JPS6013316B2 - Arrangement method for semiconductor strain gauge elements - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a method for arranging a plurality of semiconductor strain gauge elements exhibiting a piezoresistive effect, which are formed by diffusing impurities on one main surface of a circular diaphragm made of a semiconductor single crystal. .

A semiconductor single crystal is used as a circular diaphragm to respond to pressure, and an impurity is diffused onto one main surface of the diaphragm.
Semiconductor pressure-sensitive elements formed with multiple semiconductor strain gauge elements exhibiting a piezoresistance effect can be used as semiconductor pressure transducers with superior characteristics such as higher sensitivity and smaller size than conventional metal linear strain gauges. It is well known that this can be provided.

As shown in FIG. 1, this type of semiconductor pressure-sensitive element is often one in which one main surface of a semiconductor single crystal substrate 4 is processed into a concave shape to form a thin part, and this part is used as a circular diaphragm to respond to pressure. , a bridge is formed by a plurality of semiconductor strain gauge elements 1 diffused on the other main surface of the diaphragm, an electrical input is applied to the bridge via a lead wire 3 and a conductor 2, and an output voltage responsive to pressure is provided. There are many things you can get. This type of semiconductor pressure-sensitive element has excellent sensitivity characteristics especially when converting pressure into electrical output, and can obtain several tens of times the sensitivity compared to conventional metal linear strain gauges. However, with regard to the conversion accuracy, it may not only not be possible to obtain amazing superiority such as sensitivity characteristics, but may even be inferior. Furthermore, ``Sensitivity to temperature changes, which is an inherent characteristic of semiconductors, is also a major drawback of this type of semiconductor pressure-sensitive element.Various compensation methods have been proposed to date to address these drawbacks.'' ``In particular, as a method of compensating for conversion accuracy, there is a method of optimizing stress in the principal plane of a conductor diaphragm by controlling the processing shape of the diaphragm and compensating for accuracy. A method of electrically compensating for ``{3} Forming a unit bridge structure by placing a plurality of semiconductor strain gauge elements close to each other'' and ``arranging the unit bridge structure at an optimal position on the main surface of the diaphragm to compensate. In addition, many compensation methods have been proposed for the bridge output when the pressure is zero, that is, the zeq point t, and the fluctuations due to temperature, such as the output sensitivity when pressure is applied. The most common method for compensating for this temperature fluctuation is to integrate elements with equal temperature coefficients and use circuitry, which is relatively easy to achieve. Each of the above compensation methods has its drawbacks and is not satisfactory. This method attempts to compensate for accuracy by controlling the processing shape of the diaphragm so that the stress generated within the diaphragm is proportional to the pressure over a wide pressure range.
No countermeasures are taken against the nonlinearity inherent in semiconductor strain gauge elements exhibiting a piezoresistive effect, and high precision cannot be expected. Moreover, it is not easy to control the processing of the diaphragm, and it is difficult to obtain characteristics with good reproducibility. Therefore, it is difficult to achieve sufficient compensation for conversion accuracy using method '1}. The above-mentioned method (2) should be used as a last resort when compensation is impossible with the semiconductor pressure-sensitive element itself, and it is not economical even though it goes against the characteristics of miniaturization in that it increases the number of electric circuits for compensation. Conventionally, this type of semiconductor pressure-sensitive element has a plurality of semiconductor strain gauge elements formed on the main surface of a circular diaphragm. Many devices are constructed only of radial strain gauge elements whose current direction is parallel to the current direction.In the methods {1) and (2) described above, the radial strain gauge elements are also constructed by applying stress directed in opposite directions to each other within the main surface of the diaphragm. In many cases, the output sensitivity is effectively obtained by placing the sensor in the radial direction. Strain gauge element and ~
A plurality of two types of semiconductor strain gauge elements, a tangential strain gauge element in which the tangential stress acting on the main surface of the diaphragm and the current direction are parallel, are formed, and at least one of each type is placed close to each other in at least one set. This forms a unit bridge structure. The fact that output sensitivity can be effectively obtained even in such a configuration is that the topiezoresistance coefficient has opposite polarity in the current direction of the strain gauge element (hereinafter also referred to as the vertical direction) and in the orthogonal direction (hereinafter referred to as the horizontal direction). It is based on the fact that However, such a method alone cannot sufficiently compensate for accuracy. The reason for this is that the '31 method targets a composite body consisting of a plurality of semiconductor strain gauge elements called a unit bridge mechanism. The reason behind the use of such a composite structure in the glue method is that it is required to reduce the zero point unbalance of the bridge in order to compensate for the temperature fluctuations mentioned above.For this purpose, multiple strain gauge elements are formed by diffusion. It is necessary to suppress variations in resistance values as much as possible by arranging strain gauge elements in close proximity to each other. By reducing the thermal potential of the semiconductor pressure-sensitive element, it is possible to prevent characteristic drift and S/N reduction.These problems are extremely important for semiconductor pressure-sensitive devices in terms of their characteristics, but countermeasures are required. The essence of the '3: method is that too much emphasis is placed on the accuracy, resulting in incomplete compensation of accuracy. This will be explained in more detail with reference to Figure 2. Figure 2 shows the above-mentioned This figure shows an example of the relationship between the distance from the center of the circular diaphragm of the unit bridge structure and the nonlinear error of the pressure-sensitive element. The conversion accuracy above all refers to this non-linear error.In other words, in the curve showing the relationship between the applied pressure to the pressure sensitive element and the output, the point of the output Vo corresponding to zero applied pressure and the If the point of the output VMx corresponding to the maximum applied pressure of the measurement range is connected with a straight line, and the maximum output error between the straight line connecting this Vo and Vmax and the above curve is △V, then the non-linear error is N.L is expressed as follows.N.L=Obiyanagi.%.
.... 'However, VFs "Vm Matsu-Vo...
...{21 The output of this type of semiconductor pressure-sensitive element is determined by determining the applied pressure and the axial direction of the bridge from the center of the diaphragm. It depends on two variables: the distance to the construct.

