Patent Publication Number: US-2020284633-A1

Title: Fluid sensor

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     The present application is based upon and claims priority to Japanese Patent Application No. 2019-038261, filed on Mar. 4, 2019, the entire contents of which are incorporated herein by reference. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     An aspect of this disclosure relates to a fluid sensor. 
     2. Description of the Related Art 
     There are known fluid sensors for detecting the flow of a fluid such as air. A thermal fluid sensor is an example of such a fluid sensor. An example of a thermal fluid sensor is a microelectromechanical system (MEMS) fluid sensor. 
     A MEMS fluid sensor is formed by providing a heater in the middle of a membrane (thin film structure) formed in a sensor chip, and placing temperature detectors (resistors) in positions upstream and downstream of the heater. When a fluid to be detected flows over the membrane, a temperature difference corresponding to the flow of the fluid is generated between the upstream side and the downstream side of the heater. This temperature difference is detected by the two temperature detectors placed on the upstream side and the downstream side to detect the flow of the fluid. 
     In such a fluid sensor, the temperature distribution of heat generated by the heater is preferably symmetrical about the heater when no fluid is flowing. For this reason, various heater shapes suitable to achieve uniform temperature distribution have been proposed (see, for example, Japanese Patent No. 3687724 and Japanese Patent No. 3461469). 
     Japanese Laid-Open Patent Publication No. 2017-067643 discloses a fluid sensor where a pair of temperature detectors (resistors) are arranged in each of the X-axis direction and the Y-axis direction with respect to a heater to detect the direction (flow direction) of a fluid. This configuration makes it possible to detect the flow direction and the flow rate of a fluid by detecting the flow of the fluid in the X-axis direction and the Y-axis direction. 
     The fluid sensor described in Japanese Laid-Open Patent Publication No. 2017-067643 may be configured such that the temperature distribution of heat generated by the heater has a circular shape around the heater and becomes uniform. However, when the temperature detectors are arranged along the X axis and the Y axis with respect to the heater to have a temperature distribution with a circular shape as described above, compared with a case where a fluid flows along the X axis or the Y axis, the detection sensitivity of the temperature detectors becomes lower when the fluid flows in a direction other than the X-axis and Y-axis directions. 
     Thus, the detection accuracy of the flow direction and the flow rate by the fluid sensor described in Japanese Laid-Open Patent Publication No. 2017-067643 needs to be improved. 
     SUMMARY OF THE INVENTION 
     In an aspect of this disclosure, there is provided a fluid sensor that includes a primary heating resistor, a pair of X-axis temperature detectors disposed to face each other in an X-axis direction across the primary heating resistor, a pair of Y-axis temperature detectors disposed to face each other in a Y-axis direction across the primary heating resistor, and a secondary heating resistor connected to the primary heating resistor and disposed between one of the X-axis temperature detectors and one of the Y-axis temperature detectors. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a plan view exemplifying a structure of a fluid sensor according to a first embodiment; 
         FIG. 2  is a cross-sectional view taken along line A-A in  FIG. 1 ; 
         FIG. 3  is an enlarged view of a portion around a heating resistor; 
         FIG. 4  is a drawing illustrating an example of a temperature distribution when a flow rate is zero; 
         FIG. 5  is a drawing illustrating an example where a related-art temperature distribution changes depending on the flow of a fluid; 
         FIG. 6  is a drawing illustrating an example where a temperature distribution according to an embodiment changes depending on the flow of a fluid; 
         FIG. 7A  is a graph illustrating a relationship between a first sensor output signal and a second sensor output signal in a related-art example; 
         FIG. 7B  is a graph illustrating a relationship between a first sensor output signal and a second sensor output signal according to an embodiment; 
         FIG. 8  is a plan view exemplifying a structure of a fluid sensor according to a first variation; 
         FIG. 9  is an enlarged view of a portion around a heating resistor of a fluid sensor according to a second variation; 
         FIG. 10  is an enlarged view of a heating resistor of a fluid sensor according to a third variation; 
         FIG. 11  is a plan view exemplifying a structure of a fluid sensor according to a fourth variation; 
         FIG. 12  is an enlarged view of a portion around a heating resistor of a fluid sensor according to the fourth variation; and 
         FIG. 13  is a graph illustrating a temperature characteristic of a resistance temperature coefficient of vanadium oxide. 
