CN103164562A - Difference inductance simulation method - Google Patents

Abstract

The invention discloses a difference inductance simulation method. Influence of process fluctuations are considered, a line width statistical distribution correction term which reflects the fluctuations of the process is added according to a metal line width monitoring value in a process line, metal line width, metal line interval and metal line resistivity of difference induction are revised, and a simulation inductance valve and a Q value of the difference induction is obtained by conducting difference induction simulation through a regular difference inductance model according to the revised metal line width, metal line interval and metal line resistivity of the difference induction. According to the difference inductance simulation method, random differences caused by the process fluctuations can be reflected, the difference distribution of the inductance and the Q value can be obtained through simulation, and a semiconductor product which contains the difference inductance is enabled to be well forecasted before production.

Description

The differential inductance emulation mode

Technical field

The application relates to the semiconductor emulation technology, particularly a kind of differential inductance emulation mode.

Background technology

Inductance is one of requisite element in Circuits System, and it is widely used in all kinds of circuit such as amplifier, oscillator, frequency mixer.Due to the development of integrated circuit technique, traditional discrete inductance element must be integrated in chip, and the spiral inductance in chip is exactly a kind of typical form of expression.Continuous progress along with making integrated circuit technology, from early stage plane individual layer spiral inductance, develop into the structure of the numerous complicated such as multilayer stacked inductance of utilizing multiple layer metal.Along with the requirement to circuit performance improves constantly, circuit structure has the form of balance, difference usually, and in these circuit, those scripts inductance of an end ground connection in single-end circuit just is transformed into the two ends differential inductance of access differential signal respectively.Because the signal at differential inductance two ends has identical amplitude and contrary phase place, this just requires the electric property of differential inductance as far as possible symmetrical, so differential inductance has symmetrical geometric configuration usually, is also referred to as symmetrical inductance.Differential inductance wiring domain as shown in Figure 1, differential inductance has higher quality factor (Q value) and larger SRF (self-resonant frequency), offer deviser's differential inductance model, must consider that four most important inductance parameters are with inductance value required in optimized circuit, four most important inductance parameters are respectively number of inductor N, metal line-width W, inductance D outer diameter and metal wire separation S.

In practical semiconductor inductance technique, the parasitic interaction that can have influence between metal wire due to technological fluctuation changes, and all can there be a random fluctuation range in the inductance value and the Q value that after inductance parameters is fixing, obtain.But conventional differential inductance model, only consider number of inductor N, metal line-width W, tetra-parameters of inductance D outer diameter and metal wire separation S, like this at given number of inductor N, metal line-width W, after inductance D outer diameter and metal wire separation S, what by the differential inductance model emulation, obtain is a fixedly result, can't reflect the mismatch phenomenon that technological fluctuation causes, the random difference that technological fluctuation can't be caused in model reflects, can't obtain the difference distribution of inductance value and Q value by the differential inductance model emulation, make product be difficult to predict preferably before production.

The account form of the inductance value of conventional difference inductor models and Q value is:

Q＝ω*L/R；ω＝1/2πf；R＝ρ′*L/(W*δ)；

L＝F(D，N)；

F is frequency, and R is metal wire resistance, and W is metal line-width, and δ is skin depth, and L is inductance value, and N is number of inductor, and D is the inductance external diameter, and ρ is the metallic resistance rate, μ ₀be the metal electron mobility, L is the function of number of inductor N, inductance D outer diameter.

Summary of the invention

The technical matters that the application will solve is to provide a kind of differential inductance emulation mode, can reflect the mismatch phenomenon that technological fluctuation causes, and obtains the difference distribution of inductance value and Q value.

For solving the problems of the technologies described above, the differential inductance emulation mode that the application provides comprises the following steps:

One. set up the conventional difference inductor models;

Two. obtain metal line-width, metal wire separation, metal wire resistivity, number of inductor, the inductance external diameter of the differential inductance of not considering technological fluctuation;

Three. metal line-width W, metal wire separation S, the metal wire electricalresistivityρ who does not consider technological fluctuation revised, obtain revised metal line-width W ', revised metal wire separation S ', revise after the metal wire electricalresistivityρ ';

W′＝W+w _m*agauss(0，1，1)；

S′＝S+2w _m*agauss(0，1，1)；

${\mathrm{\ρ}}^{\′}=\mathrm{\ρ}+{\mathrm{\ρ}}_1*{\left(\frac{1}{\sqrt{S}}\right)}^{\mathrm{sx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right)+{\mathrm{\ρ}}_2*{\left(\frac{1}{\sqrt{W}}\right)}^{\mathrm{wx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right);$

