KR101652595B1 - Analytical calculation method for natural frequencies of chip mounted PCB module using effective modulus and Calculator using the same - Google Patents

Abstract

In the present invention, the elastic modulus of each layer of a PCB module having a plurality of layers is obtained, and the total elastic modulus and the moment of inertia are derived using the modulus of elasticity, and the effective modulus of elasticity A method of calculating a natural frequency of a PCB module having a chip mounted thereon, the method comprising: calculating elastic modulus of each layer of the plurality of layers, ; Calculating an effective elastic modulus using the elastic modulus of each of the plurality of layers; Calculating an effective moment of inertia of the PCB module; There is provided a method of calculating a natural frequency of a PCB module mounted with a chip using an effective elastic modulus that determines a natural frequency f _i of a PCB module using the calculated effective elastic modulus and the effective moment of inertia, .

Description

Technical Field [0001] The present invention relates to a method of calculating a natural frequency of a PCB module mounted with a chip using an effective elastic modulus,

The present invention relates to a method of calculating natural frequency of a PCB module and a calculation device thereof, and more particularly, to a method of calculating a natural frequency of a PCB module by using a PCB A method of calculating a natural frequency of a module, and a calculating device.

BACKGROUND ART [0002] Recently, electrical and electronic devices have been used extensively in automobile engine control devices, mobile phones, and wearable devices.

When exposed to external physical forces such as vibrations and shocks, mounted PCB modules cause vibration, and stresses generated in these situations cause damage to electrical components.

The most necessary information for predicting the vibration behavior to prevent the damage is to calculate the natural frequency of the PCB module.

In general, PCB modules mounted on PCBs are very difficult to calculate by analytical methods due to the complicated shapes of chips and parts. Therefore, although the commercial code is modeled by the finite element method, the commercial code itself is expensive, the modeling using the commercial code requires considerable skill, and the calculation time is long. A related art related to this is disclosed in Patent Publication No. 10-2014-0062816.

For example, the plastic ball grid array (PBGA) technology is the most widely used technique among the first-level package methods. The most common process for fabricating PBGA packages is outlined in the following order.

First, sawing is performed to separate the semiconductor chips formed on the wafer after the FAB (Fabrication) process for forming the integrated circuit on the wafer surface. Then, as a circuit board having wiring therein is inserted into the process, an adhesive is applied to the top surface of the circuit board to bond the cut semiconductor chip. After the chip bonding is completed, a bonding pad formed on the semiconductor chip and a predetermined The wires are electrically connected to each other by using wires. In case of Flip chip, connect with solder.

After the wire bonding is completed, a molding process of encapsulating the semiconductor chip with an epoxy molding compound (EMC) is performed. In the case of wafer level packaging, the molding process is followed by sowing. After the molding is completed, a certain pattern of solder paste is transferred onto the bottom surface of the package body made of a circuit board by screen printing, and a solder ball is attached in a predetermined pattern. Then, a reflow process as a heat treatment process is performed The solder balls are firmly fixed to the circuit board main body. Through the underfill process, the chip and the PCB are firmly attached and the solder crack is prevented. As a typical example of such a PBGA semiconductor package, a technique described in Korean Utility Model No. 20-148625 as shown in FIGS. 1 and 2 has been developed. The technical feature is that a land portion A plurality of solder balls 4 are attached to a bottom surface of the substrate 1 and a plurality of inner leads 3 are vertically and horizontally mounted on the substrate 1, And the upper surface of the semiconductor chip 3 and the upper surface of the inner lead 5 are connected to each other by a metal wire 6. The semiconductor chip 3 and the metal wire 6 are covered with the sub- A molding part 7 is formed on the upper surface of the straight 1 and the plurality of solder balls 4 are mounted on the upper surface of the substrate 8 and are firmly attached to the underfill 9

Such a PBGA packaging is attached to the PCB. To obtain the natural frequency, the calculation is impossible theoretically because of complicated structure, and it should be calculated by using a commercially available finite element program. FIG. 3 shows an example of modeling a finite element to obtain natural frequencies for a PCB having five PBGA chips. FIG. 4 is an enlarged view of one of the five chips. It shows that a complex shape is modeled and many elements are used in order to obtain an accurate natural frequency. Such finite element modeling requires expensive commercial programs, long learning of modeling techniques, and long computation time because of the large number of finite elements depending on the complexity of the package structure.

