JP3603447B2 - Flow measurement device - Google Patents

Description

【００２５】
ここで、
α_ｎ ，γ_ｎ ：振動の態様（モード）で決まる定数
Ｌ，ｈ：振動体の長さ、厚さ
Ｅ_ｅ ：実効ヤング率＝Ｅ／（１−ν^２ ）、νはポアソン比
Ｉ：振動体の断面２次モーメント
ρ：振動体材料の密度
Ａ：振動体の断面積
また振動体に加わる歪みεは、振動体に予め残留している歪みε_０ と熱応力 ε_ｈｅａｔの和で表される。
【００２６】
ε＝ε_０ ＋ε_ｈｅａｔ＝ε_０ ＋Ｋα√Ｇ
したがって、質量流量Ｇによる熱応力の変化分を考慮した振動体の共振周波数ｆ_０ は次式で表される。
【００２７】
【数２】

【００２８】
このように、計測する質量流量Ｇと振動体の共振周波数ｆ_０ との関係は１／４乗特性となる。この特性は、微小流量域では高感度（出力の傾きが大きい）で、大流量になるに伴って出力の傾きが低下して行くようなダイナミックレンジの広い理想に近い出力特性が得られることになる。
【００２９】
振動体に加わる応力に対する共振周波数の特性は、図３に示すような１／２乗特性となる。図３において、振動体の初期状態として、残留応力がゼロの点を発熱体（ヒータ）の無加熱ポイントとする。振動体をセンサとして作動させるため、予め発熱体により振動体を加熱しておくと、周囲の冷たい基板との温度差により振動体にはこれを圧縮するように応力が加わり、共振周波数ｆ_０ が低下する。
【００３０】
すなわち、所定の温度に加熱した振動体の共振周波数が、流量ゼロのときのセンサ出力となる。そして、これに空気流による冷却効果が加わると、振動体の温度が低下するため、圧縮応力が減少し、空気流量に応じて共振周波数が上昇する。
【００３１】
図３から明らかなように、圧縮応力が増大すると、振動体の共振周波数がゼロになる点がある。この点を構造力学的に座屈点と言い、このときの応力を座屈応力と言う。フローセンサとして計測のダイナミックレンジの拡大と感度の向上のためには、座屈点により近い領域における応力対周波数特性を用いるのがよいが、加熱による圧縮応力が座屈点を越えると、振動体として機能しない。
【００３２】
したがって、振動体をフローセンサとして機能させるための発熱体による加熱は、座屈点を越えない範囲で、かつ所望の感度およびダイナミックレンジが得られるように、なるべく圧縮応力の大きい側に設定する必要がある。
【００３３】
振動体の座屈点はその振動体の寸法で決定されることが知られており（オイラーの座屈点）、これを座屈歪みε_ｂ で表すと、次式のようになる（ｈ：振動体の厚さ、Ｌ：振動体の長さ）。
【００３４】
ε_ｂ ＝（−π^２ ／３）ｈ^２ ／Ｌ^２
したがって、振動体の厚さｈおよび長さＬと、振動体に予め残留する歪みε_０ と、発熱体の熱によって生じる圧縮歪みε_ｈｅａｔとが以下のような関係を満足するような設定となる。
【００３５】
ε_０ ＋ε_ｈｅａｔ＞（−π^２ ／３）ｈ^２ ／Ｌ^２
また、ε_ｈｅａｔを発熱体の加熱温度Ｔとの関係に直すと
ε_ｂ ＋αＴ＞（−π^２ ／３）ｈ^２ ／Ｌ^２
すなわち、本発明では、発熱体の加熱温度Ｔ、振動体の残留応力ε_０ および振動体の寸法（ｈ，Ｌ）が上式を満足させる関係にあることも特徴となっている。
【００３６】
また、フローセンサとして振動体を用いた場合、出力が周波数出力となり、Ａ／Ｄコンバータが不要となるから、センサの計測レンジおよび精度がＡ／Ｄコンバータの性能により制限を受けるという従来技術の問題点が解決される。そしてこの場合、センサ出力をエンジン制御用コンピュータのタイマカウンタポートに直接入力することができ、コンピュータの時間計測が高精度なこと相俟って、空気流量の高精度、高分解能計測が可能になる。また、センサ出力が周波数変調信号であるため、電磁ノイズやグラウンドノイズ等に影響されず、誤差の少ない信号伝送が実現できる。
【００３７】
発熱体の近傍に配設された両持ち梁に加わる熱応力変化の計測は、必ずしも上記両持ち梁が振動体でなくても可能ではあるが、振動体は応力に対する検出感度が極めて高く、微妙な温度変化に対しても十分検出できるほどの周波数変化をもたらす。したがって、従来技術のように発熱体の温度を高温にしておく必要がなく、信頼性および耐久性が著しく向上する。
【００３８】
また、振動体は、上述のように温度変化に敏感であるため、発熱体自身の空気流による直接の冷却効果だけでなく、振動体付近の熱分布の変化にも敏感に反応する。
【００３９】
ところで、発熱体を有するセンサ構造体上における発熱体の周囲の２次元温度分布を温度等高線で表すと、図４（ａ）に示すように、発熱体を中心に左右対称になるが、発熱体の表面上を空気流が流れると、空気流の流量とともに流れの方向によって２次元温度分布が変化する。そこで、空気流による発熱体の温度低下をフィードバック制御によって補って、発熱体の温度を常に一定に保った状態にしておくと、図４（ｂ）に示すように、発熱体の上流と下流とで熱分布に差異を生じる。
【００４０】
したがって、このような熱分布が変化する部分に、温度変化を検出する振動体を配置することにより、発熱体と振動体とを配設したセンサ基板上における２次元的な熱分布の空気流による変化も検出できるエアフローセンサが実現できる。特に熱分布の変化は、質量流量のみでなく、流れの方向成分の情報を含んでいるから、流れの方向により温度に差異の発生する複数位置にそれぞれ振動体を配設することにより、流れの方向も検出可能なエアフローセンサが実現できる。図４（ｂ）においては、発熱体に対し、空気流の上流側と下流側とに振動体を対称的に配設し、各振動体の出力周波数信号の差分を算出することにより、逆流も検出可能なエアフローセンサが実現され、自動車エンジンの高精度空燃比制御に貢献することができる。
【００４１】
【発明の実施の形態】
以下、本発明の実施の形態について、図面を参照して説明する。
【００４２】
図５は本発明による流量測定装置の第１の実施の形態を示す振動式エアフローセンサの斜視図、図６はその要部の拡大斜視図、図７は図６の ＶＩＩ−ＶＩＩ 線に沿った拡大断面図、図８は振動体の拡大断面図である。
【００４３】
図５において、２０はシリコン単結晶基板１からなるセンサ構造体で、基板１の上面１ａは、例えば図７に示すように、シリコン単結晶のミラー指数で表される（１００）面となっている。２はこのシリコン単結晶基板１からエッチング加工により一体に削出された両持ち梁構造を有する三角柱からなる振動体である。
【００４４】
この振動体２の断面形状は、基板面１ａである（１００）面が二等辺三角形の底面になり、二等辺の部分はともに（１１１）面になっている。上記底面と二等辺とのなす角度は、結晶面から見て（１００）面と（１１１）面との交わる角度である５４．７度となっており、振動体２の長手方向は、基板面１ａ内での＜１１０＞方向に平行であり、振動体２はその両端を固定端としてシリコン単結晶基板１に支持され、両持ち梁構造を構成している。一例として、振動体２の寸法を以下に記す（図８参照）。
【００４５】
振動体長さＬ： １．６ｍｍ
振動体高さｈ： ２０μｍ
振動体幅ｂ ： ２８．３μｍ
基板面１ａ上には、白金の薄膜により形成された発熱体３，３が振動体２の各固定端近傍にそれぞれ配設されており、さらに、図６に示すように、振動体２の一方の固定端から振動体２の面上に延びる駆動用抵抗４と、振動体２の他方の固定端から振動体２の面上に延びる振動検出用抵抗（ピエゾ抵抗）５とが拡散抵抗により形成されている。
【００４６】
シリコン単結晶基板１は、裏面からエッチング加工等によって深く掘られ、発熱体３，３や振動体２が配設されている部分はダイアフラム構造を有している。これは、少ない電力で発熱体の温度を上昇させるためと、センサの感度と応答性を向上させるために、熱容量を下げる必要があるからである。
【００４７】
図９は、振動体２に振動を励起させ、かつその振動を検出する回路の一例を示す概略図である。図６に示すように、振動体２上には駆動用抵抗４が拡散により形成されており、この駆動用抵抗４に交番電流を供給して交番的に発熱させることによって、振動体２に交番応力をかけ振動を励起させる。振動体２上には検出用ピエゾ抵抗５が拡散により形成されているので、このピエゾ抵抗５が振動体２が振動により曲がることにより発生する応力を検出用抵抗５の抵抗変化ととして読み出せばよい。
