CN103164562B - Difference inductance simulation method - Google Patents

Abstract

This application discloses a kind of difference inductance simulation method, consider the impact of technological fluctuation, the live width statistical distribution correction term of reaction process fluctuation is added according to the metal live width monitoring value in processing line, the metal line-width of differential inductance, metal wire separation, metallic resistance rate are revised, according to metal line-width, metal wire separation, the metallic resistance rate of revised differential inductance, by conventional difference inductor models, differential inductance is emulated, obtain simulated inductor value and the Q value of differential inductance.The difference inductance simulation method of the application, the random difference that technological fluctuation can be caused reflects, and emulation can obtain the difference distribution of inductance value and Q value, and the semiconductor product comprising differential inductance can be predicted before manufacture preferably.

Description

Difference inductance simulation method

Technical field

The application relates to semiconductor emulation technology, particularly a kind of difference inductance simulation method.

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.Along with the continuous progress making integrated circuit technology, from early stage planar monolayer spiral inductance, develop into the structure of the numerous complicated such as the multilayer stacked inductance utilizing multiple layer metal.Improve constantly along with to the requirement of circuit performance, circuit structure has the form of balance, difference usually, and in these circuits, those scripts inductance of one end ground connection in single-end circuit is just transformed into the differential inductance of two ends difference access differential signal.Signal due to differential inductance two ends has identical amplitude and contrary phase place, and this just requires that the electric property of differential inductance is as far as possible symmetrical, and therefore 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), be supplied to the differential inductance model of deviser, must consider that four most important inductance parameters are with inductance value required in optimized circuit, four most important inductance parameters are number of inductor N, metal line-width W, inductance outer diameter D and metal wire separation S respectively.

In practical semiconductor inductance technique, the parasitic interaction that can have influence between metal wire due to technological fluctuation changes, and the inductance value obtained after inductance parameters is fixed and Q value all can exist a random fluctuation range.But the differential inductance model of routine, only consider number of inductor N, metal line-width W, inductance outer diameter D and metal wire separation S tetra-parameters, like this at given number of inductor N, metal line-width W, after inductance outer diameter D and metal wire separation S, by the just fixing result that differential inductance model emulation obtains, the mismatch phenomenon that technological fluctuation causes cannot be reflected, the random difference that technological fluctuation cannot be caused in a model reflects, the difference distribution of inductance value and Q value cannot be obtained by differential inductance model emulation, product is made to be difficult to good prediction before manufacture.

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

Q＝ω*L/R；ω＝1/2πf；R＝ρ'*L/(W*δ)；

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 inductance external diameter, and ρ is metallic resistance rate, and μ 0 is metal electron mobility, and L is the function of number of inductor N, inductance outer diameter D.

Summary of the invention

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

For solving the problems of the technologies described above, the difference inductance simulation method that the application provides, comprises the following steps:

One. set up conventional difference inductor models;

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

Three. to not considering that metal line-width W, metal wire separation S, the metal wire resistance rate ρ of technological fluctuation revise, obtaining revised metal line-width W', revised metal wire separation S ＇, revising rear metal wire resistance rate ρ ';

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 the metal line-width W not considering technological fluctuation, w _mfor metal line-width correction factor, S ＇ is revised metal wire separation, and S is the metal wire separation not considering technological fluctuation, and ρ ' is metal wire resistance rate after revising, and ρ is the metal wire resistance rate 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, agauss (0,1,1) be Gaussian function, in its bracket, the central value of the 0 expression Gaussian function of the 1st of (0,1,1) is 0, in bracket, the 2nd 1 represents 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 represents that the sigma number of Gaussian function is 1;

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

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 as the correction term of spice language respectively:

(2). the +/-3sigma with reference to the metal line-width of differential inductance in processing line monitors the metal line-width W of the differential inductance of statistical implantation and domain demarcation, obtains metal width correction factor w _m; According to metal line-width W, number of inductor N, the inductance outer diameter D of the differential inductance that domain is demarcated, calculate metal wire separation S; Metal line-width W, the metal wire resistance rate ρ of the differential inductance demarcated according to domain and the metal wire separation S that calculates, obtain revised metal line-width W', revised metal wire separation S ＇ by above-mentioned correction term, revise after metal wire resistance rate ρ ';

