JP4007484B2 - Resistivity measuring method and resistivity meter - Google Patents

Description

【００１１】
（ｔは、面内等方性材料の厚さ、ｑ(Ｐ)、ｇ_BC(Ｐ)、ｇ_EF(Ｐ)は、面内等方性材料の寸法と電極探針の座標で決まる関数）
により算出することを特徴とする。
請求項２に係わる固有抵抗率計の発明では、面内等方性材料の面内方向の抵抗率ρ_ipと厚さ方向の抵抗率ρ_zとを測定する固有抵抗率計であって、一対の通電用電極探針と、二対の第１、第２の測定用電極探針とから成る６本の電極探針を有し、前記面内等方性材料の表面に接触させるプローブと、前記通電用電極探針間に電流を供給する励磁回路と、前記第１、第２の測定用電極探針間の各電位差Ｖ_BC、Ｖ_EFを検出して、その比Ｖ_EF／Ｖ_BCをＰとして、前記面内方向の抵抗率ρ_ipと厚さ方向の抵抗率ρ_zを、次式
【００１２】
【数４】

【００１３】
（ｔは面内等方性材料の厚さ、ｑ(Ｐ)、ｇ_BC(Ｐ)、ｇ_EF(Ｐ)は、面内等方性材料の寸法と探針の座標で決まる関数）
により算出する演算手段と、前記演算手段に前記関数ｑ(Ｐ)、ｇ_BC(Ｐ)、ｇ_EF(Ｐ)（面内等方性材料の寸法と探針の座標で決まる関数）及び電流値を入力する入力手段と、前記算出した面内方向の固有抵抗率ρ_ipと厚さ方向の固有抵抗率ρ_zを表示する表示手段とを備えたことを特徴とする。
【００１４】
プローブの６本の電極探針が面内等方性材料の表面に接触されて励磁回路から通電用電極探針間に電流が流れると、二対の第１、第２の測定用電極探針間に電位差Ｖ_BC、Ｖ_EFが発生する。演算手段は、これらの電位差Ｖ_BC、Ｖ_EFを入力して、入力手段から入力された面内等方性材料の厚さ、長さ、形状及び探針の位置に対して予め記憶されている関数ｑ(Ｐ)、ｇ_BC(Ｐ)、ｇ_EF(Ｐ)を読み出し、これらを使って、演算式に沿って演算処理を行い、前記面内等方性材料の面内抵抗率ρ_ip、及び厚さ方向の抵抗率ρ_zを算出して表示手段に表示する。これにより、面内等方性材料の面内方向の抵抗率ρ_ipと厚さ方向の抵抗率ρ_zを迅速に、且つ簡単に測定することができる。
【００１５】
【発明の実施の形態】
以下、本発明に係わる抵抗率測定方法を図面により詳細に説明する。
図２は、本発明に係る抵抗率測定方法の説明図である。図２において抵抗率を測定すべき材料（試料）１は、面内方向と厚さ方向の特性が異なる即ち、面内方向の抵抗率と厚さ方向の抵抗率とが異なる異方性材料、所謂面内等方性材料で、薄い直方体形状をなし、図示のように（Ｘ、Ｙ、Ｚ）座標系に置かれているものとする。そして、この面内等方性材料１のＸ軸に平行な辺１ａの長さをlx、Ｙ軸に平行な辺１ｂの長さをly、Ｚ軸方向の辺１ｃの長さ（厚さ）をｔとする。
【００１６】
材料１の表面（上面）１ｓには、例えば、辺１ａの中心を通りＹ軸方向に平行な直線La上にＹ軸方向に沿って６本の電極探針ａ、ｂ、ｃ、ｄ、ｅ、ｆが所定の間隔で一列に配置されている。これらの６本の電極探針ａ〜ｆは、各先端が被接触面としての表面１ｓに点接触している。尚、これらの電極探針ａ〜ｆの表面１ｓへの接触点を電極Ａ、Ｂ、Ｃ、Ｄ、Ｅ、Ｆで表す。
【００１７】
これら６本の電極探針のうち、一対の電極探針ａとｄが励磁電源に接続されて電流（直流電流）を流すための通電用の電極探針、二対の電極探針ｂとｃ、及び電極探針ｅとｆが電位差Ｖ_BC、及びＶ_EFを測定する測定用の電極探針とされており、一度に二つの電位差Ｖ_BC、Ｖ_EFを測定する。この材料１は、測定対象となる未知の抵抗率が、Ｘ―Ｙ平面内の抵抗率ρ_ip（＝ρ_x＝ρ_y）と、Ｚ方向の抵抗率ρ_zの二つである。そして、これらの二つの電位差Ｖ_BC、Ｖ_EFの測定値から逆解析により二つの抵抗率ρ_ipとρ_zを求める。
【００１８】
さて、図１に示すように（Ｘ、Ｙ、Ｚ）座標系に置かれた直方体の面内等方性材料１の表面１ｓに点電極ａ、ｄを介して電流を流す場合の電位分布を考える。前述したように、Ｘ―Ｙ平面内の抵抗率をρ_ip（＝ρ_x＝ρ_y）、Ｚ（厚さ）方向の抵抗率ρ_zとすると、材料１内に生じる電位分布は、電位をΦとすると、次式で表される。
【００１９】
【数５】

【００２０】
ここで、次のような座標変換を考えると、
【００２１】
【数６】

【００２２】
上式（１）は、
【００２３】
【数７】

【００２４】
のように等方性材料の電位分布を表すラプラスの方程式となる。
このとき、座標変換後の（Ｘ、Ｙ、Ｚ）座標系における抵抗率をρ'（≡ρ_u≡ρ_ｖ≡ρ_ｗ）、材料１の厚さをｔ'とおくと、夫々次式のように与えられる。
【００２５】
【数８】

【００２６】
即ち、面内等方性材料１内の電位分布は、等方性材料の電位分布の解と式（４）、式（５）のような座標変換に伴う諸量の変換式を利用して求めることができる。
等方性材料の直方体に一組の点電極を介して電流を流した場合の電位分布に関する問題はすでに解析されており、座標変換に伴う諸量の変換式と電位、Φの解を使用してＢＣ間、及びＥＦ間の電位差V_BC、V_EFを求めると次式のように表される。
【００２７】
【数９】

【００２８】
ここで、１／Ｆ_BC及び１／Ｆ_EFは、面内等方性材料１の寸法、電極の座標によって決まる係数（形状係数）である。尚、これらの係数１／Ｆ_BC及び１／Ｆ_EFは、無限級数で表される複雑な関数であり、省略する。
次に、上記電位差Ｖ_BC、Ｖ_EFから抵抗率ρ_ipとρ_zを求める。そこで、電位差Ｖ_EFのＶ_BCに対する比をＰとおくと、上式（６）、（７）は、次式で表される。
【００２９】
【数１０】

