JP2002039888A - Method of setting position of gage resistance of semiconductor pressure sensor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an efficient method of setting the positions of the gage resistances of a semiconductor pressure sensor, for reducing the pressure nonlinearity, NLP, of the sensor characteristic. SOLUTION: The method of setting the positions of the plurality of gage resistances 41 to 44 in the semiconductor pressure sensor S1 having a diaphragm 3 formed on one side of a semiconductor substrate 1 for detecting pressure and the plurality of gage resistances 41 to 44 arranged on the diaphragm 3, with the resistance values of the resistances being varied by the effect of piezoelectric resistance. The method involves determining, through finite element analysis, the relationship between the position and rate of change of resistance value of each individual gage resistance, to set the positions of the plurality of gage resistances such that the gage resistances RA and RB differing the direction of variation in resistance values assume positions where the rates of change of their resistance values are approximately equal. During the finite element analysis, the positions of the plurality of gage resistances are set while allowing for the nonlinearity errors of the resistance values with respect to pressures.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a pressure sensing diaphragm formed on one surface of a semiconductor substrate, and a plurality of gauge resistors whose resistance values change by a piezoresistive effect form a bridge circuit on the diaphragm. The present invention relates to a method of setting the positions of a plurality of gauge resistors in a semiconductor pressure sensor arranged in a semiconductor device.

[0002]

2. Description of the Related Art Semiconductor pressure sensors of this kind are generally
The semiconductor device includes a semiconductor substrate such as a silicon substrate, a pressure detection diaphragm formed on one surface side of the semiconductor substrate, and a plurality of gauge resistors arranged on the diaphragm and having a resistance value changed by a piezoresistance effect.

The plurality of gauge resistors have different resistance value changing directions, and constitute a bridge circuit. When pressure is applied to the diaphragm, the bridge circuit causes the diaphragm to deform. By converting the corresponding resistance change into an electrical signal,
The applied pressure is detected.

[0004]

In such a semiconductor pressure sensor, pressure-nonlinearity (non-linearity-pressu) of the sensor characteristics as shown in FIG.
re, hereinafter referred to as NLP), that is, there is a non-linear relationship between the output voltage V and the pressure P. Here, this NL
The magnitude of P is expressed assuming that the full-scale output voltage width is FS.
It is indicated by 100 · ΔV / FS (%).

For this reason, it is desired to dispose a gauge resistor so as to reduce the NLP. However, in a conventional semiconductor pressure sensor, the position setting of the resistance gauge on the diaphragm is a trial-and-error method, and is efficiently performed. There was no specific way to set the position.

SUMMARY OF THE INVENTION The present invention has been made in view of the above circumstances, and has as its object to provide an efficient method for setting the gauge resistance position of a semiconductor pressure sensor for reducing NLP.

[0007]

SUMMARY OF THE INVENTION According to the present invention, the change in the resistance value with respect to the pressure in the gauge resistance is non-linear, and the non-linearity error of the resistance value with respect to the pressure differs for each gauge resistance. Focusing on the occurrence of NLP, this is based on the idea that the balance of the above-described non-linearity error may be adjusted between the gauge resistors.

According to the first aspect of the present invention, the relationship between the position of each of the gauge resistors (41 to 44) and the rate of change of the resistance value is determined by the finite element method analysis, so that the resistance of the gauge resistance varies in different directions. The position of a plurality of gauge resistors is set so that the rate of change in resistance value between (RA, RB) is substantially equal. In the finite element method analysis, the nonlinearity error of the resistance value with respect to pressure is reduced. It is characterized in that the positions of a plurality of gauge resistors are set in consideration of this.

According to this, by the finite element method analysis,
When calculating the relationship between the position and the rate of change in resistance value of each gauge resistor, by taking into account the non-linear error of the resistance value with respect to pressure, the relationship between the position and the rate of change of resistance value in each gauge resistor is: It is possible to obtain a relationship in which the nonlinearity error of the resistance value with respect to the pressure is considered.

Then, from the obtained relationship, a plurality of positions at which the resistance value change rates of the gauge resistors having different resistance value change directions are substantially equal to each other are obtained, whereby a plurality of NLPs capable of accurately reducing the NLP can be obtained. The position of the gauge resistor can be set. Therefore, according to the present invention, it is possible to provide a method for efficiently setting the position of the gauge resistance of the semiconductor pressure sensor for reducing the NLP.