(3). select the frequency between fixing 3MHz to 30MHz, according to revised metal line-width W', revised metal wire separation S ＇, number of inductor N, the inductance outer diameter D of revising rear metal wire resistance rate ρ ' and differential inductance, by conventional difference inductor models, Monte Carlo simulation is carried out to differential inductance, 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, obtains 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 difference inductance simulation method of the application, consider the impact of technological fluctuation, the live width statistical distribution correction term of reaction process fluctuation is added according to the metal live width monitoring value in processing line, metal line-width W, the metal wire separation S of differential inductance, metallic resistance rate ρ are revised, according to metal line-width W ＇, metal wire separation S ＇, the metallic resistance rate ρ ' of revised differential inductance, by conventional difference inductor models, differential inductance is emulated, obtain simulated inductor value and the Q value of differential inductance.The difference inductance simulation method of the application, consider the impact of technological fluctuation on the metal line-width of differential inductance, metal wire separation, metallic resistance rate, the mismatch phenomenon that reflection technological fluctuation causes, the random difference caused by technological fluctuation in a model reflects, the difference distribution of inductance value and Q value can be obtained by differential inductance model emulation, the semiconductor product comprising differential inductance can be predicted before manufacture preferably.

Accompanying drawing explanation

In order to be illustrated more clearly in the technical scheme of the application, below the accompanying drawing used required for the application is briefly described, apparently, accompanying drawing in the following describes is only some embodiments of the application, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 is differential inductance wiring domain schematic diagram;

Fig. 2 is the difference inductance simulation method process flow diagram of the application.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present application, be clearly and completely described the technical scheme in the embodiment of the present application, obviously, described embodiment is only some embodiments of the present application, instead of whole embodiments.Should be appreciated that preferred embodiment described herein is only for instruction and explanation of the application, and be not used in restriction the application.And when not conflicting, the embodiment in the application and the feature in embodiment can combine mutually.Based on the embodiment in the application, the every other embodiment that those of ordinary skill in the art obtain, all belongs to the scope of the application's protection.

Cause a lot of because have of inductance technological fluctuation, but mainly should be reflected in metal line-width W and metal wire separation S two aspects, be then indirectly reflected in the physical characteristics of metal.Suppose that the resistivity causing metal wire 1 and metal wire 2 due to technological fluctuation produces random difference, 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 ' is metal wire resistance rate after the correction of consideration technological fluctuation, and ρ does not consider technological fluctuation metal wire resistance rate, and Δ ρ is the metal wire resistance rate 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 withIntegrated Circuit Emphasis), in its bracket (0, 1, 1) the 1st 0 represent that the central value of Gaussian function is 0, 1 of bracket the 2nd represents that the maximum sigma amplitude of Gaussian function curve from central value 0 to the right and left is 1, in bracket in the 3rd 1 represents that the sigma number of Gaussian function is 1.

Suppose that in differential inductance model, metal line-width W can by deviser's free adjustment, then what formula (1) reflected is diminishing along with metal wire separation S and metal line-width W, and the mismatch of the resistivity between metal wire and metal wire can increase.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 metal mobility, f is frequency;

Suppose that again metal line-width W exists a fluctuation, then 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 metal width correction factor.

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

S'＝S+2w _m*agauss(0,1,1) (4)

Embodiment one

Difference inductance simulation method one embodiment of the application as shown in Figure 2, comprises the following steps:

One. set up conventional difference inductor models;

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

Three. to not considering that metal line-width W, metal wire separation S, the metallic resistance rate ρ of technological fluctuation revise, obtaining revised metal line-width W', revised metal wire separation S ＇, revising 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 the metal line-width W not considering technological fluctuation, w _mfor metal line-width correction factor, S ＇ is revised metal wire separation, and S is the metal wire separation not considering technological fluctuation, and ρ ' is metal wire resistance rate after revising, and ρ is the metal wire resistance rate 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, agauss (0,1,1) be Gaussian function, in its bracket, the central value of the 0 expression Gaussian function of the 1st of (0,1,1) is 0, in bracket, the 2nd 1 represents 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 represents that the sigma number of Gaussian function is 1;