【００４８】
振動体２の自励発振は、振動の検出信号を駆動用抵抗４に正帰還させることにより発生させる。図９においては、検出用抵抗５を含むブリッジ回路６で検出した検出出力をプリアンプ７で増幅して得られた周波数出力を駆動用抵抗４に帰還させる正帰還ループに、増幅率を制御して駆動用抵抗４に供給される電力を一定にコントロールするＡＧＣアンプ８を介在させて、正帰還による無限大発振を防止している。
【００４９】
図１０は、空気流の流量が０〜１５０ｇ／ｓｅｃ の範囲において発熱体３，３の温度が約５０℃変化すると仮定した場合の空気流の質量流量と振動体２の共振周波数特性を示すグラフである。図１０から明らかなように、０〜１５０ｇ／ｓｅｃ の流量範囲で共振周波数の変化範囲は２３．３ｋＨｚ 〜３９．９ｋＨｚ となる。この場合、エンジン制御用コンピュータ内のカウンタ／タイマ機能を用いて、１ＭＨｚ の基準クロックと１ｍｓｅｃの時間で周波数計測を行なう場合において、１．０ｇ／ｓｅｃ の微小流領域から１５０ｇ／ｓｅｃ まで±３％の精度分解能をもって計測することができる。このように、本実施の形態によれば、１５０倍のダイナミックレンジの領域を精度良く計測することが可能な高感度流量測定装置を得ることができる。
【００５０】
図１１は、図５〜図８に示す振動体２の製造方法の一例を説明する工程図である。
【００５１】
工程１：先ず基板面が（１００）面であるシリコンウエハ（シリコン単結晶基板）１０を用意する。
【００５２】
工程２：エッチングマスクにするためのシリコン酸化膜１１をシリコンウエハ１０の表面に付ける。ここでは、通常の半導体集積回路の製造工程で用いられる熱酸化による方法あるいはＣＶＤによる膜形成法等を適用すればよい。なお、このエッチングマスクは、酸化膜に限定されるものでなく、窒化膜その他、強アルカリ溶液による後工程でのエッチングに対し十分な耐性を有する膜材料であればよい。
【００５３】
工程３：振動体２の形状を決定するため、酸化膜１１のパターニングを行なって、作成すべき振動体２の幅に等しい間隔を隔てて＜１１０＞方向に延びる互いに平行でかつ作成すべき振動体２の長さに等しい長さを有する一対の開口１２，１２を備えた酸化膜マスク１３をシリコンウエハ１０の表面に形成する。このパターニングは、フォトレジスト等を用いたフォトリソグラフィ工程の後、エッチング液としてフッ酸水溶液等を用いて行なう。
【００５４】
工程４：酸化膜マスク１３をエッチングマスクとして、シリコン基板に対して開口１２，１２を通じてエッチングを行なって、基板面に対してほぼ垂直な壁面を備えた互いに平行な一対の凹溝１４，１４を形成する。この場合のエッチングは、フッ素系のガスを用いたＲＩＥ（リアクティブ イオンエッチング）法を用いて行なう。
【００５５】
工程５：同じ酸化膜マスク１３をエッチングマスクとして、凹溝１４，１４に対してＫＯＨやＴＭＡＨ（テトラメチルアンモニウムハイドロオキサイド）等の強アルカリ溶液によってエッチングを行なう。
【００５６】
このように、シリコン単結晶材料を上記のような特定の強アルカリ溶液によってエッチングを行なうと、シリコン単結晶の特定の結晶面によってエッチング速度が著しく異なる性質がある。例えばシリコン単結晶の（１００）面や（１１０）面に対して（１１１）面のエッチングされる速度は非常に遅く、速度比で約１００：１程度になる。このような性質から、この工程でのエッチングは、エッチング速度の速い（１１０）面を進行面としてその両端部に（１１１）面が残る状態で結晶異方性エッチングが進行して行く。
【００５７】
工程６：最終的には振動体２となる部分の両側から（１１０）面を進行面として横方向にエッチングが進行して行き、両凹溝１４，１４間がそれらの底部において互いに連通し、振動体２となる部分の下方に空間１５が形成されることによって、残った２つの（１１１）面と１つの（１００）面とによって囲まれた三角柱からなる梁を得る。最終的に梁の上面を覆う酸化膜マスク１３をエッチング等で除去すればよい。
【００５８】
このような結晶異方性エッチングを実施すれば、エッチング後の形状がエッチング条件（温度や撹拌等）によらず高い精度で予測でき、加工が容易となる。
【００５９】
このような製造工程によって得られた、１つの（１００）面と、極めてエッチング速度が遅い２つの（１１１）面とで構成された三角柱からなる振動体２は、結晶面上の幾何学的特性から、その形状がほぼ決定される。すなわち、振動体２の幅ｂが酸化膜マスク１３上のパターニングで決定されれば、三角柱断面における高さｈは一義的に決まってしまう。
【００６０】
ｈ＝ｔａｎ（５４．７°）・ｂ／２
このことは、振動体２の幅ｂの加工精度を高めておけば、高さｈの寸法精度が自動的に向上することを意味する。
【００６１】
一般に、エッチングによって深さ方向の加工を行なう場合、その加工精度はエッチングの終点を判断するのが困難なためその寸法精度は悪い。たとえばＲＩＥ等でシリコンのエッチングを行なう場合でも、深さ寸法の加工の絶対値で±５％程度のばらつきが生じたり、加工の均一性においてもウエハ面内で±５％いないの精度を得るのに極めて複雑なエッチング装置を用いなければならない。一方、フォトリソグラフィによるパターニングで代表される面上での加工精度は、半導体集積回路の製造工程の進歩に見られるように極めて高精度な加工（絶対、相対加工精度で±１％以下）が比較的容易に得られる。
【００６２】
したがって、上述した製造方法によれば、その製造工程と得られる構造体の構造的特徴とから、深さ方向の加工精度（ここでは三角断面の高さｈ）についても面内のパターニング精度と同程度の精度が容易に実現できる。
【００６３】
上記工程４においては、ＲＩＥによるエッチング加工を施しているが、この工程でのエッチング加工は、振動体２の下部の中空になる部分が貫通できるだけの深さがあればよく、次式に示すようにその下限より深くエッチングすれば事足りることになる（エッチング壁面が基板面に対して９０°をなす場合）。
【００６４】
エッチング深さｄ＞ｂｔａｎ（５４．７°）
次に、図１２は本発明による流量測定装置の第２の実施の形態を示す振動式エアフローセンサの斜視図である。
【００６５】
本実施の形態のエアフローセンサの特徴は、空気流の流量のみでなく流れの方向をも検出可能な点にある。
【００６６】
図１２に示すセンサ構造体３０は、図５と同様のシリコン単結晶基板３１上に特性の一致した２つの振動体２，２を、計測する空気流に対して中央の発熱体３３を挾んで上流側と下流側に配置してある。センサ構造体３０は、図５に示す第１の実施の形態と同様のダイアフラム構造を有し、また振動体２，２の構造およびそれらの自励振動の機構と動作も第１の実施の形態と同様である。
【００６７】
空気流量の測定には、いずれか一方の振動体２の共振周波数を測定することにより達成できる。また、発熱体３３の下流側よりも上流側の方が温度低下が大きいことから、空気流の方向の検出は、２つの振動体２，２の共振周波数の差を求め、その正負を判定することにより達成できる。すなわち、振動体２，２の共振周波数のうち、上流側をｆ_ｕｐ、下流側をｆ_ｄｏｗｎとすると、
ｆ_ｕｐ−ｆ_ｄｏｗｎ＜０で順流、ｆ_ｕｐ−ｆ_ｄｏｗｎ＞０で逆流となる。
【００６８】
発熱体３３の駆動には、空気流の冷却効果による温度低下を補うべく、温度検出用抵抗と、外部回路とを用いて、発熱体３３の温度を一定に保つようにしている。すなわち、発熱体３３は、図１３に示すように、発熱用抵抗Ｒ_Ｈ と発熱温度をモニタする温度検出用抵抗Ｒ_ＨＴからなり、さらに基準温度（ここでは空気温）を測定するための抵抗Ｒ_Ｔ を図１４に示す外部回路に設けてあり、抵抗Ｒ_ＨＴ，Ｒ_Ｔ と定抵抗Ｒ_１ ，Ｒ_２ とによってブリッジ回路を構成している。そして冷却により発熱体３３の温度が低下するとブリッジ回路のバランスが崩れ、ブリッジ出力に電位差が発生する。この電位差を演算増幅器３４を通じて増幅して、その出力により、発熱用抵抗Ｒ_ＨＴに対する供給電流を増加させて、発熱体３３を加熱するように構成されている。このようなフィードバック回路を用いることにより、発熱体３３の温度が基準温度（空気温）に対して所定の温度差を有する温度の制御される。
