Low temperature CMOS carrier mfp and microscopic parameter extraction method and system

Abstract

The application discloses a kind of low-temperature CMOS carrier MFP and microcosmic parameter extraction method and system, they are corresponding scheme, in scheme: using the geometric scaling law of quasi-ballistic transport, with the existing effective mobility extraction technique, eliminate the carrier MFP extraction model of microcosmic unknown quantity is constructed, and based on the self-consistency of macroscopic current and voltage data with the change of channel length, without pre-existing effective mass, fermi velocity, scattering time foundation, so as to ensure that the MFP extracted by carrier MFP extraction model is pure experimental observation value;Meanwhile, on this basis, microcosmic parameters are decoupled, so that the decoupled microcosmic parameters are extracted one by one;Compared with prior art, the present application can be directly applied to the wafer level test platform of industry standard, can quickly count the MFP distribution of hundreds of devices, and provides a feasible engineering scheme for low-temperature process monitoring.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of low-temperature CMOS (Complementary Metal Oxide Semiconductor) carrier MFP and microscopic parameter extraction technology, and particularly relates to a low-temperature CMOS carrier MFP and microscopic parameter extraction method and system. BACKGROUND

[0002] With the rapid development of quantum computing, deep space exploration and high-sensitivity sensor technology, low-temperature CMOS (Cryo-CMOS) circuits working in the liquid helium temperature region (such as 4K, K for Kelvin) have become the core interface technology for realizing quantum bit control and readout. With the semiconductor process node entering the deep sub-micron (Deep Sub-micron) and even nanometer scale, the channel length L of the transistor is continuously reduced, gradually approaching or even less than the average free path (Mean Free Path, MFP) of the carrier. At this scale, the carrier transport mechanism fundamentally changes from the traditional drift-diffusion (Drift-Diffusion) mode to the quasi-ballistic transport (Quasi-ballistic Transport) region. In this region, the average free path and ballistic efficiency replace the traditional mobility to become the core physical quantity that determines the ultimate performance (such as the ultimate transconductance, injection speed) of the device and the circuit design.

[0003] At the industrial application level, with the scaling up of low-temperature electronics from the laboratory to large-scale applications, new challenges are posed for device characterization:

[0004] (1) The demand for wafer-level process monitoring (WAT): Foundry urgently needs a method that can quickly monitor the interface quality and process fluctuations at low temperature. However, traditional microscopic parameter measurement (such as SdH oscillation, Hall effect) relies on expensive superconducting magnets and special Hall bar structures, and the test cycle is long, which cannot be deployed on the automatic probe station of the production line.

[0005] (2) The demand for accurate PDK modeling: The existing industry standard compact model (such as BSIM) is mostly developed based on room temperature physics. When directly extrapolated to low temperature (such as 4K), due to the inability to accurately describe ballistic transport and quantum effects, it often leads to large errors in current and timing prediction.

[0006] However, accurately extracting the carrier MFP and related microscopic physical parameters (such as effective mass , thermal injection speed , etc.) at low temperature faces great challenges. The current mainstream extraction methods mainly include the following three, but they all have significant defects in actual engineering applications.

[0007] (1) Magnetic transport measurement: This is the gold standard in fundamental physics research. By measuring the oscillation of conductivity (SdH effect) or Hall effect under strong magnetic field, researchers can accurately separate the quantum lifetime of carriers from the transport lifetime. However, its drawbacks are: it requires extremely low temperature at millikelvin (mK) level and strong magnetic field at several Tesla, which is extremely difficult to achieve in a testing environment. More importantly, it requires a special Hall Bar geometry structure, which cannot be directly applied to standard MOSFET transistors in large-scale integrated circuits. Therefore, this method is only limited to laboratory fundamental material research, and cannot meet the needs of industrial rapid screening, process monitoring and modeling of wafer-level devices.

[0008] For example, magnetic transport measurement can be found in document 1: Ben Shalom M et al. Shubnikov-De Haas Oscillations in SrTiO3 / LaAlO3 Interface. Phys Rev Lett, 2010, 105(20): 206401.

[0009] (2) Theoretical derivation based on micro-physical parameters: A common approach is to derive based on physical constitutive relationship where represents the macroscopic mobility, and q represents the charge quantity. However, its drawbacks are: although the above physical constitutive relationship is rigorous, it is extremely difficult to apply in actual nanodevices. This is because under extremely low temperature and nanometer confined space, the effective mass and thermal injection velocity of carriers are no longer bulk constants, but are strongly modulated by quantum confinement, mechanical stress engineering and non-ideal Fermi-Dirac distribution. It is almost impossible to accurately measure these micro-quantities in a specific device, and researchers are often forced to use room temperature or bulk material theoretical values in calculations, which introduces a huge systematic error, resulting in a significant reduction in the reliability of the extracted MFP values.

