CN101770528B - Method for obtaining inductor models in integrated circuits - Google Patents
Method for obtaining inductor models in integrated circuits Download PDFInfo
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- CN101770528B CN101770528B CN 200810205262 CN200810205262A CN101770528B CN 101770528 B CN101770528 B CN 101770528B CN 200810205262 CN200810205262 CN 200810205262 CN 200810205262 A CN200810205262 A CN 200810205262A CN 101770528 B CN101770528 B CN 101770528B
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Abstract
The invention provides a method for obtaining inductor models in integrated circuits, which comprises the following steps: providing parameters from X1, X2 to Xn of a plurality of groups of inductors and an inductor feature value; changing the parameter X1 into a plurality of different numerical values to obtain the functional relationship between the inductor feature value and the parameter X1, wherein the expression of the functional relationship comprises coefficients from a1, a2 to ai; changing the parameter X2 into a plurality of different numerical values, and repeating the former steps under each numerical value to obtain the functional relationship between the coefficients from a1, a2 to ai, wherein the expression of the functional relationship comprises coefficients from b1, b2 to bj; and changing other parameters through imitating the former steps; obtaining the expression of the functional relationship between the inductor feature value and the parameters from X1, X2 to Xn, wherein the expression is the inductor model. The invention has the advantages that complicated formulas and calculation are not needed, and the manufacture efficiency is improved.
Description
[technical field]
The present invention relates to method for manufacturing integrated circuit, relate in particular to a kind of method of obtaining inductance eigenwert and inductance parameters Relations Among in the integrated circuit.
[background technology]
In current integrated circuit (IC) design field, the development of radio frequency integrated circuit (RFIC) is very swift and violent.As a kind of important passive device, spiral inductance (spiralinductor) is widely used in this field.Yet in the practical application of radio frequency integrated circuit, because calculation of complex is not also set up a comparatively perfect inductor models at present.
The common method of finding the solution the inductor models parameter is the physical model method, these methods of utilizing the physical model calculating parameter value are because various technological processs are very complicated, and a lot of physical influences are difficult to the complete expression of physical equation, therefore Shortcomings part on degree of accuracy.In order to improve the degree of accuracy of model, just need complicated calculating is done in the ghost effect of high-order, so, the formula of employing and computation process are often loaded down with trivial details tediously long, and is very inconvenient.
Therefore, developing a kind of method of obtaining comparatively accurately inductance model in integrated circuit, need not simultaneously complicated formula and calculating, is necessary.
[summary of the invention]
Technical matters to be solved by this invention is, a kind of method of obtaining inductance eigenwert and inductance parameters Relations Among in the integrated circuit is provided, and in the situation of the degree of accuracy that guarantees model, reduced the complexity of formula and the quantity of calculating.
In order to address the above problem, the invention provides a kind of method of obtaining inductance model in integrated circuit, comprise following steps:
(1) provides the parameter X of some groups of inductance
1, X
2... X
n, and an inductance eigenwert A, wherein, n is the integer greater than 2;
(2) change parameter X
1Be a plurality of different numerical value, and keep other parameter constant, to form first group of inductance parameters, adopt described first group of inductance parameters to make one group of inductance, and measure described inductance eigenwert A, thereby obtain first group of funtcional relationship expression formula, described first group of funtcional relationship expression formula is used for describing described inductance eigenwert and parameter X
1Between funtcional relationship, the coefficient in described first group of funtcional relationship expression formula is a
1, a
2... a
i, wherein, i is positive integer;
(3) change parameter X
2Be a plurality of different numerical value, and keep other parameter constants, to form second group of inductance parameters, choose successively each inductance parameters of second group of inductance parameters, repeated execution of steps (2), thereby obtain second group of funtcional relationship expression formula, described second group of funtcional relationship expression formula is used for describing each coefficient a
1, a
2... a
iRespectively with parameter X
2Between funtcional relationship, the coefficient in described second group of funtcional relationship expression formula is b
1, b
2... b
j, wherein j is positive integer;
(4) change successively all the other parameters, parameter of each change, all copy the narration of step (2) and (3) to repeat the step of front, thereby obtain the funtcional relationship between the coefficient in the funtcional relationship expression formula that reformed parameter and previous step obtain;
(5) respectively organize funtcional relationship according to what obtain in the above-mentioned steps, to obtain described inductance eigenwert A and described parameter X
1, X
2... X
nThe funtcional relationship expression formula, namely get access to described inductor models.
As optional technical scheme, the value of n is 3 in the described step (1);
As optional technical scheme, described inductance is spiral inductance.