【００６９】
図１５は本発明による流量測定装置の第３の実施の形態を示す振動式エアフローセンサの斜視図、図１６はその要部の拡大断面図である。
【００７０】
本実施の形態におけるエアフローセンサのセンサ構造体４０は、シリコン単結晶基板４１上に２つの振動体２，２を、計測する空気流に対して中央の発熱体３３を挾んで上流側と下流側に配置してある点、および空気流の流量のみでなく流れの方向をも検出可能な点で、図１２に示す第２の実施の形態と同様であるが、本実施の形態においては、センサ構造体４０の発熱体３３および振動体２，２が配設されているダイヤフラム構造部が、図１６に示すように、このダイヤフラム構造部との間に所定の間隙４４を形成したガラスキャップ４５で封止された構成を有する。この封止された間隙４４は１０〜３Ｔｏｒｒ程度の真空に保たれていることにより、振動体２，２の空気粘性による振動の減衰効果が減少し、極めて安定で高純度の共振振動が得られる。上記ガラスキャップ４５は、陽極接合法等により、基板４１の上面に気密に接合されている。
【００７１】
このように、上面を封止された構造の場合、空気流はダイヤフラム構造部の裏面に沿って流れるように構成される。そのため、基板４１の側面がエッチング加工等により削られた形状になっており、また、ダイヤフラム構造部は、発熱体３３の熱が裏面に十分に作用するような厚さに設定されている。
【００７２】
また、本実施の形態においては、振動体２に振動を励起させるために、駆動用抵抗に代えて、基板４１の上面とガラスキャップ４５の下面との間に形成された間隙４４を利用した駆動用静電電極を用いている。すなわち、図１６に示すように、振動体２の上面に下部電極４６が設けられ、この下部電極４６に対向する上部電極４７がガラスキャップ４５の下面に設けられている。そして、両電極４６，４７間に交番電圧を印加することにより、静電気力によって振動体２が振動せしめられる。振動体２の振動は、前述の実施の形態と同様に、振動体２の一方の固定端付近に設けられたピエゾ抵抗４８によってその抵抗変化として検出される。
【００７３】
図１７は、振動体２に振動を励起させ、かつその振動を検出する回路の一例を示す概略図である。
【００７４】
振動体２の自励発振は、駆動用電極４６，４７に正帰還させることにより発生させる。図９と同様に、検出用ピエゾ抵抗４８を含むブリッジ回路４９で検出した検出出力をプリアンプ５０で増幅して得られた周波数出力を駆動用電極４６，４７に帰還させる正帰還ループに、増幅率を制御して駆動用電極４６，４７に供給される電力を一定にコントロールするＡＧＣアンプ５１を介在させて、正帰還による無限大発振を防止している。
【００７５】
以上の実施の形態においては、空気流の冷却効果による発熱体３，３３の温度変化に基づく両持ち梁の熱応力変化をすべて両持ち梁構造を有する振動体２の共振周波数の変化として検出しているが、これは前述したように、振動体２が極めて検出感度が良いからである。しかしながら、本発明は、両持ち梁の熱応力変化を直接ピエゾ抵抗等を用いて検出する形式の流量測定装置をも含むことは言うまでもない。
【図面の簡単な説明】
【図１】両端を固定した剛体棒を加熱することにより剛体棒に応力が発生する機構を説明する図
【図２】両持ち梁構造を有する振動体を加熱することにより振動体に応力が発生する機構を説明する図
【図３】両持ち梁構造を有する振動体に加わる応力に対する共振周波数の変化を示す特性図
【図４】センサ構造体上における発熱体近傍の２次元温度分布を示す図
【図５】本発明による流量測定装置の第１の実施の形態を示す振動式エアフローセンサの斜視図
【図６】図５の要部拡大斜視図
【図７】図６の ＶＩＩ−ＶＩＩ 線に沿った拡大断面図
【図８】振動体の拡大断面図
【図９】振動検出回路の一例を示す概略図
【図１０】空気流の質量流量に対すると振動体の共振周波数特性を示すグラフ
【図１１】振動体の製造方法を説明する工程図
【図１２】本発明による流量測定装置の第２の実施の形態を示す振動式エアフローセンサの斜視図
【図１３】同 要部の概略的平面図
【図１４】同 発熱体の温度を一定に保つ装置の回路図
【図１５】本発明による流量測定装置の第３の実施の形態を示す振動式エアフローセンサの斜視図
【図１６】同 要部の拡大断面図
【図１７】同 振動検出回路の概略図
【符号の説明】
１，３１，４１ シリコン単結晶基板
２ 振動体
３，３３ 発熱体
４ 駆動用抵抗
５，４８ 振動検出用抵抗
８，５１ ＡＧＣアンプ
２０，３０，４０ センサ構造体
４４ 間隙
４５ ガラスキャップ
４６，４７ 電極[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to a flow measurement device suitable for use as a measurement device for an intake air amount in, for example, an automobile engine equipped with an electronically controlled fuel injection device.
[0002]
[Prior art]
Conventionally, as an airflow sensor used in a measurement device for the amount of intake air for engine control, a heated resistor is exposed to an airflow, and the temperature change of the resistor due to the cooling effect of the airflow is measured as a resistance change to measure the airflow. Things to detect are known.
[0003]
These thermal airflow sensors include a hot wire type using a thin platinum wire as a heating resistor and a hot film type using a thin film resistor such as platinum.The silicon substrate is thinned by fine processing such as etching, and the platinum A semiconductor hot-film type air flow sensor having a thin film resistor such as the one described above has also been proposed (see Japanese Patent Application Laid-Open No. Hei 7-159215).
[0004]
[Problems to be solved by the invention]
Recently, in lean-burn engines that reduce environmental pollution and save fuel, the control sensor has been designed to reduce exhaust purification catalyst capacity and achieve engine control that balances fuel efficiency and driving at a high level. High functionality is an important issue. In particular, the need to realize high sensitivity, high precision measurement of intake air volume required for precise air-fuel ratio control, and backflow detection, and to expand the dynamic range of air flow measurement required for highly supercharged engines, etc. are apparent. Is becoming