[0010] (3) Traditional I-V (current-voltage) characteristic extraction method: This method attempts to extract only from the linear region characteristics, with the lowest cost, where is the drain-source current, is the gate-source voltage, but the existing technology usually has serious model defects: (3.1) incomplete parasitic resistance de-embedding: at low temperature, due to the freeze-out of impurities in the drain-source region, the drain-source parasitic resistance increases sharply, and if not accurately removed (3.2) Extraction algorithm failure: Existing Y-function method (Ref. 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 varies with gate voltage in a bell shape, which is often not true in low-temperature short-channel devices; the method based on linear regression of channel resistance and length (Ref. 3: Niu G, Cressler J D, Mathew S J, 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, ignoring the ballistic enhancement effect in short channels; while the method based on small-signal output conductance (Ref. 4: Jazaeri F, Pezzotta A, Enz C. Free carrier mobility extraction in FETs. IEEE Transactions on Electron Devices, 2017, 64(12): 5279-5283.) is extremely sensitive to test noise at low temperature; (3.2) Physical mechanism confusion: Traditional methods cannot distinguish the contribution of different scattering mechanisms (such as Coulomb scattering and surface roughness scattering), resulting in the extraction result being a mixed average of multiple mechanisms, and the physical picture being blurred.

[0011] 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 depend on preset micro-parameters, and can accurately remove the influence of parasitic resistance, to support process optimization and accurate modeling of low-temperature chips. SUMMARY

[0012] The application aims to provide a low-temperature CMOS carrier MFP and micro-parameters extraction method and system, which does not require special test structures, does not depend on preset micro-parameters, and can accurately eliminate the influence of parasitic resistance, and the whole scheme constructs a complete physical logic chain from micro-constitutive relation to macro-transport model, realizes self-consistent extraction of parameters through strict mapping between macro-observation and micro-physical quantity, and can support process optimization and accurate modeling of low-temperature chips.

[0013] The application aims to achieve the above technical scheme.

[0014] A low-temperature CMOS carrier MFP and micro-parameters extraction method, comprising:

[0015] Based on the quasi-ballistic transport model and the effective mobility extraction technology, a carrier MFP extraction model eliminating micro-unknown quantities is constructed, which is expressed as: ; wherein the strong field scattering term and the weak field scattering term are obtained based on the effective mobility extraction technology, is the strong field scattering term; is a base value coefficient, is a length modulation coefficient, B is a power index, , and B are fitting parameters in the carrier MFP extraction model, and they are all parameters obtained by using the weak field scattering term, is an effective gate overdrive voltage; is a carrier MFP, and MFP is a mean free path;

[0016] In a temperature range lower than a set temperature, a group of CMOS devices with different channel lengths are measured, and the effective gate overdrive voltage is extracted from the current and voltage data obtained by measurement; wherein CMOS is a complementary metal oxide semiconductor;

[0017] 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;

[0018] The solved fitting parameters and the effective gate overdrive voltage are brought into the carrier MFP extraction model to obtain the carrier MFP varying with the effective gate overdrive voltage;

[0019] Based on the carrier MFP varying 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.

[0020] A low-temperature CMOS carrier MFP and micro-parameters extraction system for realizing the above method, comprising:

[0021] The carrier MFP extraction model construction unit is configured to construct a carrier MFP extraction model eliminating micro unknowns based on a quasi-ballistic transport model and an effective mobility extraction technique, and is expressed as: ; wherein the strong field scattering term and the weak field scattering term are obtained based on the effective mobility extraction technique, is the strong field scattering term; is a base value coefficient, is a length modulation coefficient, B is a power index, , and B are fitting parameters in the carrier MFP extraction model, and they are all parameters obtained by using the weak field scattering term, is an effective gate overdrive voltage; is a carrier MFP, and MFP is a mean free path;

[0022] The current and voltage data acquisition and preprocessing unit is configured to measure a group of CMOS devices with different channel lengths at a temperature zone lower than a set temperature, and extract the effective gate overdrive voltage from the measured current and voltage data; wherein CMOS is a complementary metal oxide semiconductor;

[0023] The effective mobility decoupling and fitting parameter solving unit is configured to decouple the effective mobility based on the effective gate overdrive voltage, and solve the fitting parameters in the carrier MFP extraction model;

[0024] The carrier MFP extraction unit is configured to bring the solved fitting parameters and the effective gate overdrive voltage into the carrier MFP extraction model, and obtain the carrier MFP varying with the effective gate overdrive voltage;

[0025] The micro parameter decoupling and extraction unit is configured to decouple the micro parameters based on the carrier MFP varying with the effective gate overdrive voltage and the measured current data, and extract the decoupled micro parameters one by one.