     
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Embodiments of the present invention are described below with reference to the accompanying drawings. Throughout the accompanying drawings, the same reference number is assigned to the same component, and repeated descriptions of the same component may be omitted. 
     First Embodiment 
     [Structure of Fluid Sensor] 
       FIG. 1  is a plan view exemplifying a structure of a fluid sensor  1  according to a first embodiment.  FIG. 2  is a cross-sectional view taken along line A-A in  FIG. 1 .  FIG. 3  is an enlarged view of a portion around a heating resistor  40 . 
     The fluid sensor  1  includes a semiconductor substrate  10 , a multilayer structure  20 , X-axis temperature detectors  31   a  and  31   b , Y-axis temperature detectors  32   a  and  32   b , the heating resistor  40 , fixed resistors  50   a - 50   d , and bonding pads (which are hereafter referred to as “pads”)  60   a - 60   p.    
     In  FIGS. 1 through 3 , axes parallel to two orthogonal sides of the multilayer structure  20  are referred to as an X axis and a Y axis, and the thickness direction of the multilayer structure  20  orthogonal to the X axis and the Y axis is referred to as a Z axis. 
     As illustrated in  FIG. 2 , the semiconductor substrate  10  is a frame-shaped silicon substrate including an opening  10   x . The multilayer structure  20  has a structure formed by stacking multiple insulating films  21 - 25 , and is disposed on the semiconductor substrate  10  to close the opening  10   x . The multilayer structure  20  has, for example, a circular shape in plan view. A region of the multilayer structure  20  above the opening  10   x  is referred to as a membrane (thin film structure)  20   t . The multilayer structure  20  has a thickness of about 0.5 to about 5 μm. 
     The membrane  20   t  has, for example, a square shape in plan view. Because the membrane  20   t  is not in contact with the semiconductor substrate  10 , the heat capacity of the membrane  20   t  is small, and the temperature of the membrane  20   t  tends to increase. The upper surface of the membrane  20   t  is a detection surface for detecting the flow of a fluid that is a detection target. 
     The multilayer structure  20  includes the X-axis temperature detectors  31   a  and  31   b , the Y-axis temperature detectors  32   a  and  32   b , the heating resistor  40 , and the fixed resistors  50   a - 50   d . Also, pads  60   a - 60   p  are provided on the multilayer structure  20 . 
     The opening  10   x  is a cylindrical cavity formed by, for example, dry-etching the semiconductor substrate  10 . The insulating film  21  is comprised of, for example, a silicon dioxide film (SiO 2 ), and is formed on the semiconductor substrate  10 . The insulating film  21  is formed by, for example, a thermal oxidation method or a chemical vapor deposition (CVD) method. The insulating film  22  comprised of, for example, a silicon nitride film (SiN) is formed on the insulating film  21 . The insulating film  22  is formed by, for example, a thermal CVD method. 
     On the insulating film  22 , the X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detectors  32   a  and  32   b  comprised of, for example, vanadium oxide (VO 2 ) are formed. The X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detectors  32   a  and  32   b  are formed by, for example, a sol-gel method. 
     The insulating film  23  comprised of, for example, a silicon dioxide film (SiO 2 ) is formed on the insulating film  22  to cover the X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detectors  32   a  and  32   b . The insulating film  23  is formed by, for example, a sputtering method or a plasma CVD method. 
