JPH06176113A - Analysis method for temperature in heating object - Google Patents

Abstract

PURPOSE:To provide a temperature analysis method by which the storage capacity of an electronic computer is reduced and calculation time is shortened when a temperature distribution in an object having a number of minute heat generating elements is analyzed by using the electronic computer, namely, the heat design of the internal structure of an LSI chip. CONSTITUTION:The calculation expression of the temperature rise distribution when the heat of one minute heat generating element 3 spreads all over the object is previously obtained. Temperature rise due to influence from the respective heat generating elements 3 are calculated by using the calculation expression. They are added and are corrected to satisfy a given temperature boundary condition. Thus, the temperature distribution including the influence of all the head generating elements 1-3 is obtained. Thus, calculation cost can be made inexpensive without deteriorating calculation precision, and a calculated result can speedily be obtained.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a temperature analysis method used for thermal design of the internal structure of a semiconductor LSI chip, and in particular, it analyzes the temperature distribution inside an object having a large number of minute heating elements using an electronic computer. On how to do.

[0002]

2. Description of the Related Art As a conventional method for analyzing the temperature inside a heat-generating object, for example, as described in the 28th Japan Heat Transfer Symposium Proceedings, Volume 3, page 709 (published in May 1991). , The inside of the object is divided into many fine calculation elements and calculation nodes, the energy equation and the motion equation are discretized by the difference method and the finite element method, and the matrix of the one-dimensional simultaneous equations in which the temperature of the calculation node is an unknown number is repeated or It was solved by the direct method. The calculation elements and calculation nodes finely divided the area in the vicinity of all the heating elements.

[0003]

When the temperature distribution inside an object having a large number of minute heating elements is analyzed using the above-mentioned conventional technique, the calculation elements and calculation of the area in the vicinity of each heating element are performed. Since the nodes are finely divided, the total number of calculation elements and calculation nodes of an object having a large number of heating elements becomes enormous, which requires a large memory capacity of an electronic computer and also takes a long calculation time. There was a problem that the calculation cost was large.

An object of the present invention is to provide a temperature analysis method for reducing the storage capacity of an electronic computer and shortening the calculation time when analyzing the temperature distribution inside an object having a large number of minute heating elements. To do.

[0005]

In order to achieve the above object, the present invention carries out theoretical analysis to calculate a temperature rise distribution when heat generated by one minute heating element spreads over the entire object. It is obtained in advance as a function of the dimensional structure of the heating element and the amount of heat generation. Roughly divide the entire body of a large number of heating elements by calculation elements and calculation nodes, and use the above formula to calculate the temperature rise value due to the influence of each heating element for given heating and structural conditions. Then, the temperature distribution including the influence of all the heating elements is obtained by correcting the values so as to satisfy the given temperature boundary conditions. Furthermore, only the designated local region is divided into fine calculation elements and calculation nodes to analyze the temperature distribution with high accuracy. Further, instead of the calculation formula of the temperature rise distribution when the heat is generated by one heating element, the temperature rise distribution when the heat is generated by only one heating element is obtained by the numerical analysis of the electronic computer. At that time, numerical analysis is performed by combining one-dimensional analysis, two-dimensional analysis and three-dimensional analysis.

[0006]

Since the whole body having a large number of heating elements is not divided by thin calculation elements and calculation nodes, the storage capacity of the computer can be small. Further, the temperature distribution calculation of an object having a large number of heating elements is a calculation using a calculation formula or a numerical analysis result which has been obtained in advance, and in addition, the calculation is performed by the correction, and the calculation time is short, The calculation cost can be reduced. Furthermore, a highly accurate temperature distribution can be obtained for the required local region.