Therefore, by calculating the output when pressure is applied from zero to the maximum of the measurement range at a position at an arbitrary distance from the center of the diaphragm of the bridge structure, the position dependence of the nonlinear error can be calculated by the result and definition. Can calculate. Second
The figure shows an example of this, and shows calculation results for a conventional example as shown in FIG. That is, Fig. 3 is {10
0} plane orientation n-type Si single crystal substrate 4 110>
A unit bridge structure 5 consisting of a p-type radial strain gauge element 6 and a tangential strain gauge element lr along the wisteria direction.
The opposite surface of the substrate is processed into a concave shape so that the bridge member is located within the main surface of the circular diaphragm and near the end of the diaphragm. As shown in FIG. 2, in the conventional example shown in FIG. 3, there is a position A of the bridge structure where the extraneous error is calculated to be zero near the end of the diaphragm. However, as is clear from the figure, the shape of the curve showing the position dependence of the non-linear error is extremely steep near the position where it is calculated to be zero. This tendency is common when considering the position dependence of nonlinear error using a set of strain gauge element aggregates called a bridge structure, and is not limited to the example shown in FIG. 3.
Therefore, the above-mentioned leg method requires technical means to form the bridge structure in a predetermined position, such as a diaphragm recess, since variations in the position of the bridge structure on the diaphragm surface have a very large influence on non-linear errors. This requires extremely high processing precision in shaping techniques, making it difficult to manufacture pressure-sensitive elements that exhibit the same characteristics in a simple and stable manner. In the conventional example shown in Fig. 3, anticipating the instability of such characteristics, ``four sets of characteristically equivalent unit bridge structures are formed near the rocky part on the diaphragm surface, and one set of them is selected. It is used as a pressure sensitive element.This takes advantage of the azimuthal equivalence of the piezoresistance coefficient.However, in this case, the four unit bridge structures are used, for example, depending on the pressure measurement range. It is not possible to make effective use of each of the four sets, and the azimuthal equivalence of the piezoresistance coefficients cannot be effectively utilized.
In particular, the various problems that the method '3} had were solved using completely different technical means.

That is, the present invention aims to provide a high-precision semiconductor pressure transducer that can sufficiently compensate for the shortcomings in conversion accuracy of semiconductor pressure-sensitive elements, by effectively reducing the diaphragm surface of each semiconductor strain gauge element. The aim is to provide a convenient arrangement method. The present invention provides a device in which a plurality of semiconductor strain gauge elements exhibiting a piezoresistance effect formed by diffusing impurities are arranged on one main surface of a circular diaphragm made of a semiconductor single crystal. A radial strain gauge element in which a radial stress acting on one main surface of the diaphragm is parallel to the current direction, and a tangential strain gauge element in which the tangential stress acting on one main surface of the diaphragm is parallel to the current direction. After arranging the tangential strain gauge element near the center of the diaphragm, the radial strain gauge element is arranged in a non-linear manner with the distance from the diaphragm center of the radial strain gauge element. The curve representing the relationship with the error is arranged in the vicinity of the point where the nonlinear error intersects the zero straight line in the process of changing from the center of the diaphragm toward the periphery.

The vicinity of the center of the diaphragm refers to a portion located inside a position half of the radius connecting the center of the diaphragm and its outer periphery. The distance from the center of the diaphragm of the strain gauge element means the distance between the center of the strain gauge element and the center of the diaphragm, and the center of the strain gauge element means the center of the part that predominantly contributes to the resistance change of the element. Furthermore, the vicinity of the point where the non-linear error intersects the straight line with zero includes the range within which the required accuracy can be satisfied. When pressure is applied to the circular diaphragm, each strain gauge element formed on the diaphragm surface receives stress and exhibits a resistance change.