     On the insulating film  23 , the heating resistor  40  and the fixed resistors  50   a - 50   d , which are comprised of, for example, platinum (Pt), nichrome (NiCr), or polysilicon, are formed. The heating resistor  40  and the fixed resistors  50   a - 50   d  are formed by, for example, a sputtering method. 
     The insulating film  24  comprised of, for example, a silicon dioxide film (SiO 2 ) is formed on the insulating film  23  to cover the heating resistor  40  and the fixed resistors  50   a - 50   d . The insulating film  24  is formed by, for example, a sputtering method or a plasma CVD method. 
     The pads  60   a - 60   p  comprised of, for example, aluminum (Al) or gold (Au) are formed on the insulating film  24 . The pads  60   a - 60   p  are formed by, for example, a sputtering method. Also, in addition to the pads  60   a  to  60   p , wiring is formed on the insulating film  24 . 
     On the insulating film  24 , the insulating film  25  comprised of, for example, a silicon nitride film (SiN) is formed so as to cover the wiring and expose at least parts of the upper surfaces of the pads  60   a - 60   p . The insulating film  25  is formed by, for example, a low-temperature CVD method. 
     Contact plugs  26  for connecting the X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detectors  32   a  and  32   b  to the wiring are formed in the insulating film  23  and the insulating film  24 . The contact plugs  26  are formed by filling contact holes in the insulating films  23  and  24  with a conductive material such as tungsten. The contact holes are formed by, for example, wet etching using buffered hydrofluoric acid (BHF). Here, because gaps exist in parts of vanadium oxide forming the X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detectors  32   a  and  32   b , buffered hydrofluoric acid may penetrate into a lower layer below the vanadium oxide during wet etching. To prevent the lower layer from being etched, the insulating film  22 , which is the lower layer below the X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detectors  32   a  and  32   b , is preferably formed of silicon nitride (SiN) that has a high resistance to buffered hydrofluoric acid. 
     As illustrated in  FIG. 1 , the heating resistor  40  is formed in the center of the membrane  20   t . The X-axis temperature detectors  31   a  and  31   b  are disposed to face each other in the X-axis direction across the heating resistor  40 . The Y-axis temperature detectors  32   a  and  32   b  are disposed to face each other in the Y-axis direction across the heating resistor  40 . The X-axis temperature detectors  31   a  and  31   b  detect a temperature difference in the X-axis direction based on a difference in resistance values. The Y-axis temperature detectors  32   a  and  32   b  detect a temperature difference in the Y-axis direction based on a difference in resistance values. 
     The X-axis temperature detector  31   a  is connected to the pad  60   a  via a wire  71  and connected to the pad  60   b  via a wire  72 . The X-axis temperature detector  31   b  is connected to the pad  60   c  via a wire  73  and connected to the pad  60   d  via a wire  74 . The Y-axis temperature detector  32   a  is connected to the pad  60   e  via a wire  75  and connected to the pad  60   f  via a wire  76 . The Y-axis temperature detector  32   b  is connected to the pad  60   g  via a wire  77  and connected to the pad  60   h  via a wire  78 . 
     Each of the fixed resistors  50   a - 50   d  is a resistor with a meander structure that is formed by bending a straight line multiple times. The meander structure is employed to increase the resistance value. One end of the fixed resistor  50   a  is connected to the pad  60   i  via a wire  81 , and another end of the fixed resistor  50   a  is connected to one end of the fixed resistor  50   b  via a wire  82 . Another end of the fixed resistor  50   b  is connected to the pad  60   j  via a wire  83 . 
     One end of the fixed resistor  50   c  is connected to the pad  60   j  via a wire  84 , and another end of the fixed resistor  50   c  is connected to one end of the fixed resistor  50   d  via a wire  85 . Another end of the fixed resistor  50   d  is connected to the pad  60   k  via a wire  86 . 
     The fixed resistors  50   a - 50   d  form a bridge circuit together with the X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detectors  32   a  and  32   b . The temperature distribution of heat generated by the heating resistor  40  can be detected using this bridge circuit. 