[0005]
However, the dynamic range of the conventional thermal airflow sensor is not sufficient even with a semiconductor hot film sensor in which the heat capacity of the detection unit is minimized. Therefore, the heating element (hot wire, hot film) is barely cleared by raising the temperature to 200 ° C. or higher. In this case, however, the durability of the heating element deteriorates due to the high temperature of the heating element. Has become.
[0006]
In addition, in the conventional thermal airflow sensor, since the temperature change of the resistor due to the cooling effect of the airflow is detected as a resistance change, it is difficult to say that the sensitivity is high, and a large temperature change of the resistor is required. There is also a problem.
[0007]
Furthermore, since the sensor output is an analog signal that reads the resistance change as a voltage, an A / D converter must be interposed when inputting the signal to the engine control computer. However, since an A / D converter having a large number of resolution bits is required to obtain a measurement accuracy that satisfies the entire required measurement area, the measurement range and accuracy of the sensor are limited by the performance of the A / D converter. Inconvenience.
[0008]
Further, in an electric bad environment such as the vicinity of an engine of a car, an output signal which is an analog signal is always affected by electromagnetic noise, ground noise, and the like, so that high-accuracy measurement cannot be expected.
[0009]
In view of the above circumstances, an object of the present invention is to provide a flow rate measuring device which is extremely sensitive, has high reliability and durability, and does not require an A / D converter.
[0010]
[Means for Solving the Problems]
In the flow rate measuring device according to the present invention, a heating element and a doubly supported beam are arranged close to each other on a substrate, and thermal stress generated in the doubly supported beam due to heat of the heating element causes cooling according to the mass flow rate of the fluid. The present invention is characterized in that a change due to a temperature change of the heating element due to the effect is detected as a mechanical change of the doubly supported beam.
[0011]
In this case, the doubly supported beam was integrally cut from the silicon single crystal substrate, and was supported by the silicon single crystal substrate with both ends as support ends.Configuration.
[0012]
Further, the doubly-supported beam is formed of a vibrating body having a doubly-supported beam structure. It is preferable to comprise a means for measuring
[0013]
The thickness h and length L of the vibrating body, and the strain ε due to the longitudinal stress pre-existing in the vibrating body₀And the compressive strain ε caused by the heat of the heating element_heatPreferably has a relationship represented by the following equation.
[0014]
ε₀+ Ε_heat> (− Π²/ 3) h²/ L²
Further, the flow rate measuring apparatus according to the present invention may be provided with a means for compensating for a decrease in the temperature of the heating element due to the cooling effect of the fluid, and the means may be configured to keep the temperature of the heating element substantially constant.