【００３０】
上式（８）において、Ｆ_BC、Ｆ_EF及びここで定義したＰは、材料１の長さlx、ly及び電極探針の座標を決めると、ｔ'のみの関数となる。これを夫々次式のように表す。
Ｆ_BC＝ｆ_BC(ｔ') 、Ｆ_EF＝ｆ_EF(ｔ') 、Ｐ＝ｐ(ｔ')
図３にこれらの関数の一例を示す。図２は、図１に示す面内等方性材料１の寸法を、lx＝ly＝100mmとし、探針ａ〜ｆをその中央部にＹ軸に平行に５mm間隔で配置する場合について、ｔ'を変数にＦ_BC、Ｆ_EF、Ｐを計算している。図３からＰの範囲を適当に選ぶことで、Ｐよりｔ'を逆に求めることができることが確認できる。即ち、ｐの逆関数が定義可能であり、この逆関数をｑとして次のように表す。
【００３１】
ｔ'＝ｑ(Ｐ) （９）
また、前式（６）、（７）をρ_ipについて解くと次式で表される。
【００３２】
【数１１】

【００３３】
ここで、ｇ_BC(Ｐ)＝ｆ_BC(ｑ(Ｐ)）、ｇ_EF(Ｐ)＝ｆ_EF(ｑ(Ｐ))である。
従って、値Ｐを上式（１０）、（１１）の何れかに代入して、面内方向の抵抗率ρ_ipを求めることが可能である。また、前式（５）をρ_zについて解けば、
【００３４】
【数１２】