[0026] As can be seen from the technical solutions provided by the above-mentioned application, the geometric scaling law of quasi-ballistic transport is used together with the existing effective mobility extraction technique to construct a carrier MFP extraction model eliminating micro unknowns, and based on the self-consistency of the macro current and voltage data varying with the channel length, the effective mass, Fermi velocity and scattering time do not need to be known in advance, so that the MFP extracted by the carrier MFP extraction model is a pure experimental observation value; at the same time, the micro parameters are decoupled on this basis, so that the decoupled micro parameters are extracted one by one; compared with the existing solutions, the application can be directly applied to the wafer level test table of the industry standard, and the MFP distribution of hundreds of devices can be quickly counted, thereby providing a feasible engineering solution for low-temperature process monitoring. BRIEF DESCRIPTION OF DRAWINGS

[0027] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed in the embodiments description. Obviously, the drawings in the following description only show some of the embodiments of the present application, and those skilled in the art can obtain other drawings according to these drawings without any creative effort.

[0028] Figure 1 A flow chart of a low-temperature CMOS carrier MFP and microscopic parameter extraction method provided by the embodiments of the present application.

[0029] Figure 2 A schematic diagram of a low-temperature CMOS carrier MFP and microscopic parameter extraction system provided by the embodiments of the present application. DETAILED DESCRIPTION

[0030] The technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without any creative effort fall within the protection scope of the present application.

[0031] First, the terms possibly used in the present application are explained as follows:

[0032] The terms "include", "contain", "have", "possess" or other similar semantic descriptions should be interpreted as non-exclusive inclusion. For example, the inclusion of a technical feature element (such as raw materials, components, ingredients, carriers, dosage forms, materials, sizes, parts, components, mechanisms, devices, steps, processes, methods, reaction conditions, processing conditions, parameters, algorithms, signals, data, products or articles, etc.) should be interpreted as not only including the explicitly listed technical feature element, but also including other technical feature elements not explicitly listed in the art.

[0033] The term "consisting of" means excluding any technical feature element not explicitly listed. If this term is used in the claims, the term will make the claim closed, so that it does not contain technical feature elements other than the explicitly listed technical feature elements, except for conventional impurities related thereto. If the term only appears in a certain clause of the claim, it only limits the elements explicitly listed in that clause, and the elements recorded in other clauses are not excluded from the overall claim.

[0034] The low-temperature CMOS carrier MFP and micro parameter extraction method and system provided by the present application are described in detail below. The contents not described in detail in the embodiments of the present application belong to the prior art known to those skilled in the art. The specific conditions not specified in the embodiments of the present application are performed according to the conventional conditions in the art or the conditions recommended by the manufacturer. The instruments used in the embodiments of the present application are all conventional products that can be obtained by market purchase, unless otherwise specified.

[0035] Embodiment one

[0036] The embodiments of the present application provide a low-temperature CMOS carrier MFP and micro parameter extraction method, as shown in the following formula (1), which mainly includes the following steps: Figure 1

[0037] Step 1: Based on the quasi-ballistic transport model and the effective mobility extraction technology, a carrier MFP extraction model eliminating micro unknown quantities is constructed.

[0038] The preferred embodiments of this step are as follows:

[0039] (1) The quasi-ballistic transport model refers to the device channel conductance G DS which is determined by the ballistic limit conductance G bal and the transmission probability , and is expressed as:

[0040] ;

[0041] Among them, the transmission probability represents the probability that the carrier successfully crosses the channel without being scattered back to the source, and the transmission probability depends on the ratio of the channel length L to the MFP, and is expressed as: .

[0042] (2) In the traditional drift-diffusion model, the device channel conductance in the linear region is related to the effective mobility and the channel length L, and is expressed as:

[0043] ;

[0044] Among them, is the carrier concentration, is the channel width, and q represents the charge amount. In the diffusion limit case (L ), the transmission probability , and the two can be obtained by combining:

[0045] ;

[0046] . ​

[0047] Returning to the general case of the transmission coefficient formula from ballistic to diffusion full range:

[0048] ;

[0049] wherein, is the effective mobility, is the diffusion mobility, is much larger than the sign.

[0050] (3) By simplifying the above general formula and getting the reciprocal, we get:

[0051] .

[0052] Based on the effective mobility extraction technology, the reciprocal of the effective mobility is decomposed into a strong field scattering term and a weak field scattering term, which is expressed as:

[0053] ;

[0054] wherein, is the strong field scattering term, is the weak field scattering term, is the effective gate overdrive voltage.

[0055] Weak field scattering term is expressed as:

[0056] ;

[0057] wherein, is the bias-dependent weak field scattering term function, is the geometric scaling factor related to the device channel length L, A is the amplitude parameter introduced in modeling, is the weak field scattering term coefficient related to the channel length L, which is expressed as: , is the base value coefficient, is the length modulation coefficient; B is the power index, , and B are fitting parameters in the carrier MFP extraction model, which are obtained by the weak field scattering term.