[0015]
In this case, the vibrator is arranged at a position on the substrate where the two-dimensional distribution of the substrate temperature near the heating element changes according to the fluid flow rate, and the change in the resonance frequency of the vibrator caused by the change in the two-dimensional distribution of the substrate temperature. Based on the measurement, a fluid flow measurement is made.
[0016]
Further, a plurality of vibrators are arranged on the substrate along the direction of the flow of the fluid, and the flow rate and the direction of the flow of the fluid are measured based on a difference in a resonance frequency change between the plurality of vibrators. It can be configured to be.
[0017]
【The invention's effect】
The relationship between the heat quantity Q theoretically deprived of the heating element and the mass flow rate G is as follows.
[0018]
Q = K√G (K is a constant)
Therefore, the temperature change ΔT acting on the doubly supported beam is also expressed by the following equation.
[0019]
ΔT = K√G
The thermal stress acting on the doubly supported beam is generated by a temperature difference between the vicinity of the doubly supported beam and other substrate portions. FIGS. 1 and 2 show the outline of the generation mechanism. FIG. 1 shows a state in which when a rigid rod whose both ends are fixed to an immovable wall is heated, the rod tends to expand due to thermal expansion, so that a compressive stress is generated in the rod. FIG. 2 shows a state in which stress is generated by heating in a vibrating body having a doubly supported structure. FIG. 2A shows a type in which a vibrator is directly heated, and FIG. It is a type that heats it.
[0020]
When the above-mentioned doubly supported beam is integrally cut out of the silicon single crystal substrate including the supporting portions at both ends by etching or the like, the internal stress becomes almost zero, and when this doubly supported beam is used as a vibrating body. In addition, the sensor characteristics can be easily controlled. In addition, since silicon single crystal can be easily obtained as a substrate material of a semiconductor integrated circuit with extremely high purity, a stable and uniform mechanical property can be obtained, contributing to stabilization of the resonance characteristics of the vibrating body. can do.
[0021]
Assuming that the thermal expansion coefficient of the material constituting the vibrating body is α and the temperature difference between the vibrating body and the substrate portion is T, the generated stress σ is as follows.
[0022]
σ = εE = αTE (E: Young's modulus, ε: generated strain)
Therefore, the relationship between the temperature change ΔT and the thermal stress change σ due to the cooling effect is as follows.
[0023]
ε_heat= Kα√G
On the other hand, the resonance frequency change of the vibrating body with respect to the generated strain is theoretically expressed by the following equation.
[0024]
(Equation 1)

[0025]
here,
α_n, Γ_n: Constant determined by the mode (mode) of vibration
L, h: length and thickness of vibrator
E_e: Effective Young's modulus = E / (1-ν)²), Ν is Poisson's ratio
I: Second moment of area of vibrating body
ρ: Density of vibrator material
A: Cross-sectional area of vibrator
The strain ε applied to the vibrating body is the strain ε remaining in the vibrating body in advance.₀And thermal stress ε_heatIt is expressed by the sum of
[0026]
ε = ε₀+ Ε_heat= Ε₀+ Kα√G
Therefore, the resonance frequency f of the vibrating body in consideration of the change in the thermal stress due to the mass flow rate G₀Is represented by the following equation.
[0027]
(Equation 2)

[0028]
Thus, the mass flow rate G to be measured and the resonance frequency f of the vibrating body are₀Is a 1/4 power characteristic. This characteristic is that high-sensitivity (slope of the output is large) in the micro flow rate range and output characteristics close to ideal with a wide dynamic range such that the output slope decreases as the flow rate increases. Become.
[0029]
The resonance frequency characteristic with respect to the stress applied to the vibrating body is a half-square characteristic as shown in FIG. In FIG. 3, a point where the residual stress is zero is set as a non-heating point of the heating element (heater) as an initial state of the vibration element. If the vibrating body is heated by a heating element in advance to operate the vibrating body as a sensor, a stress is applied to the vibrating body to compress the vibrating body due to a temperature difference from a surrounding cold substrate, and the resonance frequency f₀Decreases.
[0030]
That is, the resonance frequency of the vibrating body heated to the predetermined temperature becomes the sensor output when the flow rate is zero. When the cooling effect of the air flow is added to this, the temperature of the vibrating body decreases, so that the compressive stress decreases and the resonance frequency increases according to the air flow rate.
[0031]
As is clear from FIG. 3, there is a point where the resonance frequency of the vibrating body becomes zero when the compressive stress increases. This point is called a buckling point in structural mechanics, and the stress at this time is called a buckling stress. In order to expand the dynamic range of measurement and improve sensitivity as a flow sensor, it is better to use stress versus frequency characteristics in the area closer to the buckling point, but if the compressive stress due to heating exceeds the buckling point, the vibrator Does not work as
[0032]
Therefore, the heating by the heating element for causing the vibrating element to function as a flow sensor needs to be set within a range not exceeding the buckling point and on the side where the compressive stress is as large as possible so as to obtain a desired sensitivity and dynamic range. There is.
[0033]
It is known that the buckling point of a vibrating body is determined by the size of the vibrating body (Euler's buckling point)._bThe following equation (h: thickness of the vibrating body, L: length of the vibrating body) is obtained.
[0034]
ε_b= (-Π²/ 3) h²/ L²
Therefore, the thickness h and the length L of the vibrating body and the strain ε that remains in the vibrating body in advance₀And the compressive strain ε caused by the heat of the heating element_heatAre set so as to satisfy the following relationship.
[0035]
ε₀+ Ε_heat> (− Π²/ 3) h²/ L²
Also, ε_heatIs converted into the relationship with the heating temperature T of the heating element.
ε_b+ ΑT> (− π²/ 3) h²/ L²
That is, in the present invention, the heating temperature T of the heating element and the residual stress ε₀Another characteristic is that the dimensions (h, L) of the vibrating body satisfy the above equation.
[0036]
In addition, when a vibrating body is used as a flow sensor, the output becomes a frequency output, and an A / D converter is not required. Therefore, the conventional technology has a problem that the measurement range and accuracy of the sensor are limited by the performance of the A / D converter. The point is solved. In this case, the sensor output can be directly input to the timer counter port of the engine control computer, and the high accuracy and high resolution measurement of the air flow rate can be performed in combination with the high accuracy of the time measurement of the computer. . Further, since the sensor output is a frequency modulated signal, signal transmission with little error can be realized without being affected by electromagnetic noise or ground noise.
[0037]
The measurement of the change in thermal stress applied to the doubly-supported beam placed in the vicinity of the heating element is not necessarily required even if the doubly-supported beam is not a vibrating body, but the vibrating body has extremely high detection sensitivity to stress and is subtle. A frequency change that can be sufficiently detected even with a change in temperature is brought about. Therefore, it is not necessary to keep the temperature of the heating element high as in the prior art, and the reliability and durability are significantly improved.