【００３５】
従って、予めｔの値（材料１の厚さ）が分かっていれば、上式（１２）にｔ'、ρ_ip及びｔの値を代入して材料１のＺ軸方向（厚み方向）の抵抗値ρ_zを算出することが可能である。
図３において、ｔ'の小さな範囲では、ｆ_BC(ｔ')、ｆ_EF(ｔ')、ｐ(ｔ')は、何れもｔ'に無関係に一定の値（約2.8）となる。これは、ｔ'が或る程度小さくなると材料内の電流の流れが二次元的になるためである。また、ｔ'が大きくなるとｐ(ｔ')の変化が次第に小さくなり、ｐ(ｔ')が約1.5付近に漸近する。これは、ｔ'が電流密度の高い領域の深さに比べて十分大きくなり、材料１の表面１ｓにおける電位分布が、ｔ'＝∞の材料に電流を流したときの値に近づくためである。
【００３６】
測定可能な範囲の検討は、Ｐとｔ'の関係、ｔ'(Ｐ)とＦ_BCの関係（即ち、ＰとＦ_BCの関係）、ｔ'(Ｐ)とＦ_EFの関係（即ち、ＰとＦ_EFの関係）について行うものであるが、Ｐとｔ'の関係が最も厳しいので、これについて検討を行えば合理的である。従って、図３において測定可能な範囲を示せば、点線で囲った範囲となる。
【００３７】
図３と同じ条件における関数ｑ(Ｐ)を図４に、関数ｇ_BC(Ｐ)、ｇ_EF(Ｐ)を図５に示す。これらの関数は、順解析により求めた図３に示す関係をＰを変数に書き換えた関係であり、離散的に与えられる。図４から、関数ｑ(Ｐ)は、Ｐの値が1.6以下及び2.0以上で、図５から、関数ｇ_BC(Ｐ)、ｇ_EF(Ｐ)は、Ｐの値が1.6以下で夫々Ｐの変化に敏感となり、急激に変化している。従って、このような急激に変化する領域における前記各関数ｑ(Ｐ)、ｇ_BC(Ｐ)、ｇ_EF(Ｐ)は、逆解析には実用的ではない。
【００３８】
本発明の測定方法では、電位差Ｖ_BC、Ｖ_EF、電流値Ｉ、面内等方性材料１の厚さｔを測定して、これらの各値を前式（８）〜（１２）に代入して抵抗率を算出するものであり、測定値には、誤差が含まれることは不可避であるので、計算過程における誤差の拡大を検討しておくことが重要となる。そこで、現在の測定装置の精度を考慮して全ての測定値の相対誤差を0.1％以下と仮定して抵抗率に伝播する相対誤差の限界を求めた結果を図６に示す。図６において、Ｐの範囲を 1.53〜2.04の範囲に限定すると、抵抗率ρ_ip、ρ_zを計算するときの最終的な相対誤差の限界が共に５％以内になり、十分に実用にかなう範囲である。
【００３９】
上述した0.1％以下の測定誤差に対して抵抗率ρ_ip、ρ_zの最終的な相対誤差の限界が共に５％以内となるＰの範囲をＰの有効範囲と称することにする。図１に示す６本の探針ａ〜ｆの間隔（ピッチ）が変わると、関数ｑ(Ｐ)、ｇ_BC(Ｐ)、ｇ_EF(Ｐ)が変化するので、これに伴いＰの有効範囲も変化する。図７は、６本の電極探針ａ〜ｆの間隔を2.5mm〜10mmの範囲で変えて、その範囲の変化の結果を示す。図７に示すようにＰの有効範囲は、曲線Ｉ（Ｐ min）、II（Ｐmax）に示すように電極探針ａ〜ｆの間隔大きくなるとＰの大きい方へ移行し、且つ広くなる（曲線II）。
【００４０】
また、Ｐの有効範囲が定まると、同時にｔ'の範囲も決定される（式（９））。そこで、電極探針ａ〜ｆの間隔とｔ'の範囲の関係を図８の曲線III（ｔ'min）、IV（ｔ'max）で示す。図７に示すように電極探針ａ〜ｆの間隔が広くなると、ｔ'の範囲は厚い方向に移行し、且つ著しく広くなる（曲線IV）。
また、前式（５）に示すようにｔ'は、材料１の厚さｔと抵抗率の比ρ_z／ρ_ipの関数であり、従って、厚さｔを求めれば、ρ_z／ρ_ipの範囲が決まる。そこで、ｔ＝１、２、４、８mmとして、図７に示した結果に対してρ_z／ρ_ipの範囲を求めた結果を図８（ａ）、（ｂ）、（ｃ）、（ｄ）に示す。この図８は、0.1％の相対誤差に対して抵抗率を誤差５％以内で測定することができるρ_z／ρ_ipの範囲と電極探針ａ〜ｆの間隔の関係を示しており、測定に際して抵抗率が大凡予測できる場合には、適切な探針間隔と材料の厚さとを選択することができる。
【００４１】
上述したように本願発明の測定方法によれば、６本の電極探針を材料１の表面１ｓに押し付けて接触させるだけで、面内方向の抵抗率ρ_ipと厚さ方向の抵抗率ρ_zとを迅速且つ容易に測定することが可能である。
尚、上記実施形態においては、６本の電極探針ａ〜ｆを一直線上に一列に配置し、一対の通電用電極探針ａとｄの内側及び外側に二対の測定用電極探針ｂとｃ、ｅとｆを配置した場合について記述したが、かかる配置に限定されるものではない。即ち、測定用電極探針ｂとｃ、ｅとｆは、通電用電極探針ａとｄにより面内等方性材料１に通電したときに当該面内等方性材料１に発生する電圧を測定できればよく、従って、上記三対の電極探針ａとｄ、ｂとｃ、及びｅとｆは、所望の位置に設定すればよい。また、各一対の電極探針間の間隔も所望の間隔に設定すればよい。
【００４２】
図９は、前述した抵抗率測定方法を適用した固有抵抗率計の実施形態を示すブロック図である。図９において面内等方性材料としての材料１は、測定対象となる未知の抵抗率が、表面（Ｘ−Ｙ平面）１ｓ内の抵抗率ρ_ip（＝ρ_x＝ρ_y）と、厚さ（Ｚ軸）方向の抵抗率ρ_zの二つである。固有抵抗率計１０のプローブ（探触子）１１は、例えば、６本の電極探針１１ａ〜１１ｆが一列に所定の間隔で配列されており、各先端が材料１の表面１ｓに同時に所定の接触圧で点接触可能とされている。そして、これらの電極探針１１ａ〜１１ｆの接触点を電極Ａ〜Ｆで表す。
【００４３】
６本の電極探針１１ａ〜１１ｆのうち、一対の電極探針１１ａと１１ｄが電流を流すための通電用電極探針とされ、これらの通電用電極探針１１ａと１１ｄの、内側の一対の電極探針１１ｂと１１ｃ、外側の一対の電極探針１１ｅと１１ｆが夫々電位差を検出する測定用（検出用）の電極探針とされている。通電用電極探針１１ａと１１ｄは、励磁回路１２に接続されて材料１の電極ＡとＤとの間に電流（直流電流）Ｉを流すようになっている。測定用電極探針１１ｂと１１ｃは、電極ＢとＣとの間の電位差Ｖ_BCを検出し、測定用電極探針１１ｅと１１ｆは、電極ＥとＦとの間の電位差Ｖ_EFを検出する。これら測定用電極探針１１ｂ〜１１ｆは切換回路１３に接続されている。この切換回路１３は、後述する演算手段としてのコンピュータ１８により切換制御されて、測定用電極探針１１ｂと１１ｃ間の電位差Ｖ_BCと測定用電極探針１１ｅと１１ｆ間の電位差Ｖ_EFを選択的に（交互に）出力する。
【００４４】
入力手段としてのキーボード１４は、コンピュータ１８に各種パラメータ即ち、材料の形状（円形、正方形又は長方形）、形状に応じた寸法、探針の位置、電流値及びメモリ番号を入力する。メモリ番号とは、ユーザによって測定すべき材料の形状、寸法、探針位置及び電流値が特定している場合において、これらの情報をメモリに記憶させたときに、これらの情報の組合せについて付ける番号である。この番号を入力することで、これらの情報の入力の手間が省ける。
【００４５】
前述したように関数ｑ(Ｐ)、ｇ_BC(Ｐ)、ｇ_EF(Ｐ)は、形状係数１／Ｆ_BC、１／Ｆ_EFをｔ'について計算した結果を整理して与えられる。なお、形状係数１／Ｆ_BC、１／Ｆ_EFは、無限級数で表される関数であり、これらの計算をその都度行うと計算に長時間を要する。そこで、数種類の試料の形状、寸法と探針位置に対して予め前述した関数Ｐ、ｑ(Ｐ)、ｇ_BC(Ｐ)、ｇ_EF(Ｐ)のデータ列がコンピュータ１８のメモリ部に格納されている。これにより、コンピュータ１８は、検出した電位差Ｖ_BC、Ｖ_EFに基づいて抵抗率ρ_ip、ρ_zを迅速に演算することができる。
【００４６】
前段増幅回路１５、後段増幅回路１６は、切換回路１３から出力された電位差Ｖ_BC、Ｖ_EFを順次増幅して所定の電圧として出力する。負帰還回路１７は、前段増幅回路１５、後段増幅回路１６に接続されており、接点電圧即ち、検出された電位差Ｖ_BC、Ｖ_EF、増幅回路１５、１６の残留電圧を、負帰還を掛けて測定前の０（零）値を取るためのものである。
【００４７】
コンピュータ１８は、励磁回路１２を制御して通電用電極探針１１ａ、１１ｄに加える電流Ｉの方向を所定時間毎に電極探針１１ａ→１１ｄ、１１ｄ→１１ａへと所定回数切り換える。また、コンピュータ１８は、電極探針１１ａ〜１１ｆの材料１への接触時及び離隔時にアークの発生を防止するために、測定開始時に６本の電極探針が全て材料１の表面１ｓに接触した後に通電用電極探針１１ａ、１１ｄ間に通電させ、所定回測定後電流を遮断する。また、コンピュータ１８は、前段増幅回路１５、後段増幅回路１６の各増幅率を最適な値に切換制御して後段増幅器１６から所定の電圧を出力させる。電源回路２０は、前記各回路１２、１３、１５〜１８に所定の電源を供給する。
【００４８】
以下に動作を説明する。
コンピュータ１８は、測定に際して、測定用電極探針１１ｂと１１ｃとの間、１１ｅと１１ｆとの間を短絡させてゼロ調節する。また、通電用電極探針１１ａと１１ｄとの間の電流Ｉが０（開放時）のときに前段増幅回路１５と後段増幅回路１６の各オフセット電圧をキャンセルして、測定前のゼロを取る。
【００４９】
次いで、オペレータがプローブ１１の６本の電極探針１１ａ〜１１ｆの先端を材料１の表面１ｓに押し付けて接触させる。図１０（ａ）に示すように通電用電極探針１１ａから１１ｄに電流Ｉが流れると電極Ａ、Ｄの周りに円形状に同心的に電位が発生し、電極Ａが正電位、電極Ｄが負電位となり、電極ＢとＣ間に電位差Ｖ_BCが発生し、電極ＦとＥとの間に電位差Ｖ_EFが発生する。電極探針１１ａ〜１１ｆの間隔を変えると、同図（ｂ）に示すように電極ＢとＣ間に発生する電位差Ｖ_BC、電極ＦとＥ間に発生する電位差Ｖ_EFが変化する。尚、図１０は、材料１に発生する電位差を分かりやすく描いたものである。
【００５０】
コンピュータ１８は、切換回路１３から出力されて前段増幅回路１５及び後段増幅回路１６で増幅された電位差Ｖ_BC、Ｖ_EFを入力して、キーボード１４から入力された材料の厚さ、長さ、形状及び探針の位置に対して読み出した関数ｑ(Ｐ)、ｇ_BC(Ｐ)、ｇ_EF(Ｐ)より、前式（１０）〜（１２）に沿って演算処理を行い、材料１の面内抵抗率ρ_ip、及び厚さ方向の抵抗率ρ_zを算出する。即ち、検出した二つの電位差Ｖ_BC、Ｖ_EFから前述した逆解析の演算を実行して二つの抵抗率ρ_ipとρ_zとを算出する。コンピュータ１８は、前述したように通電用電極探針１１ａと１１ｄとの間の電流Ｉの方向を切り換えて所定回数例えば、１０回抵抗率ρ_ip、ρ_zを算出してその平均値を算出する。これにより、抵抗率ρ_ip、ρ_zを精度よく測定することが可能となる。コンピュータ１８は、この算出した面内方向の抵抗率ρ_ipと厚さ方向の抵抗率ρ_zを表示回路１９に表示すると共に、現在の形状、プローブの探針の位置を併せて補足表示する。これにより、面内等方性材料１の面内方向の抵抗率ρ_ipと厚さ方向の抵抗率ρ_zを迅速に、且つ簡単に測定することができる。
【００５１】
この固有抵抗率計は、非破壊検査の分野の機器に応用することができる。例えば、材料の内部欠陥の分布状況の評価や、材料の不均一性の管理等に応用することができる。
尚、上記実施形態においては、プローブ１１の６本の電極探針１１ａ〜１１ｆを一直線上に一列に配置し、一対の通電用電極探針１１ａと１１ｄの内側及び外側に二対の測定用電極探針１１ｂと１１ｃ、１１ｅと１１ｆを配置した場合について記述したが、かかる配置に限定されるものではない。即ち、測定用電極探針１１ｂと１１ｃ、１１ｅと１１ｆは、通電用電極探針１１ａと１１ｄにより面内等方性材料１に通電したときに当該面内等方性材料１に発生する電圧を測定できればよく、従って、上記三対の電極探針１１ａと１１ｄ、１１ｂと１１ｃ、及び１１ｅと１１ｆは、所望の位置に設定すればよい。また、各電極探針間の間隔についても所望の間隔に設定すればよい。
【００５２】
【発明の効果】
以上説明したように、請求項１の発明では、面内等方性材料の面内と厚さ方向の抵抗率を迅速に、且つ容易に測定することが可能となり、薄膜状の材料の厚さ方向の抵抗率を評価することが可能となる。
請求項２の発明では、６本の電極探針を測定すべき面内等方性材料の表面に接触させるだけで、面内方向と厚さ方向の二つの抵抗率を迅速に、且つ容易に測定することが可能となる。これにより、材料の内部欠陥の分布状況の評価や、材料の不均一性の管理等の非破壊検査の分野の機器に応用することができる。また、構成が簡単であり、取り扱いも容易である。
【図面の簡単な説明】
【図１】４探針法により異方性材料の面内方向と厚さ方向の二つの抵抗率を測定する場合の説明図である。
【図２】本発明に係る抵抗率測定方法により面内等方性材料の面内方向と厚さ方向の二つの抵抗率を測定する場合の説明図である。
【図３】図２に示す抵抗率測定方法により抵抗率を逆解析により演算する場合に使用する関数の一例を示す図である。
【図４】図３に示すｔ'とその相対誤差の拡大率を示す図である。
【図５】図３に示すＦ_BC、Ｆ_EFとその相対誤差の拡大率を示す図である。
【図６】図２に示す抵抗率測定方法における抵抗率の評価に伝播する測定誤差の説明図である。
【図７】図３に示すＰとｔ'の有効範囲と電極探針間隔との関係を示す図である。
【図８】 0.1％の測定誤差に対して抵抗率を５％以内で評価できるρ_ip／ρ_zの範囲と電極探針間隔との関係を示す図である。
【図９】本発明に係る抵抗率測定方法を用いた固有抵抗率計の実施形態を示すブロック図である。
【図１０】図９に示す固有抵抗率計による測定時における面内等方性材料に発生する電位差を分かりやすく描いた説明図である。
【符号の説明】
１ 面内等方性材料
１ｓ 表面（Ｘ−Ｙ平面）
ａ〜ｆ 電極探針
Ａ〜Ｆ 電極
ｔ 面内等方性材料の厚さ
ρ_ip 面内方向の抵抗率
ρ_z 厚み方向の抵抗率
Ｖ_BC 測定用電極探針ｂ-ｃ間の電位差
Ｖ_EF 測定用電極探針ｅ-ｆ間の電位差
１０ 固有抵抗率計
１１ プローブ
１１ａ〜１１ｆ 電極探針
１２ 励磁回路
