JPS6013315B2 - 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, which are made up of multiple semiconductor strain gauge elements exhibiting a piezoresistive effect, have excellent 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 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, and an electrical input is given to the bridge via a lead wire 3 and a conductor 2 to generate an output voltage responsive to pressure. There is a lot to be gained.This type of semiconductor pressure-sensitive element has particularly excellent sensitivity characteristics when converting pressure into electrical output, and can obtain several tens of times the sensitivity compared to conventional metal linear strain gauges, etc. However, in terms of conversion accuracy, it may not be possible to obtain amazing superiority such as sensitivity characteristics, or it may even be inferior.Furthermore, it is sensitive to temperature changes, which is a characteristic unique to semiconductors. This is a major drawback of this type of semiconductor pressure-sensitive element. Various compensation methods have been proposed to date for these drawbacks, and in particular, as a compensation method for conversion accuracy, "{1} A method of optimizing internal stress by controlling the processed shape of the diaphragm and compensating for accuracy; 2) A method of electrically compensating for accuracy by providing an external electric circuit; 3) A method of using multiple semiconductor strain gauges. A method has been used to compensate by placing elements close together to form a unit bridge structure and arranging the unit bridge structure at an optimal position on the main surface of the diaphragm. Many compensation methods have been proposed to date for temperature-related variations in the bridge output, or zero point, and output sensitivity when pressure is applied.To compensate for this temperature variation, elements with equal temperature coefficients are integrated. The most common method is to use circuitry to compensate for conversion accuracy, and it is relatively easy to implement. The above-mentioned Kawa method is such that when pressure is applied to a diaphragm, the stress generated in the main surface of said diaphragm forming a semiconductor strain gauge element is proportional to the pressure over a wide pressure range. It attempts to control the machining shape of the diaphragm and compensate for accuracy.
There is no countermeasure against the inherent nonlinearity of a semiconductor strain gauge element having a piezoresistance effect, and high accuracy 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 with the method {1'. The above-mentioned method (■) should be used as a last resort when compensation is not possible with the semiconductor pressure-sensitive element itself, and it goes against the characteristic of miniaturization in that it increases the number of compensation circuits, so it is not suitable for economic reasons. It is clear that this would be a disadvantage. 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, with only radial strain gauge elements in which the radial stress acting on the diaphragm surface is parallel to the current direction. There are many components. In the above-mentioned method, most of the radial strain gauge elements are arranged in stress regions oriented in opposite directions on the main surface of the diaphragm to effectively obtain output sensitivity. As a result, no countermeasure has been taken to sufficiently compensate for the accuracy.However, in the method [31] mentioned above, the radial strain gauge element, the tangential stress acting on the main surface of the diaphragm, and the current direction are parallel to each other. A plurality of semiconductor strain gauge elements are constituted by two types of semiconductor strain gauge elements, including tangential strain gauge elements, and at least one of each type is placed close to each other to form at least one unit bridge structure. The fact that output sensitivity can be effectively obtained even in such a configuration is that the piezoresistance coefficient is opposite in the current direction of the strain gauge element (hereinafter referred to as the vertical direction) and in the orthogonal direction (hereinafter referred to as the lateral direction). However, this method alone cannot sufficiently compensate for the accuracy.The reason for this is that method {3} consists of multiple semiconductor strain gauge elements called a unit bridge structure. This is based on the fact that the leg method uses such a composite structure because it is required to reduce the zero point unbalance of the bridge in order to compensate for the temperature fluctuations mentioned above. , Therefore, it is necessary to minimize the variation in resistance value when forming a plurality of strain gauge elements by diffusion by arranging the strain gauge elements close to each other.
In addition, by arranging each strain gauge element close to each other, they are exposed to almost the same ambient conditions, and by reducing the thermoelectric potential between adjacent bridge arms, drift in the L characteristic and a decrease in the S/N ratio can be avoided. These problems are extremely important for the characteristics of semiconductor pressure-sensitive devices, but it is said that too much emphasis is placed on countermeasures, which inevitably results in incomplete compensation for accuracy. This is the substance of the method {3}. This will be explained in more detail with reference to Figure 2. Figure 2 shows the relationship between the distance of the unit bridge structure from the center of the circular diaphragm and the nonlinear error of the pressure-sensitive element. Here, the non-linear error is defined as below, and the conversion accuracy described so far refers to this non-linear error. In the curve showing the relationship between the pressure applied to the pressure element and the output, the output V corresponding to zero applied pressure
The output V where the point o and the applied pressure correspond to the maximum of the measurement range
When connecting the max point with a straight line, this Vo and Vma
If the maximum output error between the straight line connecting x and the above curve is ΔV, the non-linear error N can be expressed as below. N
QL=Tsuba side% -.・・・．・{1} However, VFS NiVm-V.

