CN117540683A - Extraction method of BSIM4 model characteristic parameters of MOS device - Google Patents
Extraction method of BSIM4 model characteristic parameters of MOS device Download PDFInfo
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- CN117540683A CN117540683A CN202311602990.1A CN202311602990A CN117540683A CN 117540683 A CN117540683 A CN 117540683A CN 202311602990 A CN202311602990 A CN 202311602990A CN 117540683 A CN117540683 A CN 117540683A
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- 238000000605 extraction Methods 0.000 title claims abstract description 19
- 238000000034 method Methods 0.000 claims abstract description 28
- 238000012216 screening Methods 0.000 claims abstract description 16
- 230000035945 sensitivity Effects 0.000 claims abstract description 13
- 238000004458 analytical method Methods 0.000 claims description 9
- 238000004364 calculation method Methods 0.000 claims description 8
- 238000011156 evaluation Methods 0.000 claims description 4
- 238000012546 transfer Methods 0.000 claims description 3
- 238000005259 measurement Methods 0.000 description 5
- 230000008569 process Effects 0.000 description 5
- 230000000694 effects Effects 0.000 description 4
- 230000006872 improvement Effects 0.000 description 4
- 238000013461 design Methods 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 3
- 230000009286 beneficial effect Effects 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 230000010354 integration Effects 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 239000004065 semiconductor Substances 0.000 description 2
- 101000955967 Deinagkistrodon acutus Thrombin-like enzyme acutin Proteins 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 101150014330 dfa2 gene Proteins 0.000 description 1
- 101150061638 dfa3 gene Proteins 0.000 description 1
- 101150000999 dfa4 gene Proteins 0.000 description 1
- 238000004141 dimensional analysis Methods 0.000 description 1
- 230000005669 field effect Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000003860 storage Methods 0.000 description 1
Classifications
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/30—Circuit design
- G06F30/36—Circuit design at the analogue level
- G06F30/367—Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods
Abstract
The invention discloses a BSIM4 model characteristic parameter extraction method of a MOS device, and relates to the technical field of transistor devices. The extraction method comprises the following steps: setting a using method of a lexical method, wherein a definite type finite automaton is used for identifying a section of characters as a Token sequence; screening sensitivity; selecting parameters; and solving the identified Token sequence, and obtaining parameters to be fitted based on the generation formula of the grammar G.
Description
Technical Field
The invention relates to the technical field of transistor devices, in particular to a BSIM4 model characteristic parameter extraction method of a MOS device.
Background
Metal-oxide-semiconductor field effect (MOSFET) transistors are the basic building blocks of integrated circuits. A unipolar transistor by majority carrier to transfer current has the features of small size, simple process, easy control of device parameters, etc. The fabrication of large scale integrated circuits using MOS technology is a dominant technology in the semiconductor industry. The integration of MOS integrated circuits has grown at a remarkable rate, mainly due to the smaller size of MOS transistors and the improvement in process technology. MOSFET device models are key ties that relate IC design and IC product functions to performance. As the size of integrated devices becomes smaller and the integration scale becomes larger, the process of integrated circuits becomes more complex and the precision requirements on device models become higher. The primary problem that IC CAD designers need to solve is how to build an accurate MOSFET model.
BSIM series models are developed by BSIM model development groups of the university of Berkeley, short channel MOSFET transmission characteristics are described by a simple DC model from a first generation BSIM1 model to a second generation BSIM2 model, the BSIM model is based on a semi-empirical model, the BSIM4 model of the third generation is completely established on a physical basis, the BSIM model is based on a physical model of quasi-two-dimensional analysis, physical characteristics related to devices in operation are mainly solved, influences of process parameters and device sizes are considered, fitting parameters are introduced for improving accuracy in specific use to modify errors when equations describe certain device characteristics, and BSIM3V3 is widely applied in industry standards. As devices enter the deep submicron regime, the BSIM4 model was released in 2000, which improved over BSIM3V3 in terms of high frequency applications. BSIM4 meets the requirements of most digital circuit, analog circuit and radio frequency high frequency circuit design manufacturers, has higher model precision and simulation efficiency, and is a mainstream model in the industry so far.