In above formula, W ' is revised metal line-width, and W is not for considering the metal line-width W of technological fluctuation, w _mfor the metal line-width correction factor, S ' is revised metal wire separation, and S is not for considering the metal wire separation of technological fluctuation, and ρ ' is metal wire resistivity after revising, and ρ is the metal wire resistivity of not considering technological fluctuation, ρ ₁the mismatch correction factor that resistivity changes with metal wire separation, ρ ₂it is the mismatch correction factor that resistivity changes with metal line-width, sx is metal wire separation index correction term, wx is metal line-width index correction term, and agauss (0,1,1) be Gaussian function, in its bracket, the 1st of (0,1,1) the 0 means that the central value of Gaussian function is 0, in bracket, the 2nd 1 means that the maximum sigma amplitude of Gaussian function curve from central value 0 to the right and left is 1, and 1 in bracket in the 3rd means that the sigma number of Gaussian function is 1;

Four. according to metallic resistance rate after the number of inductor of not considering technological fluctuation, inductance external diameter and revised metal line-width, revised metal wire separation, correction, to differential inductance emulation, obtain simulated inductor value and the Q value of differential inductance by the conventional difference inductor models.

Metal line-width correction factor w _m, the mismatch correction factor ρ that changes with metal wire separation of resistivity ₁, the mismatch correction factor ρ that changes with metal line-width of resistivity ₂, metal wire separation index correction term sx and metal line-width index correction term wx, can determine in the following manner;

(1). by formula:

W′＝W+w _m*agauss(0，1，1)、S′＝S+2w _m*agauss(0，1，1)、

${\mathrm{\ρ}}^{\′}=\mathrm{\ρ}+{\mathrm{\ρ}}_1*{\left(\frac{1}{\sqrt{S^{\′}}}\right)}^{\mathrm{sx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right)+{\mathrm{\ρ}}_2*{\left(\frac{1}{\sqrt{W^{\′}}}\right)}^{\mathrm{wx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right),$ Write respectively as the correction term of spice language:

(2). the metal line-width W of the differential inductance of demarcating with reference to +/-3sigma monitoring statistical distribution value and the domain of the metal line-width of differential inductance on processing line obtains metal width correction factor w _m; Metal line-width W, number of inductor N, the inductance D outer diameter of the differential inductance of demarcating according to domain, calculate metal wire separation S; Metal line-width W, the metal wire electricalresistivityρ of the differential inductance of demarcating according to domain and the metal wire separation S calculated, by above-mentioned correction term obtain revised metal line-width W ', revised metal wire separation S ', revise after the metal wire electricalresistivityρ ';

(3). select fixing 3MHz to the frequency between 30MHz, according to revised metal line-width W ', revised metal wire separation S ', revise after metal wire electricalresistivityρ ' and number of inductor N, the inductance D outer diameter of differential inductance, by the conventional difference inductor models, differential inductance is carried out to Monte Carlo simulation, obtain the emulation Q value of the differential inductance under this frequency;

(4). the distribution of the actual measurement Q value of differential inductance under the distribution of the emulation Q value of differential inductance and same frequency condition is compared, by matching, obtain the mismatch correction factor ρ that resistivity changes with metal wire separation ₁, the mismatch correction factor ρ that changes with metal line-width of resistivity ₂, metal wire separation index correction term sx, metal line-width index correction term wx.

The application's differential inductance emulation mode, consider the impact of technological fluctuation, add the live width statistical distribution correction term of reaction process fluctuation according to the metal live width monitoring value on processing line, metal line-width W, metal wire separation S, metallic resistance rate ρ to differential inductance are revised, metal line-width W ', metal wire separation S ', metallic resistance rate ρ ' according to revised differential inductance, to differential inductance emulation, obtain simulated inductor value and the Q value of differential inductance by the conventional difference inductor models.The application's differential inductance emulation mode, considered the impact of technological fluctuation on the metal line-width of differential inductance, metal wire separation, metallic resistance rate, the mismatch phenomenon that the reflection technological fluctuation causes, the random difference in model, technological fluctuation caused reflects, can obtain the difference distribution of inductance value and Q value by the differential inductance model emulation, the semiconductor product that comprises differential inductance can be predicted preferably before production.