[0038]
Further, since the vibrating body is sensitive to the temperature change as described above, the vibrating body responds not only to the direct cooling effect due to the air flow of the heating element itself but also to a change in the heat distribution near the vibrating body.
[0039]
By the way, when the two-dimensional temperature distribution around the heating element on the sensor structure having the heating element is represented by temperature contours, as shown in FIG. When the airflow flows on the surface of the airflow, the two-dimensional temperature distribution changes depending on the flow direction together with the flow rate of the airflow. Accordingly, if the temperature of the heating element is compensated for by a feedback control to keep the temperature of the heating element constant at all times, as shown in FIG. Causes a difference in heat distribution.
[0040]
Therefore, by arranging the vibrating body for detecting a temperature change in such a portion where the heat distribution changes, the two-dimensional heat distribution due to the air flow on the sensor substrate on which the heating element and the vibrating body are disposed is provided. An airflow sensor capable of detecting a change can be realized. In particular, the change in the heat distribution includes not only the mass flow rate but also information on the direction component of the flow.Therefore, by disposing the vibrators at a plurality of positions where the temperature differs depending on the flow direction, the flow An airflow sensor capable of detecting the direction can be realized. In FIG. 4 (b), the vibrating body is symmetrically arranged on the upstream side and the downstream side of the airflow with respect to the heating element, and the difference between the output frequency signals of the vibrating bodies is calculated, so that the backflow also occurs. A detectable air flow sensor is realized, which can contribute to high-precision air-fuel ratio control of an automobile engine.
[0041]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
[0042]
FIG. 5 is a perspective view of a vibrating air flow sensor showing a first embodiment of the flow measuring device according to the present invention, FIG. 6 is an enlarged perspective view of a main part thereof, and FIG. 7 is a view taken along line VII-VII of FIG. FIG. 8 is an enlarged sectional view of the vibrating body.
[0043]
In FIG. 5, reference numeral 20 denotes a sensor structure composed of a silicon single crystal substrate 1, and an upper surface 1a of the substrate 1 has a (100) plane represented by a Miller index of the silicon single crystal, for example, as shown in FIG. I have. Reference numeral 2 denotes a vibrating body composed of a triangular prism having a double-supported beam structure, which is integrally cut out of the silicon single crystal substrate 1 by etching.
[0044]
The cross-sectional shape of the vibrator 2 is such that the (100) plane, which is the substrate surface 1a, is a bottom surface of an isosceles triangle, and both isosceles portions are (111) planes. The angle between the bottom surface and the isosceles is 54.7 degrees, which is the angle at which the (100) plane intersects with the (111) plane when viewed from the crystal plane. The vibrating body 2 is supported by the silicon single crystal substrate 1 with both ends thereof being fixed ends, and constitutes a doubly supported structure. As an example, the dimensions of the vibrating body 2 are described below (see FIG. 8).
[0045]
Vibrator length L: 1.6mm
Vibrator height h: 20 μm
Oscillator width b: 28.3 μm
On the substrate surface 1a, heating elements 3 and 3 formed of a thin film of platinum are provided near the fixed ends of the vibrating body 2, respectively. Further, as shown in FIG. A driving resistor 4 extending from the fixed end of the vibrating body 2 on the surface of the vibrating body 2 and a vibration detecting resistor (piezoresistor) 5 extending from the other fixed end of the vibrating body 2 on the surface of the vibrating body 2 are formed by diffusion resistance. Have been.
[0046]
The silicon single crystal substrate 1 is dug deep from the back surface by etching or the like, and a portion where the heating elements 3 and 3 and the vibrating element 2 are disposed has a diaphragm structure. This is because it is necessary to reduce the heat capacity in order to raise the temperature of the heating element with a small amount of power and to improve the sensitivity and responsiveness of the sensor.
[0047]
FIG. 9 is a schematic diagram illustrating an example of a circuit that excites the vibration of the vibrating body 2 and detects the vibration. As shown in FIG. 6, a driving resistor 4 is formed on the vibrating body 2 by diffusion, and an alternating current is supplied to the driving resistor 4 to generate heat alternately. Apply stress to excite vibration. Since the detection piezoresistor 5 is formed on the vibrating body 2 by diffusion, if the piezoresistor 5 reads out the stress generated when the vibrating body 2 bends due to vibration as the resistance change of the detection resistor 5. Good.
[0048]
The self-excited oscillation of the vibrating body 2 is generated by positively feeding back a vibration detection signal to the driving resistor 4. In FIG. 9, the amplification factor is controlled by a positive feedback loop in which a detection output detected by a bridge circuit 6 including a detection resistor 5 is amplified by a preamplifier 7 and a frequency output obtained is fed back to a driving resistor 4. An infinite oscillation due to positive feedback is prevented by interposing an AGC amplifier 8 for controlling the power supplied to the driving resistor 4 to be constant.
[0049]
FIG. 10 is a graph showing the mass flow rate of the air flow and the resonance frequency characteristics of the vibrating body 2 assuming that the temperature of the heating elements 3 and 3 changes by about 50 ° C. in the range of the air flow rate of 0 to 150 g / sec. It is. As is clear from FIG. 10, in the flow rate range of 0 to 150 g / sec, the change range of the resonance frequency is 23.3 kHz to 39.9 kHz. In this case, when the frequency is measured using a counter / timer function in the engine control computer with a reference clock of 1 MHz and a time of 1 msec, ± 3% from a micro flow region of 1.0 g / sec to 150 g / sec. Can be measured with an accuracy resolution of As described above, according to the present embodiment, it is possible to obtain a high-sensitivity flow measurement device capable of accurately measuring a region having a dynamic range of 150 times.
[0050]
FIG. 11 is a process chart illustrating an example of a method of manufacturing the vibrating body 2 illustrated in FIGS. 5 to 8.
[0051]
Step 1: First, a silicon wafer (silicon single crystal substrate) 10 having a (100) substrate surface is prepared.
[0052]
Step 2: A silicon oxide film 11 for use as an etching mask is provided on the surface of the silicon wafer 10. Here, a method by thermal oxidation or a film forming method by CVD, which is used in a normal semiconductor integrated circuit manufacturing process, may be applied. The etching mask is not limited to an oxide film, but may be a nitride film or any other film material having sufficient resistance to etching in a subsequent step using a strong alkaline solution.
