity and the ballistic rate in the saturation zone. .

[0109] Based on the aforementioned low field strength inversion region ( The effective quality of the extracted The theoretical heat injection rate is calculated based on the following formula. : ; In the above formula, here These are extracted constants. It is a variable, the effective gate overdrive voltage in the saturation region. .

[0110] Calculated Substituting the formula for the saturation current in the quasi-ballistic model, the saturation current rate over the entire voltage range can be obtained. : .

[0111] III. Explanation of the effects of the above-mentioned solution of the present invention.

[0112] The extraction method proposed in this invention represents a significant technological advancement in the field of low-temperature CMOS device characterization, primarily in the following three aspects.

[0113] 1. Independence and robustness of MFP extraction.

[0114] The core MFP extraction scheme of this invention has unique physical advantages, solving the problems of "inaccuracy in measurement" and "incorrect calculation" in existing technologies. Specifically: (E1) Completely independent of microscopic parameter assumptions (Parameter-Free Extraction): Existing methods typically rely on constitutive equations To reverse the process, this leads to a situation where "in order to measure..." We must first assume The circular reasoning trap, and At the nanoscale, the details are often unknown. This invention innovatively utilizes the geometric scaling laws of quasi-ballistic transport (…). By separating the length-dependent term (ballistic correction term) and the length-independent term (diffusion limit term) in the reciprocal of the effective mobility, and then directly calculating using the relationship between the two, the effective mobility can be further optimized. This process relies solely on the self-consistency of macroscopic current-voltage data as a function of channel length, without requiring prior knowledge of carrier effective mass, Fermi velocity, or scattering time, thus ensuring that the extracted MFP is a pure experimental observation.

[0115] (E2) Precise parasitic resistance de-embedding and mechanism decoupling: At low temperatures (e.g., 4K), drain-source parasitic resistance ( The drain-source parasitic resistance increases significantly, and traditional methods often misinterpret this voltage drop as channel scattering, leading to a severe underestimation of the MFP. This invention combines higher-order derivative analysis and the length-scaling method to mathematically and rigorously separate the drain-source parasitic resistance, which is independent of the length. The text describes a series of parameters, including a length-independent strong-field scattering term (corresponding to surface roughness) and a length-linearly dependent weak-field scattering term (corresponding to Coulomb / ballistic effects). This deep physical decoupling ensures that the extracted λ truly reflects the intrinsic transport limit within the channel, rather than being an artifact of contact characteristics.

[0116] (E3) Simplified testing requirements and high throughput: Compared to complex characterization methods that rely on strong magnetic fields (such as SdH oscillations) or RF S-parameters, this invention only requires conventional DC current-voltage scanning. This allows the method to be directly applied to industry-standard wafer-level probing, enabling rapid statistical analysis of the MFP distribution of hundreds or thousands of devices, providing a feasible engineering solution for cryogenic process monitoring.

[0117] 2. Microscopic parameter extraction and non-equilibrium state diagnosis capabilities.

[0118] Based on the accurate MFP extraction results described above, this invention further expands the ability to characterize the microscopic physical properties of devices: (F1) Physically Consistent Acquisition of True Effective Mass: This invention abandons the traditional approach of directly using the effective mass of the bulk material (0.19m0). By combining data from the linear region (low energy state) and the saturated region (high energy state), this invention can accurately "weigh" the effective mass modulated by nanoscale quantum confinement and stress effects in the low-field-strength inversion region. Experimental results show that this value is often greater than the theoretical value, revealing non-ideal factors in practical low-temperature devices.

[0119] (F2) Quantitative Diagnosis of Non-equilibrium Transport: This invention proposes using the ballistic rate in the linear region as a benchmark to verify the drain-source current in the saturation region. The deviation between the two can directly quantify the degree of suppression of ballistic transport by high-energy scattering mechanisms (such as optical phonon emission). This provides a quantitative physical criterion for understanding why cryogenic devices cannot reach the ideal ballistic limit, and points out specific directions for improving device performance through interface optimization or stress engineering.

[0120] 3. Industrial application value.

[0121] (G1) Low-cost wafer-level process monitoring: This method requires only conventional DC current-voltage scanning, without the need for magnetic fields or radio frequency equipment. This makes it possible to rapidly screen the microstructure (such as interface roughness and scattering intensity) of thousands of transistors on the foundry production line using standard automated probe stations, greatly reducing the testing costs and timelines for cryogenic process development.