In order to solve the problem of the method of calculating the natural frequency of a PCB module using the conventional finite element method as described above, the PCB module having the chip mounted therein is modeled into a structure composed of several layers, and the effective elastic modulus And the total effective elastic modulus and the moment of inertia are derived using the calculated elastic modulus and the inertia moment, and by using the theoretical calculation formula, the chip module is mounted on the PCB module using the effective elastic modulus, And to provide a calculation method and a calculation device of the natural frequency.

The present invention relates to a method of calculating a natural frequency of a PCB module having a plurality of layers, the method comprising the steps of: determining an effective elastic modulus of each layer of the plurality of layers; Calculating a total effective elastic modulus using the effective modulus of elasticity of each layer of the plurality of layers; Calculating an effective moment of inertia of the PCB module; And calculating the natural frequency of the PCB module using the calculated total effective elastic modulus and the calculated effective moment of inertia.

Wherein the step of determining the effective elastic modulus of each layer can be performed by using the mixing law of the elastic modulus of each layer, and the step of determining the effective modulus of elasticity of each layer is characterized in that, 1].

Ef: effective modulus of elasticity of the layer

E _c1 , E _c2 ... E _cn : modulus of elasticity of the constituent material of the layer

υ ₁ , υ ₂ , ... υ _n : Volume ratio of each material

In the step of obtaining the total effective elastic modulus, the total effective modulus of elasticity can be calculated using the mixing law, and the total effective modulus of elasticity can be calculated using the following equation (2).

E _eff : total effective modulus of elasticity

E ₁ to E _n : effective elastic modulus of each layer

υ ₁ υ _n ~: volume ratio of the layers

The PCB module may be formed by sequentially stacking a PCB, a solder layer, a substrate, a chip, and a molding compound layer. In the step of determining the effective moment of inertia (I _eff ), the effective moment of inertia , And the step of determining the effective moment of inertia I _eff may be calculated using Equation (3) and Equation (4).

I ₁ : moment of inertia when the chip completely covers the surface of the PCB

I ₂ : Moment of inertia of PCB alone except chip

υa: Chip volume ratio

b: width of section

h: height of section

The natural frequency (f _i ) of the PCB module can be determined by the following equation (5).

E: effective modulus of elasticity

I: moment of inertia

m: mass per unit length

L: Length

λ _i : a constant determined according to the fixed state of both ends of the beam in the theoretical equation for obtaining the natural frequency of the beam

On the other hand, the present invention can provide a PCB module frequency calculation device for calculating a natural frequency of a PCB module using the natural frequency calculation method.

The natural frequency calculation method according to the present invention calculates the elastic modulus of each layer of a PCB on which chips having a plurality of layers are mounted and derives the total effective elastic modulus and the moment of inertia by using them, It is possible to calculate the natural frequency of the entire PCB more easily than in the conventional case.

1 is a conceptual diagram of a conventional PBGA semiconductor package.
2 is a cross-sectional view of a conventional PBGA semiconductor package.
3 is a finite element modeling diagram of a PCB in which five PBGA chips are mounted.
4 is an enlarged view of the chip portion of FIG. 3;
5 is a flowchart of a natural frequency calculation method according to an embodiment of the present invention.
6 is a cross-sectional view of a PCB module in which a natural frequency is calculated by a natural frequency calculation method according to an embodiment of the present invention and a schematic view of a PCB module according to a calculation procedure.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, terms and words used in the present specification and claims should not be construed as limited to ordinary or dictionary terms, and the inventor should appropriately interpret the concepts of the terms appropriately The present invention should be construed in accordance with the meaning and concept consistent with the technical idea of the present invention.

5 and 6, a natural frequency calculation method according to an embodiment of the present invention includes determining elastic modulus of each layer (S100), determining an effective elastic modulus (S200), calculating an effective moment of inertia (S300) and determining a natural frequency (S400).

In one embodiment of the present invention, the natural frequency is calculated based on the PBGA packing structure disclosed in FIG. Although the present embodiment has been described on the basis of the PBGA packaging structure, since the PCB module is slightly different depending on the packaging form of the chip, it can be basically modeled as a stacked structure, so that the present invention can be applied to various PCB modules Of course.