At present, the MOSFETs are extracted at home and abroad, and because of the lack of some effect models, the established models are inaccurate. And a complete parameter extraction technology is not provided for MOSFET devices, so that development of a self-adaptive parameter extraction method is urgently needed.
Disclosure of Invention
The invention aims to solve the problem of how to directly, automatically and accurately position the most suitable model according to measurement data for extracting parameters for so many models in a model library when MOSFET devices extract parameters.
Object of the invention
The invention aims to provide a method for extracting characteristic parameters of a BSIM4 model of a MOS device, which aims to solve the problem of how to directly, automatically and accurately position a most suitable model for parameter extraction according to measurement data in a BSIM4 model library of the MOS device.
(II) technical scheme
In order to solve the above problems, the present invention provides a method for extracting a BSIM4 model feature parameter of a MOS device, where the method includes:
setting a using method of a lexical method, wherein a definite type finite automaton is used for identifying a section of characters as a Token sequence;
screening sensitivity;
selecting parameters;
solving the identified Token sequence, wherein a grammar G is provided, and the generation formula of the grammar G is as follows:
S→E
E→B_l EB_r|Eδ_2E|δ_1B_l EB_r|P|C
P→p
δ_2→+,-,×,÷,…
δ_1→sin,cos,tan,…
B_l→(
B_r→)
C→c
and obtaining parameters to be fitted based on the generation formula of the grammar G.
Optionally, before obtaining the parameters to be fitted based on the generation formula of the grammar G, the method further includes:
eliminating left recursion, extracting left common factors to obtain LL grammar, and generating a prediction analysis table;
performing grammar analysis to obtain a CFG analysis tree;
and generating an inverse Polish expression of the calculation sequence, and performing arithmetic formula shifting by using the Polish expression to obtain parameters to be fitted.
Optionally, the method for using the set lexical words further includes:
the model formula is expressed generically for all non-PDE models using the model formula M, where M ε L (M), L (M) can be expressed as:
L(M)＝f(Σ,δ,B)；
wherein the identifier set Σ= { P u C }, P is a parameter set, C is a constant set,the operator set δ= { δ_1 ∈δ_2}, δ_1 is a single operator, δ_1 (a) =b, δ_2 is a binary operator, δ_2 (a, b) =c; a. b, c e Σ delimiter set b= { (,) }.
Optionally, screening the sensitivity comprises:
making an initial assumption of all parameters;
utilizing the characteristics of the parameter library to perform preliminary screening on formulas in specific parameter solving;
and carrying out sensitivity evaluation on the formula set obtained after the preliminary screening.
Optionally, generating an inverse polish expression of the calculation sequence, performing a formula shift by using the polish expression, and obtaining the parameters to be fitted includes:
and carrying out parameter solving by using a Levenberg-Marquadt method to obtain parameters to be fitted.
(III) beneficial effects
The technical scheme of the invention has the following beneficial technical effects:
1. the self-adaptive extraction of parameters can not reconstruct a model from an underlying structure due to the addition of some new effects, and the new parameters are directly added.
2. When parameter extraction is fitted, the technical scheme can enable the model function to be converged during calculation.
Drawings
FIG. 1 is a schematic flow chart of the extraction method of the present invention;
FIG. 2 is a schematic equivalent circuit diagram of the extraction of Vuic of a selected HTB device using the extraction method of the present invention;
FIG. 3 is a finite automaton of the deterministic type for identifying parameters in accordance with the present invention;
FIG. 4 is a finite automaton of the deterministic type for identifying unsigned constants in accordance with the present invention;
FIG. 5 is a finite automaton of the deterministic type of identification delimiters according to the invention;
FIG. 6 is a deterministic finite automaton for recognizing Token sequences according to the present invention;
FIG. 7 is a graph of the fitting effect of the method used in the present invention.
Detailed Description
The objects, technical solutions and advantages of the present invention will become more apparent by the following detailed description of the present invention with reference to the accompanying drawings. It should be understood that the description is illustrative only and is not intended to limit the scope of the invention. In addition, in the following description, descriptions of well-known structures and techniques are omitted so as not to unnecessarily obscure the present invention.