...[21 When the temperature is constant, the output of this type of semiconductor pressure-sensitive element is determined by determining the shape and plane of the diaphragm and the axial direction in which the bridge structure is arranged. 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 from the result and definition. FIG. 2 shows an example of this, and shows the calculation results for the subordinate example shown in FIG. That is, Fig. 3 is {100}
A unit bridge structure 5 consisting of a p-type radial strain gauge element 6 and a tangential strain gauge element 7 is formed by diffusion along the <110> bag orientation of an n-type Si single crystal substrate 4 having both orientations. The opposite surface of the substrate is processed into a concave shape so that the bridge structure is located in the thin section of the circular diaphragm and near the end of the thick section 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 near the end of the diaphragm where the nonlinear error is calculated to be zero. However, as is clear from the figure, the shape of the curve showing the position dependence of the nonlinear error becomes extremely steep near the position where it is calculated to be zero. This is common when considering the position dependence of non-linear errors in terms of aggregates, and is not limited to the example shown in FIG.
Therefore, in the above-mentioned method {3}, since variations in the position of the bridge structure on the diaphragm surface have an extremely large effect on nonlinear errors, technical means for forming the bridge structure at a predetermined position, such as This requires extremely high processing precision in the diaphragm's concave processing technology, making it difficult to manufacture pressure-sensitive elements that exhibit the same characteristics in a simple and stable manner. Anticipating the instability of such characteristics, the dependent example shown in Figure 3 forms four sets of characteristically equivalent unit bridge structures near the ends on the diaphragm surface, and selects one of them. It is used as a pressure-sensitive element. This utilizes the equivalence of piezoresistance coefficients. However, this method has the following drawbacks. '1}
Although four sets of unit bridge structures can be formed, only one of them is used, so it is difficult to effectively use the four sets of bridge structures, such as using each of the four sets depending on the measurement pressure range. Can not. {2' When the diaphragm is made smaller, even if four sets of equivalent bridge structures are formed as shown in Figure 3, each individual bridge structure will not exhibit good characteristics as a Fuji pressure element. become unable. This is because there are technical limits to the size of the individual strain gauge elements, which prevent them from being able to cope with the miniaturization of the diaphragm and to exhibit effective sensitivity to the pressure applied to the diaphragm. Therefore, 4
In a method in which an effective pressure-sensitive element can only be obtained by forming a pair of equivalent bridge structures, that is, in the method shown in Fig. 3, there is a technical limit to miniaturizing the diaphragm, and pressure conversion is difficult. This is very disadvantageous in terms of making the vessel smaller. The present invention has been able to solve the various problems that the '3- method had as a background, as described above, by using completely different technical means.

That is, the present invention aims at obtaining an effective semiconductor pressure transducer on the diaphragm surface of each semiconductor strain gauge element in order to obtain a high-precision semiconductor pressure transducer that can sufficiently compensate for the shortcomings in conversion accuracy that semiconductor pressure-sensitive elements have. The purpose is to provide a distribution method. The present invention provides a semiconductor strain gauge element 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 the radial stress acting on one main surface of the diaphragm is parallel to the current direction, and a radial strain gauge element in which the tangential stress acting on one main surface of the diaphragm is parallel to the current direction. The radial strain gauge element is arranged near the periphery of the diaphragm, and then the tangential strain gauge element is arranged at a distance from the center of the diaphragm of the tangential strain gauge element. In the process in which the curve representing the relationship between the curve and the non-linear error changes from the center of the diaphragm toward the periphery, the curve is arranged near a point where the non-linear error intersects or touches the straight line of zero.

In particular, when the curve intersects a straight line with zero non-linear error, there are two intersecting points, and the first intersecting point, that is, the vicinity of the point near the center of the diaphragm is desirable. Note that the vicinity of the periphery of the diaphragm refers to a portion located outside of 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 of the element that predominantly contributes to resistance change. do. In addition, the vicinity of the point where the nonlinear error intersects or touches the straight line with zero includes the range that satisfies the required accuracy or sensitivity.When pressure is applied to the circular diaphragm, each point formed on the diaphragm surface The strain gauge element in this case exhibits a change in resistance when subjected to stress. It is a well-known fact that this is due to the piezoresistance effect, and the resistance value of each strain gauge element in this case can be approximated by the following formula if the temperature is kept constant. It is already well known that it can be expressed as Rr3R.