The accompanying drawing explanation

In order to be illustrated more clearly in the application's technical scheme, below the accompanying drawing of the required use of the application is briefly described, apparently, accompanying drawing in the following describes is only some embodiment of the application, for those of ordinary skills, under the prerequisite of not paying creative work, can also obtain according to these accompanying drawings other accompanying drawing.

Fig. 1 is differential inductance wiring domain schematic diagram;

Fig. 2 is the application's differential inductance emulation mode process flow diagram.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present application, the technical scheme in the embodiment of the present application is clearly and completely described, obviously, described embodiment is only the application's part embodiment, rather than whole embodiment.Should be appreciated that preferred embodiment described herein is only for description and interpretation the application, and be not used in restriction the application.And, in the situation that do not conflict, embodiment and the feature in embodiment in the application can combine mutually.Embodiment based in the application, the every other embodiment that those of ordinary skills obtain, belong to the scope that the application protects.

Cause the factor of inductance technological fluctuation to have a lot, but should mainly be reflected in metal line-width W and two aspects of metal wire separation S, then indirectly be reflected on the physical characteristics of metal.Suppose to produce random difference because technological fluctuation has caused the resistivity of metal wire 1 and metal wire 2, express with formula:

${\mathrm{\ρ}}^{\′}=\mathrm{\ρ}+\mathrm{\Δ\ρ}=\mathrm{\ρ}+{\mathrm{\ρ}}_1*{\left(\frac{1}{\sqrt{S}}\right)}^{\mathrm{sx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right)+{\mathrm{\ρ}}_2*{\left(\frac{1}{\sqrt{W}}\right)}^{\mathrm{wx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right)---\left(1\right)$

In formula (1), ρ ' considers metal wire resistivity after the correction of technological fluctuation, and ρ does not consider technological fluctuation metal wire resistivity, and Δ ρ is the metal wire resistivity difference that technological fluctuation causes, ρ ₁the mismatch correction factor that resistivity changes with metal wire separation, ρ ₂it is the mismatch correction factor that resistivity changes with metal line-width, sx is metal wire separation index correction term, wx is metal line-width index correction term, sx, wx is empirical parameter, agauss (0, 1, 1) be the built-in Gaussian function of SPICE (Simulation Program with Integrated Circuit Emphasis), in its bracket (0, 1, the central value of the 0 expression Gaussian function of the 1st 1) is 0, the maximum sigma amplitude of 1 expression Gaussian function curve from central value 0 to the right and left that bracket is the 2nd is 1, in bracket in the 3rd 1 means that the sigma number of Gaussian function is 1.

Suppose that in the differential inductance model, metal line-width W can be by deviser's free adjustment, formula (1) reflects is that the mismatch of the resistivity between metal wire and metal wire can increase along with the diminishing of metal wire separation S and metal line-width W.During high frequency, the fluctuation of metal skin effect is subject to the impact of resistivity:

$\mathrm{\δ}=\sqrt{\frac{{\mathrm{\ρ}}^{\′}}{\mathrm{\π}\·{\mathrm{\μ}}_0\·f}}---\left(2\right)$

In formula (2), δ is skin depth, μ ₀for the metal mobility, f is frequency;

Suppose that again there is a fluctuation in metal line-width W, W need add a correction:

W′＝W+ΔW＝W+w _m*agauss(0，1，1) (3)

In formula (3), W ' is revised metal line-width, w _mfor the metal width correction factor.

The fluctuation of the metal wire separation S of differential inductance can be regarded the remote effect of metal line-width W fluctuation as, revised metal wire separation S ':

S′＝S+2w _m*agauss(0，1，1) (4)

Embodiment mono-

The application's differential inductance emulation mode one embodiment as shown in Figure 2, comprises the following steps:

One. set up the conventional difference inductor models;

Two. obtain metal line-width W, metal wire separation S, metal wire electricalresistivityρ, number of inductor N, the inductance D outer diameter of the differential inductance of not considering technological fluctuation;

Three. metal line-width W, metal wire separation S, the metallic resistance rate ρ that does not consider technological fluctuation revised, obtain revised metal line-width W ', revised metal wire separation S ', revise rear metallic resistance rate ρ ';

W′＝W+ΔW＝W+w _m*agauss(0，1，1)；

S′＝S+2w _m*agauss(0，1，1)；

${\mathrm{\ρ}}^{\′}=\mathrm{\ρ}+\mathrm{\Δ\ρ}=\mathrm{\ρ}+{\mathrm{\ρ}}_1*{\left(\frac{1}{\sqrt{S}}\right)}^{\mathrm{sx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right)+{\mathrm{\ρ}}_2*{\left(\frac{1}{\sqrt{W}}\right)}^{\mathrm{wx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right);$