Further, in the invention of claim 2, a first step of obtaining a relationship between a position in each gauge resistance (41 to 44) and a resistance value change rate ΔR / R by a finite element method analysis; The relationship between the resistance change rate ΔR / R and the non-linearity error NLR of the resistance value with respect to the pressure is obtained by actually measuring the resistance value of the gauge resistance at different positions.
By replacing the resistance change rate ΔR / R in the relation obtained in the first step with the nonlinearity error NLR using the relation obtained in the second step, A third step of determining the relationship between the position and the non-linearity error NLR and setting the positions of the plurality of gauge resistances at positions where the non-linearity errors NLR of the plurality of gauge resistances substantially coincide with each other;
And a step of:

According to the present invention, the relationship between the position of each gauge resistor and the resistance value change rate ΔR / R (this is referred to as a first relation), the resistance value change rate ΔR / R and the resistance value with respect to the pressure, A relationship with the nonlinearity error NLR (this is referred to as a second relationship) is obtained, and the resistance value change rate ΔR / R in the first relationship is replaced with the nonlinearity error NLR using the second relationship. Thus, the relationship between the position in each gauge resistor and the nonlinearity error NLR (this is referred to as a third relationship) is obtained.

From the third relationship, by obtaining a position where the nonlinearity errors NLR between the plurality of gauge resistors substantially coincide with each other, a plurality of gauge resistors capable of accurately reducing the NLP can be obtained. Can be set. Therefore, according to the present invention, it is possible to provide a method for efficiently setting the position of the gauge resistance of the semiconductor pressure sensor for reducing the NLP.

According to the third aspect of the present invention, when each of the gauge resistors (41 to 44) is a pattern in which a plurality of straight lines are connected in a folded shape, the finite element method analysis is performed.
This method is characterized in that the analysis is performed in accordance with the pattern shape of the gauge resistor. By performing the finite element method analysis corresponding to the pattern shape, highly accurate analysis can be performed.

Note that the reference numerals in parentheses of the above means are examples showing the correspondence with specific means described in the embodiments described later.

[0016]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram showing a first embodiment of the present invention. FIG. 1 is a schematic sectional view of a semiconductor pressure sensor S1 according to an embodiment of the present invention, and FIG.
It is the schematic plan view seen from the arrow A direction inside. Reference numeral 1 denotes a semiconductor substrate made of a single crystal silicon substrate or the like. In the semiconductor substrate 1, a concave portion 2 which is concave from one surface of the semiconductor substrate 1 is formed by etching or the like.

A diaphragm 3 for detecting pressure is formed on the bottom surface side of the concave portion 2 which has become thinner due to the formation of the concave portion 2. The surface of the diaphragm 3 (semiconductor substrate 1)
On the other side), four gauge resistors 41, 42, 43, and 44 whose resistance values change due to the piezoresistance effect are formed by a semiconductor process such as diffusion. Each gauge resistance 41
Are disposed on the inner side and the outer side of the diaphragm 3 across the respective sides of the planar rectangular diaphragm 3.

FIG. 3 is an enlarged view of the plane shape of each gauge resistor. Each of the gauge resistors 41 to 44 forms the same pattern in which a plurality of straight lines are connected in a folded shape. . In this pattern, the folded portion 4
Has a thicker wiring width than that of the straight portion 5, and in effect, the sum of the resistance values of the plurality of straight portions 5 is equal to the gauge resistance 41.
４４44.

In the gauge resistors 41 and 43, the straight portion 5 is orthogonal to the side of the diaphragm 3 and
In (44) and (44), the straight portion 5 is parallel to the side of the diaphragm 3. Therefore, the gauge resistances 41 and 43 and the gauge resistances 42 and 44 differ in the direction of change in resistance value with respect to pressure.

Here, each of the gauge resistors 41 to 44 is shown in FIG.
And a Wheatstone bridge. The bridge circuit generates an electric signal based on the distortion of the diaphragm 3 when the pressure is applied, and the applied pressure can be detected. Also,
Although not shown, the gauge resistances 41 to 41 are provided on the semiconductor substrate 1.
44, a wiring and the like for exchanging signals between the bridge circuit and the external circuit are formed.