As optional technical scheme, described parameter X
1Be number of inductor; The span of described number of inductor is 3.5～5.5; The value of described number of inductor is respectively 3.5,4.5 and 5.5.
As optional technical scheme, described parameter X
2Be internal coil diameter; The span of described internal coil diameter is 30um～90um; The value of described internal coil diameter is respectively 30um, 60um and 90um.
As optional technical scheme, described parameter X
3Be the inductor wire diameter; The span of described inductor wire diameter is 1.5um～2um; The value of described inductor wire diameter is respectively 1.5um and 2um.
As optional technical scheme, inductance value, scattering parameter or admittance parameter that described inductance eigenwert is inductance.
The invention has the advantages that, in the practical application of radio frequency integrated circuit, set up a comparatively perfect inductor models.The invention provides a kind of method of obtaining comparatively accurately inductance model in integrated circuit, need not simultaneously complicated formula and calculating, improved manufacturing efficient.
[description of drawings]
Fig. 1 is the process flow diagram of the specific embodiment of the invention;
Fig. 2 to Figure 10 is the function synoptic diagram in the specific embodiment of the invention.
[embodiment]
Below in conjunction with accompanying drawing the embodiment of obtaining the method for inductance eigenwert and inductance parameters Relations Among in the integrated circuit provided by the invention is elaborated.
Referring to Fig. 1, be the process flow diagram of the specific embodiment of the invention.This embodiment comprises the steps: step S10, and the parameter X of some groups of inductance is provided
1, X
2... X
n, and an inductance eigenwert A, wherein, n is the integer greater than 2; Step S11 changes parameter X
1Be a plurality of different numerical value, and keep other parameter constant, to form first group of inductance parameters, adopt described first group of inductance parameters to make one group of inductance, and measure described inductance eigenwert A, thereby obtain first group of funtcional relationship expression formula, described first group of funtcional relationship expression formula is used for describing described inductance eigenwert and parameter X
1Between funtcional relationship, the coefficient in described first group of funtcional relationship expression formula is a
1, a
2... a
i, wherein, i is positive integer; Step S12 changes parameter X
2Be a plurality of different numerical value, and keep other parameter constants, to form second group of inductance parameters, choose successively each inductance parameters of second group of inductance parameters, repeated execution of steps (2), thereby obtain second group of funtcional relationship expression formula, described second group of funtcional relationship expression formula is used for describing each coefficient a
1, a
2... a
iRespectively with parameter X
2Between funtcional relationship, the coefficient in described second group of funtcional relationship expression formula is b
1, b
2... b
j, wherein j is positive integer; Step S13, change successively all the other parameters, each change a parameter, all copy the narration of step S11 and S12 to repeat the step of front, thereby obtain the funtcional relationship between the coefficient in the funtcional relationship expression formula that reformed parameter and previous step obtain; Step S14 respectively organizes funtcional relationship according to what obtain in the above-mentioned steps, to obtain described inductance eigenwert A and described parameter X
1, X
2... X
nThe funtcional relationship expression formula, namely get access to described inductor models.
Wherein, described inductance eigenwert is generally inductance value (Ls), scattering parameter (S parameter) or the admittance parameter (Y parameter) of inductance.
For spiral inductance, the parameter that often adopts in the industry at present is number of inductor, inductor wire diameter, internal coil diameter, and for other inductance, type and the number of the parameter of selection are not quite similar.As a rule, choosing of inductance parameters is to arrange according to its power to inductance eigenwert influence factor.In this embodiment, in order to guarantee that model is representative and to save the time of obtaining inductance eigenwert and inductance parameters Relations Among, the value of number of inductor is respectively 3.5,4.5 and 5.5, the value of internal coil diameter is respectively 30um, 60um and 90um, and the value of inductor wire diameter is respectively 1.5um and 2um.
Step S10 provides the parameter X of some groups of inductance
1, X
2... X
n, and an inductance eigenwert A, wherein, n is the integer greater than 2, in this embodiment, the value of n is 3; Selecting All Parameters X
1Be number of inductor T, X
2Be internal coil diameter R, X
3Be inductor wire diameter S, inductance eigenwert A is inductance value Ls.
Step S11 changes parameter X
1Be a plurality of different numerical value, and keep other parameter constant, to form first group of inductance parameters, adopt described first group of inductance parameters to make one group of inductance, and measure described inductance eigenwert A, thereby obtain first group of funtcional relationship expression formula, described first group of funtcional relationship expression formula is used for describing described inductance eigenwert and parameter X
1Between funtcional relationship, the coefficient in described first group of funtcional relationship expression formula is a
1, a
2... a
i, wherein, i is positive integer.
