CN100570618C - Be applied to the ferroelectric capacitor behavior model in the SPICE circuit simulation program - Google Patents
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Abstract
The invention belongs to the integrated circuit (IC) design technical field, relate to the integrated circuit (IC) design of using ferroelectric capacitor, relate in particular to the ferroelectric capacitor behavior model in a kind of SPICE of being applied to circuit simulation program.This model utilizes the expression formula function in the SPICE program to set up the nonlinear capacitance original paper, cooperate differentiating circuit as control circuit, the physical behavio(u)r of simulation ferroelectric capacitor, this model component comprises: a linear capacitance, a nonlinear capacitance, a voltage controlled voltage source and a differentiating circuit; Contact with voltage controlled voltage source, differentiating circuit successively by the parallel circuit that described linear capacitance, nonlinear capacitance are formed.With respect to prior art, by the nonlinear capacitance performance, available expression carries out accurate assignment fully in the electricity behavior of ferroelectric capacitor in the invention.The work control of this model is finished by differentiating circuit fully, and control procedure is simple, is beneficial to the raising simulation velocity.Because control signal is the input voltage time differential, therefore be more suitable for transient state emulation.
Description
Technical field
The invention belongs to the integrated circuit (IC) design technical field, relate to the integrated circuit (IC) design of using ferroelectric capacitor, relate in particular to the ferroelectric capacitor behavior model in a kind of SPICE of being applied to circuit simulation program.
Background technology
Ferroelectric capacitor is a kind of capacity cell that utilizes ferroelectric material to make, and in the design of current integrated circuit (IC) design especially memory circuitry, has more and more important position.For standard and accurate circuit design, be absolutely necessary based on the circuit simulation of EDA (Electronic Design is auxiliary) software.Yet ferroelectric capacitor does not also obtain independently analogy model as a kind of novel element in various eda softwares, brought very big difficulty to integrated circuit (IC) design.Therefore the ferroelectric capacitor modelling that is fit to eda software at present remains the work of a very challenging property.The ferroelectric capacitor model can be divided into two kinds substantially: physical model and behavior model.Physical model can intuitively react the physical characteristics of ferroelectric material, but the structural physical model needs darker physical basis, and lacks circuit description intuitively, is difficult in the eda software and realizes.Behavior model is then cast aside the details of ferroelectric theory, just merely observes macroscopical electrical characteristic of ferroelectric material from the angle of circuit, and is described, and does not need deep ferroelectric physical knowledge background, thereby realizes than being easier to.Below briefly introduce existing several behavior models.
(1) two capacitor models: this is an early stage model that is based upon on the ferroelectric hysteresis loop basis.This model is similar to ferroelectric hysteresis loop two straight lines of drawing on two of longitudinal axis the right, every corresponding linear capacitance of straight line, and capacitance is the slope of straight line, and model parameter can obtain by extracting from empirical curve, and model structure is with reference to Fig. 3.But because ferroelectric hysteresis loop is not only relevant with the ferroelectric capacitor size, also relevant with added signal waveform, therefore after changing signal, parameter needs to extract again.In the actual storage circuit, the signal amplitude and the waveform that are added on the ferroelectric capacitor are unforeseen, and the model parameter under so different situations can only be set very roughly, has very mistake in realistic simulation.Therefore this model is a very coarse capacitor model.
(2) numerical model: simulate loop line with a hyperbolic tangent function.Numerical model provides a kind of good method for the ferroelectric capacitor static characteristics analysis, but uncomfortable cooperation transient analysis, because it does not comprise any parameter relevant with transient performance.
(3) distributed adverse field model: when adding enough electric fields on dipole, dipole can be another kind of state from a kind of state turnover, and making the critical electric field of dipole generation polarised direction upset is coercive electric field.For the ferroelectrics of single domain, this coercive electric field is with the coercive field unanimity of the ferroelectric hysteresis loop of this material; For the multidomain ferroelectrics, because the direction of electricdomain has nothing in common with each other, different electricdomains are reversed under different impressed voltages.When the electricdomain number is very big, the electricdomain number that counter-rotating takes place down different voltages forms Gaussian distribution to voltage, like this, suppose that the polarization of each electricdomain is identical to the contribution of total polarization intensity, the increase of the polarization intensity that then every increase unit voltage is caused also meets Gaussian distribution to voltage.This model is compared with numerical model, is similar in essence.