It is a well-known fact that this is due to the piezoresistance effect.
It is already well known that the resistance value of each strain gauge element in this case can be approximately expressed by the following equation if the temperature is constant. Rr;R. (1000 r. r + trot)
...{3, Rt3R. (10 tot 10 or tt.r)
...[4} Here, Rr and Rt are the resistance values of the radial strain gauge element and tangential strain gauge element, respectively, Ro is the resistance value when the pressure is zero, mr and lt are the resistance values of the radial strain gauge element, respectively. , the longitudinal piezoresistance coefficient of the tangential strain gauge element, tr, and u are the transverse piezoresistance coefficients of the radial strain gauge element and the tangential strain gauge element, respectively. Also,. (The enemies are the radial stress and the tangential stress that act on the diaphragm surface, respectively, and if the diaphragm is fixed at its outer circumference, they can be approximately expressed by the following equations.

r3-kure (hatake) 2-p {(・+shi)−(3+shi)sa}
... wind enemy - delicious nose) 2・p {(・10y) - (113re) pier} ...'6)
Here, a and h are the radius and thickness of the diaphragm, p is the pressure,
Poisson's ratio, r, is the distance from the center of the diaphragm. Inferring from equations {3' to [6}, the resistance values Rr and Rt of each strain gauge element can be determined by determining the pressure p and distance by determining the shape and material of the diaphragm and the orientation of the lamination axis of each strain gauge element. It can be seen that it is a function of r. Therefore, by using the formula 6i, it is possible to calculate the resistance value corresponding to any pressure at any position on the diaphragm surface, and by further applying this to the well-known bridge output calculation formula, the sensitivity of the semiconductor pressure-sensitive element can be approximated. Determined exactly. However, {3'~
As is clear from the '61 formula, the resistance value is in a proportional relationship with the pressure in this case, and it is not possible to calculate accuracy with this. Conventionally, this type of semiconductor pressure-sensitive element has been difficult in terms of accuracy because the stress distribution and piezoresistance effect cannot be completely expressed as in equations '3' to {6} and include nonlinear terms. None other than that. stress. r. t is not necessarily proportional to the pressure p as shown in the equation [5}, and the resistance values Rr and Rt are [3
1. Stress as shown in '4-Equation. It cannot be expressed only by the linear terms of r and ot. Therefore, the inventors analyzed the relationship between stress and pressure, including nonlinear terms, and calculated the respective resistance values using the expansion formula shown below.
From this, we calculated the bridge output and examined its nonlinear error. Note that although the following equation describes only up to the second-order term of each stress, it is considered that even higher-order terms are included and further act on the strain gauge element. rL. It is clear that more accurate results can be obtained if calculations are performed taking into account stresses other than those above. Rr2R. (10 towns of 10 towns
rot + 汀2rbir2 10m2trhit2)
[7}Rt2R. (10 powers,
tot+ ttor juchuhada 02 jutake 2tt 2)
'8} Here, mar,
21t is the second-order longitudinal piezoresistance coefficient of the radial strain gauge element and the tangential strain gauge element, respectively, and mar and 2tt are the respective second-order lateral piezoresistance coefficients. The curve shown in FIG. 4 was obtained as a result of the study using the method described above. From the viewpoint of output sensitivity, it is often preferable to arrange the tangential strain gauge element near the center of the diaphragm. Figure 4 shows the relationship between the nonlinear error and the distance of the radial strain gauge element from the center of the diaphragm x R when the tangential strain gauge element is placed near the center of the diaphragm. It is. According to this figure, "The curve intersects the straight line with zero nonlinear error at point B, and if the radial strain gauge element is placed near this position, the nonlinear error of the pressure sensitive element will be zero in principle. As a result, a highly accurate pressure transducer can be obtained.Figure 5 shows the relationship between nonlinear error and radial strain gauge element when the distance of the tangential strain gauge element from the center of the diaphragm is slightly changed. This figure shows the relationship between the distance from the center of the diaphragm and one curve corresponds to one position of the tangential strain gauge element.Let the curve corresponding to the turtle figure be x',
The position of the tangential strain gauge element corresponding to this curve is ±△
Consider the curves XT+ΔX and XT−ΔX in the case of changing ×. It is naturally expected that the position of each strain gauge element will deviate from its optimally designed position during the manufacturing process of pressure-sensitive elements, and in that case, it is required to minimize the influence in order to produce products with stable characteristics. . Examining point B in Figure 5 from this perspective, we can see that the nonlinear error changes from a to b for a position change of 2△×, but the slope of the change is gentler than the slope of each curve. I understand that there is something. This is based on the fact that the tangential strain gauge element is placed near the center of the diaphragm.If the tangential strain gauge element is placed near the periphery of the diaphragm, the gradient of change corresponding to a to b in the figure will change. It has also been confirmed that the slope will become steeper. Therefore, after first placing the tangential strain gauge element near the center of the diaphragm, the radial strain gauge element is placed at a point corresponding to point B in FIG. By placing the characteristic curve showing the relationship between A stable pressure transducer can be obtained.
Furthermore, if the strain gauge element arrangement method of the present invention is adopted, it is not necessary to form four equivalent bridge sets for one type of pressure range in the accuracy compensation method described in subsection [3]. Therefore, at least two or more types of pressure ranges can be covered by multiple sets of bridges, and it becomes possible to effectively utilize the axial equivalence of piezoresistance coefficients. Example 1 FIG. 6 shows two sets of p-type tangential strain gauge elements along the 450 direction from the 110> axis and the <100> axis of an n-type Si single crystal substrate having {110} plane orientation. It is formed symmetrically about an axis, and two sets of p-type radial strain gauge elements are formed symmetrically about the axis along the <111> direction.