１３ 切換回路
１４ キーボード（入力手段）
１５、１６ 増幅回路
１７ 負帰還回路
１８ コンピュータ（演算手段）
１９ 表示回路（表示手段）
２０ 電源回路[0001]
BACKGROUND OF THE INVENTION
The present invention provides two in-plane resistivity and in-plane isotropic materials such as conductive films, semiconductor wafers, magnetic films, multilayer resistive films, and other conductive in-plane isotropic materials. The present invention relates to a resistivity measurement method and a specific resistivity meter useful for evaluation.
[0002]
[Prior art]
In recent years, new materials such as conductive films, semiconductor wafers, magnetic films, and multilayer resistive films have been rapidly developed, and quick and simple evaluations have been required for the properties of these developed materials. However, the same applies to the resistivity. For example, in a conductive plastic as an electrode paper developed for capacitors, measurement of resistivity in the thickness direction has become important.
[0003]
The resistivity measurement method for isotropic materials with the same resistivity in the in-plane direction and the out-of-plane direction includes the four-terminal method and the four-probe method, which are anisotropic with different in-plane and out-of-plane characteristics. There is a Montgomery method as a method for measuring the resistivity of the sexual material.
In the 4-terminal method or 4-probe method, four electrode terminals or electrode probes arranged on a straight line are brought into contact with the sample, and a current is passed through the sample by a pair of electrode terminals or electrode probes arranged on the outside. A potential difference is measured by a pair of electrode terminals or electrode probes. In the 4-terminal method, the resistivity is calculated from the current value, the potential difference, the cross-sectional area of the sample, and the distance between the inner electrode terminals. In the 4-probe method, the resistance is calculated from the current value, the potential difference, the thickness of the sample, and the shape factor. Calculate the rate.
[0004]
When measuring the resistivity of an anisotropic material, the simplest method is to repeat the number of anisotropic main axes by the four-probe method. For example, in the resistivity measurement of an in-plane isotropic material (an anisotropic material having two different resistivity), as shown in FIG. 1, the resistivity ρ _{ip is} different in the XY plane and in the z direction. For the material 1 having (= ρ _x = ρ _y ) and ρ _z , the thin and thin samples 2 and 3 are cut out from the directions of XY and XZ, and four samples for each of these samples 2 and 3 are cut out. The resistivity ρ _ip in the in-plane direction and the resistivity ρ _z in the thickness direction are calculated by applying the electrode probe. The same applies when the four-terminal method is used.
[0005]
In the Montgomery method, a rectangular parallelepiped sample in which each side coincides with the direction of the anisotropic main axis is cut out from an anisotropic material, electrodes are arranged at four corners of one side, and a pair of electrodes arranged on one side are arranged. A potential difference is measured with a pair of electrodes arranged on opposite sides by passing an electric current. This is performed twice by rotating the electrode arrangement by 90 °, and the in-plane resistivity measured from the result and the sample dimensions is calculated (calculated).
[0006]
[Problems to be solved by the invention]
However, in the resistivity measurement method for anisotropic materials by the four-probe method, the measurement must be repeated as many times as the number of the anisotropic main axes, and it takes a lot of work to cut out the exact dimensions of the sample. There is a problem of requiring a lot of labor.
In the Montgomery method, only one sample is prepared, and the sample cutting process is reduced compared to the four-probe method. However, it is possible to prepare an accurate rectangular parallelepiped sample, attach an electrode accurately, etc. It is difficult and requires a lot of effort. In some cases, the sample dimensions must be adjusted so that the potential difference falls within the measurement range of the measurement apparatus.
[0007]
Furthermore, in any measurement method, when the thickness of the sample is thin, it is very difficult to measure the resistivity in the thickness direction, and it may be impossible depending on conditions. For example, the conductive plastic described above is extremely thin with a thickness of about several tens of μm. When the resistivity in the thickness direction is measured by the four-probe method, the sample becomes an extremely small sample, It is almost impossible to cut out the sample.
[0008]
The present invention has been made in view of the above points, and a resistivity measuring method and a specific resistance capable of quickly and easily measuring the resistivity in the in-plane direction and the thickness direction of the in-plane isotropic material. The purpose is to provide a rate meter.
[0009]
[Means for Solving the Problems]
In order to achieve the above object, in the invention of the resistivity measuring method according to claim 1, the resistivity for measuring the in-plane resistivity ρ _ip and the thickness direction resistivity ρ _z of the in-plane isotropic material. A measuring method, wherein six electrode probes comprising a pair of energizing electrode probes and two pairs of first and second measuring electrode probes are brought into contact with the surface of the in-plane isotropic material. Then, a current is passed between the energizing electrode probes, and the ratio between the potential difference V _BC generated between the first measuring electrode probes and the potential difference V _EF generated between the second measuring electrode probes. When V _EF / V _BC is P, the resistivity ρ _{ip in the in-} plane direction and the resistivity ρ _z in the thickness direction are expressed by the following equations:
[Equation 3]