(4) based on ferromagnetic model: ferroelectrics and ferromagnet have many similar parts, therefore can utilize existing ferromagnetic core model to come the ferroelectric model of emulation.The voltage scale that will be added on the ferroelectric capacitor based on the model on ferromagnetic basis is converted to current source, be added on the magnetic core, produce voltage, again voltage scale is converted to electric current by ferroelectric capacitor based on magnetic hysteresis loop, model structure is referring to Fig. 4, and wherein K1, K2 are two scale-up factors.If the magnetic core model accuracy improves, the precision of ferroelectric capacitor class magnetic model also can further improve, but this model is unsuitable for doing transient analysis, because the two does not have general character on transient response.
(5) intensify the counter-rotating model based on electric current: this model both can have been done static analysis also can do transient analysis.Model is regarded ferroelectric capacitor as electric capacity and a current source parallel connection.Electric capacity determines that by the small-signal dielectric coefficient of ferroelectric material current source is represented the Switching Currents of electric capacity, obtains by electric capacity is carried out pulse test.For every kind of different pulse height, the current source parameter need redefine, and the complicacy that this has increased model is unfavorable for the practical application of model, because the voltage that is added on the ferroelectric capacitor is ignorant in advance.Model parameter also has dependent form to the time constant of circuit in addition.
(6) zero reversing time transient model (ZSTT): the polarization reversal time of model assumption ferroelectric capacitor is zero, and the polarization reversal that is far longer than ferroelectric capacitor when the RC of research circuit constant supposes that the error of being brought is negligible during the time.Reversing time is zero to mean that the increase of ferroelectric capacitor polarization charge is instantaneous, and the increment of electric charge is the function that impressed voltage closes the ferroelectric capacitor original state, and it had nothing to do with the time.The circuit of ZSTT ferroelectric capacitor model mainly is made up of two parts, and the one, the switch of control ferroelectric capacitor state exchange, the 2nd, C
0(V
0) and C
1(V
1) two nonlinear capacitances, model structure is referring to Fig. 5, and wherein S01, S02, S11 and S12 are the electric capacity state switch.The logic control of capacitance switch needs complicated circuit, is unfavorable for simulation.Simultaneously, the value of two nonlinear capacitances adopts piecewise linear data list usually, and to different electric capacity, change mass data could emulation.
Above various models or accurate inadequately, or use inconvenience, or complex structure is restive, all inconvenience to some extent when therefore being applied in the eda tool.SPICE is present the most frequently used EDA circuit simulation tools, becomes extremely important at the ferroelectric capacitor model of this instrument.
Summary of the invention
In view of the deficiencies in the prior art, the objective of the invention is to design a kind of ferroelectric capacitor model of being convenient to be applied in the SPICE eda tool, can realize quick, high-precision emulation, the while is simple in structure, control is convenient.
A kind of ferroelectric capacitor behavior model that is applied in the SPICE circuit simulation program, this model utilizes the expression formula function in the SPICE program to set up the nonlinear capacitance original paper, and cooperate differentiating circuit as control circuit, simulate the physical behavio(u)r of ferroelectric capacitor, the ingredient of this model comprises: positive end points, negative terminal, first linear capacitance, a nonlinear capacitance, a voltage controlled voltage source and a differentiating circuit;
Be the parallel circuit of being made up of described first linear capacitance, nonlinear capacitance and voltage controlled voltage source between described positive end points, negative terminal, the positive output end of described voltage controlled voltage source links to each other with differentiating circuit, and negative output terminal connects earth terminal.
Described differentiating circuit, its ingredient comprises: an ideal operational amplificr, the linear resistance and second linear capacitance;
Wherein: described ideal operational amplificr has n+, and n-, three links of out, linear capacitance are connected between the positive output end and n+ end of voltage controlled voltage source, and linear resistance is connected between n+ and the out end, and the n-end connects earth terminal;
The signal of described out end is the control signal of model.