A layer structure schematic diagram according to an embodiment of the present invention is shown in the drawings. The figures are not drawn to scale, wherein certain details may be exaggerated and some details may be omitted for clarity. The shapes of the various regions, layers and relative sizes, positional relationships between them shown in the drawings are merely exemplary, may in practice deviate due to manufacturing tolerances or technical limitations, and one skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions as actually required.
It will be apparent that the described embodiments are some, but not all, embodiments of the invention. All other embodiments, which can be made by one of ordinary skill in the art without undue burden on the person of ordinary skill in the art based on embodiments of the present invention, are intended to be within the scope of the present invention.
In addition, the technical features of the different embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention will be described in more detail below with reference to the accompanying drawings. Like elements are denoted by like reference numerals throughout the various figures. For clarity, the various features of the drawings are not drawn to scale.
The present invention will be described in detail with respect to the existing components which are not related to the point of improvement of the present invention, with or without a brief description, and with emphasis on the components which make improvements over the prior art.
Referring to fig. 1 to 7, the present embodiment provides a method for extracting a BSIM4 model feature parameter of a MOS device, where the method includes:
setting a using method of a lexical method, wherein a definite type finite automaton is used for identifying a section of characters as a Token sequence;
screening sensitivity;
selecting parameters;
solving the identified Token sequence, there is grammar G, which has the following formula:
S→E
E→B_l EB_r|Eδ_2E|δ_1B_l EB_r|P|C
P→p
δ_2→+,-,×,÷,…
δ_1→sin,cos,tan,…
B_l→(
B_r→)
C→c
eliminating left recursion, extracting left common factors to obtain LL grammar, and generating a prediction analysis table;
performing grammar analysis to obtain a CFG analysis tree;
and generating an inverse Polish expression of the calculation sequence, and performing arithmetic formula shifting by using the Polish expression to obtain parameters to be fitted.
Further, the method for using the set lexical words further comprises:
the model formula is expressed generically for all non-PDE models using the model formula M, where M ε L (M), L (M) can be expressed as:
L(M)＝f(Σ,δ,B)；
wherein the identifier set Σ= { P u C }, P is a parameter set, C is a constant set,the operator set δ= { δ_1 ∈δ_2}, δ_1 is a single operator, δ_1 (a) =b, δ_2 is a binary operator, δ_2 (a, b) =c; a. b, c e Σ delimiter set b= { (,) }. And (5) carrying out grammar assistance, and calibrating the calculation priority of the grammar segments.
Preferably, for a piece of text, it is identified as a Token sequence using a deterministic finite automaton (DFA, deterministic Finite automata).
Like the DFA1 of the identification parameters of fig. 3, the DFA2 of the identification unsigned constant of fig. 4, the DFA3 of the identification delimiter of fig. 5, and the DFA4 of the Token sequence of fig. 6.
Further, screening sensitivity includes:
making an initial assumption of all parameters;
utilizing the characteristics of the parameter library to perform preliminary screening on formulas in specific parameter solving;
and carrying out sensitivity evaluation on the formula set obtained after the preliminary screening.
That is, an assumption is made that all parameters have initial values. The formula storage simultaneously shows the characteristics of the Token sequence and the parameter library, and the characteristics of the parameter library can be utilized to carry out primary screening on the formula in solving a specific parameter. Screening is carried out on the formula set obtained after preliminary screening for sensitivity evaluation.
Further, the selecting parameters includes:
step 1, selecting parameters with weights larger than preset values from experimental data, and solving;
step 2, solving a formula with single parameter solving selection sensitivity larger than a specified set threshold value;
and 3, repeatedly executing the step 1 and the step 2 until the error of the model parameter reaches the set standard and the optimization is finished.
That is, parameters with larger weights in experimental data are selected and solved, and then a formula with sensitivity larger than a certain specified threshold value is selected for solving the single parameters to perform joint solving. This process is repeated until the error of the model parameters reaches a certain criterion, ending the optimization. That is, disturbance is applied, fluctuation conditions are observed, and no matter how large the proportion of the fluctuation to the whole size is, the fluctuation is obvious.
