JPH0542608B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION <Technical Field to Which the Invention Pertains> The present invention relates to a pressure sensor that utilizes the piezoresistive effect of a semiconductor.

<Prior art> Generally, a pressure sensor that utilizes the piezoresistance effect of a semiconductor has a pressure receiving diaphragm formed by etching on a single crystal semiconductor substrate made of silicon, for example.
A gauge resistor is provided on the pressure-receiving diaphragm using diffusion technology or the like, stress based on the pressure difference applied to both sides of the pressure-receiving diaphragm is applied to the gauge resistor, and the pressure difference is detected from the change in the resistance value of the gauge resistor. Usually, two or four gauge resistors are provided on the pressure receiving diaphragm to form a half bridge or full bridge to obtain a signal representing the pressure difference across the diaphragm. However, in this type of pressure sensor, the gauge resistance has a large temperature dependence, so it is affected by changes in ambient temperature and has the disadvantage that the output fluctuates.

Therefore, output fluctuations are generally compensated for by controlling the power supply voltage of the bridge according to temperature changes using a temperature sensing element such as a thermistor, posistor, or transistor. In order to perform accurate compensation using this method, it is necessary to match the temperature characteristics of the gauge resistance and the temperature sensing element for compensation.
However, it is not easy to match these, and highly accurate compensation is difficult. Moreover, the adjustment man-hours required for such compensation are reduced by using a constant temperature bath.
The temperature characteristics of the gauge resistance and the compensation temperature sensing element must be measured one by one, which accounts for nearly half of the total assembly man-hours of the pressure sensor.

In addition, a gauge resistor for temperature compensation is provided on the fixed part of the board to compensate for the temperature of the measured value, but the temperature coefficient β of the piezoresistance coefficient of the gauge resistor is
Cannot be canceled until then.

For this reason, it is necessary to take measures such as giving the power supply voltage a temperature coefficient of -β.

<Object of the Invention> The present invention is directed to realizing a pressure sensor having a structure that can effectively compensate for the influence of changes in ambient temperature.

<Means for Solving the Problem> In order to achieve this object, the present invention provides a pressure receiving diaphragm and a cantilever provided on a single crystal semiconductor substrate, and a pressure receiving diaphragm and a cantilever provided on the pressure receiving diaphragm and the cantilever, respectively. at least two gauge resistors provided on either one of them; a base to which the single crystal semiconductor substrate is fixed by applying a predetermined displacement to the cantilever in advance so as to generate a predetermined stress on the cantilever; The temperature coefficient of the gauge resistance and the temperature coefficient of the piezo resistance coefficient are calculated from the three relational expressions related to the measured pressure obtained from the resistance values of the three gauge resistances, the temperature coefficient of the gauge resistance, and the temperature coefficient of the piezo resistance coefficient. The pressure sensor is configured to include a calculation section that calculates the measured pressure.

<Example> FIG. 1 is a perspective view showing an example of the pressure sensor of the present invention, and FIG. 2 is a sectional view of FIG. 1. In both figures, 10 is a single-crystal semiconductor substrate such as silicon having a (100) plane orientation, 11 is a rectangular pressure-receiving diaphragm formed on the substrate 10 by anisotropic etching, and 12
1 is a cantilever formed on the substrate 10 by anisotropic etching, and 13 is a fixing portion of the substrate 10. As shown in FIG. 3, a slight initial step δ (for example, 4000 Å) is provided between the tip 12 _a of the cantilever 12 and the fixed portion 13 . 21,2
2, 23, 24 are gauge resistors such as diffused resistors, 21, 22 are formed close to each other with their longitudinal direction (current direction) perpendicular to the surface of the pressure receiving diaphragm 11, and 23, 24 are cantilevers. 1
The longitudinal direction thereof is perpendicular to the surface of 2 and is formed close to it. Reference numeral 30 denotes a base made of silicon, glass, etc., on which the fixing part 13 of the single crystal semiconductor substrate 10 is mounted.
The back side of the plate is fixed by anodic bonding or low melting point glass bonding. This board 10 and base 30
By joining, a constant displacement δ based on the initial step is given to the cantilever 12 in advance. Further, the base 30 is provided with an opening 31 for applying a reference pressure P ₀ (for example, atmospheric pressure) to the back surface of the pressure receiving diaphragm 11. As a result, the pressure receiving diaphragm 1
1 is sensitive to the measured pressure P _M (difference from the reference pressure P ₀ ) applied to its surface. Note that the cantilever 12 is balanced with respect to the pressure to be measured P _M , and its tip 12 _a is not joined to the base 30 .