[0058] The expression of is combined with the reciprocal of the effective mobility decomposition expression to obtain the following relationship:

[0059] .

[0060] 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.

[0061] (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:

[0062] .

[0063] Preferably, the general formula based on effective mobility is... The expression establishes a physical mapping and modifies the above relation, including:

[0064] Establish the following physical mapping: , ;in, It is the reciprocal of the diffusion mobility. This is a ballistic correction item.

[0065] 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 unknown, i.e., the diffusion mobility. ,get:

[0066] .

[0067] Simplifying the above equation yields the carrier MFP extraction model that eliminates microscopic unknowns.

[0068] 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. ).

[0069] The preferred implementation method for this step is as follows:

[0070] (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.

[0071] The setting temperature can be set according to actual conditions, for example, between 70K and 30K, and for example, the low-temperature temperature zone can be 1K~70K or 1K~30K.

[0072] (2) For linear region test, the gate-source voltage is calculated. The effective gate overdrive voltage of the linear region is calculated. .

[0073] (3) For saturation region test, the linear region drain-source current and the saturation region drain-source current are combined to construct a target function in the subthreshold region, to find the optimal voltage shift, and the linear region threshold voltage and the optimal voltage shift are used to calculate the saturation region threshold voltage , and the effective gate overdrive voltage of the saturation region is calculated. .

[0074] Preferably, the construction of the target function in the subthreshold region, the finding of the optimal voltage shift, and the calculation of the saturation region threshold voltage using the linear region threshold voltage and the optimal voltage shift include:

[0075] The linear region drain-source current and the saturation region drain-source current of the same CMOS device are selected, and the following target function is constructed in the subthreshold region to find the optimal voltage shift:

[0076] .

[0077] wherein, represents the optimal voltage shift, represents any voltage shift, and the function represents the when the minimum value of the mode is taken as the optimal voltage shift.

[0078] The linear region threshold voltage and the optimal voltage shift are used to calculate the saturation region threshold voltage , which is represented as: .

[0079] Step 3: 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.

[0080] The preferred embodiment of this step is as follows:

[0081] (1) Using the effective gate overdrive voltage in the linear region , a resistance model containing the drain-source parasitic resistance is constructed :

[0082] ;

[0083] wherein W is the channel width, L is the channel length, is the unit area capacitance of the gate oxide layer; is the strong field scattering term, is the weak field scattering term, and the two terms are obtained by decomposing the reciprocal of the effective mobility and bringing the effective gate overdrive voltage in the linear region into the effective mobility extraction technology.

[0084] (2) Based on the effective mobility extraction technology, the drain-source parasitic resistance can be removed and the strong field scattering term and the weak field scattering term are physically separated, wherein the parameters and can be derived based on the effective mobility extraction technology. Specifically, referring to the example of the effective mobility extraction technology provided in the foregoing, the intercept and the slope of the linear fitting of can be derived using the enhanced resistance model , wherein is the partial derivative symbol, is the n-th order partial derivative. The principle of the enhanced resistance model involved here can also be seen from the example of the effective mobility extraction technology provided in the foregoing, and thus is not described in detail. Then, the linear fitting is performed on , and the fitting parameter in the carrier MFP extraction model is obtained. .

[0085] Step 4, the fitting parameters obtained are brought into the carrier MFP extraction model with the effective gate overdrive voltage, and the carrier MFP varying with the effective gate overdrive voltage is obtained.

[0086] In the embodiment of the application, the fitting parameters obtained and the effective gate overdrive voltage in the linear region are brought into the carrier MFP extraction model, and the carrier MFP varying with the effective gate overdrive voltage is calculated.

[0087] Step 5, based on the carrier MFP varying with the effective gate overdrive voltage and the current data obtained by measurement, the micro-parameters are decoupled, and the decoupled micro-parameters are extracted one by one.

[0088] In the embodiment of the present application, the carrier MFP varying with the effective gate overdrive voltage is used to calculate the linear region ballistic rate , combined with the saturation region drain-source current The micro-parameters are decoupled, and the decoupled micro-parameters are calculated one by one, including effective mass, theoretical thermal injection speed, and saturation region ballistic rate .

[0089] Preferably, the way of calculating the effective mass comprises:

[0090] Based on the saturation region ballistic injection model, it is obtained that:

[0091] ;

[0092] Wherein, W is the channel width, is the unit area capacitance of the gate oxide layer, is the thermal injection speed; BE is the ballistic rate, and the linear region ballistic rate is taken into account, then the preliminarily calculated thermal injection speed is obtained:

[0093] .