[0011]
(T is the thickness of the in-plane isotropic material, q (P), g _BC (P), and g _EF (P) are functions determined by the dimensions of the in-plane isotropic material and the coordinates of the electrode probe)
It is characterized by calculating by.
The specific resistivity meter according to claim 2 is a specific resistivity meter for measuring an in-plane resistivity ρ _ip and a thickness direction resistivity ρ _{z of} an in-plane isotropic material, A probe having six electrode probes each comprising a pair of first and second measurement electrode probes, and contacting the surface of the in-plane isotropic material; Each potential difference V _BC , V _EF between the excitation circuit for supplying current between the energizing electrode probe and the first and second measuring electrode probes is detected, and the ratio V _EF / V _BC is calculated. As P, the resistivity ρ _{ip in the in-} plane direction and the resistivity ρ _z in the thickness direction are expressed by the following equation:
[Expression 4]

[0013]
(T is the thickness of the in-plane isotropic material, q (P), g _BC (P), and g _EF (P) are functions determined by the dimensions of the in-plane isotropic material and the coordinates of the probe)
, The function q (P), g _BC (P), g _EF (P) (a function determined by the dimensions of the in-plane isotropic material and the coordinates of the probe) and the current value input means for inputting a, and further comprising a display means for displaying the resistivity [rho _z of resistivity [rho _ip the thickness direction of the calculated in-plane direction.
[0014]
When the six electrode probes of the probe are brought into contact with the surface of the in-plane isotropic material and a current flows between the excitation electrode probe and the energizing electrode probe, two pairs of first and second measurement electrode probes Potential differences V _BC and V _EF are generated between them. The calculation means inputs these potential differences V _BC and V _EF and stores them in advance for the thickness, length, shape, and probe position of the in-plane isotropic material input from the input means. The functions q (P), g _BC (P), and g _EF (P) are read out, and using these, calculation processing is performed according to the calculation formula, and the in-plane resistivity ρ _ip of the in-plane isotropic material is calculated. And the resistivity ρ _z in the thickness direction is calculated and displayed on the display means. Thereby, the in-plane resistivity ρ _ip and the thickness direction resistivity ρ _z of the in-plane isotropic material can be measured quickly and easily.
[0015]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, the resistivity measurement method according to the present invention will be described in detail with reference to the drawings.
FIG. 2 is an explanatory diagram of a resistivity measuring method according to the present invention. The material (sample) 1 whose resistivity is to be measured in FIG. 2 is an anisotropic material having different in-plane characteristics and thickness-direction characteristics, that is, in-plane-direction resistivity and thickness-direction resistivity are different. It is assumed that a so-called in-plane isotropic material has a thin rectangular parallelepiped shape and is placed in the (X, Y, Z) coordinate system as shown. Then, the length of the side 1a parallel to the X axis of the in-plane isotropic material 1 is lx, the length of the side 1b parallel to the Y axis is ly, and the length (thickness) of the side 1c in the Z-axis direction. Is t.
[0016]
The surface (upper surface) 1s of the material 1 has, for example, six electrode probes a, b, c, d, e along the Y-axis direction on a straight line La passing through the center of the side 1a and parallel to the Y-axis direction. , F are arranged in a line at a predetermined interval. The tip ends of these six electrode probes a to f are in point contact with the surface 1s as a contacted surface. The contact points of the electrode probes a to f with respect to the surface 1s are represented by electrodes A, B, C, D, E, and F.
[0017]
Among these six electrode probes, a pair of electrode probes a and d are connected to an excitation power source and an energizing electrode probe for flowing a current (DC current), two pairs of electrode probes b and c. , And the electrode probes e and f are electrode probes for measurement for measuring the potential differences V _BC and V _EF , and two potential differences V _BC and V _EF are measured at a time. This material 1 has two unknown resistivity to be measured: resistivity ρ _ip (= ρ _x = ρ _y ) in the XY plane and resistivity ρ _{z in} the Z direction. Then, a two resistivity [rho _ip and [rho _z These two potential V _BC, inverse analysis from measurements of V _EF.
[0018]
Now, as shown in FIG. 1, the potential distribution when current is passed through the surface 1s of the in-plane isotropic material 1 of the rectangular parallelepiped placed in the (X, Y, Z) coordinate system via the point electrodes a and d is shown. Think. As described above, when the resistivity in the XY plane is ρ _ip (= ρ _x = ρ _y ) and the resistivity ρ _z in the Z (thickness) direction, the potential distribution generated in the material 1 is the potential. If Φ, it is expressed by the following equation.
[0019]
[Equation 5]