[0007]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to FIGS. Here, an example of analyzing the temperature distribution inside the semiconductor LSI chip during operation will be described. FIG. 3 shows a part of an LSI chip (area size is 100 μm × 60
FIG. 3 is a plan view of an electronic device arrangement of μm). 4 is shown in FIG.
It is sectional drawing of the II cross section shown in FIG. The main heating elements in the electronic device are the transistor elements 1 and 2 and the resistance element 3. In the case of FIG. 3, there are 29 heating elements. There are two types of transistor elements: an element 1 formed directly on the surface layer portion of the silicon substrate 4 and an element 2 formed inside a silicon rectangular parallelepiped region 6 surrounded by the SiO ₂ insulating film 5 on the surface layer portion of the silicon substrate 4. The resistance element 3 is S
It is formed in the iO ₂ insulating film 7. A multilayer aluminum wiring layer 8 is formed above them. Figure 5 is LS
The vertical cross-sectional view of the state which assembled the I chip in the cooling structure is shown. The LSI chip 9 is housed inside a package 11 having a cooling structure 10 and attached to a board 12. The upper surface of the silicon substrate 4 of FIG. 4 corresponds to the lower surface 13 of the LSI chip 9 of FIG. 5, and the heat generated in the heating elements 1, 2, and 3 is conducted to the inside of the silicon substrate 4, and the cooling structure is obtained. It is transmitted to the object 10 and radiated into the air.

An analysis method for calculating such a temperature distribution inside the LSI chip by using an electronic computer will be described below. FIG. 6 shows a flow chart of the analysis method of this example. Step 1: The worker determines the structure to be calculated, the physical property value,
Boundary conditions, heat generation conditions, and local region position data that require detailed analysis are input to a computer. Step 2:
The analysis area is automatically divided into calculation elements and calculation nodes inside the electronic computer. FIG. 1 is a plan view after division into calculation elements and calculation nodes, and FIG. 2 is a vertical cross-sectional view of the I-I section shown in FIG. Computational nodes 14 that are roughly divided into five equal parts in each direction, and computational nodes 16 that are finely divided inside the local region 15 that requires detailed analysis,
The nodes 17 around the input heating elements 1, 2 and 3 are combined to make a total calculation node. All electronic device positions are on the surface of the silicon substrate, and their thickness is ignored. Ignore the aluminum wiring layer 8 that has little effect on the overall temperature distribution. Step 3: As detailed below,
In advance, a calculation formula of a temperature distribution when heat generated by one minute heating element spreads through heat conduction throughout a large object is obtained as a function of the amount of heat generation and the element size. The temperature rise value at each node is calculated by using the calculation formula and adding the influences from all the heating elements. Step 4: As will be described later in detail, the temperature increase value at each node is used to calculate the temperature at each node so as to satisfy the boundary condition. Step 5: Perform accurate analysis using a finite element method or a difference method inside a local region that requires detailed analysis. In this analysis, the temperature around the local region obtained by the above method is used as the boundary condition. Step 6: Finally, output the calculation result.

A formula for calculating a temperature rise value when heat generated by one minute heating element spreads throughout the object and a calculation for adding influences from all the heating elements will be described below. As shown in FIG. 7, if the minute heating element 18 has a hemispherical shape on the surface of the infinite object 4 and the heat generation amount is Q (W), the temperature at a position separated by a distance r (m) from the element generates heat. Value that temperature rises due to the influence of the element ΔT (℃)
Is calculated by the following formula by theoretical analysis.

[0010]

[Equation 1]

Here, k is the thermal conductivity (W / mK) of the material of the silicon substrate, and π is the circular constant.

For a node at a position that does not enter the inside of the heating element, the temperature rise value obtained by adding the effects of all the heating elements is given by the following equation.

[0013]

[Equation 2]

Here, i = 1 to N are the numbers of the heating elements, Qi is the heat generation amount (W) of each heating element, and ri is the distance (m) from each heating element.

Like the transistor element 1 in which minute heating elements are formed directly on the surface layer of the silicon substrate, the influence of all the heating elements at the node where the heating elements having the rectangular parallelepiped shape 19 in FIG. The added temperature rise value is given by the following equation.

[0016]

[Equation 3]

Where j is the number of the heating element of its own,
a, b, and c are the length, width, and height (m) of the heating element.

