JP2806245B2 - Derivation method of wiring equivalent circuit - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a system for deriving an equivalent circuit of a wiring.

[0002]

2. Description of the Related Art With the increase in the speed of active elements such as transistors, high-frequency components of signals transmitted through wirings increase.
In addition to treating the wiring as a lossy transmission line, it has become necessary to consider the frequency dependence of the loss. One method of analyzing a lossy transmission line is to construct an equivalent circuit and proceed with the analysis (CHU-SU
NYEN, et. al. Proc. of the
IEEE, Vol. 70, no. 7, pp. 750-7
59, July 1982, VIJA K. TRIP
ATHI, et. al. , IEEE Trans. on
Microwave Theory and Tec
huniques, Vol. 36, no. 2, pp. 2
56-262, February 1988). As a means for constructing the equivalent circuit, there is a method in which a three-dimensional electromagnetic field analysis is performed by finite element analysis to calculate a current density distribution, and then an equivalent circuit is derived by fitting. (U
TTAM GHOSHAL, et. al. Proc.
4th IEEE VLSIM Multilevel I
interconnection Conf. Pp. 2
65-272, June 1987, CLAUDE H
ILBERT, et. al. Proc. NEPCON
West, pp. 1391-1403, 1990).
However, this method requires a great deal of labor and calculation time for the electromagnetic field analysis and alignment work, and the wiring length, wiring width, wiring thickness, wiring resistivity, insulator thickness and dielectric constant, etc. If the calculation is performed every time for various combinations of parameters, there is a problem that it takes an enormous amount of analysis time.

[0003]

SUMMARY OF THE INVENTION An object of the present invention is to easily derive an equivalent circuit of a wiring from parameters of a wiring pattern.

[0004]

According to the present invention, an equivalent circuit of a wiring has a ladder stage structure in which a resistance element and an inductor are connected in parallel, and a plurality of lossless transmission lines and the like are connected in series. Take the method of expressing by a network. That is, a geometric progression of frequencies at which the film thickness of the wiring becomes equal to the skin depth due to the skin effect is obtained, and a set of inductor values is calculated from a value proportional to their square root.

Further, the invention is characterized in that an equivalent circuit is efficiently derived by calculating a resistance value connected in parallel thereto from a product of a frequency and an inductor value.
The specific calculation method will be described below.

First, how many divisions of the wiring to be modeled
Is determined. The finer the division, the more accurate the characteristics
It can be expressed, but the calculation time becomes longer. Generally,
The rule of thumb is that the length of the wiring after splitting is
Is not necessary. Let the propagation speed of the signal be v,
The rise time of the input wave is T_rAnd the signal propagation delay is T_D ,
Assuming that the wiring length is 1 and the number of divisions is M, first, a distributed constant line
Equation 1 must be satisfied in order not to require
Must.

_Tr > 2.5 × T _D Equation 1 Since T _D is represented by Equation 2, the number of divisions M must satisfy Equation 2 ′.

T _D = 1 / (v · M) Formula 2 M> 2.5 · 1 / (v · T _r ) Formula 2 ′ where v is

[0009]

(Equation 2)

Where c ₀ is the speed of light in a vacuum,

[0011]

[Outside 1]

Is the relative permittivity, and μ _r is the magnetic permeability (1 if not a magnetic material).

Next, a ladder circuit expressing the frequency dependence of the loss is obtained. First, the first-stage resistance R ₀ is equal to the wiring film thickness t.
₀ , the wiring length l _M (= l / M), the wiring width W, and the wiring resistivity ρ are calculated as R ₀ = ρ · l _M / (W · t ₀ ) (Equation 4). Then, Skin-depth (σ) exactly wiring t ₀ thickness becomes equal such frequency f ₀
Is calculated from the following equation.

F ₀ = ρ / (π · μ · t ₀ ² ) Equation 5 The maximum value f _{M in the} frequency domain where an equivalent circuit is desired to be expressed is calculated from the rise time _{Tr as} follows.

F _M = 2.2 / (2 · π · T _r ) Equation 6 A geometric progression f _{i of} frequencies for f _M is determined by the following equation 7.

F _i = 4 ^{−1 + i} · f _0/2 (i = 1, 2,..., N) Expression 7 where the value of N is a minimum value that satisfies Expression 8. It is an integer.

[0017] _{^{4 -1 + N · f 0/}} 2> 4 · f M ··· formula 8 Then, using each of the f _i,

[0018]

(Equation 3)

[0019] seek from L _i. Next, calculate the R _i from _{R i = 2 · π · f} i · L i / a i ··· formula ^{_{10 a i = K · 2 1}} -i ··· formula 11. Here, K is a parameter related to the wiring shape.