[0020]
Here, consider the following coordinate transformation:
[0021]
[Formula 6]

[0022]
The above formula (1) is
[0023]
[Expression 7]

[0024]
Thus, the Laplace equation representing the potential distribution of the isotropic material is obtained.
At this time, if the resistivity in the (X, Y, Z) coordinate system after coordinate transformation is ρ ′ (≡ρ _u ≡ρ _v ≡ρ _w ) and the thickness of the material 1 is t ′, As given.
[0025]
[Equation 8]

[0026]
That is, the potential distribution in the in-plane isotropic material 1 is obtained by using the solution of the potential distribution of the isotropic material and the conversion formulas of various quantities associated with the coordinate conversion such as the equations (4) and (5). Can be sought.
The problem of potential distribution when a current is passed through a rectangular parallelepiped of isotropic material through a pair of point electrodes has already been analyzed. Te between BC, and the potential difference V _BC between EF, when determining the V _EF is expressed by the following equation.
[0027]
[Equation 9]

[0028]
Here, 1 / F _BC and 1 / F _EF are coefficients (shape factors) determined by the dimensions of the in-plane isotropic material 1 and the coordinates of the electrodes. Note that these coefficients 1 / F _BC and 1 / F _EF are complicated functions represented by an infinite series and are omitted.
Next, the resistivity ρ _ip and ρ _z are obtained from the potential differences V _BC and V _EF . Therefore, when the ratio of the potential difference V _EF to V _BC is P, the above equations (6) and (7) are expressed by the following equations.
[0029]
[Expression 10]

[0030]
In the above equation (8), F _BC , F _EF and P defined here are functions of only t ′ when the length lx, ly of the material 1 and the coordinates of the electrode probe are determined. This is expressed as follows.
F _BC = f _BC (t ′), F _EF = f _EF (t ′), P = p (t ′)
FIG. 3 shows an example of these functions. FIG. 2 shows a case where the dimension of the in-plane isotropic material 1 shown in FIG. 1 is lx = ly = 100 mm, and the probes a to f are arranged in the center thereof at intervals of 5 mm parallel to the Y axis. F _BC , F _EF , and P are calculated using 'as a variable. It can be confirmed that t ′ can be obtained in reverse from P by appropriately selecting the range of P from FIG. That is, an inverse function of p can be defined, and this inverse function is represented as q as follows.
[0031]
t ′ = q (P) (9)
Furthermore, Equation (6), is expressed by the following equation is solved for [rho _ip (7).
[0032]
[Expression 11]

[0033]
Here, g _BC (P) = f _BC (q (P)) and g _EF (P) = f _EF (q (P)).
Therefore, it is possible to determine the resistivity ρ _ip in the in-plane direction by substituting the value P into any of the above formulas (10) and (11). Also, if the previous equation (5) is solved for ρ _z ,
[0034]
[Expression 12]