(10 enemies ror 10 games.t) ...{3IRt2R.
(10 strokes, tot 10 '.r) ...,. ．． ■R here
r and Rt are the resistance values of the radial strain gauge element and the tangential strain gauge element, respectively. is the resistance value when the pressure is zero,
mr, t, and t are the longitudinal piezoresistance coefficients of the radial strain gauge element and tangential strain gauge element, mtr, mt, respectively.
t is the transverse piezoresistance coefficient of the radial strain gauge element and the tangential strain gauge element, respectively. Also,. r. t
are the radial stress acting on the diaphragm surface, respectively,
This is a tangential stress, and when the outer periphery of the diaphragm is fixed, it is approximately expressed by the following equations. .

r; - Kurashi - (Tai) 20 p {(1 + shi) - (3 + shi) (ki) 2} ‐-‐‐‐‐'51 2nd body (climb) 2‐p {(1 + shi) - (1 13y) (ki)2}
‐‐‐‐‐[6} Here, a and h are the radius and thickness of the diaphragm, p is the pressure, Poisson's ratio, and r is the distance from the center of the diaphragm. Inferring from formula 6, the resistance values Rr and Rt of each strain gauge element can be determined as a function of pressure p and distance r by determining the shape and material of the diaphragm and the orientation of each strain gauge element. I know what will happen. Therefore, by using Equation 61, the resistance value corresponding to any pressure at any position on the diaphragm surface can be calculated, and by further applying this to the well-known bridge output calculation formula, the sensitivity of the semiconductor pressure-sensitive element can be approximated. It can be found exactly. However, as is clear from equation t31 ~ [6}, the resistance value is proportional to the pressure in this case,
This makes it impossible to calculate accuracy. Conventionally, this type of semiconductor pressure-sensitive element has been difficult in terms of accuracy because the stress calculation and piezoresistance effect cannot be completely expressed as in equations ``3'' to ``6'' and include nonlinear terms. None other than that. '6' (
6} Each stress as shown in formula. r. [is pressure p
The resistance values Rr and Rt are not necessarily proportional to stress, as shown in equations [3}'4). r. It cannot be expressed only by the linear term of t. Therefore, the present inventors calculated the respective resistance values using the expansion formula shown below, taking into account the relationship between stress and pressure that includes nonlinear mounds, calculated the bridge output from this, and examined its nonlinear error. did. Although the following equation describes only up to the second-order term of each stress, higher-order terms are also included, and it is thought that it also acts on the strain gauge element. It goes without saying that more accurate results can be obtained by including stresses other than those above. .

r2R. (10 r. r + middle hi. t 10 yo. r2 10 bamboo skin ot2) ...[7] R
T Engineering R. (10 t enemy 10 mtt r + others, tot 2 1 bamboo 2 comparison r 2) …,. , where mar and ke21t are the second-order longitudinal piezoresistance coefficients of the radial strain gauge element and tangential strain gauge element, respectively, and the bamboo fence and ke2tt are the respective second-order lateral piezoresistance coefficients. . A curve or a group of curves as shown in FIGS. 4 and 5 were obtained as a result of examination using the method described above. From the point of view of output sensitivity,
Preferably, the radial strain gauge element is located near the periphery of the diaphragm. Figure '1 shows that when done like this,
That is, it shows the relationship between the non-linear error and the distance X of the tangential strain gauge element from the center of the diaphragm when the radial strain gauge element is disposed near the periphery of the diaphragm. According to this figure, the curve intersects the straight line with zero nonlinear error at points B and C, so if a tangential strain gage element is placed near either of these positions, the pressure-sensitive element In principle, the nonlinear error becomes zero, and a highly accurate pressure transducer can be obtained. Also, by slightly changing the position of the radial strain gauge element,
A curve may intersect with a straight line with zero non-linearity error at only 1 point, 211 points, {3} neither intersect nor touch. In the case of one leg, a tangential strain gauge element may be placed near one of the legs. In the case of {3', the curve may be placed near the point where the non-traditional line error approaches the straight line of zero. Among the positions of the tangential strain gauge element as described above, the position showing the most excellent characteristics is near point B shown in FIG. This is the fifth
This will be explained using figures. Figure 5 shows the relationship between the nonlinear error and the distance from the diaphragm center of the tangential strain gauge element when the distance from the diaphragm center of the radial strain gauge element is changed. Corresponds to one position of the radial strain gauge element. Now, the fourth
Let the curve corresponding to the figure be XR, and consider the curves XR+ΔX and ×R−ΔX when the position of the radial strain gauge element corresponding to this curve is changed by ±Δ×. It is naturally expected that the position of each strain gauge element will deviate from its optimally designed position during the manufacturing process of a pressure sensitive element, and in order to produce a stable product, it is necessary to minimize the influence in such a case. Considering points B and C in Figure 5 from this perspective, the nonlinear error changes from a to b at point B and from c to d at point C for a position change of 2△×, respectively. It can be seen that the amount of change is much larger at point C. Therefore, after arranging the radial strain gauge element near the periphery of the diaphragm, the tangential strain gauge element is placed in the fourth position.
The point corresponding to point B in the figure, that is, the characteristic curve showing the relationship between the nonlinear error and the distance from the diaphragm center of the tangential strain gauge element, is near the point where the nonlinear error first intersects the straight line with zero. By arranging them, it is possible to obtain a highly sensitive and highly accurate pressure sensing element, and it is possible to obtain a stable pressure transducer with small variations in characteristics between products. Furthermore, if the strain gauge element arrangement method of the present invention is adopted, the method described in {3} of the conventional accuracy compensation method, that is, 1
It is no longer necessary to form four sets of bridges equivalent to different types of pressure ranges, and an effective method of covering at least two or more types of pressure ranges with multiple sets of bridges becomes possible. Furthermore, since each strain gauge element is arranged and formed independently, the size of the pressure sensitive element can be easily reduced compared to the conventional method '3'. Example 1 Figure 6 shows two sets of p-type radial strain gauge elements formed symmetrically along the <111> direction of an n-type Si single crystal substrate having both {110} orientations. 110> axis and <1
Two sets of p-type tangential strain gauge elements are formed symmetrically along the direction 45o from the 00> axis.