[0094] According to the semiconductor carrier statistical theory, the thermal injection speed and the effective mass satisfy the Fermi-Dirac statistical relationship as follows:

[0095] ;

[0096] Wherein, is the Boltzmann constant, is the absolute temperature, is the circular constant, e is the natural constant, and ln is the natural logarithm, is the Fermi-Dirac integral, is the reduced Fermi energy level.

[0097] When the carrier is in a strong degenerate state, the above formula is rewritten to obtain the following analytical relationship:

[0098] ;

[0099] Wherein, is the reduced Planck constant, is the unit area capacitance of the gate oxide layer, is the Fermi speed, and q is the charge amount.

[0100] The preset field strength inversion region is selected as the extraction window, and the effective gate overdrive voltage in the extraction window is taken into the analytical relationship as the effective gate overdrive voltage The initially calculated heat injection rate Substituting the analytical relation as Calculate the effective mass .

[0101] Preferably, the theoretical thermal injection velocity and the ballistic rate in the saturation zone are calculated. The method is as follows:

[0102] 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. ;

[0103] 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 .

[0104] 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.

[0105] I. Overall Description of the Plan

[0106] 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.

[0107] 1. Derivation of the constitutive relationship between microscopic parameters and macroscopic mobility.

[0108] 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:

[0109] (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:

[0110] .

[0111] (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:

[0112] .

[0113] (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:

[0114] ;

[0115] 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).

[0116] (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:

[0117] .

[0118] 2. Derivation of the mapping between the quasi-ballistic transport model and the IV decoupling parameters.

[0119] In order to achieve effective quality without prior knowledge and heat injection rate Directly extract the mean free path in the case of The present application introduces quasi-ballistic transport model and establishes its mathematical mapping with experimental decoupling parameters.

[0120] (B1) Quasi-ballistic conductance: Device channel conductance G DS is determined by ballistic limit conductance G bal and transport probability , which is expressed as:

[0121] ;

[0122] where transport probability represents the probability of carriers successfully crossing the channel without being scattered back to the source, according to the quasi-ballistic transport model, transport probability depends on the ratio of channel length L to MFP, which is expressed as: .

[0123] (B2) The above quasi-ballistic conductance is combined with the traditional diffusion transport conductance expression , where is the inversion layer charge density. When (i.e. long channel limit), transport degenerates into diffusion dominance, and mobility tends to diffusion mobility . By calibrating the model, the general formula of effective mobility is obtained:

[0124] ;

[0125] where is effective mobility, is diffusion mobility, is much larger than the symbol.

[0126] (B3) Inverse form linearization and physical mapping: taking the inverse of the above general formula, we get:

[0127] .

[0128] At the same time, based on the effective mobility extraction technology, the inverse of the effective mobility is decomposed into strong field scattering term and weak field scattering term, which is expressed as:

[0129] ;

[0130] where is the strong field scattering term, is the weak field scattering term, is the effective gate overdrive voltage.

[0131] Weak field scattering term is expressed as:

[0132] .

[0133] By analyzing the data extracted from CMOS devices with different channel length L, it is verified that varies linearly with 1 / L, and the linear fitting gives .

[0134] ;

[0135] where is the coefficient of the weak-field scattering term related to channel length L, is the base value coefficient, is the length modulation coefficient.

[0136] Combining the expression of with the decomposition expression of the effective mobility inverse, the following relationship between the effective mobility inverse and 1 / L is obtained:

[0137] .

[0138] Based on the general expression of the effective mobility and the expression of , the physical mapping is established as follows:

[0139] where is the inverse of the diffusion mobility, and the above physical mapping verifies that the strong-field scattering term and the base value coefficient are independent of channel length L, corresponding to the diffusion limit under long channel.

[0140] where is the ballistic correction term, and the above physical mapping verifies that varies linearly with 1 / L, reflecting the quasi-ballistic effect under short channel.

[0141] (B4) Construct a carrier MFP extraction model that eliminates microscopic unknowns.

[0142] Based on the above physical mapping, the ratio of the ballistic correction term to the inverse of the diffusion mobility is calculated, which eliminates the microscopic unknown, i.e., the diffusion mobility , and obtains:

[0143] .

[0144] Simplifying the above equation, we obtain the carrier MFP extraction model that eliminates microscopic unknowns, which is expressed as:

[0145] .

[0146] 2. Physical differences between linear and saturated ballistic rates and microscopic parameter backstepping.

[0147] ​In the embodiment of the present application, linear region test and saturation region test are respectively performed on a group of CMOS devices with different channel lengths L, the average free path is extracted by using the data obtained by the linear region test and combining the aforementioned carrier MFP extraction model, and the micro parameters are derived by combining the data obtained by the saturation region test.