Referring to FIG. 2, the PBGA packaging structure has a multilayer structure in which a PCB layer, an underfill and a solder layer, a substrate layer, a silicon chip and a molding compound layer, and a pure molding compound layer are stacked from the bottom.

The step of determining the effective elastic modulus of each layer (S100) calculates the effective elastic modulus of each layer in the PCB module composed of a plurality of layers.

In each layer, a layer made of a single material can be used as it is to represent the two materials constituting each layer in the underfill and the solder layer in which the two materials coexist and the silicon chip and the molding compound layer, The elastic modulus is calculated.

There are many calculation equations derived by using micro-mechanics in the method of obtaining the effective elastic modulus, but in the present embodiment, the calculation is performed using the rule of mixture. The mixing law is the simplest of the various methods of obtaining effective physical properties based on the assumption that stress occurs equally in each material forming the layer in the transverse direction and strain occurs in the longitudinal direction . Of course, the effective modulus of elasticity can be obtained by using various other equations in addition to the mixing law.

In the present embodiment, the elastic modulus in the transverse direction in the form in which the solder and the underfill are mixed can be calculated by the following formula (1).

[Equation 1]

Ef: effective modulus of elasticity of the layer

E _c1 , E _c2 ... E _cn : modulus of elasticity of the constituent material of the layer

υ ₁ , υ ₂ , ... υ _n : Volume ratio of each material

In the present embodiment, the elastic modulus of each layer is calculated using the simplest equation of the lateral mixing law, which is also possible to calculate the elastic modulus of each layer .

In one embodiment of the present invention, the natural frequency of the PCB module 100, which comprises the PCB 110, the solder ball layer 120, the substrate 130, the silicon chip 140, and the molding compound 150, is calculated.

Since the elastic modulus of each layer is made of a single material in the case of the PCB 110, the BT substrate 130 and the molding compound (EMC) 150, 1] and specify the modulus of elasticity of each layer.

[Table 1]

The solder ball layer made of two or more materials and the layer including the silicon chip calculate the elastic modulus of each layer using Equation (1).

[Equation 1]

Ef: effective modulus of elasticity of the layer

E _c1 , E _c2 ... E _cn : modulus of elasticity of the constituent material of the layer

υ ₁ , υ ₂ , ... υ _n : Volume ratio of each material

That is, in the case of the solder ball layer 120, the elastic modulus and the volume ratio of the solder ball 121 are determined, and the elastic modulus and the volume ratio of the underfill 122 are obtained. Subsequently, the elastic modulus and the volume ratio of the underfill 122 are substituted into the formula (1) The elastic modulus Ef of the elastic member 120 is derived.

The elastic modulus and the volume ratio of the silicon chip 140 are determined and the elastic modulus and the volume ratio of the molding compound 150 formed on the side surface of the silicon chip 140 are determined Then, the effective elastic modulus of the layer is derived using the above-mentioned formula (1).

The elastic modulus of each component is derived from [Table 1], and the volume ratio (υ) of each component can be easily obtained by a general calculator since the dimensions for each component are already known.

When the elastic modulus of each layer is determined in this manner, the effective modulus of elasticity of the entire layer is determined. (S200)

The total effective elastic modulus can be calculated based on the effective elastic modulus of each layer and the volume ratio of each layer.

The total effective elastic modulus is calculated by the following equation (2).

&Quot; (2) "

E _eff : total effective modulus of elasticity

E ₁ to E _n : effective elastic modulus of each layer

υ ₁ υ _n ~: volume ratio of the layers

The total effective modulus of elasticity in the present embodiment is determined by the effective elastic modulus of the PCB 110 * the volume ratio of the PCB 110 + the effective elastic modulus of the solder ball layer 120 * the volume ratio of the solder ball layer 120 + The effective elastic modulus of the layer including the silicon chip 140 the volume ratio of the layer including the silicon chip 140 the effective elastic modulus of the molding compound layer 150 the molding ratio The volume ratio of the compound (150) layer is calculated.

In the present embodiment, the total effective elastic modulus is calculated using the above-mentioned expression (2), but it is of course possible to calculate the total effective elastic modulus using other analytical expressions.