Each strain gauge element has a configuration in which four mutually parallel pongee strips are connected in series via a low resistance region. The diaphragm was shaped as shown in FIG. For example, 5k
g/S for ground pressure measurement with a thickness of 0.2 and a diameter of 8 ribs.
i.A radial strain gauge element and a tangential strain gauge element are placed on the strain-generating part of the diaphragm from the center of the diaphragm to 3.2 parts of each shoe: o. 8), o. 8 females = o. 2) When the bridge is excited with a constant current so that the voltage between the input terminals is 3.5V, the output voltage sensitivity is 200V.
The VFS/3.5V non-linear error of 0 was less than 0.1%FS. Here, FS means the maximum pressure in the pressure measurement range. In addition, for pressure measurement on 100k9' ground, a radial strain gauge element and a tangential strain gauge element are placed on the strain-generating part of an Sj diaphragm with a thickness of 0.8 grade and a diameter of 8 bars, respectively, from the 343rd side to the 343rd side from the center of the diaphragm. o-8)
, 1-6 side (ki: o-4) and when the bridge was excited with a constant current in the same manner as above, almost the same characteristics as in the pressure measurement of 5k9' were obtained. Embodiment 2 FIG. 7 shows two sets of p-type radial strain gauge elements formed symmetrically along the 110>bag direction of an n-type Si single crystal substrate having {110} plane orientation, Two sets of p-type tangential strain gauge elements are formed symmetrically along the 100>axis.

With this arrangement method, a radial strain gauge element and a tangential strain gauge element are placed on the strain generating part of a Si diaphragm with a thickness of 0.23 mm and a diameter of 8 columns for pressure measurement of 5K9'. Fence (ki=o-8), 2
-4 legs are formed as =o-6), and when this bridge is excited with a constant current as in the implementation side, the output voltage sensitivity is 200±
20VFS/3.5V "Non-linear error is ±0.1%FS
It was below. Other examples and application examples are shown in Table 1.

The present invention is not necessarily limited to these examples. Furthermore, it is also possible to realize an n-type strain gauge element or a semiconductor single crystal other than Si such as Ge. Table 1 As described above, according to the present invention, it is possible to provide a semiconductor pressure transducer with high sensitivity and small variations in characteristics between products.

Brief description of the drawings Figure 1 is a schematic cross-sectional view of a Si diaphragm, Figure 2 is a characteristic diagram corresponding to the conventional arrangement pattern shown in Figure 3, Figure 3 is a conventional layout diagram, Figures 4 and 5. The figure is a characteristic diagram for explaining the present invention, and FIGS. 6 and 7 are layout diagrams showing embodiments of the present invention.

6... Radial strain gauge element, 7... Tangential strain gauge element.

younger brother diagram Figure 2 Figure 3 Figure 4 Hair S figure figure to wear Figure 7

Claims (1)

[Scope of Claims] 1. 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, wherein the semiconductor The strain gauge element is a radial strain gauge element in which a radial stress acting on one main surface of the diaphragm is parallel to a current direction, and a tangential stress acting on one main surface of the diaphragm and a current direction are parallel to each other. The radial strain gauge element is positioned near the periphery of the diaphragm, and then the tangential strain gauge element is positioned in the vicinity of the tangential strain gauge element. A method of arranging a semiconductor strain gauge element, characterized in that it is determined at a point where non-linear errors are reduced. 2. In claim 1, the position of the tangential strain gauge element is determined by a curve indicating the relationship between the distance of the tangential strain gauge element from the center of the diaphragm and the non-linear error from the center of the diaphragm to the periphery. 1. A method of arranging a semiconductor strain gauge element, characterized in that the non-linear error is set in the vicinity of a point where it first intersects a zero line in the process of changing direction.