     For example, a power supply voltage is applied to one of the pad  60   i  and the pad  60   k , and the other one of the pad  60   i  and the pad  60   k  is set at the ground potential to use a potential appearing at the pad  60   j  as a reference potential. Also, the pad  60   a  and the pad  60   c  are connected to each other via external wiring, a power supply voltage is applied to one of the pad  60   b  and the pad  60   d , and another one of the pad  60   b  and the pad  60   d  is set at the ground potential. In this case, a first sensor output signal is obtained by detecting a difference between the potential appearing at the pad  60   a  and the pad  60   c  and the reference potential with a sensor amplifier. The first sensor output signal is a signal corresponding to the temperature difference between the X-axis temperature detectors  31   a  and  31   b , and becomes substantially zero when there is no temperature difference. 
     Further, the pad  60   e  and the pad  60   g  are connected to each other via external wiring, a power supply voltage is applied to one of the pad  60   f  and the pad  60   h , and another one of the pad  60   f  and the pad  60   h  is set at the ground potential. In this case, a second sensor output signal corresponding to the temperature distribution in the Y direction is obtained by detecting a difference between the potential appearing at the pad  60   e  and the pad  60   g  and the reference potential with a sensor amplifier. The second sensor output signal is a signal corresponding to the temperature difference between the Y-axis temperature detectors  32   a  and  32   b , and becomes substantially zero when there is no temperature difference. 
     As illustrated in  FIG. 3 , the heating resistor  40  includes one primary heating resistor  41  and four secondary heating resistors  42   a - 42   d . The primary heating resistor  41  is disposed in the center of the membrane  20   t . In the present embodiment, the primary heating resistor  41  is separated into a first heating resistor  41   a  and a second heating resistor  41   b . Each of the first heating resistor  41   a  and the second heating resistor  41   b  has a meander structure. When the X axis and the Y axis are defined to intersect at the center of the membrane  20   t , the first heating resistor  41   a  and the second heating resistor  41   b  are symmetrical with respect to the X axis. 
     Each of the secondary heating resistors  42   a - 42   d  is disposed apart from the intersection between the X axis and the Y axis in a direction that forms an angle of 45 degrees with each of the X axis and the Y axis. Each of the secondary heating resistors  42   a - 42   d  has a meander structure formed by bending an extension of a wire of the primary heating resistor  41  multiple times. 
     The secondary heating resistor  42   a  is connected to one end of the first heating resistor  41   a . The secondary heating resistor  42   b  is connected to another end of the first heating resistor  41   a . That is, the first heating resistor  41   a , the secondary heating resistor  42   a , and the secondary heating resistor  42   b  are formed by bending parts of one wire into meander shapes. The secondary heating resistor  42   a  is substantially disposed between the X-axis temperature detector  31   a  and the Y-axis temperature detector  32   a . The secondary heating resistor  42   b  is substantially disposed between the Y-axis temperature detector  32   a  and the X-axis temperature detector  31   b . The secondary heating resistor  42   a  and the secondary heating resistor  42   b  are symmetrical with respect to the Y axis. 
     The secondary heating resistor  42   c  is connected to one end of the second heating resistor  41   b . The secondary heating resistor  42   d  is connected to another end of the second heating resistor  41   b . That is, the second heating resistor  41   b , the secondary heating resistor  42   c , and the secondary heating resistor  42   d  are formed by bending parts of one wire into meander shapes. The secondary heating resistor  42   c  is substantially disposed between the X-axis temperature detector  31   a  and the Y-axis temperature detector  32   b . The secondary heating resistor  42   d  is substantially disposed between the Y-axis temperature detector  32   b  and the X-axis temperature detector  31   b . The secondary heating resistor  42   c  and the secondary heating resistor  42   d  are substantially symmetrical with respect to the Y axis. 