[0148] (C1) Area difference of ballistic probability : In the linear region (low ), the carrier energy is low, and it is mainly affected by elastic scattering, and the extracted ballistic probability is defined as In the saturation region (high ), the carrier obtains energy rapidly at the source end, and a non-elastic scattering mechanism such as optical phonon emission may be excited. At this time, the real saturation region ballistic probability is often smaller than the value derived in the linear region. This difference directly reflects the inhibitory effect of high-energy scattering mechanisms on transport.

[0149] (C2) Self-consistent extraction of micro parameters: saturation region drain-source current follows the ballistic injection model: wherein is proportional to If it is forcibly assumed that and are substituted into the formula, the inverse solution of will contain the deviation caused by scattering (for example is significantly larger than the theoretical value). The present application uses this feature to obtain the effective mass by anchoring the extraction value in the low-field inversion region (a window in which high-energy scattering has not yet dominated), and further quantifies the high-energy scattering loss in the saturation region.

[0150] II. Detailed introduction of the scheme.

[0151] Considering that the main technical details of constructing a carrier MFP extraction model that eliminates micro unknowns have been described in detail in the previous embodiments, no further description is given, and the following mainly describes the measurement of current and voltage data and preprocessing, and the related carrier MFP and micro parameter extraction process in detail.

[0152] 1. Measurement of current and voltage data and preprocessing.

[0153] In a low-temperature (such as 4K) environment, a group of CMOS devices with different channel lengths L are measured, and the specific steps are as follows:

[0154] The current and voltage data corresponding to the linear region test are the linear region drain-source current and the 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 )

[0155] 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.

[0156] 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.

[0157] 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:

[0158] ;

[0159] 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.

[0160] Using the threshold voltage of the linear region The threshold voltage of the saturation region is calculated using the optimal voltage shift. , represented as: .

[0161] 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.

[0162] 2. Linear region mobility scattering decoupling.

[0163] Processing linear region data based on effective mobility extraction techniques:

[0164] Construct a system that includes drain-source parasitic resistance Resistance model:

[0165] ;

[0166] Where W is the channel width and L is the channel length. The capacitance per unit area of ​​the gate oxide layer; This is a strong-field scattering term. 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.

[0167] 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.

[0168] 3. Extract the mean free path and the ballistic rate in the linear region.

[0169] 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:

[0170] ;

[0171] in, The MFP represents the carrier that varies with the effective gate over-drive voltage.

[0172] 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 overdrive voltage, expressed as:

[0173] ;

[0174] in, This represents the ballistic rate in the linear region.

[0175] 4. Extraction and analysis of micro-parameters from combined saturation region data.

[0176] The linear region ballistic mobility As a reference, the saturation region drain-source current is combined to decouple the microscopic parameters.

[0177] (D1) Extract the hot injection velocity and analyze the non-ideality.

[0178] Based on the saturation region ballistic injection model, we have:

[0179] ;

[0180] In the above equation, BE is the ballistic mobility, and the linear region ballistic mobility is substituted into the equation to obtain the preliminary calculated hot injection velocity :

[0181] ;

[0182] where, is the preliminary calculated hot injection velocity.

[0183] The trend of the hot injection velocity with the effective gate overdrive voltage is analyzed. If there is a deviation from the ideal square root law (such as linear or saturation) at high field strength, it indicates that the true saturation region ballistic mobility is significantly lower than the linear region ballistic mobility due to high-energy scattering (such as optical phonon emission).

[0184] (D2) Extract the effective mass.

[0185] To obtain accurate microscopic parameters, the low-field inversion region is selected as the extraction window, and the effective gate overdrive voltage in the extraction window is denoted as , which is exemplified as: Within this extraction window, high-energy scattering has not yet dominated, and it satisfies , which is used as a known condition to decouple the hot injection velocity from the saturation current.

[0186] According to the semiconductor carrier statistical theory, the hot injection velocity and the effective mass satisfy the following Fermi-Dirac statistical relationship:

[0187] ;

[0188] where, is the constant pi, e is the natural constant, ln is the natural logarithm, is the Fermi-Dirac integral, is the reduced Fermi energy level.

[0189] Under the specific condition of low temperature (e.g. 4K) strong inversion region, the carriers are in a strong degenerate state , based on the aforementioned derivation of the statistical properties of the two-dimensional electron gas (i.e. the aforementioned A3 section), the above relationship takes the limit approximation, and its thermal injection speed is determined by the Fermi velocity and its coefficient , which is expressed as:

[0190] .

[0191] Using the analytical relationship derived above, the thermal injection speed preliminarily calculated in the foregoing is fitted to calculate the effective mass .

[0192] If the calculated effective mass is close to the theoretical value (e.g. 0.19m0 for the transverse mass of silicon electrons), it indicates that the CMOS device is close to ideal ballistic transport. If the calculated effective mass is significantly greater than the theoretical value (e.g. > 0.3m0), the increment reflects the additional scattering loss in the saturation region, which can be used to quantify the non-equilibrium transport efficiency of the device; where m0 is the inertial mass of an electron.