In the pressure sensor of the present invention configured as described above, first, a stress σ MX acts on the gauge resistors 21 and 22 provided on the pressure receiving diaphragm 11 in the longitudinal direction of the gauge resistor 21 in accordance with the measured pressure P _M , and a stress σ _MX acts in the vertical direction. A stress σ _MY acts on . Gauge resistance 21, 22
The resistance values R _M1 and R _M2 are R ₀ the initial resistance at the reference temperature t ₀ , α the resistance temperature coefficient of R ₀ , and α the resistance temperature coefficient at the reference temperature t _{0
When _}
Letting t be the temperature change from the reference temperature _t0 , each is given by the following equation.

R _M1 = R ₀ (1+αt) {1+(π _l0 σ _MX +π _t0 σ _MY ) (1+βt)}(1) R _M2 = R ₀ (1+αt) {1+(π _l0 σ _MY +π _t0 σ _MX ) (1+βt) }(2) Then, if constants determined by the structure of the pressure receiving diaphragm 11 and the arrangement positions of the gauge resistors 21 and 22 are k ₁ and k ₂ , then the following relationship holds true.

π _l0 σ _MX +π _t0 σ _MY =k ₁ P _M (3) π _l0 σ _MY +π _t0 σ _MX =k ₂ P _M (4) Next, the distance from the tip to the surface of the cantilever 12 is
A stress σ _S as shown in the following equation acts on the gauge resistors 23 and 24 provided at l ₁ due to a constant displacement δ based on the initial step difference.

σ _S =3/2・dE/l ³・δ・l ₁ (4) Here, d: Cantilever thickness l: Cantilever effective length E: Young's modulus The temperature coefficient of this response σ _S is Substrate 10
It is almost determined by the temperature coefficient of Young's modulus of , and when the substrate 10 is silicon, it is sufficiently small at about ⁴³
σ _S is hardly affected by changes in ambient temperature.
Furthermore, the cantilever 12 is balanced against the measured pressure P _M , and σ _S does not change even with P _M.
That is, σ _S becomes a reference stress that is not affected by changes in ambient temperature or changes in measured pressure. Therefore, the resistance values R _S1 and R _S2 of the gauge resistors 23 and 24 are values based on the standard stress σ _S and are given by the following equations.

R _S1 = R ₀ (1+αt) {1+π _l0 σ _S (1+βt)} (6) R _S2 = R ₀ (1+αt) {1+π _t0 σ _S (1+βt)} (7) Therefore, gauge resistance 21, 22, 23 , 24 resistance values R _M1 , R _M2 , R _S1 , R _S2 based on the following equation, R _M1 − R _M2 / R _S1 − R _S2 = kP _M (8) Here, k=k ₁ −k ₂ /(π _l0 −π _t0 )σ _S , and the terms of temperature coefficients α and β can be removed. That is, a signal representing the pressure to be measured P _M can be obtained with high accuracy without being affected by changes in ambient temperature. Moreover, it is no longer necessary to measure the temperature characteristics of the gauge resistance by using a constant temperature bath, and it is only necessary to check the standard stress σ _S , thereby reducing the number of steps required to assemble the pressure sensor.

Furthermore, with regard to disturbance forces such as residual stress caused by the bonding between the single crystal semiconductor substrate 10 and the base 30, the influence thereof is generally reduced by increasing the thickness of the substrate 10 and the bonding width. Furthermore, since the stress caused by the disturbance force acts on the gauge resistors 21 and 22 and 23 and 24 in the same way, the resulting changes in the resistance values of the gauge resistors 21 and 22 and 23 and 24 are the same, and the calculation of equation (8) By doing so, the effects of disturbance forces can also be canceled out.

FIG. 4 is a connection diagram showing an example of a signal processing circuit used with the pressure sensors of FIGS. 1 and 2. FIG. In the signal processing circuit 40 of FIG. 4, 41 _a ,
41 _b , 41 _c , and 41 _d are sensor amplifiers, and a gauge resistor 21 is connected to the feedback circuit of the sensor amplifier 41 _a .
Gauge resistor 22 is added to the feedback circuit of sensor amplifier 41 _b .
However, a gauge resistor 23 is connected to the feedback circuit of the sensor amplifier _41c , and a gauge resistor 24 is connected to the feedback circuit of the sensor amplifier _41d . 42 is an error amplifier whose output E _C is connected to the resistor 4 with the same resistance value.
3 _a , 43 _b , 43 _c , and 43 _d to the inputs of sensor amplifiers 41 _a , 41 _b , 41 _c , and 41 _d , respectively. 44 and 45 are subtraction circuits, respectively. The subtraction circuit 44 includes four operational resistors 44 _b , _{44 c} , 44 _d , 4 having the same resistance value as the operational amplifier 44 a.
4 _e , calculate the difference E S1 −E _S2 between the output E _S1 of the sensor amplifier 41 _c and the output E _S2 of the sensor amplifier _{41 d} , and connect the resistor 42 _a to the input terminal (-) of the error amplifier 42. Add via. The subtraction circuit 45 includes an operational amplifier 45 _a and four operational resistors 45 _b having the same resistance value.
_45c , _45d , _45e , sensor amplifier 4
The difference (E _M1 - E _M2 ) between the output E _M1 of the sensor amplifier 1 _a and the output E M2 of the sensor amplifier _{41 b} is calculated and applied to the output terminal OUT as an output voltage E _O. 46 is a reference voltage source;
Connect the constant voltage E _R to the input terminal (+) of the error amplifier 42
give to In the signal processing circuit having such a configuration, if the resistance values of the resistors 43 _a , 43 _b , 43 _c , and 43 _d are selected to be equal and that value is R _C , then each of the sensor amplifiers 41 _a , 41 _b , 41 _c , 41 The output of _d E _M1 ,
E _M2 , E _S1 , and E _S2 are each given by the following equations.