Described nonlinear capacitance, its capacitance is determined by following expression formula
Wherein:
Wherein, C
1(V) the expression description is half on the right side, the C of the ferroelectric capacitor behavior curve of parameter with voltage V
2(V) the expression description is half on a left side, a, the c of the ferroelectric capacitor behavior curve of parameter with voltage V
u, c
dThe parameter of two shape facilities about ferroelectric capacitor behavior curve is described in expression;
V represents to be applied to the voltage at positive end points of ferroelectric capacitor behavior model and negative terminal two ends;
V
cThe coercive voltage of expression ferroelectric capacitor also is a parameter of describing the ferroelectric capacitor feature;
The voltage of V (out) expression end points out;
A, c in the formula
uAnd c
dBe to describe C
1(V) and C
2(V) parameter of curve shape obtains from the capacity measurement extracting data;
Sgn () is-symbol function is used for the symbol of judgment variable, if positive sign, then value is 1; If negative sign, then value is 0.
Beneficial effect of the present invention:
The present invention and the comparison that has several models now
The electricity behavior of ferroelectric capacitor by the nonlinear capacitance performance, can be carried out accurate assignment with expression formula fully among the present invention, and degree of accuracy improves a lot than former method (1).The work control of this model is finished by differentiating circuit fully, and compare and existing method: method (5), method (6), it is many that control procedure is simple, helps improving simulation velocity.Compare and existing method: method (2), (3), and (4), because control signal is the input voltage time differential, promptly therefore voltage change ratio is more suitable for transient state emulation.This model has simple in structure, and simulation velocity is fast, the simulation accuracy advantages of higher.
Description of drawings
Fig. 1 is a kind of ferroelectric capacitor behavior model structure that is applied in the SPICE circuit simulation program;
Fig. 2 is the capacitance curve and the ferroelectric hysteresis loop of the linear capacitance in the capacitor model;
Fig. 3 is two capacitor model structures;
Fig. 4 is based on ferromagnetic model structure;
Fig. 5 is the ZSTT model structure.
Embodiment
Embodiment below in conjunction with this model of description of drawings:
Fig. 1 is a kind of ferroelectric capacitor behavior model based on the voltage delay behavior, shown among the figure 1:
This model utilizes the expression formula function in the SPICE program to set up the nonlinear capacitance original paper, and cooperate differentiating circuit as control circuit, simulate the physical behavio(u)r of ferroelectric capacitor, the ingredient of this model comprises: positive end points, negative terminal, the first linear capacitance Cy, a nonlinear capacitance Cx, a voltage controlled voltage source and a differentiating circuit;
Be the parallel circuit of being made up of the described first linear capacitance Cy, nonlinear capacitance Cx and voltage controlled voltage source between described positive end points, negative terminal, the positive output end of described voltage controlled voltage source links to each other with differentiating circuit, and negative output terminal connects earth terminal.
Described differentiating circuit, its ingredient comprises: an ideal operational amplificr, the linear resistance and the second linear capacitance C;
Be specially:
This capacitor model comprises two end points (+,-), is connecting the main element of describing the electric capacity behavior on these two end points: linear capacitance (Cy) and nonlinear capacitance (Cx); The signal voltage V that electric capacity is applied is added on these two end points; Voltage V be applied to simultaneously gain be 1 voltage controlled voltage source VCVS input end (V+, V-), be transformed into output terminal (O+, O-) on, therefore (O+, O-) voltage of port equals that (V+, the V-) voltage of port promptly equals V.From (O+, O-) voltage that comes out of port is applied on the differentiating circuit, and the magnitude of voltage of this differentiating circuit output terminal out promptly is the differential value of voltage V, and we then have with the magnitude of voltage that V (out) represents port out
Linear capacitance (Cy) is a common capacity cell, and its size is a model parameter; The size of nonlinear capacitance (Cx) is by the value decision of expression formula.We can describe with reference to the diagram of figure 2:
Fig. 2 is the capacitance curve and the ferroelectric hysteresis loop of the linear capacitance in the capacitor model;
Transverse axis represents to apply voltage V among Fig. 2, Vm and-Vm represents forward maximal value and the maximum negative value of V; The longitudinal axis is a capacitance for capacitance curve, is charge value for ferroelectric hysteresis loop.Capacitance curve is the bimodal curve of V axle top, and ferroelectric hysteresis loop is centrosymmetric square loop line.Ferroelectric hysteresis loop and capacitance curve all comprise two branches as shown in the figure, and peak, the right side correspondence of the ACB branch of ferroelectric hysteresis loop and capacitance curve the process that voltage V changes to Vm from-Vm that applies; Peak, the left side correspondence of the BDA branch of ferroelectric hysteresis loop and capacitance curve the process that voltage V changes to-Vm from Vm that applies; Two processes are shown in the direction of arrow among the figure.The expression formula of nonlinear capacitance (Cx) is divided into C1 that describes the peak, right side and the C2 that describes the peak, left side, and their size is by applying voltage V decision, and the formula of embodying is:
Since the process that the corresponding voltage in peak, right side rises, the process that the corresponding voltage in peak, left side descends, so C
1The corresponding voltage derivative value that applies is on the occasion of, C
2The corresponding voltage derivative value that applies is a negative value, just can determine that by the sign of judging V (out) which expression formula this select calculate the value of Cx, therefore:
Sgn () is-symbol function in the expression formula is used for the symbol of judgment variable, if positive sign, then value is 1; If negative sign, then value is 0.We can find the Cx=C when being negative sign as V (out) by this simple calculating
1, V (out) Cx=C when being positive sign
2
The ingredient of differentiating circuit comprises: an ideal operational amplificr (OP), a linear resistance (R) and a linear capacitance (C)
Wherein: described ideal operational amplificr has n+, and n-, three links of out, linear capacitance are connected between the positive output end and n+ end of voltage controlled voltage source, and linear resistance is connected between n+ and the out end, and the n-end connects earth terminal;
The signal of described out end is the control signal of model.
As shown in FIG.:
Therefore V (out) can be used to refer to the symbol that applies voltage V differential, can find
Be V (out) symbol and the opposite in sign that applies voltage V differential.Ideal operational amplificr can be described with the behavior description voltage source in the SPICE software.
Contrast this model and common electric capacity, the two all is to have two end points, so this model also can be directly connected on the port of required connection as common electric capacity in use.Utilize this model can finish the various breadboardins that utilize ferroelectric capacitor.
Above-described embodiment is a more preferably embodiment of the present invention, and common variation that those skilled in the art carries out in the technical solution of the present invention scope and replacement all should be included in protection scope of the present invention.
Claims (3)
1. ferroelectric capacitor behavior model that is applied in the SPICE circuit simulation program, it is characterized in that, this model utilizes the expression formula function in the SPICE program to set up the nonlinear capacitance original paper, and cooperate differentiating circuit as control circuit, simulate the physical behavio(u)r of ferroelectric capacitor, the ingredient of this model comprises: positive end points, negative terminal, first linear capacitance, a nonlinear capacitance, a voltage controlled voltage source and a differentiating circuit;
Be the parallel circuit of being made up of described first linear capacitance, nonlinear capacitance and voltage controlled voltage source between described positive end points, negative terminal, the positive output end of described voltage controlled voltage source links to each other with differentiating circuit, and negative output terminal connects earth terminal.
2. the ferroelectric capacitor behavior model that is applied in the SPICE circuit simulation program according to claim 1 is characterized in that, described differentiating circuit, and its ingredient comprises: an ideal operational amplificr, the linear resistance and second linear capacitance;
Wherein: described ideal operational amplificr has n+, and n-, three links of out, second linear capacitance are connected between the positive output end and n+ end of voltage controlled voltage source, and linear resistance is connected between n+ and the out end, and the n-end connects earth terminal;
The signal of described out end is the control signal of model.
3. the ferroelectric capacitor behavior model that is applied in the SPICE circuit simulation program according to claim 1 is characterized in that, described nonlinear capacitance, and its capacitance is determined by following expression formula
Wherein:
Wherein, C
1(V) the expression description is half on the right side, the C of the ferroelectric capacitor behavior curve of parameter with voltage V
2(V) the expression description is half on a left side, a, the c of the ferroelectric capacitor behavior curve of parameter with voltage V
u, c
dThe parameter of two shape facilities about ferroelectric capacitor behavior curve is described in expression;
V represents to be applied to the voltage at positive end points of ferroelectric capacitor behavior model and negative terminal two ends;
V
cThe coercive voltage of expression ferroelectric capacitor also is a parameter of describing the ferroelectric capacitor feature;
The voltage of V (out) expression end points out;
A, c in the formula
uAnd c
dBe to describe C
1(V) and C
2(V) parameter of curve shape obtains from the capacity measurement extracting data;
Sgn () is-symbol function is used for the symbol of judgment variable, if positive sign, then value is 1; If negative sign, then value is 0.
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