[0035]
Accordingly, if the value of t (the thickness of the material 1) is known in advance, the resistance of the material 1 in the Z-axis direction (thickness direction) is substituted by substituting the values of t ′, _ρip, and t into the above equation (12). The value ρ _z can be calculated.
In FIG. 3, in a small range of t ′, f _BC (t ′), f _EF (t ′), and p (t ′) are all constant values (about 2.8) regardless of t ′. This is because the current flow in the material becomes two-dimensional when t ′ is reduced to some extent. Further, as t ′ increases, the change in p (t ′) gradually decreases, and p (t ′) gradually approaches about 1.5. This is because t ′ is sufficiently larger than the depth of the region where the current density is high, and the potential distribution on the surface 1 s of the material 1 approaches the value when a current is passed through the material of t ′ = ∞. .
[0036]
Examination of the measurable range includes the relationship between P and t ′, the relationship between t ′ (P) and F _BC (ie, the relationship between P and F _BC ), and the relationship between t ′ (P) and F _EF (ie, P The relationship between P and t _EF is the most severe, and it is reasonable to examine this because it is the most severe. Therefore, if a measurable range is shown in FIG. 3, it is a range surrounded by a dotted line.
[0037]
FIG. 4 shows the function q (P) under the same conditions as FIG. 3, and FIG. 5 shows the functions g _BC (P) and g _EF (P). These functions are relationships obtained by rewriting the relationship shown in FIG. 3 obtained by forward analysis with P as a variable, and are given discretely. From FIG. 4, the function q (P) has P values of 1.6 or less and 2.0 or more, and from FIG. 5, the functions g _BC (P) and g _EF (P) have P values of 1.6 or less and P Sensitive to change and changing rapidly. Accordingly, the functions q (P), g _BC (P), and g _EF (P) in such a rapidly changing region are not practical for inverse analysis.
[0038]
In the measurement method of the present invention, the potential differences V _BC , V _EF , the current value I, and the thickness t of the in-plane isotropic material 1 are measured, and these values are substituted into the previous equations (8) to (12). Thus, the resistivity is calculated, and it is inevitable that the measurement value includes an error. Therefore, it is important to consider the expansion of the error in the calculation process. Therefore, FIG. 6 shows the result of obtaining the limit of the relative error that propagates to the resistivity assuming that the relative error of all the measured values is 0.1% or less in consideration of the accuracy of the current measuring apparatus. In FIG. 6, when the range of P is limited to the range of 1.53 to 2.04, the limits of the final relative error when calculating the resistivity ρ _ip and ρ _z are both within 5%, and the range is sufficiently practical. It is.
[0039]
The range of P in which the final relative error limits of the resistivity ρ _ip and ρ _z are both within 5% with respect to the measurement error of 0.1% or less is referred to as an effective range of P. Since the functions q (P), g _BC (P), and g _EF (P) change when the interval (pitch) between the six probes a to f shown in FIG. 1 changes, the effective range of P is changed accordingly. Also changes. FIG. 7 shows the result of changing the distance between the six electrode probes a to f in the range of 2.5 mm to 10 mm. As shown in FIG. 7, the effective range of P shifts to a larger P and becomes wider as the distance between the electrode probes a to f increases as shown by the curves I (P min) and II (Pmax) (curves). II).
[0040]
When the effective range of P is determined, the range of t ′ is also determined at the same time (formula (9)). Therefore, the relationship between the distance between the electrode probes a to f and the range of t ′ is shown by curves III (t′min) and IV (t′max) in FIG. As shown in FIG. 7, when the distance between the electrode probes af increases, the range of t ′ shifts in the thick direction and becomes significantly wider (curve IV).
Further, as shown in the previous equation (5), t ′ is a function of the ratio of the thickness t of the material 1 to the resistivity ρ _z / ρ _ip , and therefore, if the thickness t is obtained, ρ _z / ρ _ip The range of is determined. Therefore, assuming t = 1, 2, 4, and 8 mm, the results of obtaining the range of ρ _z / ρ _{ip with} respect to the result shown in FIG. 7 are the results of FIGS. 8A, 8 B, 8 C, and 8 D. ). FIG 8 shows the relationship between 0.1% relative error intervals ranging electrode probe a~f of ρ _z / ρ _ip capable of measuring the resistivity within 5% error with respect to the measurement In this case, if the resistivity can be roughly predicted, an appropriate probe interval and material thickness can be selected.
[0041]
As described above, according to the measurement method of the present invention, the resistivity ρ _ip in the in-plane direction and the resistivity ρ _{z in the} thickness direction can be obtained simply by pressing the six electrode probes against the surface 1s of the material 1 and bringing them into contact with each other. Can be measured quickly and easily.
In the above-described embodiment, six electrode probes a to f are arranged in a line on a straight line, and two pairs of measurement electrode probes b are provided inside and outside the pair of energizing electrode probes a and d. Although c, e, and f have been described, the present invention is not limited to such an arrangement. That is, the measurement electrode probes b and c, e, and f generate voltages generated in the in-plane isotropic material 1 when the in-plane isotropic material 1 is energized by the energization electrode probes a and d. Therefore, the three pairs of electrode probes a and d, b and c, and e and f may be set at desired positions. Moreover, what is necessary is just to set the space | interval between each pair of electrode probes to a desired space | interval.
[0042]
FIG. 9 is a block diagram showing an embodiment of a specific resistivity meter to which the resistivity measurement method described above is applied. In FIG. 9, the material 1 as the in-plane isotropic material has an unknown resistivity to be measured, a resistivity ρ _ip (= ρ _x = ρ _y ) in the surface (XY plane) 1 s, and a thickness. are two are (Z-axis) direction of the resistivity [rho _z. The probe (probe) 11 of the specific resistivity meter 10 has, for example, six electrode probes 11 a to 11 f arranged in a line at a predetermined interval, and each tip is simultaneously formed on the surface 1 s of the material 1 with a predetermined value. Point contact is possible with contact pressure. The contact points of these electrode probes 11a to 11f are represented by electrodes A to F.
[0043]
Of the six electrode probes 11a to 11f, the pair of electrode probes 11a and 11d is an energizing electrode probe for flowing current, and the inner pair of these energizing electrode probes 11a and 11d. The electrode probes 11b and 11c and the pair of outer electrode probes 11e and 11f are used as measurement (detection) electrode probes for detecting a potential difference. The energization electrode probes 11a and 11d are connected to the excitation circuit 12 so as to pass a current (DC current) I between the electrodes A and D of the material 1. The measurement electrode probes 11b and 11c detect a potential difference V _BC between the electrodes B and C, and the measurement electrode probes 11e and 11f detect a potential difference V _EF between the electrodes E and F. These measurement electrode probes 11 b to 11 f are connected to a switching circuit 13. This switching circuit 13 is switched and controlled by a computer 18 as arithmetic means described later, and selectively selects a potential difference V _BC between the measuring electrode probes 11b and 11c and a potential difference V _EF between the measuring electrode probes 11e and 11f. (Alternately).
[0044]
The keyboard 14 as input means inputs various parameters, that is, the shape of the material (circular, square, or rectangular), the size according to the shape, the position of the probe, the current value, and the memory number. The memory number is the number assigned to the combination of information when the shape, size, probe position and current value of the material to be measured are specified by the user and the information is stored in the memory. It is. By inputting this number, the labor of inputting such information can be saved.
[0045]
As described above, the functions q (P), g _BC (P), and g _EF (P) are given by organizing the results of calculating the shape factors 1 / F _BC and 1 / F _EF for t ′. Note that the shape factors 1 / F _BC and 1 / F _EF are functions represented by an infinite series, and it takes a long time to perform these calculations each time. Therefore, the data strings of the above-described functions P, q (P), g _BC (P), and g _EF (P) are stored in the memory unit of the computer 18 in advance for several types of sample shapes, dimensions, and probe positions. ing. As a result, the computer 18 can quickly calculate the resistivity ρ _ip , ρ _z based on the detected potential differences V _BC , V _EF .