     Also, the secondary heating resistor  42   a  and the secondary heating resistor  42   c  are symmetrical with respect to the X axis. Further, the secondary heating resistor  42   b  and the secondary heating resistor  42   d  are symmetrical with respect to the X axis. 
     An end of the secondary heating resistor  42   a , which is located opposite the first heating resistor  41   a , is connected to the pad  601  via a wire  91 . An end of the secondary heating resistor  42   b , which is located opposite the first heating resistor  41   a , is connected to the pad  60   m  via a wire  92 . 
     An end of the secondary heating resistor  42   c , which is located opposite the second heating resistor  41   b , is connected to the pad  60   n  via a wire  93 . An end of the secondary heating resistor  42   d , which is located opposite the second heating resistor  41   b , is connected to the pad  60   o  via a wire  94 . 
     The pad  601  and the pad  60   n  are connected to each other via a wire  95 . Also, the pad  60   m  and the pad  60   o  are connected to each other via a wire  96 . Here, the pad  60   p  is a dummy pad. 
     By applying a potential difference between the pads  601  and  60   n  and the pads  60   m  and  60   o , an electric current flows through a path connecting the first heating resistor  41   a , the secondary heating resistor  42   a , and the secondary heating resistor  42   b , and through a path connecting the second heating resistor  41   b , the secondary heating resistor  42   c , and the secondary heating resistor  42   d . As a result, a temperature distribution is formed on a detection surface due to heat generated by the heating resistor  40 . 
     As illustrated in  FIG. 1 , the X-axis temperature detectors  31   a  and  31   b , the Y-axis temperature detectors  32   a  and  32   b , the heating resistor  40 , the fixed resistors  50   a - 50   d , the pads  60   a - 60   p , and the wires  71 - 78 ,  81 - 86 , and  91 - 96  form a pattern that is substantially symmetrical with respect to the X axis and the Y axis. 
     [Temperature Distribution] 
     Next, a temperature distribution of heat generated by the heating resistor  40  of the present embodiment is described.  FIG. 4  is a drawing illustrating an example of a temperature distribution when the flow rate is zero. In  FIG. 4 , a temperature distribution D 1  indicates the shape of a temperature distribution formed by the heating resistor  40  of the present embodiment. A temperature distribution D 0  indicates the shape of a temperature distribution formed when the secondary heating resistors  42   a - 42   d  are not provided and only the primary heating resistor  41  is provided. Thus, while the related-art temperature distribution D 0  has a substantially circular shape, the temperature distribution D 1  in the present embodiment has a substantially square shape. 
       FIG. 5  is a drawing illustrating an example where a related-art temperature distribution changes depending on the flow of a fluid. In  FIG. 5 , a first temperature distribution D 0   a  is formed when the flow direction is parallel to the Y-axis direction (arrow A). A second temperature distribution D 0   b  is formed when the flow direction is at an angle of 45 degrees with each of the X-axis direction and the Y-axis direction (arrow B). 
     Thus, in the related-art example, the temperature distribution D 0  has a substantially circular shape when the flow rate is zero, and when the flow rate is not zero, the shape of the temperature distribution D 0  rotates in a direction corresponding to the flow direction. Accordingly, with the first temperature distribution D 0   a , the temperature difference between the Y-axis temperature detectors  32   a  and  32   b  becomes large, and the second sensor output signal increases. With the second temperature distribution D 0   b , the temperature difference between the Y-axis temperature detectors  32   a  and  32   b  decreases, and the second sensor output signal decreases; and the temperature difference between the X-axis temperature detectors  31   a  and  31   b  increases, and the first sensor output signal increases. In the related-art example, the temperature difference between each pair of the X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detectors  32   a  and  32   b , which results from the change from the first temperature distribution D 0   a  to the second temperature distribution D 0   b , is small. Therefore, both of the first sensor output signal and the second sensor output signal are small, and the detection sensitivity is low. 