E _M1 = −R _M1 /R _C E _C E _M2 = −R _M2 /R _C E _C E _S1 = −R _S1 /R _C E _C E _S2 = −R _S2 /R _C E _C (9) And the error Since the input voltage E _C of the sensor amplifiers 41 _a , 41 _b , 41 _c , and 41 _d is controlled by the amplifier 42 so that the output (E _S1 −E _S2 ) of the subtraction circuit 44 becomes equal to the reference voltage E _R , The following relationship holds true.

1/R _C (R _S1 −R _S2 )E _C =E _R (10) Therefore, the output voltage E _O (=E _M1 −E _M2 ) obtained at the output terminal of the subtraction circuit 45 is E _O =R _M1 −R _M2 /R _S1 −R _S2 E _R (11) Therefore, the calculation of equation (8) can be executed, and the signal voltage E _O representing the measured pressure P _M can be obtained without being affected by changes in the ambient temperature. be able to. Note that the signal processing circuit includes each gauge resistor 21, 22, 23,
24, the voltage drop of each gauge resistance is converted into a digital quantity by an A/D converter, and then a microcomputer performs digital calculations corresponding to equation (8). I can do it. Furthermore, by forming the signal processing circuit 40 on the single crystal semiconductor substrate 10, it is possible to improve the S/N and reduce the size.

In addition, if the change in resistance value of each gauge resistor 21 to 24 due to disturbance force is equal, either one of gauge resistor 22 and gauge resistor 24 is omitted and the measured pressure P _M is calculated by the following formula. Good too.

(R _M1 −R _S2 )+k ₃ (R _S1 −R _S2 )/k ₁ /k ₁ −k ₂ (R _S1 −R
_S2 )=kP _M (12) (R _M1 − R _M2 ) (1+k ₃ )/(R _S1 − R _M2 )+k ₂ /k ₁ −k ₂
(R _M1 −R _M2 )=kP _M (13) Here, k ₃ =π _t0 /π _l0 −π _t0 FIGS. 5 and 6 are cross-sectional views of other embodiments of the pressure sensor of the present invention. 5 and 6 differ from the embodiment shown in FIG. 2 in that the length h of the tip end _12a of the cantilever 12 is shortened. This is because the materials of the cantilever 12's tip _12a and the base 30 are normally selected and manufactured so that no bulges act on the contact area, but if bulges are present, the coefficient of thermal expansion of the two will decrease. Due to the difference, a massing force F based on temperature is generated, and a constant moment M (=
Fh) occurs. As a result, this constant moment M
The stress caused by this acts on the gauge resistors 23 and 24, and changes the resistance values R _S1 and R _S2 of the gauge resistors 23 and 24. Therefore, the length h of the tip portion _12a of the cantilever 12 is shortened to keep the constant moment M small even if there is a lump in the contact portion, and the fluctuations in R _S1 and R _S2 are made sufficiently small. Note that the tip 12 _a of the cantilever 12 and the base 30 may be joined to avoid being affected by the massing force.

FIG. 7 is a perspective view of another embodiment of the pressure sensor of the present invention. 7, the difference from the embodiment shown in FIG. 1 is that the distance l ₂ from the tip of the cantilever 12
The longitudinal direction is perpendicular to the position (near the tip 12 _a ),
In addition, by providing the gauge resistors 25 and 26 formed close to each other, it is possible to remove the influence of the constant moment M due to the stiffness of the contact portion between the tip 12 _a of the cantilever 12 and the base 30 by calculation. be. That is, gauge resistances 23, 24, 25, 2
The resistance values R _S1 , R _S2 , R _S3 , and R _S4 of No. 6 are given by the following equations, respectively, where σ _N (=6M/bd ² ) is the stress due to the constant moment M acting on the tip of the cantilever 12.