A pedestal 6 made of glass, silicon, or the like is joined to one surface of the semiconductor substrate 1 so as to cover the recess 2. By the joining of the pedestals 6, a pressure reference chamber 7 defined by the pedestals 6 and the recesses 2 is formed. The pressure in the pressure reference chamber 7 is a reference pressure for detecting the pressure received from the surface of the diaphragm 3.

In the pressure sensor S1, the detection of the pressure is performed as follows. When pressure is applied to the diaphragm 3 from the surface of the diaphragm 3 in the direction of the white arrow shown in FIG. 1, the diaphragm 3 is deformed and deformed. At this time,
The input terminals Ia and Ia of the Wheatstone bridge shown in FIG.
When the constant DC voltage V is applied between the output terminals Pa and Pb, this deformation appears as a change in the resistance value of the strain gauge resistors 41 to 44, and a voltage Vout of a level corresponding to the detected pressure is output from between the output terminals Pa and Pb. Is output, and pressure detection is performed.

Next, a method for setting the positions of the gauge resistors 41 to 44 in the pressure sensor S1 will be described. Here, the gauge resistors 41 and 43 having the same direction of change in resistance value with respect to pressure are referred to as gauge resistors RA, and the gauge resistors 42 and 44 having different resistance value change directions from the gauge resistor RA are referred to as gauge resistors RB.

First, the relationship between the position (gauge position) and the rate of change of the resistance value ΔR / R with respect to the pressure in each of the gauge resistors RA and RB is obtained by a finite element method analysis (FEM analysis) (first step). ). The gauge position was defined as shown in FIG. That is, the gauge position is
Is defined as the distance x that the outermost sides of the gauge resistors RA and RB protrude from the ends of the gauge resistance. -Is the time when it enters.

Further, in order to accurately analyze the gauge resistors RA and RB having the above-mentioned folded pattern, a finite element method analysis was performed corresponding to the gauge resistor pattern shape. That is, each gauge resistance is
Although the entire outer shape including the gap between the linear portions 5 is a plane rectangle, the stress generated in the gap between the linear portions 5 does not match the actual shape, instead of being analyzed as such a rectangle. It was analyzed as one.

Further, the rate of change of resistance value against pressure ΔR / R
Is a value (absolute value) obtained by dividing the width ΔR of the resistance value that changes at the full scale of the pressure measurement range in the pressure sensor by the initial resistance value R. Specifically, using a relational expression indicating a resistance change rate ΔR / R when the piezoresistance coefficient is π44 and the stress generated in the gauge resistance at a certain pressure is σ as shown in the following equation 1, / R can be determined.

[0027]

ΔR / R = 0.5 · π44 · σ Then, for each of the gauge resistors RA and RB, a resistance value change rate ΔR / R when the gauge position x is changed is obtained, and is shown in FIG. , Gauge resistance RA (black diamond mark)
The relationship between the gauge position x (μm) and the resistance change rate ΔR / R (absolute value) for the gauge resistance RB (black square mark) (hereinafter referred to as x-ΔR / R relationship) was obtained.

From the x-.DELTA.R / R relationship shown in FIG. 6, each of the gauge resistors RA and RB has a different resistance value changing direction so that the resistance change rates .DELTA.R / R between the RBs are substantially equal. , RB gauge position x,
The pressure non-linearity (NLP) of the sensor characteristics is not sufficiently small. This is because the x-ΔR / R relationship does not take into account a non-linear error of the resistance value with respect to pressure, which will be described later.

Then, next, a step (hereinafter referred to as ΔR / R-NLR relation) between the resistance value change rate ΔR / R and the nonlinearity error NLR of the resistance value with respect to the pressure (hereinafter referred to as ΔR / R-NLR relation) is described.
Step). In the present embodiment, the individual gauge resistors R
The ΔR / R-NLR relationship is obtained by actually measuring the resistance values of A and RB while changing the gauge position x.

The resistance values of the individual gauge resistors RA and RB are:
The measurement was performed using a measurement sample (TEG) as shown in FIG. This TEG (Test Element Group) forms a gauge resistance for measurement in a region T (region surrounded by a broken line in FIG. 7) on the semiconductor substrate 1 on which the diaphragm 3 is formed. 1, a wiring T0 for measuring a resistance value and the like are formed around the outer periphery of the diaphragm 3 on the substrate 1.