Further, generating an inverse Polish expression of the calculation sequence, performing an arithmetic transfer by using the Polish expression, and obtaining parameters to be fitted includes:
and carrying out parameter solving by using a Levenberg-Marquadt method to obtain parameters to be fitted.
The accuracy of the extraction method is verified as follows:
step one:
the device dimensions were chosen for a W/L of 10 μm/10 μm, at v_bs=0, -0.375, -0.750, -1.125, -1.500 (units V), v_ds yielding a total of 170 (34 x 5) measurements of i_ds and v_gs at 0.05V, under which conditions the measurements are suitable for extracting VTH0, K1, K2.
Step two:
text format of threshold voltage v_th model in input BISM 4:
V_th＝VTH0+K1*(sqrt(phi_s-V_bs)-sqrt(phi_s)-K2*V_bs
step three:
the measurements under this condition are then suitable for extracting VTH0, K1, K2.
Step four:
the original values of VTH0, K1 and K2 are substituted into the formula, and the measured data of VTH0, K1 and K2 are substituted and used, so that the obtained parameters are shown in the table 1, and the error between the obtained parameters and the actual values is within 3%.
As shown in fig. 7, this method can be demonstrated to be effective by comparison of the original parameters with the extracted parameters and fitting of the curve.
It is to be understood that the above-described embodiments of the present invention are merely illustrative of or explanation of the principles of the present invention and are in no way limiting of the invention. Accordingly, any modification, equivalent replacement, improvement, or the like, which does not depart from the spirit and scope of the present invention, should be included in the protection zone of the present invention. Furthermore, the appended claims are intended to cover all such changes and modifications that fall within the metes and bounds of the appended claims, or equivalents of such metes and bounds.
TABLE 1 V_th parameter in BSIM4 model
Claims (5)
1. The extraction method of the BSIM4 model characteristic parameters of the MOS device is characterized by comprising the following steps:
setting a using method of a lexical method, wherein a definite type finite automaton is used for identifying a section of characters as a Token sequence;
screening sensitivity;
selecting parameters;
solving the identified Token sequence, wherein a grammar G is provided, and the generation formula of the grammar G is as follows:
S→E
E→B_l EB_r|Eδ_2E|δ_1 B_l EB_r|P|C
P→p
δ_2→+,-,×,÷,…
δ_1→sin,cos,tan,…
B_l→(
B_r→)
C→c
and obtaining parameters to be fitted based on the generation formula of the grammar G.
2. The extraction method according to claim 1, further comprising, before deriving parameters to be fitted based on the formula of the grammar G:
eliminating left recursion, extracting left common factors to obtain LL grammar, and generating a prediction analysis table;
performing grammar analysis to obtain a CFG analysis tree;
and generating an inverse Polish expression of the calculation sequence, and performing arithmetic formula shifting by using the Polish expression to obtain parameters to be fitted.
3. The extraction method according to claim 1, wherein the method of using the set vocabulary further comprises:
the model formula is expressed generically for all non-PDE models using the model formula M, where M ε L (M), L (M) can be expressed as:
L(M)＝f(Σ,δ,B)；
wherein the identifier set Σ= { P u C }, P is a parameter set, C is a constant set,the operator set δ= { δ_1 ∈δ_2}, δ_1 is a unitary operator, δ_1 (a) =b, δ_2 is a binary operatorOperator, δ_2 (a, b) =c; a. b, c e Σ delimiter set b= { (,) }.
4. The extraction method according to claim 1, wherein screening sensitivity comprises:
making an initial assumption of all parameters;
utilizing the characteristics of the parameter library to perform preliminary screening on formulas in specific parameter solving;
and carrying out sensitivity evaluation on the formula set obtained after the preliminary screening.
5. The extraction method according to any one of claim 1 to 4, wherein,
generating an inverse Polish expression of the calculation sequence, performing arithmetic formula transfer by using the Polish expression, and obtaining parameters to be fitted comprises:
and carrying out parameter solving by using a Levenberg-Marquadt method to obtain parameters to be fitted.
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