       FIG. 6  is a drawing illustrating an example where a temperature distribution according to the present embodiment changes depending on the flow of a fluid. In  FIG. 6 , a first temperature distribution D 1   a  is formed when the flow direction is parallel to the Y-axis direction (arrow A). A second temperature distribution D 1   b  is formed when the flow direction is at an angle of 45 degrees with each of the X-axis direction and the Y-axis direction (arrow B). 
     In the present embodiment, because the temperature distribution D 1  has a substantially square shape instead of a circular shape when the flow rate is zero, the temperature distribution D 1  takes a shape formed by stretching a part of the square in a direction corresponding to the flow direction when the flow rate is not zero. Similarly to the related-art example, with the first temperature distribution D 1   a , the temperature difference between the Y-axis temperature detectors  32   a  and  32   b  is large, and the second sensor output signal increases. With the second temperature distribution D 1   b , the temperature difference between the Y-axis temperature detectors  32   a  and  32   b  decreases, and the second sensor output signal decreases; and the temperature difference between the X-axis temperature detectors  31   a  and  31   b  increases, and the first sensor output signal increases. 
     In the present embodiment, however, the temperature difference between each pair of the X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detector  32   a  and  32   b , which results from the change from the first temperature distribution D 1   a  to the second temperature distribution D 1   b , is large. Accordingly, both of the first sensor output signal and the second sensor output signal increase, and the detection sensitivity is improved. 
       FIG. 7A  is a graph illustrating the relationship between the first sensor output signal and the second sensor output signal in the related-art example.  FIG. 7B  is a graph illustrating the relationship between the first sensor output signal and the second sensor output signal in the present embodiment. In each of  FIG. 7A  and  FIG. 7B , a dotted line indicates values (ideal values) of the first sensor output signal and the second sensor output signal in an ideal state where the detection sensitivity is not decreased. A solid line indicates simulation values that are obtained when the flow rate is set at 6 m/s, and are normalized by the ideal values. 
     As illustrated in  FIG. 7A , in the conventional example, when the flow direction forms an angle of 45 degrees with each of the X-axis direction and the Y-axis direction, the detection sensitivity is greatly reduced. In contrast, as illustrated in  FIG. 7B , in the present embodiment, the values of the first sensor output signal and the second sensor output signal are close to the ideal values, and the decrease in the detection sensitivity is suppressed. Thus, the present embodiment makes it possible to improve the accuracy of detecting the flow direction and the flow rate. 
     Next, variations of the present embodiment are described. 
     &lt;First Variation&gt; 
       FIG. 8  is a plan view exemplifying a structure of a fluid sensor  1   a  according to a first variation. The fluid sensor  1   a  according to the first variation is different from the fluid sensor  1  of the first embodiment in that the membrane  20   t  has a substantially square shape in plan view. Other configurations of the fluid sensor  1   a  are substantially the same as those of the fluid sensor  1  of the first embodiment. Thus, the planar shape of the membrane  20   t  is not limited to a circular shape, but may also be a square shape. 
     &lt;Second Variation&gt; 
       FIG. 9  is an enlarged view of a portion around the heating resistor  40  of a fluid sensor according to a second variation. In the second variation, slits  43  are provided around the primary heating resistor  41  at positions between the secondary heating resistor  42   a  and the secondary heating resistor  42   b , between the secondary heating resistor  42   b  and the secondary heating resistor  42   d , between the secondary heating resistor  42   d  and the secondary heating resistor  42   c , and between the secondary heating resistor  42   c  and the secondary heating resistor  42   a . In the area of each slit  43 , the multilayer structure  20  is removed. Other configurations of the fluid sensor are substantially the same as those of the fluid sensor  1  of the first embodiment. 