In FIG. 7, two linear portions 5 indicated by oblique hatching are formed, and measurement wirings T0 indicated by dotted dots are formed therearound. Pads T1 to T7 corresponding to the respective wirings T0 are formed. Are formed. The wiring T0 is formed by diffusion or ion implantation, for example, like the gauge resistance.

Then, for example, a current flows between the pads T2 and T7 with respect to the lower linear portion 5 in FIG. 7 and the voltage between the pads T1 and T3 at this time is obtained. The resistance value of the linear portion 5 can be measured.
As described above, by using the four-terminal method, the resistance value can be accurately obtained.

According to the actual measurement method of the resistance value, the applied pressure is set at three points (P
1, P2, P3) and measure the resistance values (R1, R2, R3) at each applied pressure. By this measurement, a relationship between the pressure and the resistance value as shown in FIG. 8 (hereinafter referred to as a PR relationship) is obtained.

From the PR relationship shown in FIG. 8, the change in the resistance value with respect to the pressure in the gauge resistance is represented by an ideal straight line (in the figure,
(Indicated by a dashed line), and it can be seen that it is non-linear. Here, ΔR in FIG. 8 is (R3−R1), which corresponds to ΔR in the resistance value change rate ΔR / R in the first relationship.

Further, ΔΔR indicates the degree of deviation from the ideal straight line, and is obtained by dividing ΔΔR by ΔR.
Multiplied by 100 · ΔΔR / ΔR is the nonlinearity error NLR of the resistance value with respect to the pressure. Note that the unit of NLR is% FS (% full scale), which is ΔR
Is the width ΔR of the resistance value that changes at the full scale of the pressure measurement range in the pressure sensor.

By changing the gauge position x and actually measuring the resistance values of the gauge resistors RA and RB, various PR relationships can be obtained. Plotting the various ΔR / R and NLR values obtained from these various PR relationships,
As shown in FIG. 9, a ΔR / R-NLR relationship is obtained. This is the second step.

Next, the x-ΔR / R obtained in the first step
The resistance change rate ΔR / R in the relationship is calculated by using the ΔR / R-NLR relationship obtained in the second step to obtain the nonlinearity error NL.
By substituting R for each gauge resistance RA, R
The relationship between the gauge position x and the non-linearity error NLR at B (hereinafter referred to as x-NLR relationship) is obtained, and the positions of the plurality of gauge resistances are set to the positions where the non-linearity errors NLR between the plurality of gauge resistors substantially match. Set (third step).

That is, ΔR / R-NLR shown in FIG.
From the relationship, the resistance value change rate ΔR / R is calculated as the nonlinearity error NLR.
By replacing the resistance change rate ΔR / R in FIG. 6 with the value of the non-linear error NLR. Then, an x-NLR relationship is obtained as shown in FIG.
Then, in FIG. 10, a gauge position x at which the non-linearity error NLR substantially matches the gauge resistance RA (black diamond mark) and the gauge resistance RB (black square mark) is obtained.

For example, FIG. 10 shows that each gauge resistor R
The gauge position x where A and RB are set is −10 μm ± 5
μm or +16 μm ± 5 μm. This is the third step, and x obtained by this third step is
The -NLR relationship can be said to be a relationship in which the nonlinear error NLR is considered in the x-ΔR / R relationship shown in FIG.

As described above, according to the gauge resistance position setting method in the present embodiment, the finite element method analysis
When determining the relationship between the gauge position x and the resistance value change rate ΔR / R in each of the gauge resistances RA and RB, by taking into account the nonlinearity error NLR of the resistance value with respect to pressure,
In the relationship between the gauge position x and the resistance value change rate ΔR / R in each of the gauge resistors RA and RB, a relationship in which the nonlinear error NLR is considered can be obtained.

Then, from the obtained relationship, a position where the resistance change rates of the gauge resistors RA and RB having different resistance value changes are substantially equal to each other is determined to obtain the pressure non-linearity NLP of the sensor characteristics. A gauge position x that can be reduced with high accuracy can be set. Therefore, according to the present embodiment, it is possible to provide a method for efficiently setting the position of the gauge resistance of the semiconductor pressure sensor for reducing the NLP.

When the gauge resistors RA and RB are actually arranged at the gauge positions x obtained by executing the first to third steps of the present embodiment, the nonlinearity error NLR
The NLP can be reduced from -0.29% FS to -0.18% FS as compared to the case where the gauge is positioned at the gauge position x obtained from the x-ΔR / R relationship shown in FIG. did it.