[0053]
Step 3: In order to determine the shape of the vibrator 2, the oxide film 11 is patterned, and vibrations extending in the <110> direction at an interval equal to the width of the vibrator 2 to be produced are parallel to each other and are to be produced. An oxide film mask 13 having a pair of openings 12, 12 having a length equal to the length of the body 2 is formed on the surface of the silicon wafer 10. This patterning is performed by using a hydrofluoric acid aqueous solution or the like as an etching solution after a photolithography process using a photoresist or the like.
[0054]
Step 4: The silicon substrate is etched through the openings 12 and 12 using the oxide film mask 13 as an etching mask to form a pair of mutually parallel concave grooves 14 and 14 having wall surfaces substantially perpendicular to the substrate surface. Form. The etching in this case is performed by RIE (reactive ion etching) using a fluorine-based gas.
[0055]
Step 5: Using the same oxide film mask 13 as an etching mask, the concave grooves 14 are etched with a strong alkaline solution such as KOH or TMAH (tetramethylammonium hydroxide).
[0056]
As described above, when the silicon single crystal material is etched with the above-described specific strong alkaline solution, the etching rate is significantly different depending on the specific crystal plane of the silicon single crystal. For example, the etching rate of the (111) plane with respect to the (100) plane and the (110) plane of silicon single crystal is extremely low, and the rate is about 100: 1. Due to such properties, in the etching in this step, the crystal anisotropic etching proceeds with the (110) plane having a high etching rate as a progress plane and the (111) planes remaining at both ends.
[0057]
Step 6: The etching proceeds in the lateral direction from both sides of the portion that will eventually become the vibrating body 2 with the (110) plane as the advancing surface, and the two concave grooves 14, 14 communicate with each other at their bottoms, By forming the space 15 below the portion that will be the vibrating body 2, a beam composed of a triangular prism surrounded by the remaining two (111) planes and one (100) plane is obtained. Finally, the oxide film mask 13 covering the upper surface of the beam may be removed by etching or the like.
[0058]
If such crystal anisotropic etching is performed, the shape after etching can be predicted with high accuracy regardless of the etching conditions (temperature, stirring, etc.), and processing becomes easy.
[0059]
The vibrator 2 composed of a triangular prism composed of one (100) plane and two (111) planes having an extremely low etching rate, obtained by such a manufacturing process, has a geometrical characteristic on a crystal plane. , The shape is almost determined. That is, if the width b of the vibrating body 2 is determined by patterning on the oxide film mask 13, the height h in the triangular prism cross section is uniquely determined.
[0060]
h = tan (54.7 °) · b / 2
This means that if the processing accuracy of the width b of the vibrating body 2 is increased, the dimensional accuracy of the height h is automatically improved.
[0061]
Generally, when processing is performed in the depth direction by etching, the dimensional accuracy of the processing accuracy is poor because it is difficult to determine the end point of the etching. For example, even when silicon is etched by RIE or the like, the absolute value of the processing of the depth dimension may vary by about ± 5%, and the uniformity of the processing may be as high as ± 5% within the wafer surface. A very complicated etching apparatus must be used. On the other hand, the processing accuracy on the surface represented by patterning by photolithography is compared with extremely high-precision processing (absolute, relative processing accuracy of ± 1% or less) as seen in the progress of semiconductor integrated circuit manufacturing processes. The target is easily obtained.
[0062]
Therefore, according to the above-described manufacturing method, the processing accuracy in the depth direction (here, the height h of the triangular cross section) is the same as the in-plane patterning accuracy, based on the manufacturing process and the structural characteristics of the obtained structure. A degree of accuracy can be easily realized.
[0063]
In the above step 4, the etching process by RIE is performed. However, the etching process in this step only needs to have a depth enough to penetrate a hollow portion below the vibrating body 2, and as shown in the following equation: It suffices to etch deeper than the lower limit (when the etching wall is at 90 ° to the substrate surface).
[0064]
Etching depth d> btan (54.7 °)
Next, FIG. 12 is a perspective view of a vibrating airflow sensor showing a second embodiment of the flow measuring device according to the present invention.
[0065]
The feature of the airflow sensor according to the present embodiment is that not only the flow rate of the airflow but also the direction of the airflow can be detected.
[0066]
A sensor structure 30 shown in FIG. 12 has two vibrators 2 and 2 having the same characteristics on a silicon single crystal substrate 31 similar to that shown in FIG. It is located upstream and downstream. The sensor structure 30 has a diaphragm structure similar to that of the first embodiment shown in FIG. 5, and the structures of the vibrators 2 and 2 and the mechanism and operation of self-excited vibration thereof are also the same as those of the first embodiment. Is the same as
[0067]
The measurement of the air flow rate can be achieved by measuring the resonance frequency of one of the vibrators 2. Further, since the temperature drop is greater on the upstream side than on the downstream side of the heating element 33, the direction of the air flow is detected by determining the difference between the resonance frequencies of the two vibrators 2 and determining whether the difference is positive or negative. This can be achieved by: That is, of the resonance frequencies of the vibrators 2 and 2, the upstream side is f_up, The downstream side is f_downThen
f_up−f_down<0 for forward flow, f_up−f_downWhen> 0, a reverse flow occurs.
[0068]
The driving of the heating element 33 uses a temperature detecting resistor and an external circuit to keep the temperature of the heating element 33 constant in order to compensate for a temperature drop due to the cooling effect of the airflow. In other words, as shown in FIG._HAnd a temperature detecting resistor R for monitoring the heat generation temperature_HTAnd a resistance R for measuring a reference temperature (air temperature in this case)._TAre provided in the external circuit shown in FIG._HT, R_TAnd constant resistance R₁, R₂A bridge circuit is constituted by these. When the temperature of the heating element 33 decreases due to cooling, the balance of the bridge circuit is lost, and a potential difference occurs in the bridge output. This potential difference is amplified through an operational amplifier 34, and the output thereof is used to generate a heating resistor R_HTAnd the heating element 33 is heated by increasing the supply current to the heating element 33. By using such a feedback circuit, the temperature of the heating element 33 is controlled to have a predetermined temperature difference from a reference temperature (air temperature).
[0069]
FIG. 15 is a perspective view of a vibrating air flow sensor showing a third embodiment of the flow measuring device according to the present invention, and FIG. 16 is an enlarged sectional view of a main part thereof.