In above formula, W ' is revised metal line-width, and W is not for considering the metal line-width W of technological fluctuation, w _mfor the metal line-width correction factor, S ' is revised metal wire separation, and S is not for considering the metal wire separation of technological fluctuation, and ρ ' is metal wire resistivity after revising, and ρ is the metal wire resistivity of not considering technological fluctuation, ρ ₁the mismatch correction factor that resistivity changes with metal wire separation, ρ ₂it is the mismatch correction factor that resistivity changes with metal line-width, sx is metal wire separation index correction term, wx is metal line-width index correction term, and agauss (0,1,1) be Gaussian function, in its bracket, the 1st of (0,1,1) the 0 means that the central value of Gaussian function is 0, in bracket, the 2nd 1 means that the maximum sigma amplitude of Gaussian function curve from central value 0 to the right and left is 1, and 1 in bracket in the 3rd means that the sigma number of Gaussian function is 1;

Four. according to metallic resistance rate ρ ' after the number of inductor N that does not consider technological fluctuation, inductance D outer diameter and revised metal line-width W ', revised metal wire separation S ', correction, to differential inductance emulation, obtain simulated inductor value and the Q value of differential inductance by the conventional difference inductor models.

Metal line-width correction factor w _m, the mismatch correction factor ρ that changes with metal wire separation of resistivity ₁, the mismatch correction factor ρ that changes with metal line-width of resistivity ₂, metal wire separation index correction term sx and metal line-width index correction term wx, can determine in the following manner;

(1). by formula:

W′＝W+w _m*agauss(0，1，1)、S′＝S+2w _m*agauss(0，1，1)、

${\mathrm{\ρ}}^{\′}=\mathrm{\ρ}+{\mathrm{\ρ}}_1*{\left(\frac{1}{\sqrt{S^{\′}}}\right)}^{\mathrm{sx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right)+{\mathrm{\ρ}}_2*{\left(\frac{1}{\sqrt{W^{\′}}}\right)}^{\mathrm{wx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right),$ Write respectively as the correction term of spice language:

(2). the metal line-width W of the differential inductance of demarcating with reference to +/-3sigma monitoring statistical distribution value and the domain of the metal line-width of differential inductance on processing line obtains metal width correction factor w _m; Metal line-width W, number of inductor N, the inductance D outer diameter of the differential inductance of demarcating according to domain, calculate metal wire separation S; Metal line-width W, the metallic resistance rate ρ of the differential inductance of demarcating according to domain and the metal wire separation S calculated, obtain revised metal line-width W ', revised metal wire separation S ', revise rear metallic resistance rate ρ ' by above-mentioned correction term;

(3). select fixing higher (3MHz is to 30MHz) frequency, number of inductor N, inductance D outer diameter according to metallic resistance rate ρ ' and differential inductance after revised metal line-width W ', revised metal wire separation S ', correction, by the conventional difference inductor models, differential inductance is carried out to Monte Carlo simulation, obtain the emulation Q value of the differential inductance under this frequency;

(4). the distribution of the actual measurement Q value of differential inductance under the distribution of the emulation Q value of differential inductance and same frequency condition is compared, by matching, obtain the mismatch correction factor ρ that resistivity changes with metal wire separation ₁, the mismatch correction factor ρ that changes with metal line-width of resistivity ₂, metal wire separation index correction term sx, metal line-width index correction term wx.

The application's differential inductance emulation mode, consider the impact of technological fluctuation, add the live width statistical distribution correction term of reaction process fluctuation according to the metal live width monitoring value on processing line, metal line-width W, metal wire separation S, metallic resistance rate ρ to differential inductance are revised, metal line-width W ', metal wire separation S ', metallic resistance rate ρ ' according to revised differential inductance, to differential inductance emulation, obtain simulated inductor value and the Q value of differential inductance by the conventional difference inductor models.The application's differential inductance emulation mode, considered the impact of technological fluctuation on the metal line-width of differential inductance, metal wire separation, metallic resistance rate, the mismatch phenomenon that the reflection technological fluctuation causes, the random difference in model, technological fluctuation caused reflects, can obtain the difference distribution of inductance value and Q value by the differential inductance model emulation, the semiconductor product that comprises differential inductance can be predicted preferably before production.

The foregoing is only the application's preferred embodiment, not in order to limit the application, all within the application's spirit and principle, any modification of making, be equal to replacement, improvement etc., within all should being included in the scope of the application's protection.