Each strain gauge element has a configuration in which four sets of mutually parallel pongee strips are connected in series via a low resistance region. This is because by doing so, the required resistance value can be obtained in a small area. The diaphragm was shaped as shown in FIG. For example, thickness 0 for pressure measurement of 5k9/
．． 2. Place a tangential strain gauge element and a radial strain gauge element on a Si diaphragm with a diameter of 8 ribs, respectively, from the center of the diaphragm to o-8 ribs (ki=o-2) and 3 ribs.
-2 skin =o-8) and when the bridge is excited with constant current so that the voltage between the input terminals is 3.5V, the output voltage sensitivity is 10% of VFS of 200, and the nonlinear error is It was less than 0.1%FS. Here, FS means the maximum range in the pressure measurement range. In addition, for pressure measurement of a 100k9' block, a tangential strain gauge element and a radial strain gauge element are placed on the super-curved part of a Si diaphragm with a thickness of 0.8 skin and a diameter of 8 bars, respectively, from the center of the diaphragm.
-6 legs (Ki=o-4) and 3-2 legs (Ki=0.8), and when the bridge is excited with a constant current in the same way as above, 5
Almost the same characteristics as those for pressure measurement in kg/kg were obtained. Example 2 Figure 7 shows that two sets of p-type tangential strain gauge elements are formed symmetrically along the <112> direction of an n-type moxibustion i single crystal substrate having a {110} plane orientation. 111> Two sets of p-type radial strain gauge elements are formed symmetrically along the axis.

For example, a Si diaphragm with a thickness of 0.2 mm and a diameter of 8 ribs is used to measure the pressure of 5k9/ground, and a tangential strain gauge element and a radial strain gauge element are placed on the -2 side (-2 side) from the center of the diaphragm, respectively. Ki = o-3), 3-2 side =
o-8) and when the bridge is excited with constant current as in Example 1, the output voltage sensitivity is 200VFS+1
0%, and the non-linear error was less than ±0.1%FS. Other examples and application examples are shown in Table 1. The present invention is not limited to these examples. Table 1 As stated above, according to the present invention, it is possible to provide a semiconductor pressure transducer with high sensitivity, high precision, and small variations in characteristics between products.

[Brief explanation of drawings]

Fig. 1 is a schematic cross-sectional view of a semiconductor pressure-sensitive element, Fig. 2 is a characteristic diagram corresponding to the conventional arrangement pattern shown in Fig. 3, Fig. 3 is a diagram of the conventional arrangement pattern, Fig. 4 and Fig. 5 are Characteristic diagrams illustrating the present invention, FIGS. 6 and 7 are examples of the present invention. 6... Radial strain gauge element, 7... Tangential strain gauge element. Figure 2 Figure 3 Figure 4 Figure s Figure 5 Figure 7

Claims (1)

[Claims] 1. A plurality of semiconductor strain gauge elements exhibiting a piezoresistive effect formed by diffusing impurities are arranged on one main surface of a circular diaphragm made of a semiconductor single crystal, in which the semiconductor strain gauge elements are connected to the diaphragm. a radial strain gauge element in which a radial stress acting on one main surface of the diaphragm is parallel to the current direction; and a tangential strain gauge element in which a tangential stress acting on one main surface of the diaphragm is parallel to the current direction. consisting of two types of gauge elements, with the tangential strain gauge element positioned near the center of the diaphragm;
A method for arranging a semiconductor strain gauge element, characterized in that the position of the radial strain gauge element is then determined at a point where a non-linear error of the radial strain gauge element is reduced.