Like the transistor element 2 in which a minute heating element is formed inside the silicon rectangular parallelepiped region 6 surrounded by the SiO ₂ insulating film, all of the nodes at the positions inside the rectangular parallelepiped shape 19 heating element shown in FIG. The temperature rise value, which is obtained by adding the influence of the heating element of, is given by the following equation.

[0019]

[Equation 4]

Here, K is the thermal conductivity (W / mK) of the material of the SiO ₂ insulating film, and l, m, and n are silicon rectangular parallelepiped regions 6
The vertical, horizontal, and height (m), and t are the thickness (m) of the insulating film.

Like the resistance element 3 in the SiO ₂ insulating film, the effect of all the heat generating elements at the node where the minute heat generating element enters the inside of the heat generating element of the rectangular parallelepiped shape 19 in FIG. 10 is added. The temperature rise value is given by the following equation.

[0022]

[Equation 5]

Here, t is the thickness (m) of the insulating film at the bottom of the heating element.

By using the above formula, it is possible to calculate the temperature rise value in which the influences from all the heating elements are added together at each node.

A method of calculating the temperature of each node so as to satisfy the boundary condition by using the temperature rise value at each node will be described below. As a boundary condition, if you want to fix the temperature of the specified surface, do as follows. The average temperature rise value of all the nodes included in the specified surface is calculated using the above calculation formula, and the difference from the fixed temperature is taken as the corrected temperature difference. The temperature difference at each node can be calculated by adding the corrected temperature difference to the temperature rise values at all nodes.

As a boundary condition, when the heat transfer coefficient of the designated surface is fixed, the following is performed. The temperature of the specified surface is calculated by the following formula.

[0027]

[Equation 6]

Here, Qi is the heat generation amount (W) of each heating element, Ts is the cooling air temperature (° C.), A is the designated surface area (m ² ) α is the heat transfer coefficient (W / m ² K). Is. The rest is the same as when fixing the temperature of the specified surface to the temperature obtained by this formula.

As a boundary condition, when the designated surface is to be an adiabatic surface, the following is performed. The temperature of each node can be calculated by considering the virtual surface on the opposite side with the specified surface as the symmetry surface and calculating the temperature rise value by adding the influence from the heating element in the virtual surface. .

FIG. 11 shows an example of the result of analyzing the temperature distribution inside the semiconductor LSI chip according to this embodiment. Targeting the structures shown in FIGS. 3 and 4, the temperature of the lower surface of the silicon substrate was fixed at 20 ° C. as a boundary condition.

Next, the effect of this embodiment will be shown. FIG. 1 is a plan view after applying the present invention and dividing into calculation elements and calculation nodes. FIG. 12 is a plan view after the same calculation target is divided into calculation elements and calculation nodes according to the related art.
It can be seen that the present invention can significantly reduce the number of divisions of calculation elements and calculation nodes.

Although the above description has been made with reference to the temperature distribution calculation, the same analysis method can be applied to velocity distribution calculation and stress calculation.

A second embodiment of the present invention will be described with reference to FIGS. FIG. 13 is a cross-sectional perspective view when a plurality of transistor elements having the same structure are arranged in parallel in a part of an LSI chip. In the surface layer portion of the silicon substrate 4, SiO ₂
The transistor element 2 formed inside the silicon rectangular parallelepiped region 6 surrounded by the insulating film 5 is formed. L like this
An analysis method for calculating the temperature distribution inside the SI chip by using an electronic computer will be described below. FIG. 14 shows a flow chart of the analysis method of this example. Step 1: The worker
Input the data required for analysis into the computer. Step 2: Inside the electronic computer, when one minute heating element is present on the silicon substrate, only the vicinity of one heating element is finely divided into calculation elements and calculation nodes. Step 3: Calculate the temperature rise distribution when only one minute heating element generates heat by numerical analysis using the finite element method. Numerical analysis for obtaining the temperature rise distribution when one heating element generates heat is repeated for heating elements having different element structures. Step 4: The temperature rise value at each node is calculated by using the calculation result and adding the influences from all the heating elements. At that time, in the case where the element structure is the same, it is calculated that the temperature rise value obtained by the numerical analysis is proportional to the heat generation amount of the element. Step 5: Using the temperature rise value at each node, calculate the temperature of each node so as to satisfy the boundary condition,
Finally, the calculation result is output.