[0070]
The sensor structure 40 of the airflow sensor according to the present embodiment includes two vibrators 2, 2 on a silicon single crystal substrate 41, and an upstream side and a downstream side with respect to an air flow to be measured with a central heating element 33 interposed therebetween. The second embodiment shown in FIG. 12 is the same as the second embodiment shown in FIG. 12 in that it can detect not only the flow rate of the air flow but also the direction of the flow. As shown in FIG. 16, the diaphragm structure in which the heating element 33 and the vibrating bodies 2 and 2 of the structure 40 are disposed is a glass cap 45 having a predetermined gap 44 formed between the diaphragm structure and the diaphragm structure. It has a sealed configuration. Since the sealed gap 44 is kept at a vacuum of about 10 to 3 Torr, the damping effect of vibration due to the air viscosity of the vibrators 2 and 2 is reduced, and extremely stable and high-purity resonance vibration is obtained. . The glass cap 45 is hermetically bonded to the upper surface of the substrate 41 by an anodic bonding method or the like.
[0071]
Thus, in the case of the structure in which the upper surface is sealed, the air flow is configured to flow along the back surface of the diaphragm structure. For this reason, the side surface of the substrate 41 has a shape cut off by etching or the like, and the diaphragm structure is set to a thickness such that the heat of the heating element 33 sufficiently acts on the back surface.
[0072]
Further, in the present embodiment, in order to excite the vibrating body 2 to vibrate, the driving using the gap 44 formed between the upper surface of the substrate 41 and the lower surface of the glass cap 45 instead of the driving resistor. Use electrostatic electrodes. That is, as shown in FIG. 16, the lower electrode 46 is provided on the upper surface of the vibrating body 2, and the upper electrode 47 facing the lower electrode 46 is provided on the lower surface of the glass cap 45. Then, by applying an alternating voltage between the electrodes 46 and 47, the vibrating body 2 is vibrated by the electrostatic force. The vibration of the vibrating body 2 is detected as a resistance change by a piezo resistor 48 provided near one fixed end of the vibrating body 2 as in the above-described embodiment.
[0073]
FIG. 17 is a schematic diagram illustrating an example of a circuit that excites the vibration body 2 and detects the vibration.
[0074]
The self-excited oscillation of the vibrating body 2 is generated by positively feeding back the driving electrodes 46 and 47. Similarly to FIG. 9, a positive feedback loop for amplifying the detection output detected by the bridge circuit 49 including the detection piezoresistor 48 with the preamplifier 50 and feeding back the frequency output to the driving electrodes 46 and 47 is provided. The AGC amplifier 51 for controlling the power supplied to the driving electrodes 46 and 47 at a constant level to prevent the infinite oscillation due to the positive feedback is prevented.
[0075]
In the above embodiment, all changes in the thermal stress of the doubly supported beam based on the temperature change of the heating elements 3 and 33 due to the cooling effect of the airflow are detected as changes in the resonance frequency of the vibrating body 2 having the doubly supported structure. However, this is because the vibrating body 2 has extremely high detection sensitivity as described above. However, it goes without saying that the present invention also includes a flow rate measuring device of the type that directly detects a change in the thermal stress of the double-ended beam using piezoresistance or the like.
[Brief description of the drawings]
FIG. 1 is a view for explaining a mechanism in which a rigid rod having both ends fixed is heated to generate stress in the rigid rod.
FIG. 2 is a diagram illustrating a mechanism in which stress is generated in a vibrating body by heating the vibrating body having a doubly supported structure.
FIG. 3 is a characteristic diagram showing a change in resonance frequency with respect to a stress applied to a vibrating body having a doubly supported structure.
FIG. 4 is a diagram showing a two-dimensional temperature distribution near a heating element on a sensor structure;
FIG. 5 is a perspective view of a vibrating air flow sensor showing a first embodiment of the flow measuring device according to the present invention.
FIG. 6 is an enlarged perspective view of a main part of FIG. 5;
FIG. 7 is an enlarged sectional view taken along line VII-VII of FIG. 6;
FIG. 8 is an enlarged sectional view of a vibrating body.
FIG. 9 is a schematic diagram illustrating an example of a vibration detection circuit.
FIG. 10 is a graph showing a resonance frequency characteristic of a vibrating body with respect to a mass flow rate of an air flow.
FIG. 11 is a process diagram illustrating a method for manufacturing a vibrating body.
FIG. 12 is a perspective view of a vibrating airflow sensor showing a second embodiment of the flow measuring device according to the present invention.
FIG. 13 is a schematic plan view of the main part.
FIG. 14 is a circuit diagram of a device for keeping the temperature of the heating element constant.
FIG. 15 is a perspective view of a vibration type air flow sensor showing a third embodiment of the flow measuring device according to the present invention.
FIG. 16 is an enlarged sectional view of a main part of the same.
FIG. 17 is a schematic diagram of the vibration detection circuit.
[Explanation of symbols]
1,31,41 Silicon single crystal substrate
2 vibrator
3,33 heating element
4 Driving resistor
5,48 Vibration detection resistor
8,51 AGC amplifier
20, 30, 40 sensor structure
44 gap
45 glass cap
46, 47 electrodes

Claims (6)

A heating element disposed on the substrate,
A doubly supported beam arranged near the heating element,
Means for measuring a mechanical change caused by a thermal stress change applied to the doubly supported beam based on a temperature change of the heating element or a substrate in the vicinity thereof due to a cooling effect of a fluid flowing along the surface of the substrate. ,
Measuring the flow rate of the fluid based on the measurement of the mechanical change of the doubly supported beam by the means ;
A flow rate measuring apparatus , wherein the doubly supported beam is integrally cut from a silicon single crystal substrate, and is supported by the silicon single crystal substrate with both ends as support ends . The doubly-supported beam includes a vibrating body having a doubly-supported beam structure, and the means for measuring a mechanical change of the doubly-supported beam due to a thermal stress change applied thereto measures a change in a resonance frequency of the vibrating body. 2. The flow measuring device according to claim 1, comprising means. The thickness h and length L of the vibrator, the strain ε ₀ due to the longitudinal stress existing in the vibrator in advance, and the compressive strain ε _heat generated by the heat of the heating element are represented by the following equations. 3. The flow measurement device according to claim 2 , wherein the flow measurement device has a relationship.
_{ε 0 + ε heat> (-} π 2/3) h 2 / L 2 3. The flow measuring device according to claim 2 , further comprising means for compensating for a decrease in the temperature of the heating element due to the cooling effect of the fluid, and the means keeping the temperature of the heating element substantially constant. The vibrator is disposed at a position on the substrate where the two-dimensional distribution of the substrate temperature near the heating element changes according to the fluid flow rate, and the change in the resonance frequency of the vibrator caused by the change in the two-dimensional distribution of the substrate temperature. The flow rate measuring device according to claim 4 , wherein the flow rate of the fluid is measured based on the measurement. A plurality of the vibrators are arranged on the substrate along a flow direction of the fluid, and a flow rate and a flow direction of the fluid are measured based on a difference in a resonance frequency change between the plurality of vibrators. The flow measurement device according to claim 5, wherein

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