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

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 as the correction term of spice language respectively:

(2). the +/-3sigma with reference to the metal line-width of differential inductance in processing line monitors the metal line-width W of the differential inductance of statistical implantation and domain demarcation, obtains metal width correction factor w _m; According to metal line-width W, number of inductor N, the inductance outer diameter D of the differential inductance that domain is demarcated, calculate metal wire separation S; Metal line-width W, the metallic resistance rate ρ of the differential inductance demarcated according to domain and the metal wire separation S that calculates, obtain revised metal line-width W', revised metal wire separation S ＇ by above-mentioned correction term, revise after metallic resistance rate ρ ';

(3). select fixing higher (3MHz to 30MHz) frequency, according to revised metal line-width W', revised metal wire separation S ＇, number of inductor N, the inductance outer diameter D of revising rear metallic resistance rate ρ ' and differential inductance, by conventional difference inductor models, Monte Carlo simulation is carried out to differential inductance, 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, obtains 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 difference inductance simulation method of the application, consider the impact of technological fluctuation, the live width statistical distribution correction term of reaction process fluctuation is added according to the metal live width monitoring value in processing line, metal line-width W, the metal wire separation S of differential inductance, metallic resistance rate ρ are revised, according to metal line-width W ＇, metal wire separation S ＇, the metallic resistance rate ρ ' of revised differential inductance, by conventional difference inductor models, differential inductance is emulated, obtain simulated inductor value and the Q value of differential inductance.The difference inductance simulation method of the application, consider the impact of technological fluctuation on the metal line-width of differential inductance, metal wire separation, metallic resistance rate, the mismatch phenomenon that reflection technological fluctuation causes, the random difference caused by technological fluctuation in a model reflects, the difference distribution of inductance value and Q value can be obtained by differential inductance model emulation, the semiconductor product comprising differential inductance can be predicted before manufacture preferably.

The foregoing is only the preferred embodiment of the application, not in order to limit the application, within all spirit in the application and principle, any amendment made, equivalent replacements, improvement etc., all should be included within scope that the application protects.

Claims (2)

1. a difference inductance simulation method, is characterized in that, comprises the following steps:

One. set up conventional difference inductor models;

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

Three. to not considering that metal line-width W, metal wire separation S, the metal wire resistance rate ρ of technological fluctuation revise, obtaining revised metal line-width W', revised metal wire separation S ＇, revising rear metal wire resistance rate ρ ';

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 the metal line-width not considering technological fluctuation, w _mfor metal line-width correction factor, S ＇ is revised metal wire separation, and S is the metal wire separation not considering technological fluctuation, and ρ ' is metal wire resistance rate after revising, and ρ is the metal wire resistance rate 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, agauss (0,1,1) be Gaussian function, in its bracket, the central value of the 0 expression Gaussian function of the 1st of (0,1,1) is 0, in bracket, the 2nd 1 represents 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 represents that the sigma number of Gaussian function is 1;

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

2. difference inductance simulation method 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 as the correction term of spice language respectively:

(2). the +/-3sigma with reference to the metal line-width of differential inductance in processing line monitors the metal line-width W of the differential inductance of statistical implantation and domain demarcation, obtains metal width correction factor w _m; According to metal line-width W, number of inductor N, the inductance outer diameter D of the differential inductance that domain is demarcated, calculate metal wire separation S; Metal line-width W, the metal wire resistance rate ρ of the differential inductance demarcated according to domain and the metal wire separation S that calculates, obtain revised metal line-width W', revised metal wire separation S ＇ by above-mentioned correction term, revise after metal wire resistance rate ρ ';

(3). select the frequency between fixing 3MHz to 30MHz, according to revised metal line-width W', revised metal wire separation S ＇, number of inductor N, the inductance outer diameter D of revising rear metal wire resistance rate ρ ' and differential inductance, by conventional difference inductor models, Monte Carlo simulation is carried out to differential inductance, 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, obtains 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.