R _S1 = R ₀ (1+αt) {1+π _l0 (σ _S1 +σ _N ) (1+βt)}(14) R _S2 = R ₀ (1+αt) {1+π _t0 (σ _S1 +σ _N )(1+βt)}(15) R _S3 = R ₀ (1+αt) {1+π _l0 (σ _S2 +σ _N ) (1+βt)}(16) R _S4 = R ₀ (1+αt) {1+π _t0 (σ _S2 +σ _N )(1+βt)}(17) Here, σ _S1 = 3/2・dE/l ³・δ・l ₁ σ _S2 = 3/2・dE/l ³・δ・l ₂ Therefore, gauge resistance 21, 22, 23, 24, 2
5, 26 resistance values R _M1 , R _M2 , R _S1 , R _S2 , R _S3 ,
If the following formula is calculated based on R _S4 , R _M1 − R _M2 / (R _S1 − R _S2 ) − (R _S3 − R _S4 )=kP _M (18) Here, k=k ₁ − _{k 2} /(π _l0 −π _t0 )σ _S ,σ _S =σ _S1
−σ _S2 , and the influence of the constant moment M can be removed. In addition, the gauge resistance 23, 24, due to disturbance force
If the changes in resistance values of 25 and 26 are equal, the gauge resistors 24 and 26 can be omitted. Further, the tip portion 12 _a of the cantilever 12 and the base 30 may be joined.

Note that in the above description, the case where a single crystal semiconductor substrate 10 having a plane orientation of (100) is used as an example,
It may be one with plane orientation (110) or (111). Further, although the shape of the pressure receiving diaphragm 11 is rectangular, it goes without saying that it may be circular. In addition, cantilever 12
As shown in the perspective view of Fig. 8, the shape of
The width b may be small. Furthermore, if the gauge resistors 21, 22 (and 23, 24) are integrally formed as shown in FIG. 9, the characteristics can be made more uniform and the compensation accuracy can be improved. Furthermore, when the gauge resistors 21 and 22 are separately provided at two points on the pressure receiving diaphragm where the stress based on the measured pressure P _M differentially changes, it is not necessary that they be orthogonal to each other.

<Effects of the Invention> In the present invention, (1) Since at least two gauge resistors are provided on either the pressure receiving diaphragm or the cantilever, the measured pressure P _M can be determined from these at least three gauge resistance values. , three relational expressions related to the temperature coefficient α of the gauge resistance and the temperature coefficient β of the piezoresistance coefficient are obtained, so the temperature coefficient α of the gauge resistance and the temperature coefficient β of the piezoresistance coefficient are
Calculations can be erased by the arithmetic unit, and measurement pressure can be measured with high precision without being affected by changes in ambient temperature.

(2) Since it is not affected by changes in ambient temperature, there is no need to measure the temperature characteristics of the gauge resistance using a constant temperature bath, which can significantly reduce assembly man-hours.

(3) Since the gauge resistor of the compensation temperature-sensitive element is not placed in the fixed part of the single-crystal semiconductor substrate, which is susceptible to the effects of displacement of the pressure-receiving diaphragm, the measured pressure can be measured with higher accuracy. .

[Brief explanation of the drawing]

Fig. 1 is a perspective view showing an embodiment of the pressure sensor of the present invention, Fig. 2 is a cross-sectional view thereof, Fig. 3 is a cross-sectional view of main parts of the pressure sensor of the present invention, and Fig. 4 is a signal of the pressure sensor of the present invention. A connection diagram showing one embodiment of the processing section, FIGS. 5 and 6 are sectional views showing other embodiments of the pressure sensor of the present invention, and FIGS. 7 and 8 show other embodiments of the pressure sensor of the present invention. FIG. 9 is a perspective view showing an example of a gauge resistor used in the pressure sensor of the present invention. DESCRIPTION OF SYMBOLS 10... Single crystal semiconductor substrate, 11... Pressure receiving diaphragm, 12... Cantilever, 13... Fixed part, 21, 22, 23, 24, 25, 26... Gauge resistor, 30... Base, 40... signal processing circuit.

Claims (1)

[Scope of Claims] 1. A pressure receiving diaphragm and a cantilever provided on a single crystal semiconductor substrate; and at least two gauge resistors provided on each of the pressure receiving diaphragm and the cantilever, and at least two gauge resistors provided on either the pressure receiving diaphragm or the cantilever. a base on which the single crystal semiconductor substrate is fixed by applying a predetermined displacement to the cantilever in advance so as to generate a predetermined stress on the cantilever; and a measurement pressure obtained from the resistance values of these three gauge resistors. and a calculation section that calculates the measured pressure by calculating and eliminating the temperature coefficient of the gauge resistance and the temperature coefficient of the piezoresistance coefficient from three relational expressions related to the temperature coefficient of the gauge resistance and the temperature coefficient of the piezoresistance coefficient. sensor.