In the above-mentioned steps, the step of making inductance and the described inductance eigenwert A of measurement can adopt semiconductor planar technique to realize at wafer, all belongs to those skilled in the art's known technology, repeats no more herein.
In this step, change parameter X
1Be that number of inductor T is a plurality of different values, and keep parameter X
2, X
3The value that is R and S is constant, for example, when S=1.5, R=30, makes the value of T be respectively 3.5,4.5 and 5.5, makes one group of inductance with this.As shown in table 1, be the inductance parameters of this step made and the inductance value under this parameter.
Table 1
| S | R | T | Ls |
| 1.5 | 30 | 3.5 | 0.3 |
| 1.5 | 30 | 4.5 | 0.4 |
| 1.5 | 30 | 5.5 | 0.5 |
Referring to shown in Figure 2, comprise among Fig. 2 according to the function relation curve between inductance value Ls and the number of inductor T in this step of table 1 data drafting.Function curve relational expression by Fig. 2 can find out that in this embodiment, the funtcional relationship between inductance value and the number of inductor is Ls=a
1T+a
2Obtain thus first group of funtcional relationship expression formula Ls=0.1T-0.05, at this moment, coefficient a
1=0.1, a
2=-0.05.
Step S12 changes parameter X
2Be a plurality of different numerical value, and keep other parameter constants, to form second group of inductance parameters, choose successively each inductance parameters of second group of inductance parameters, repeated execution of steps (2), thereby obtain second group of funtcional relationship expression formula, described second group of funtcional relationship expression formula is used for describing each coefficient a
1, a
2... a
iRespectively with parameter X
2Between funtcional relationship, the coefficient in described second group of funtcional relationship expression formula is b
1, b
2... b
j, wherein j is positive integer.
In this step, change parameter X
2Be the value of internal coil diameter R, keep parameter X
3The value that is S is constant, under each numerical value of R, all repeats step S 11, for example, when S=1.5, makes the value of R become 60 and 90 by 30, respectively repeats steps S11.As shown in table 2, be the inductance parameters of this step made and the inductance value under this parameter.
Table 2
| S | R | T | Ls |
| 1.5 | 60 | 3.5 | 0.4 |
| 1.5 | 60 | 4.5 | 0.6 |
| 1.5 | 60 | 5.5 | 0.8 |
| 1.5 | 90 | 3.5 | 0.6 |
| 1.5 | 90 | 4.5 | 0.9 |
| 1.5 | 90 | 5.5 | 1.2 |
Same in conjunction with referring to Fig. 2, comprise among Fig. 2 according to the function relation curve between inductance value Ls and the number of inductor T in this step of table 2 data drafting.Other two groups of funtcional relationships be can obtain thus, Ls=0.2T-0.3 and Ls=0.3T-0.45 are respectively.Comprise equally coefficient a in the expression formula of these two groups of funtcional relationships
1, a
2If Ls=a1T+a2, then when Ls=0.2T-0.3, a
1=0.2, a
2=-0.3; And when Ls=0.3T-0.45, a
1=0.3, a
2=-0.45.
In conjunction with the numerical value in above-mentioned steps and table 1 and the table 2, can obtain in the situation of different R values coefficient a
1And a
2The numerical value change situation, as shown in table 3:
Table 3
| S | R | a 1 | a 2 |
| 1.5 | 30 | 0.1 | -0.05 |
| 1.5 | 60 | 0.2 | -0.3 |
| 1.5 | 90 | 0.3 | -0.45 |
During as shown in Figures 3 and 4, for S=1.5 R respectively with coefficient a
1, a
2Function relation curve.Function curve relational expression by Fig. 3 and Fig. 4 can find out in this embodiment, a is arranged
1=b
1R+b
2, a
2=b
3Ln (R)+b
4, obtain second group of funtcional relationship expression formula, i.e. R and coefficient a this moment
1, a
2The funtcional relationship expression formula:
a
1=0.0033R+2.00 * 10
-16And
a
2＝0.3637ln(R)-1.1877
Wherein, ln (R) is the logarithm of the R take e the end of as.Can obtain coefficient b thus
1, b
2, b
3And b
4Be convenient and calculate, below to the coefficient processing that rounds up.At this moment, coefficient b
1=3.33 * 10
-3, b
2=2.00 * 10
-16, b
3=3.64 * 10
-1, b
4=-1.19.
Step S13, change successively all the other parameters, each change a parameter, all copy the narration of step S11 and S12 to repeat the step of front, thereby obtain the funtcional relationship between the coefficient in the funtcional relationship expression formula that reformed parameter and previous step obtain.