[0122] (G2) High-precision PDK (Process Design Kit) model calibration: extracted hot injection rate, effective mass, and It provides key physical patches to correct compact models such as BSIM (Berkeley Short-Channel Insulated-Gate Field-Effect Transistor Model). This helps EDA (Electronic Design Automation) tools more accurately predict the drive current and timing characteristics of low-temperature circuits, avoiding chip design failures caused by model errors.

[0123] IV. Example Explanation.

[0124] Taking the thermal management and selection of quantum computing control chips as an example, the above-mentioned solution provided by this invention has specific key application value in the field of quantum computing hardware, especially in providing a physical-level solution to the problem of the "power consumption wall" in low-temperature electronics.

[0125] Example 1: Microscopic Diagnosis and Localization of Heat Sources: Quantum bits are extremely sensitive to thermal noise, and the power consumption of cryogenic control chips is the biggest bottleneck limiting the scaling of quantum computer qubit numbers. The ballistic rate in the saturation region is extracted using this method. The backscattering coefficient r of the source-end carriers can be directly quantified: ; The lower the value (meaning a higher backscattering coefficient r), the more intense the optical phonon emission occurs within the kT layer at the source, thus converting potential energy into lattice heat (Joule heating). Therefore, this method essentially provides an "electrical thermal imager" function, enabling designers to quickly identify and eliminate device units with severe localized heating due to poor interface quality or improper structural design during the chip fabrication and testing phase.

[0126] Example 2: Low-power device selection based on stress engineering: Experimental characterization results of this invention show that in PMOS (P-type metal-oxide-semiconductor field-effect transistor) devices, narrow-width structures can introduce mechanical stress, thereby significantly reducing the effective mass of charge carriers. This significantly increases the ballistic probability in the saturation zone. Using this method, circuit designers can quantify microscopic parameters under different geometries, quickly screen for optimal device structures with "low effective mass and high ballistic rate" characteristics (such as narrow-finger, wide-finger, multi-finger parallel PMOS), and prioritize their application in critical qubit drive lines. This physics-based device selection strategy can fundamentally reduce the power consumption per unit drive current of control chips, facilitating the low-temperature integration of large-scale quantum computing systems.

[0127] 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.

[0128] Example 2

[0129] This invention also provides a low-temperature CMOS carrier MFP and micro-parameter 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: The carrier MFP extraction model building unit is used to construct a carrier MFP extraction model that eliminates microscopic unknowns based on the quasi-ballistic transport model and effective mobility extraction technology, and is represented as follows: Among them, strong-field scattering and weak-field scattering terms are obtained based on the effective mobility extraction technique. This is a strong-field scattering term; Base value coefficient, B is the length modulation coefficient; B is the power exponent. , B and B are the fitting parameters in the carrier MFP extraction model, and they are all obtained using the weak field scattering term. This is the effective gate overdrive voltage; For carrier MFP, MFP is the mean free path; The current and voltage data acquisition and preprocessing unit is used to measure a group of CMOS devices with different channel lengths in a temperature range below a set temperature, and extract the effective gate over-drive voltage from the measured current and voltage data; wherein, CMOS is complementary metal-oxide semiconductor. The effective mobility decoupling and fitting parameter solving unit is used to decouple the effective mobility based on the effective gate over-drive voltage by constructing a resistance model and solving for the fitting parameters in the carrier MFP extraction model. The carrier MFP extraction unit is used to input the solved fitting parameters and the effective gate over-drive voltage into the carrier MFP extraction model to obtain the carrier MFP that varies with the effective gate over-drive voltage. The micro-parameter decoupling and extraction unit is used to decouple the micro-parameters based on the carrier MFP that varies with the effective gate over-drive voltage and the measured current data, and extract the decoupled micro-parameters one by one.

[0130] Since the main technical details of this system have been described in detail in previous embodiments, they will not be repeated here.

[0131] 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.

[0132] 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 low-temperature CMOS carrier MFP and microscopic parameter extraction, characterized in that, include: Based on the quasi-ballistic transport model and effective mobility extraction technology, a carrier MFP extraction model that eliminates microscopic unknowns is constructed, expressed as: Among them, strong-field scattering and weak-field scattering terms are obtained based on the effective mobility extraction technique. This is a strong-field scattering term; Base value coefficient, B is the length modulation coefficient, and B is the power exponent. , B and B are the fitting parameters in the carrier MFP extraction model, and they are all obtained using the weak field scattering term. This is the effective gate overdrive voltage; For carrier MFP, MFP is the mean free path; In a temperature range below a set temperature, a group of CMOS devices with different channel lengths are measured, and the effective gate overdrive voltage is extracted from the measured current and voltage data; wherein, CMOS is complementary metal-oxide semiconductor. Based on the effective gate overdrive voltage, a resistance model is constructed to decouple the effective mobility, and the fitting parameters in the carrier MFP extraction model are solved. The solved fitting parameters and the effective gate overdrive voltage are substituted into the carrier MFP extraction model to obtain the carrier MFP that varies with the effective gate overdrive voltage. The micro-parameters are decoupled based on the carrier MFP that varies with the effective gate over-drive voltage and the measured current data, and the decoupled micro-parameters are extracted one by one.