Next, the effective moment of inertia of the entire PCB module is calculated (S300)

The effective moment of inertia can be calculated using the volume fraction of the PBGA chip.

The PCB module 100 is geometrically different from the PCB module 100 in which the silicon chip is not mounted due to the mounted silicon chip 140.

In order to correct this, the effective moment of inertia is calculated using [Equation 3] and [Equation 4] for the PCB module having the chip in this embodiment.

&Quot; (3) "

I ₁ : moment of inertia when the chip completely covers the surface of the PCB

I ₂ : Moment of inertia of PCB alone except chip

υa: Chip volume ratio

&Quot; (4) "

b: width of section

h: height of section

When the effective elastic modulus and effective inertial moment of the PCB module are calculated as described above, the natural frequency (f _i ) of the PCB module is calculated using the calculated effective elastic modulus and effective inertial moment.

In this embodiment, assuming that the PCB on which the chip is mounted is a two-dimensional beam and assuming that both ends are fixed, the natural frequency of the PCB module is calculated by using Equation (5) (f _i ).

&Quot; (5) "

E: effective modulus of elasticity

I: effective moment of inertia

m: mass per unit length

L: Length

λ _i : a constant determined according to the fixed state of both ends of the beam in the theoretical equation for obtaining the natural frequency of the beam

In this embodiment, the natural frequency is calculated using the equation (5), which is the analysis equation for obtaining the natural frequency for the two-dimensional beam. However, it is of course possible to calculate the natural frequency by using other analytical equations.

As shown in FIG. 3, the natural frequency of the PCB module mounted with the chip is calculated by the finite element method and the method disclosed in the present invention, and the difference is about 3%. However, for the finite element calculation, And the present invention was able to calculate within about 5 minutes using a general calculator.

That is, the natural frequency calculation method of the PCB module according to the embodiment of the present invention can more conveniently calculate the natural frequency of the PCB module, and can also quickly and easily calculate the natural frequency of the PCB module using this calculation method The natural frequency calculation device of the PCB module can be implemented.

While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments, but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

100: PCB module 110: PCB
120: solder ball layer 130: substrate
140: Silicon chip 150: Molding compound

Claims (9)

A method of calculating a natural frequency of a PCB module having a plurality of layers,
Determining effective elastic modulus of each layer of the plurality of layers;
Calculating a total effective elastic modulus using the effective modulus of elasticity of each layer of the plurality of layers;
Calculating an effective moment of inertia of the PCB module;
Determining the natural frequency of the PCB module using the calculated total effective modulus of elasticity and the effective moment of inertia,
Wherein the step of determining the effective elastic modulus of each layer comprises:
The effective elastic modulus of each layer is calculated using the following equation (1)
[Equation 1]

Ef: effective modulus of elasticity of the layer
E _c1 , E _c2 ... E _cn : modulus of elasticity of the constituent material of the layer
υ ₁ , υ ₂ , ... υ _n : Volume ratio of each material

The total effective elastic modulus is calculated using Equation (2)
&Quot; (2) "

E _eff : total effective modulus of elasticity
E ₁ to E _n : effective elastic modulus of each layer
υ ₁ υ _n ~: volume ratio of the layers
The PCB module includes a PCB, a solder layer, a substrate, a chip, and a molding compound layer sequentially laminated,
The step of determining the effective moment of inertia (I _eff ) may be performed using the volume fraction of the chip,
The step of determining the effective moment of inertia (I _eff ) is calculated using Equation (3) and Equation (4)

&Quot; (3) "

I ₁ : moment of inertia when the chip completely covers the surface of the PCB
I ₂ : Moment of inertia of PCB alone except chip
υa: Chip volume ratio
&Quot; (4) "

b: width of section
h: height of section
The natural frequency (f _i ) of the PCB module is calculated by using the effective elastic modulus determined by Equation (5).

&Quot; (5) "

E: effective modulus of elasticity
I: moment of inertia
m: mass per unit length
L: Length
λ _i : a constant determined according to the fixed state of both ends of the beam in the theoretical equation for obtaining the natural frequency of the beam
delete delete delete delete delete delete delete An apparatus for calculating a natural frequency of a PCB module mounted with a chip using an effective elastic modulus calculating a natural frequency of the PCB module using the natural frequency calculation method of claim 1.

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