In this embodiment, copy abovementioned steps to change parameter X
3Be a plurality of different numerical value, under each numerical value, and keep other parameter constants, to form the 3rd group of inductance parameters, choose successively each inductance parameters of the 3rd group of inductance parameters, repeated execution of steps step S11 and S12, thus the 3rd group of funtcional relationship expression formula obtained, and described the 3rd group of funtcional relationship expression formula is used for describing each coefficient b
1, b
2... b
jWith parameter X
nBetween funtcional relationship, the coefficient in described the 3rd group of funtcional relationship expression formula is c
1, c
2... c
k, wherein k is positive integer.
In this step, change parameter X
3Be the value of inductor wire diameter S, the value that is about to S becomes 2 by 1.5, such as preceding method repeating step S11 and S12.As shown in table 4, be the inductance parameters of this step made and the inductance value under this parameter.
Table 4
| S | | T | Ls | |
| 2 | 30 | 3.5 | 0.4 | |
| 2 | 30 | 4.5 | 0.6 | |
| 2 | 30 | 5.5 | 0.8 | |
| 2 | 60 | 3.5 | 0.6 | |
| 2 | 60 | 4.5 | 1 | |
| 2 | 60 | 5.5 | 1.4 | |
| 2 | 90 | 3.5 | 1 | |
| 2 | 90 | 4.5 | 1.6 | |
| 2 | 90 | 5.5 | 2.2 |
According to table 4, the disposal route among repeating step S11 and the S12 can obtain, the parameters R when S=2, R change and coefficient a
1, a
2One group of relation, referring to Fig. 5 and Fig. 6, during for S=2 R respectively with coefficient a
1, a
2Function relation curve.That is:
a
1=0.0067R+3 * 10
-16And
a
2＝0.7275ln(R)-2.1754
If a
1=b
1R+b
2, a
2=b
3Ln (R)+b
4, can obtain again one group of coefficient b more than then
1, b
2, b
3And b
4, at this moment, coefficient b
1=6.67 * 10
-3, b
2=3.00 * 10
-16, b
3=7.27 * 10
-1, b
4=-2.18.Can obtain thus parameter S and coefficient b
1～b
4Between relation, as shown in table 5:
Table 5
| S | b 1 | b 2 | b 3 | b 4 |
| 1.5 | 3.33×10 -3 | 2.00×10 -16 | 3.64×10 -1 | -1.19 |
| 2 | 6.67×10 -3 | 3.00×10 -16 | 7.27×10 -1 | -2.18 |
According to table 5, and obtain parameter S and b in conjunction with the function relation curve of Fig. 7～Figure 10
1～b
4Between the funtcional relationship expression formula, can be found out by the function curve relational expression, in this embodiment, parameter S and b
1～b
4Between the funtcional relationship expression formula can be expressed as:
b
1＝c
1S+c
2
b
2＝c
3S+c
4
b
3＝c
5S+c
6
b
4＝c
7S+c
8
Namely obtain the 3rd group of funtcional relationship expression formula:
b
1＝0.0067S-0.0067
b
2＝2×10
-16S-1×10
-16
b
3=-0.728S+1.456 and
b
4＝1.98S-1.78。
Comprise coefficient c1～c8 in the above-mentioned function relation curve.Wherein, c
1=0.0067, c
2=-0.0067, c
3=2 * 10
-16, c
4=-1 * 10
-16, c
5=-0.728, c
6=1.456, c
7=1.98, c
8=-1.78.
If the value of n is greater than 3 in step S10, when namely also having chosen other parameter, then also need to copy change X
3Embodiment repeats the step of front, to obtain the funtcional relationship between the coefficient that this parameter and previous step obtained; In this embodiment, owing to only comprise number of inductor, inductor wire diameter, these three parameters of internal coil diameter, the funtcional relationship before abovementioned steps can obtain these three parameters and coefficient.
Step S14 respectively organizes funtcional relationship according to what obtain in the above-mentioned steps, to obtain described inductance eigenwert A and described parameter X
1, X
2... X
nThe funtcional relationship expression formula, namely get access to described inductor models.