[0193] (D3) Calculate the theoretical thermal injection speed and the saturation region ballistic rate .

[0194] According to the effective mass extracted in the low field strong inversion region in the foregoing, the theoretical thermal injection speed is calculated according to the following formula:

[0195] ;

[0196] In the above formula, here is the extracted constant, is a variable, and the effective gate overdrive voltage in the saturation region is brought in.

[0197] The calculated is brought into the quasi-ballistic model saturation region current formula, and the saturation region ballistic rate in the full voltage range is obtained:

[0198] .

[0199] Three, effect description of the above scheme of the present application.

[0200] The extraction method proposed by the present application has made significant technical progress in the field of characterization of low-temperature CMOS devices, mainly in the following three aspects.

[0201] 1. Independence and robustness of MFP extraction.

[0202] The core MFP extraction scheme of the present invention has unique physical advantages, solving the problems of "uncertainty" and "inaccuracy" in the prior art. Specifically:

[0203] (E1) Complete independence from microscopic parameter assumptions (Parameter-Free Extraction): Existing methods usually rely on the constitutive equation to back-calculate, which falls into the circular argument trap of "in order to measure , one must first assume ", and is often unknown at the nanoscale. The present invention innovatively utilizes the geometric scaling law of quasi-ballistic transport , separates the length-dependent term (ballistic correction term) from the length-independent term (diffusion limit term) in the effective mobility inverse, and then directly calculates using their relationship. This process only relies on the self-consistency of the macroscopic current-voltage data with channel length, without the need to know the carrier effective mass, Fermi velocity, or scattering time, thus ensuring that the extracted MFP is a pure experimental observation value.

[0204] (E2) Accurate parasitic resistance de-embedding and mechanism decoupling: At low temperatures (such as 4K), the drain-source parasitic resistance significantly increases, and traditional methods often misjudge its voltage drop as channel scattering, leading to a serious underestimate of MFP. The present invention combines high-order derivative analysis and length scaling, mathematically strictly separating the length-independent drain-source parasitic resistance , the length-independent strong-field scattering term (corresponding to surface roughness), and the length-linearly dependent weak-field scattering term (corresponding to Coulomb / ballistic effects). This deep physical mechanism decoupling ensures that the extracted λ truly reflects the intrinsic transport limit within the channel, rather than the artifact of contact characteristics.

[0205] (E3) Minimal testing requirements and high throughput: Compared to complex characterization methods that rely on strong magnetic fields (such as SdH oscillations) or radio frequency S parameters, the present invention only requires a conventional direct current-voltage scan. This enables the method to be directly applied to industry-standard wafer-level probers, allowing for the rapid statistical analysis of MFP distribution for hundreds or thousands of devices, providing a feasible engineering solution for low-temperature process monitoring.

[0206] 2. Microscopic parameter extraction and non-equilibrium state diagnosis capability.

[0207] Based on the above accurate MFP extraction results, the application further expands the characterization capability of the physical properties of the device microscopically:

[0208] (F1) Physically self-consistent real effective mass acquisition: Abandoning the traditional method of directly using the bulk material effective mass (0.19m0). By combining the data of the linear region (low-energy state) and the saturation region (high-energy state), the application can accurately "weigh" the effective mass modulated by the nanoscale quantum confinement effect and the stress effect in the low-field inversion region. Experimental results show that this value is often greater than the theoretical value, revealing the non-ideal factors in the low-temperature actual device.

[0209] (F2) Quantitative diagnosis of non-equilibrium transport: The application proposes to use the linear region ballistic rate as a reference to verify the saturation region leakage source current. The deviation between the two can directly quantify the degree of inhibition of high-energy scattering mechanisms (such as optical phonon emission) on ballistic transport. This provides a quantitative physical criterion for understanding why low-temperature devices cannot achieve the ideal ballistic limit, and points out the specific direction for improving device performance through interface optimization or stress engineering.

[0210] 3. Industrial application value.

[0211] (G1) Low-cost wafer-level process monitoring: This method only requires a conventional direct current-voltage scan, without the need for magnetic fields or radio frequency equipment. This makes it possible to use standard automatic probe stations to quickly screen the micro quality (such as interface roughness and scattering intensity) of thousands of transistors on the production line of a foundry, greatly reducing the testing cost and cycle of low-temperature process development.

[0212] (G2) High-precision PDK (Process Design Kit) model calibration: The extracted thermal injection velocity, effective mass, and This provides key physical patches for compact models such as BSIM (Berkeley Short Channel Insulated Gate Field Effect Transistor Model), which 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.

[0213] Four, example explanation.