2. The method for extracting microscopic parameters of a low-temperature CMOS carrier MFP according to claim 1, characterized in that, The carrier MFP extraction model, which eliminates microscopic unknowns, is constructed based on the quasi-ballistic transport model and effective mobility extraction technology, including: Quasi-ballistic transport model refers to the device channel conductance G DS From the ballistic limiting conductivity G bal and transmission probability A joint decision, expressed as: ； Among them, transmission probability The transport probability represents the probability that a charge carrier successfully crosses the channel without being scattered back to the source. Depends on channel length L and mean free path The ratio is expressed as: ; Based on quasi-ballistic transport theory and combined with effective mobility extraction technology, the general formula for effective mobility is obtained: ； in, For effective migration rate, For diffusion mobility; By taking the reciprocal of the above general formula and separating the components, we obtain: ； Based on the effective mobility extraction technique, the reciprocal of the effective mobility is decomposed into a strong-field scattering term and a weak-field scattering term, expressed as: ； in, This is a weak-field scattering term; Weak field scattering term Represented as: ； in, The coefficients of the weak-field scattering term related to the channel length L are expressed as: ; Will Combining the expression with the inverse decomposition expression of the effective mobility, we obtain the following relationship: ； General formula based on effective mobility and The expression establishes a physical mapping, and the above relationship is modified to obtain the carrier MFP extraction model that eliminates microscopic unknowns.

3. The method for extracting microscopic parameters of a low-temperature CMOS carrier MFP according to claim 2, characterized in that, The general formula based on effective mobility and The expression establishes a physical mapping and modifies the above relation, including: Establish the following physical mapping: , ;in, It is the reciprocal of the diffusion mobility. For ballistic correction items; Based on the above physical mapping, the ratio of the ballistic correction term to the reciprocal of the diffusion mobility is calculated to eliminate microscopic unknowns, i.e., the diffusion mobility. ,get: ； Simplifying the above equation yields the carrier MFP extraction model that eliminates microscopic unknowns.

4. The method for extracting microscopic parameters of a low-temperature CMOS carrier MFP according to claim 2, characterized in that, The step of measuring a group of CMOS devices with different channel lengths in a temperature range below a set temperature, and extracting the effective gate over-drive voltage from the measured current and voltage data, includes: Within a temperature range below a set threshold, linear region and saturation region tests were performed on a group of CMOS devices with different channel lengths to obtain corresponding current and voltage data. The current and voltage data corresponding to the linear region test were the drain-source current in the linear region. With gate-source voltage The data, including the current and voltage data corresponding to the saturation region test, represents the drain-source current in the saturation region. With gate-source voltage data; For linear region testing, gate-source voltage is used. Calculate the threshold voltage in the linear region And from this, the effective gate overdrive voltage in the linear region can be calculated. ; For saturation region testing, consider the drain-source current in the linear region. and saturation region drain-source current In the subthreshold region, an objective function is constructed to find the optimal voltage shift, and the threshold voltage in the linear region is utilized. The threshold voltage of the saturation region is calculated using the optimal voltage shift. And from this, the effective gate overdrive voltage in the saturation region can be calculated. .

5. The method for extracting microscopic parameters of a low-temperature CMOS carrier MFP according to claim 4, characterized in that, The objective function is constructed in the subthreshold region to find the optimal voltage shift, and the threshold voltage in the linear region is utilized. The threshold voltage of the saturation region is calculated using the optimal voltage shift. include: Selecting the drain-source current in the linear region and the drain-source current in the saturation region of the same CMOS device, in the subthreshold region Construct the following objective function to find the optimal voltage shift: ； in, This represents the optimal voltage shift. To represent any voltage shift, the function... This indicates the minimum value of the subsequent modulo. As the optimal voltage shift; Using the threshold voltage of the linear region The threshold voltage of the saturation region is calculated using the optimal voltage shift. , is represented as: .