Claims (2)

1. a differential inductance emulation mode, is characterized in that, comprises the following steps:

One. set up the conventional difference inductor models;

Two. obtain metal line-width, metal wire separation, metal wire resistivity, number of inductor, the inductance external diameter of the differential inductance of not considering technological fluctuation;

Three. metal line-width W, metal wire separation S, the metal wire electricalresistivityρ who does not consider technological fluctuation revised, obtain revised metal line-width W ', revised metal wire separation S ', revise after the metal wire electricalresistivityρ ';

W′＝W+w _m*agauss(0，1，1)；

S′＝S+2w _m*agauss(0，1，1)；

${\mathrm{\ρ}}^{\′}=\mathrm{\ρ}+{\mathrm{\ρ}}_1*{\left(\frac{1}{\sqrt{S}}\right)}^{\mathrm{sx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right)+{\mathrm{\ρ}}_2*{\left(\frac{1}{\sqrt{W}}\right)}^{\mathrm{wx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right);$

In above formula, W ' is revised metal line-width, and W is not for considering the metal line-width of technological fluctuation, w _mfor the metal line-width correction factor, S ' is revised metal wire separation, and S is not for considering the metal wire separation of technological fluctuation, and ρ ' is metal wire resistivity after revising, and ρ is the metal wire resistivity of not considering technological fluctuation, ρ ₁the mismatch correction factor that resistivity changes with metal wire separation, ρ ₂it is the mismatch correction factor that resistivity changes with metal line-width, sx is metal wire separation index correction term, wx is metal line-width index correction term, and agauss (0,1,1) be Gaussian function, in its bracket, the 1st of (0,1,1) the 0 means that the central value of Gaussian function is 0, in bracket, the 2nd 1 means that the maximum sigma amplitude of Gaussian function curve from central value 0 to the right and left is 1, and 1 in bracket in the 3rd means that the sigma number of Gaussian function is 1;

Four. according to metallic resistance rate after the number of inductor of not considering technological fluctuation, inductance external diameter and revised metal line-width, revised metal wire separation, correction, to differential inductance emulation, obtain simulated inductor value and the Q value of differential inductance by the conventional difference inductor models.

2. differential inductance emulation mode according to claim 1, is characterized in that,

Metal line-width correction factor w _m, the mismatch correction factor ρ that changes with metal wire separation of resistivity ₁, the mismatch correction factor ρ that changes with metal line-width of resistivity ₂, metal wire separation index correction term sx and metal line-width index correction term wx, determine in the following manner;

(1). by formula:

W′＝W+w _m*agauss(0，1，1)、S′＝S+2w _m*agauss(0，1，1)、

${\mathrm{\ρ}}^{\′}=\mathrm{\ρ}+{\mathrm{\ρ}}_1*{\left(\frac{1}{\sqrt{S^{\′}}}\right)}^{\mathrm{sx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right)+{\mathrm{\ρ}}_2*{\left(\frac{1}{\sqrt{W^{\′}}}\right)}^{\mathrm{wx}}*\mathrm{agauss}\left(\mathrm{0,1,1}\right),$ Write respectively as the correction term of spice language:

(2). the metal line-width W of the differential inductance of demarcating with reference to +/-3sigma monitoring statistical distribution value and the domain of the metal line-width of differential inductance on processing line obtains metal width correction factor w _m; Metal line-width W, number of inductor N, the inductance D outer diameter of the differential inductance of demarcating according to domain, calculate metal wire separation S; Metal line-width W, the metal wire electricalresistivityρ of the differential inductance of demarcating according to domain and the metal wire separation S calculated, by above-mentioned correction term obtain revised metal line-width W ', revised metal wire separation S ', revise after the metal wire electricalresistivityρ ';

(3). select fixing 3MHz to the frequency between 30MHz, according to revised metal line-width W ', revised metal wire separation S ', revise after metal wire electricalresistivityρ ' and number of inductor N, the inductance D outer diameter of differential inductance, by the conventional difference inductor models, differential inductance is carried out to Monte Carlo simulation, obtain the emulation Q value of the differential inductance under this frequency;

(4). the distribution of the actual measurement Q value of differential inductance under the distribution of the emulation Q value of differential inductance and same frequency condition is compared, by matching, obtain the mismatch correction factor ρ that resistivity changes with metal wire separation ₁, the mismatch correction factor ρ that changes with metal line-width of resistivity ₂, metal wire separation index correction term sx, metal line-width index correction term wx.

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