[0214] Taking the thermal management and selection of quantum computing control chips as an example, the above-mentioned scheme provided by the application has specific key application value in the field of quantum computing hardware, especially in solving the "power wall" problem of low-temperature electronics, providing a physical level solution.

[0215] Example one, micro-diagnosis and positioning of heat source: Quantum bits are extremely sensitive to thermal noise, and the power consumption of low-temperature control chips is the biggest bottleneck limiting the expansion (Scaling) of quantum bits of quantum computers. Using the saturation region ballistic rate extracted by the method The backscattering coefficient r of the source end carrier can be quantified directly:

[0216] ;

[0217] The lower (meaning the higher backscattering coefficient r), the more intense the optical phonon emission of high-energy carriers in the source end kT layer, thereby converting potential energy into lattice heat energy (Joule heat). Therefore, the method essentially provides an "electrical thermal imager" function, which can help designers quickly identify and eliminate device units that cause serious local heating due to poor interface quality or improper structural design during chip tape-out testing.

[0218] Example two, low-power device selection based on stress engineering: The experimental characterization results of the present application show that in PMOS (P-type metal-oxide-semiconductor field-effect transistor) devices, a narrow channel (Narrow Width) structure can introduce mechanical stress, thereby significantly reducing the effective mass of carriers , and greatly improving the saturation region ballistic rate . Using this method, circuit designers can quantify micro-parameters under different geometric sizes, quickly select the best device structure (such as narrow finger width multi-finger parallel PMOS) with "low effective mass and high ballistic rate" characteristics, and preferentially apply it to critical qubit drive lines. This device selection strategy based on the physical bottom layer can fundamentally reduce the unit drive current power consumption of the control chip, helping to realize the low-temperature integration of large-scale quantum computing systems.

[0219] Through the description of the above implementation, those skilled in the art can clearly understand that the above-mentioned embodiments can be implemented by software, or can be implemented by means of software plus necessary general hardware platforms. Based on such understanding, the technical solutions of the above-mentioned embodiments can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a U disk, a mobile hard disk, etc.), including a plurality of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in various embodiments of the present application.

[0220] Example two

[0221] The present application also provides a low-temperature CMOS carrier MFP and a micro-parameters extraction system, which is mainly used to realize the method provided by the above-mentioned embodiments, as shown in Figure 2 , the system mainly includes:

[0222] The carrier MFP extraction model construction unit is configured to construct a carrier MFP extraction model eliminating micro-unknown quantities based on a quasi-ballistic transport model and an effective mobility extraction technique, and is expressed as: ; wherein the strong field scattering term and the weak field scattering term are obtained based on the effective mobility extraction technique, is the strong field scattering term; is a base value coefficient, is a length modulation coefficient; B is a power index, , and B are fitting parameters in the carrier MFP extraction model, and they are all parameters obtained by using the weak field scattering term, is an effective gate overdrive voltage; is a carrier MFP, and MFP is a mean free path;

[0223] The current and voltage data acquisition and preprocessing unit is configured to measure a group of CMOS devices with different channel lengths at a temperature zone lower than a set temperature, and extract the effective gate overdrive voltage from the measured current and voltage data; wherein CMOS is a complementary metal oxide semiconductor.

[0224] The effective mobility decoupling and fitting parameter solving unit is configured to decouple the effective mobility based on the effective gate overdrive voltage, and solve the fitting parameters in the carrier MFP extraction model.

[0225] The carrier MFP extraction unit is configured to bring the solved fitting parameters and the effective gate overdrive voltage into the carrier MFP extraction model, and obtain the carrier MFP varying with the effective gate overdrive voltage.

[0226] The micro-parameter decoupling and extraction unit is configured to decouple the micro-parameters based on the carrier MFP varying with the effective gate overdrive voltage and the measured current data, and extract the decoupled micro-parameters one by one.

[0227] Since the main technical details involved in the system have been described in detail in the previous embodiments, they will not be described again.

[0228] Those skilled in the art can clearly understand that, for the convenience and brevity of description, only the division of the above functional modules is taken as an example for illustration, and in actual application, the above functions can be completed by different functional modules according to needs, that is, the internal structure of the system is divided into different functional modules to complete all or part of the functions described above.

[0229] The above description is merely preferred embodiments of the present application, but the protection scope of the present application is not limited thereto, and any changes or substitutions easily conceived by those skilled in the art within the technical scope disclosed by the present application should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims. The information disclosed in the background section of the present application is merely intended to deepen the understanding of the general background of the present application, and should not be regarded as acknowledging or implying in any form that the information constitutes the prior art known to those skilled in the art.

Claims

1. A method for extracting microscopic parameters from a low-temperature CMOS carrier MFP, 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, 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. ; 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. , 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; This is a strong-field scattering term. 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 Fermi-Dirac integration, 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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