6. The method for extracting microscopic parameters of a low-temperature CMOS carrier MFP according to claim 4, characterized in that, The method of constructing a resistance model based on the effective gate overdrive voltage to decouple the effective mobility and solving for the fitting parameters in the carrier MFP extraction model includes: Utilizing the effective gate overdrive voltage in the linear region Construct a system that includes drain-source parasitic resistance resistance model : ； Where W is the channel width and L is the channel length. The capacitance per unit area of ​​the gate oxide layer; For strong field scattering, For weak-field scattering terms, these two terms are derived by decomposing the reciprocal of the effective mobility using an effective mobility extraction technique and incorporating it into the effective gate overdrive voltage in the linear region. get; By using derivative-enhanced fitting and based on effective mobility extraction technology, drain-source parasitic resistance is eliminated. And physically separate the strong field scattering term With weak field scattering term , where parameters and It is derived based on the effective mobility extraction technique, and then... about Perform linear fitting , obtain parameters .

7. The method for extracting microscopic parameters of a low-temperature CMOS carrier MFP according to claim 4, characterized in that, Based on the carrier MFP that varies with the effective gate overdrive voltage and the measured current data, the micro parameters are decoupled, and the decoupled micro parameters are extracted one by one, including: Calculation of linear region ballistics using carrier MFP that varies with effective gate overdrive voltage Combined with the drain-source current in the saturation region The micro-parameters are decoupled, and each decoupled micro-parameter is calculated individually, including: effective mass, theoretical thermal injection rate, and ballistic rate in the saturation region. .

8. The method for extracting microscopic parameters of a low-temperature CMOS carrier MFP according to claim 7, characterized in that, Methods for calculating effective mass include: Based on the ballistic injection model in the saturation region, we obtain: ； Where W is the channel width, The capacitance per unit area of ​​the gate oxide layer. BE is the heat injection velocity; BE is the ballistic rate, which is the ballistic rate in the linear region. Then the preliminary calculated heat injection rate is obtained. : ； According to semiconductor carrier statistics, the thermal injection rate and effective mass satisfy the following Fermi-Dirac statistical relationship: ； in, Boltzmann's constant, Absolute temperature Let π be the mathematical constant, e be the natural constant, and ln be the natural logarithm. For the Fermi-Dirac integral, To reduce the Fermi level, For effective quality; When the charge carriers are in a strongly degenerate state, the above equation can be rewritten to obtain the following analytical relation: ； in, To reduce Planck's constant, The capacitance per unit area of ​​the gate oxide layer. Let q be the Fermi velocity and q be the charge. Select a preset field strength inversion region as the extraction window, and extract the effective gate overdrive voltage within the extraction window. Substituting the analytical relationship into the effective gate overdrive voltage The initially calculated heat injection rate Substituting the analytical relation as Calculate the effective mass .

9. The method for extracting microscopic parameters of a low-temperature CMOS carrier MFP according to claim 8, characterized in that, Calculate the theoretical thermal injection velocity and the ballistic rate in the saturation zone. The methods include: Combined with effective quality and the effective gate overdrive voltage in the saturation region The theoretical heat injection rate was calculated using the analytical relationship between heat injection rate and effective mass. ; Combined with the theoretical heat injection rate Drain-source current in saturation region With the effective gate overdrive voltage in the saturation region Calculate the ballistic rate in the saturation region .

10. A low-temperature CMOS carrier MFP and microscopic parameter extraction system, characterized in that, To implement the method according to any one of claims 1 to 9, comprising: The carrier MFP extraction model building unit is used to construct a carrier MFP extraction model that eliminates microscopic unknowns based on the quasi-ballistic transport model and effective mobility extraction technology, and is represented as follows: Among them, strong-field scattering and weak-field scattering terms are obtained based on the effective mobility extraction technique. This is a strong-field scattering term; Base value coefficient, B is the length modulation coefficient, and B is the power exponent. , B and B are the fitting parameters in the carrier MFP extraction model, and they are all obtained using the weak field scattering term. This is the effective gate overdrive voltage; For carrier MFP, MFP is the mean free path; The current and voltage data acquisition and preprocessing unit is used to measure a group of CMOS devices with different channel lengths in a temperature range below a set temperature, and extract the effective gate over-drive voltage from the measured current and voltage data; wherein, CMOS is complementary metal-oxide semiconductor. The effective mobility decoupling and fitting parameter solving unit is used to decouple the effective mobility based on the effective gate over-drive voltage by constructing a resistance model and solving for the fitting parameters in the carrier MFP extraction model. The carrier MFP extraction unit is used to input the solved fitting parameters and the effective gate over-drive voltage into the carrier MFP extraction model to obtain the carrier MFP that varies with the effective gate over-drive voltage. The micro-parameter decoupling and extraction unit is used to decouple the micro-parameters based on the carrier MFP that varies with the effective gate over-drive voltage and the measured current data, and extract the decoupled micro-parameters one by one.

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