     &lt;Third Variation&gt; 
       FIG. 10  is an enlarged view of a heating resistor  40   a  of a fluid sensor according to a third variation. The heating resistor  40   a  according to the third variation differs from the heating resistor  40  of the first embodiment in the shapes of the first heating resistor  41   a  and the second heating resistor  41   b  included in the primary heating resistor  41  and the shapes of the secondary heating resistors  42   a - 42   d . In the third variation, the primary heating resistor  41  has a multiple-ring shape as a whole. 
     &lt;Fourth Variation&gt; 
       FIG. 11  is a plan view exemplifying a structure of a fluid sensor  1   b  according to a fourth variation.  FIG. 12  is an enlarged view of a portion around a heating resistor  40   b  of the fluid sensor  1   b  according to the fourth variation. As illustrated in  FIG. 12 , unlike the heating resistor  40  according to the first embodiment, the primary heating resistor  41  included in the heating resistor  40   b  of the fourth variation is not divided, and has a meander structure as a whole. Accordingly, in the fourth variation, all of the primary heating resistor  41  and the secondary heating resistors  42   a - 42   d  are formed by bending one wire. 
     Also in the fourth variation, as illustrated in  FIG. 11 , the wire  95  for connecting the pad  601  and the pad  60   n  and the wire  96  for connecting the pad  60   m  and the pad  60   o  are not provided. In the fourth variation, no voltage is applied to the pad  601  and the pad  60   o  used as dummy pads, and a potential difference is applied between the pad  60   m  and the pad  60   n  to cause an electric current to flow through the heating resistor  40   b . For example, a power supply voltage is applied to the pad  60   m  and the pad  60   n  is set at the ground potential so that, as indicated by arrows, an electric current flows through the secondary heating resistor  42   b , the secondary heating resistor  42   d , the primary heating resistor  41 , the secondary heating resistor  42   a , and the secondary heating resistor  42   c  in this order. 
     [Materials of Temperature Detectors] 
     As described above, the X-axis temperature detectors  31   a  and  31   b  and the Y-axis temperature detectors  32   a  and  32   b  are preferably comprised of vanadium oxide. However, to further improve the sensitivity, a material obtained by doping vanadium oxide with aluminum (Al) and/or titanium (Ti) may be preferably used. 
       FIG. 13  is a graph illustrating a temperature characteristic of a resistance temperature coefficient of vanadium oxide. The resistance temperature coefficient indicates a percentage of change of a resistance value in relation to a temperature change. 
     In  FIG. 13 , a dotted line indicates the characteristic of vanadium oxide doped with titanium. The doping concentration of titanium is between 10% and 20%. A solid line indicates the characteristic of vanadium oxide doped with aluminum and titanium. The doping concentration of aluminum is between 1% and 10%, and the doping concentration of titanium is between 10% and 20%. 
     As indicated by the graph, doping vanadium oxide with aluminum and titanium increases the temperature range where the resistance temperature coefficient is constant. Accordingly, the sensitivity is improved by using vanadium oxide doped with aluminum and titanium as the material of the temperature detectors. 
     [Locations of Secondary Heating Resistors] 
     In the above-described embodiment, the secondary heating resistor is disposed such that a line connecting the secondary heating resistor and the center of the primary heating resistor forms an angle of 45 degrees with each of the X-axis direction and the Y-axis direction. However, as long as the secondary heating resistor is disposed between the X-axis temperature detector and the Y-axis temperature detector, the secondary heating resistor is not necessarily disposed to form an angle of 45 degrees. For example, to make the temperature distribution uniform, taking into account the variation in the sensitivity of the X-axis temperature detector and the Y-axis temperature detector, the secondary heating resistor disposed between the X-axis temperature detector and the Y-axis temperature detector may be shifted toward the X-axis temperature detector or the Y-axis temperature detector. 
     An aspect of this disclosure makes it possible to improve the accuracy of detecting a flow direction and a flow rate. 
     Fluid sensors according to the embodiments of the present invention are described above. However, the present invention is not limited to the specifically disclosed embodiments, and variations and modifications may be made without departing from the scope of the present invention.