A circuit obtained by connecting M lossless transmission lines to the resistor and inductor network obtained in this way and connecting them in series becomes an equivalent circuit of wiring in consideration of the frequency dependence of loss. . If an increase in the loss due to the skin effect is to be expressed by such an equivalent circuit, R _i must increase gradually as i increases, and conversely, L _i must decrease. To express this in a geometric progression, a geometric progression of frequencies is calculated. Here, the characteristic impedance Z _0, which is a parameter of the lossless transmission line, varies depending on the shape of the microstrip line. In the case of a microstrip line formed on a ground layer via a dielectric, an approximate expression such as May be used.

[0021]

(Equation 4)

D = 0.536 · W + 0.67 · t ₀ Equation 13 ε _eff = (0.475 · ε _r +0.67) · ε ₀ Equation 14 where h is a dielectric film The thickness, μ is the magnetic permeability, ε ₀ is the dielectric constant of vacuum, and ε _r is the relative dielectric constant of the dielectric. Expression 2 may be used for the delay time, which is another parameter of the transmission line.

In this method, the value of K is not determined, but is determined by fitting with reference to the S-parameter characteristics with respect to the frequency obtained from the electromagnetic field analysis or the like or the data of the S-parameter characteristics obtained by actual measurement.
However, if the matching operation is performed for only one wiring shape pattern, it can be predicted for the same type of wiring pattern, so that the efficiency of deriving an equivalent circuit is greatly improved.

That is, according to the present invention, it is possible to efficiently and quickly derive an equivalent circuit of a wiring.

[0025]

Next, an embodiment of the present invention will be described. FIG. 1 shows an algorithm of the present system for deriving an equivalent circuit of a wiring.

FIG. 8 shows a multi-chip module (MC
FIG. 2 is a diagram showing a structure of an IC chip mounting method called M). FIG. 9 is a diagram showing a structure of a mounting method using a printed wiring board. Unlike the mounting using the printed wiring board, the mounting by the MCM is such that the signal pads 82 and 83 are directly mounted on the wiring board 82 via the bumps 84 without packaging the IC chip 80. By doing so, it is possible to shorten the wiring length between chips, remove the influence of inductance and capacitance parasitic on the package, and aim at a high-speed system. However, on the other hand, in the wiring board of the MCM, the density of the wiring is increased and the influence of the resistance of the wiring on the signal propagation characteristics cannot be ignored. Moreover, since the wiring length is about one side of the chip, that is, on the order of several cm, it is necessary to treat the wiring as a transmission line. In order to analyze the signal propagation characteristics in the transmission line in consideration of such a loss, it is necessary to construct an equivalent circuit of the wiring.

FIGS. 2 and 3 show a wiring TEG (Test) for evaluating wiring characteristics on an MCM wiring board.
3 shows a cross-sectional structure of the element group (Element Group) and a shape viewed from above. The pads for inputting and outputting signals are arranged as GND-signal-GND in order to match the tip of a high-frequency probe such as a wafer probe head having a very low input capacitance. is there.

In this structure, the wiring width W = 20 μm,
Wiring length l = 6 cm, the wiring film thickness t ₀ = 2 [mu] m, the dielectric constant epsilon _r = 3.5 the dielectric, the measured data of the characteristic of the S ₂₁ parameter in the thickness h = 20 [mu] m of the wiring of the dielectric, the method FIG. 4 shows a simulation result of an equivalent circuit derived by using FIG. It can be seen that the measured data and the simulation result agree well.
FIG. 5 is a schematic diagram of the obtained equivalent circuit. In detecting the equivalent circuit, K = 4 · h / d (Equation 15) was used to determine the parameter K.

Using this equation (15) and equations (1) to (11), S in a pattern having a different wiring width, wiring length and wiring film thickness is obtained.
Parameter characteristics can be predicted.

FIG. 6 shows the pattern measured in FIG.
In a pattern where only the wiring width is W = 40 μm,
Shows the simulation result by the measurement data and the equivalent circuit of the S ₂₁ characteristics on the same graph. From FIG.
It can be seen that the measured data of the characteristics and the simulation result agree well. FIG. 7 is a schematic diagram of the obtained equivalent circuit.

The present invention can be similarly applied to LSI wiring and printed circuit board wiring. However, in the case of LSI wiring, since GND is a semiconductor such as Si, it may be necessary to consider the resistance on the GND plane, but it can be adjusted by matching.

[0032]

As described above, the present invention makes it possible to efficiently and quickly derive an equivalent circuit of a wiring.