In this step, according to abovementioned steps, can obtain:
Ls=a
1* T+a
2, so
Ls=(b
1* R+b
2) * T+ (b
3Ln (R)+b
4), so
Ls=[(c
1* S+c
2) * (R)+(c
3* S+c
4)] * T+[(c
5* S+c
6) * ln (R)+(c
7* S+c
8)] namely
Ls＝[(0.0067×S-0.0067)×R+(2×10
-16S-1×10
-16)]×T-[(0.726×S-0.725)×ln(R)-(1.98×S-1.78)]
Thus, inductor models be can obtain, described inductance eigenwert Ls and described parameter X namely obtained
1, X
2, X
3Funtcional relationship expression formula, that is the funtcional relationship expression formula of inductance eigenwert Ls and number of inductor T, internal coil diameter R, inductor wire diameter S.Utilize this inductor models, can make number of inductor between 3.5～5.5, internal coil diameter is that 30um～90um and inductor wire diameter are all spiral inductances of 1.5um～2um, only need by adjusting any to three in four of number of inductor, internal coil diameter, inductor wire diameter or the inductance eigenwerts, can obtain the value of its remainder, and need not loaded down with trivial details calculating.For example, when number of inductor T is 4, internal coil diameter R is 80um, and when inductor wire diameter S was 1.8um, utilizing this model can easily calculate inductance value Ls was 0.95.
The above only is preferred implementation of the present invention; should be pointed out that for those skilled in the art, without departing from the inventive concept of the premise; can also make some improvements and modifications, these improvements and modifications also should be considered within the scope of protection of the present invention.
Claims (8)
1. a method of obtaining inductance model in integrated circuit is characterized in that, comprises following steps:
(1) parameter X of some groups of inductance of setting
1, X
2And X
3, and an inductance eigenwert A, wherein said parameter X
1Be number of inductor, described parameter X
2Be internal coil diameter, described parameter X
3Be the inductor wire diameter, described inductance eigenwert A is inductance value, scattering parameter or the admittance parameter of inductance;
(2) change parameter X
1Be a plurality of different numerical value, and keep other parameter constant, to form first group of inductance parameters, adopt described first group of inductance parameters to make one group of inductance, and measure described inductance eigenwert A, thereby obtain first group of funtcional relationship expression formula, described first group of funtcional relationship expression formula is used for describing described inductance eigenwert and parameter X
1Between funtcional relationship, the coefficient in described first group of funtcional relationship expression formula is a
1, a
2A
i, wherein, i is positive integer;
(3) change parameter X
2Be a plurality of different numerical value, and keep other parameter constants, to form second group of inductance parameters, choose successively each inductance parameters of second group of inductance parameters, repeated execution of steps (2), thereby obtain second group of funtcional relationship expression formula, described second group of funtcional relationship expression formula is used for describing each coefficient a
1, a
2A
iRespectively with parameter X
2Between funtcional relationship, the coefficient in described second group of funtcional relationship expression formula is b
1, b
2... b
j, wherein j is positive integer;
(4) change parameter X
3, and copy the narration of step (2) and (3) to repeat the step of front, thereby obtain the funtcional relationship between the coefficient in the funtcional relationship expression formula that reformed parameter and previous step obtain;
(5) respectively organize funtcional relationship according to what obtain in the above-mentioned steps, to obtain described inductance eigenwert A and described parameter X
1, X
2, and X
3The funtcional relationship expression formula, namely get access to described inductor models.
2. the method for obtaining inductance model in integrated circuit according to claim 1 is characterized in that, the span of described number of inductor is 3.5～5.5.
3. the method for obtaining inductance model in integrated circuit according to claim 2 is characterized in that, the value of described number of inductor is respectively 3.5,4.5 and 5.5.
4. the method for obtaining inductance model in integrated circuit according to claim 1 is characterized in that, the span of described internal coil diameter is 30 μ m～90 μ m.
5. the method for obtaining inductance model in integrated circuit according to claim 4 is characterized in that, the value of described internal coil diameter is respectively 30 μ m, 60 μ m and 90 μ m.
6. the method for obtaining inductance model in integrated circuit according to claim 1 is characterized in that, the span of described inductor wire diameter is 1.5 μ m～2 μ m.
7. the method for obtaining inductance model in integrated circuit according to claim 6 is characterized in that, the value of described inductor wire diameter is respectively 1.5 μ m and 2 μ m.
8. the method for obtaining inductance model in integrated circuit according to claim 1 is characterized in that, described inductance is spiral inductance.
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| CN1845301A (en) * | 2005-04-08 | 2006-10-11 | 上海傲亚微电子有限公司 | Extraction method for asymmetric equivalent circuit model parameter of silicon based spiral inductor |
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| CN1845301A (en) * | 2005-04-08 | 2006-10-11 | 上海傲亚微电子有限公司 | Extraction method for asymmetric equivalent circuit model parameter of silicon based spiral inductor |
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| Title |
|---|
| 姜祁峰，李征帆.硅衬底RF集成电路中螺旋电感的建模和分析.《电子学报》.2002,(第8期),1219-1221. * |
| 黄志忠等.砷化镓衬底上螺旋电感的建模和分析.《微波学报》.2005,第21卷39-43. * |
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