In the above embodiment, the diaphragm 3
A pressure sensor of the surface pressure receiving type which receives a pressure from the surface of the diaphragm, for example, a pressure introducing hole communicating with the concave portion 2 is formed in the pedestal 6, and the pressure of the back pressure receiving type is received from the pressure introducing hole to the back surface of the diaphragm 3. The present invention is applicable to a sensor.

[Brief description of the drawings]

FIG. 1 is a schematic sectional view of a semiconductor pressure sensor according to an embodiment of the present invention.

FIG. 2 is a view taken in the direction of the arrow A in FIG.

FIG. 3 is an enlarged plan view of each gauge resistor.

FIG. 4 is a connection diagram showing a wiring state of a gauge resistor.

FIG. 5 is an explanatory diagram for defining a gauge position.

FIG. 6 is a diagram showing a relationship between a gauge position x and a resistance value change rate ΔR / R in each gauge resistance obtained by a finite element method.

FIG. 7 is a diagram showing a configuration of a TEG for measuring a resistance value of a gauge resistor.

FIG. 8 is a diagram illustrating a relationship between a pressure and a resistance value obtained by actual measurement, and illustrating a resistance value change rate ΔR / R and a non-linear error NLR of the resistance value with respect to the pressure.

FIG. 9 is a diagram showing a relationship between a resistance value change rate ΔR / R obtained by actual measurement and a nonlinear error NLR of a resistance value with respect to pressure.

FIG. 10 is a diagram showing a relationship between a gauge position x and a nonlinearity error NLR in each gauge resistance.

FIG. 11 is a diagram showing a non-linearity NLP of output voltage characteristics with respect to pressure in a pressure sensor.

[Explanation of symbols]

1 ... Semiconductor substrate, 3 ... Diaphragm, 41-44 ... Gauge resistance.

Claims (3)

[Claims] 1. A semiconductor substrate (1), a pressure detecting diaphragm (3) formed on one surface side of the semiconductor substrate (1), and a resistance value which is arranged on the diaphragm and changes by a piezoresistance effect. A plurality of gauge resistors (41 to 44), wherein the plurality of gauge resistors include gauge resistors (RA, RB) having different resistance value changing directions, and a bridge circuit constituted by the plurality of gauge resistors. A method of setting the positions of the plurality of gauge resistors in a semiconductor pressure sensor configured to convert a change in resistance value according to deformation of the diaphragm into an electric signal, wherein the individual gauge resistors are analyzed by a finite element method analysis. By determining the relationship between the position and the rate of change in resistance, the rate of change in resistance between gauge resistors having different directions of change in resistance is substantially equal. Setting the positions of the plurality of gauge resistors so that the positions of the plurality of gauge resistors are set in consideration of the non-linearity error of the resistance value with respect to pressure during the finite element method analysis. A method for setting the position of a gauge resistance of a semiconductor pressure sensor. 2. A semiconductor substrate (1), a diaphragm (3) for detecting pressure formed on one surface side of the semiconductor substrate (1), and a resistance value which is arranged on the diaphragm and changes by a piezoresistance effect. A plurality of gauge resistors (41 to 44), wherein a bridge circuit configured by the plurality of gauge resistors converts a resistance value change according to the deformation of the diaphragm into an electric signal. A method of setting positions of a plurality of gauge resistors, comprising: a first step of obtaining a relationship between a position in each of the gauge resistors and a resistance value change rate ΔR / R by a finite element method analysis; A second method for obtaining the relationship between the resistance change rate ΔR / R and the nonlinearity error NLR of the resistance with respect to the pressure by actually measuring the resistance of the resistance at different positions. And the resistance change rate Δ in the relationship obtained in the first step.
By replacing R / R with the nonlinearity error NLR using the relationship obtained in the second step, the relationship between the position in each gauge resistance and the nonlinearity error NLR is determined, Setting a position of the plurality of gauge resistors at a position where the non-linearity errors NLR of the plurality of gauge resistors coincide with each other. . 3. The individual gauge resistor (41-44).
The semiconductor pressure sensor according to claim 1, wherein: is a pattern in which a plurality of straight lines are connected in a folded shape, and the finite element analysis is performed in accordance with the pattern shape of the gauge resistance. 4. How to set the gauge resistance position.