A third embodiment of the present invention will be described next. An analysis method for calculating the temperature distribution inside the LSI chip shown in FIGS. 3 and 4 using an electronic computer will be described below. In this embodiment, the calculation target is divided into three area groups, and one-dimensional analysis, two-dimensional analysis and three-dimensional analysis are applied to each area group. A region in the vicinity of the transistor element 1 in which minute heating elements are directly formed on the surface layer of the silicon substrate is subjected to a one-dimensional analysis that spreads in the radial direction with the heating elements as the center. A three-dimensional analysis is performed on a region in the vicinity of the transistor element 2 formed inside the silicon rectangular parallelepiped region 6 in which the minute heating element is surrounded by the SiO ₂ insulating film. A region of the resistance element 3 in the vicinity of the heating element is subjected to a two-dimensional analysis that spreads in the radial direction with the elongated heating element as the central axis. Three-dimensional analysis is performed on the surface layer of the silicon substrate. One-dimensional analysis in the depth direction is performed on the region from the position away from the surface layer of the silicon substrate to the lower surface. Simultaneous numerical analysis of the entire calculation target by combining 1-dimensional analysis, 2-dimensional analysis and 3-dimensional analysis. According to the present embodiment, the whole calculation target is not divided by fine calculation elements and calculation nodes for three-dimensional analysis, so that the number of divisions of calculation elements and calculation nodes can be reduced.

[0035]

According to the present invention, since the whole body having a large number of heating elements is not divided by fine calculation elements and calculation nodes, the number of divisions of calculation elements and calculation nodes can be greatly reduced, and the computer The storage capacity of is small. Also,
To calculate the temperature distribution of an object with many heating elements, the calculation formulas or numerical analysis results that have been obtained in advance are used, their additions are made, and the corrections are made. It can be cheaper and the calculation result can be obtained quickly.

[Brief description of drawings]

FIG. 1 is a plan view of calculation elements and calculation nodes according to a first embodiment of this invention.

FIG. 2 is a cross-sectional view taken along the line II of FIG.

FIG. 3 is a plan view of an electronic device arrangement of a part of an LSI chip.

FIG. 4 is a cross-sectional view taken along the line II of FIG.

FIG. 5 is a sectional view of an LSI chip cooling structure.

FIG. 6 is a flowchart of the analysis method of the first embodiment.

FIG. 7 is an explanatory diagram showing a hemispherical heating element.

FIG. 8 is an explanatory diagram showing a rectangular parallelepiped heating element formed directly on a substrate.

FIG. 9 is an explanatory diagram showing a rectangular parallelepiped-shaped heating element formed inside an insulating film.

FIG. 10 is an explanatory diagram showing a rectangular parallelepiped heating element formed in an insulating film.

FIG. 11 is a perspective view showing an analysis result of temperature distribution.

FIG. 12 is a plan view of a conventional calculation element and calculation node.

FIG. 13 is a cross-sectional perspective view of a part of an LSI chip.

FIG. 14 is a flowchart of the analysis method of the second embodiment.

[Explanation of symbols]

1,2 ... transistor elements 3 ... resistance element, 4 ... silicon substrate, 5, 7 ... SiO ₂ insulating film, 6 ... silicon cuboid region, 9 ... LSI chip.

Claims (1)

[Claims] 1. A solid or fluid containing a plurality of heating elements inside is a calculation object, and the calculation object is divided into a large number of calculation elements and calculation nodes, and in a numerical analysis of temperature distribution using an electronic computer, first, A temperature analysis inside a heating object, characterized in that a temperature rise distribution when one heating element generates heat is obtained, and then a temperature distribution when a plurality of heating elements simultaneously generate heat is obtained using the temperature rise distribution. Method.