[Brief description of the drawings]

FIG. 1 is a diagram showing an embodiment of an algorithm in an equivalent circuit deriving method according to the present invention.

FIG. 2 is a sectional view showing a structure of a wiring board from which an equivalent circuit is derived by applying the present invention.

FIG. 3 is a top view showing a pattern of a wiring board from which an equivalent circuit is derived by applying the present invention.

FIG. 4 shows a wiring width of 20 μm obtained by comparing a simulation result of an equivalent circuit obtained by applying the present invention with measured data.
FIG. 9 is a S ₂₁ parameter characteristic diagram for a wiring having a wiring length of 6 cm and a wiring length m.

FIG. 5 is a diagram showing an equivalent circuit of a wiring having a wiring width of 20 μm and a wiring length of 6 cm obtained by applying the present invention.

FIG. 6 shows a wiring width of 40 μm obtained by comparing a simulation result of an equivalent circuit obtained by applying the present invention with measured data.
FIG. 9 is a S ₂₁ parameter characteristic diagram for a wiring having a wiring length of 6 cm and a wiring length m.

FIG. 7 is a diagram showing an equivalent circuit of a wiring having a wiring width of 40 μm and a wiring length of 6 cm obtained by applying the present invention.

FIG. 8 is a diagram showing a structure of a multi-chip module.

FIG. 9 is a diagram illustrating a projection method using a printed wiring board.

[Explanation of symbols]

 Reference Signs List 80 IC chip 81 Wiring board 82, 83 Signal pad 90, 91 IC package 92 Signal pin 100 Printed wiring board

──────────────────────────────────────────────────の Continued on the front page (58) Field surveyed (Int.Cl. ⁶ , DB name) G06F 17/50 JICST file (JOIS)

Claims (7)

(57) [Claims] 1. An equivalent circuit of a wiring is formed by a circuit network in which a resistance element, a resistance element and an inductor are connected in parallel, and a plurality of lossless transmission lines are connected in series, and a unit ladder stage structure is arranged in a straight line. In the method of deriving the equivalent circuit of the wiring to be expressed, an equivalent frequency sequence based on the frequency at which the film thickness of the wiring is equal to the skin depth due to the skin effect is obtained, and the inductance component in each unit ladder step structure is obtained from the frequency sequence, Next, an equivalent circuit deriving method, wherein a value of a resistor connected in parallel to each inductor is obtained from a product of a sequence of frequencies and a value of the inductor. 2. A wiring is divided on a computer so that it is not necessary to regard the wiring as a distributed constant line, a resistance value of a first stage of an equivalent circuit is obtained, and an equivalent circuit of the wiring is formed by a resistance element, a resistance element and an inductor. In a method for deriving an equivalent circuit of a wiring represented by a circuit network in which a plurality of non-lossy transmission lines connected in parallel and a plurality of non-loss transmission lines are connected in series, the wiring thickness is a skin due to a skin effect. A sequence of equal frequencies based on the frequency equal to the depth is determined, the inductance component in each unit ladder structure is determined from the frequency sequence, and the value of the resistance connected in parallel with each inductor is determined by the frequency sequence and the inductor. A method for deriving an equivalent circuit, wherein the equivalent circuit is obtained from a product of values of: 3. The frequency f _{0 at} which the thickness of the wiring becomes equal to the skin depth due to the skin effect is represented by f ₀ = ρ · l _M / (W /
t ₀₎ (provided that ρ wiring resistivity, l _M is the line length, W is the wiring width, t ₀ is the equivalent circuit deriving method according to claim 1 or 2, obtained by wiring film thickness). 4. An iso-frequency sequence is defined as f _i = 4 ^{-1 + N} · f _0/2.
(However, i = 1, 2, 3,... N, N is 4 ^{−1 + N} · f ₀
/ 2> 4 · f _M , f _M is the maximum value in the frequency domain where an equivalent circuit is desired to be expressed, and f _M = 2.2 / (2πT _r ), where _{R r} is the rise time. 4. The method for deriving an equivalent circuit according to claim 3, wherein 5. The inductor L _i is given by: The method for deriving an equivalent circuit according to claim 4, wherein 6. The resistance R _i is R _i = 2 · π · f _i · L _i / a
6. The method for deriving an equivalent circuit according to claim 5, wherein _{i is obtained by using i} (where a _i = K · 2 ^1-i , K is a parameter relating to wiring). 7. The method for deriving an equivalent circuit according to claim 6, wherein K is obtained by combining the measured data with the measured data, thereby obtaining R _i .