[0046]
The pre-stage amplifier circuit 15 and the post-stage amplifier circuit 16 sequentially amplify the potential differences V _BC and V _EF output from the switching circuit 13 and output them as predetermined voltages. The negative feedback circuit 17 is connected to the preamplifier circuit 15 and the postamplifier circuit 16 and applies negative feedback to the contact voltages, that is, the detected potential differences V _BC and V _EF and the residual voltages of the amplifier circuits 15 and 16. This is for taking a 0 (zero) value before measurement.
[0047]
The computer 18 controls the excitation circuit 12 to switch the direction of the current I applied to the energizing electrode probes 11a and 11d from the electrode probes 11a to 11d and 11d to 11a every predetermined time. Further, the computer 18 contacts all the electrode probes 11a to 11f with the surface 1s of the material 1 at the start of measurement in order to prevent generation of an arc when the electrode probes 11a to 11f are in contact with the material 1 and at the time of separation. After that, current is passed between the current-carrying electrode probes 11a and 11d, and the current is cut off after a predetermined number of measurements. Further, the computer 18 controls the respective amplification factors of the pre-stage amplifier circuit 15 and the post-stage amplifier circuit 16 to be optimal values and outputs a predetermined voltage from the post-stage amplifier 16. The power supply circuit 20 supplies a predetermined power to each of the circuits 12, 13, 15-18.
[0048]
The operation will be described below.
In the measurement, the computer 18 performs zero adjustment by short-circuiting between the measurement electrode probes 11b and 11c and between 11e and 11f. Further, when the current I between the energizing electrode probes 11a and 11d is 0 (when opened), the offset voltages of the preamplifier circuit 15 and the postamplifier circuit 16 are canceled, and zero before measurement is taken.
[0049]
Next, the operator presses the tips of the six electrode probes 11 a to 11 f of the probe 11 against the surface 1 s of the material 1 to make contact. As shown in FIG. 10A, when a current I flows from the current-carrying electrode probes 11a to 11d, a potential is generated concentrically in a circular shape around the electrodes A and D, the electrode A is a positive potential, and the electrode D is A negative potential is generated, a potential difference V _BC is generated between the electrodes B and C, and a potential difference V _EF is generated between the electrodes F and E. When the distance between the electrode probes 11a to 11f is changed, the potential difference V _BC generated between the electrodes B and C and the potential difference V _EF generated between the electrodes F and E are changed as shown in FIG. FIG. 10 depicts the potential difference generated in the material 1 in an easy-to-understand manner.
[0050]
The computer 18 inputs the potential differences V _BC and V _EF output from the switching circuit 13 and amplified by the pre-stage amplifier circuit 15 and the post-stage amplifier circuit 16, and the thickness, length, and shape of the material input from the keyboard 14. And the function q (P), g _BC (P), and g _EF (P) read out with respect to the probe position, the arithmetic processing is performed according to the previous equations (10) to (12), and the surface of the material 1 The internal resistivity ρ _ip and the resistivity ρ _z in the thickness direction are calculated. That is, the above-described inverse analysis is performed from the detected two potential differences V _BC and V _EF to calculate the two resistivities ρ _ip and ρ _z . As described above, the computer 18 switches the direction of the current I between the energization electrode probes 11a and 11d, calculates the resistivity ρ _ip , ρ _z a predetermined number of times, for example, 10 times, and calculates the average value. . This makes it possible to accurately measure the resistivity ρ _ip and ρ _z . The computer 18 displays the calculated resistivity ρ _ip in the in-plane direction and resistivity ρ _z in the thickness direction on the display circuit 19 and additionally displays the current shape and the probe probe position together. Thereby, the resistivity ρ _ip in the in-plane direction and the resistivity ρ _z in the thickness direction of the in-plane isotropic material 1 can be measured quickly and easily.
[0051]
This resistivity meter can be applied to equipment in the field of nondestructive inspection. For example, the present invention can be applied to evaluation of the distribution state of internal defects of materials, management of material non-uniformity, and the like.
In the above embodiment, the six electrode probes 11a to 11f of the probe 11 are arranged in a line on a straight line, and two pairs of measurement electrodes are provided inside and outside the pair of energizing electrode probes 11a and 11d. Although the case where the probes 11b and 11c and 11e and 11f are arranged has been described, the present invention is not limited to such arrangement. That is, the measurement electrode probes 11b and 11c, 11e and 11f generate a voltage generated in the in-plane isotropic material 1 when the in-plane isotropic material 1 is energized by the energization electrode probes 11a and 11d. Therefore, the three pairs of electrode probes 11a and 11d, 11b and 11c, and 11e and 11f may be set at desired positions. Moreover, what is necessary is just to set the space | interval between each electrode probe to a desired space | interval.
[0052]
【The invention's effect】
As described above, according to the first aspect of the present invention, the in-plane and in-thickness resistivity of the in-plane isotropic material can be measured quickly and easily, and the thickness of the thin film material can be measured. It becomes possible to evaluate the resistivity in the direction.
According to the second aspect of the present invention, the two resistivity in the in-plane direction and the thickness direction can be quickly and easily achieved by simply bringing the six electrode probes into contact with the surface of the in-plane isotropic material to be measured. It becomes possible to measure. Thereby, it can apply to the apparatus of the field | area of the nondestructive inspection, such as evaluation of the distribution condition of the internal defect of material, and management of the nonuniformity of material. Further, the configuration is simple and the handling is easy.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram in the case of measuring two resistivity values in an in-plane direction and a thickness direction of an anisotropic material by a four-probe method.
FIG. 2 is an explanatory diagram in the case of measuring two resistivity values in an in-plane direction and a thickness direction of an in-plane isotropic material by the resistivity measurement method according to the present invention.
FIG. 3 is a diagram illustrating an example of a function used when the resistivity is calculated by inverse analysis using the resistivity measurement method illustrated in FIG. 2;
4 is a diagram showing an enlargement ratio of t ′ and its relative error shown in FIG. 3; FIG.
FIG. 5 is a diagram illustrating an enlargement ratio of F _BC and F _EF shown in FIG. 3 and their relative errors.
6 is an explanatory diagram of a measurement error propagated to resistivity evaluation in the resistivity measuring method shown in FIG.
7 is a diagram showing a relationship between an effective range of P and t ′ shown in FIG. 3 and an electrode probe interval. FIG.
FIG. 8 is a diagram showing a relationship between a range of ρ _ip / ρ _{z where} the resistivity can be evaluated within 5% with respect to a measurement error of 0.1% and an electrode probe interval.
FIG. 9 is a block diagram showing an embodiment of a specific resistivity meter using the resistivity measuring method according to the present invention.
10 is an explanatory diagram depicting the potential difference generated in the in-plane isotropic material at the time of measurement by the specific resistivity meter shown in FIG. 9 in an easy-to-understand manner.
[Explanation of symbols]
1 In-plane isotropic material 1s surface (XY plane)
a to f electrode probes A to F electrode t thickness of in-plane isotropic material ρ _{ip in-} plane resistivity ρ _z thickness direction resistivity V _BC potential difference V _ec between electrode probes _bc Potential difference between measurement electrode probes ef 10 Specific resistivity meter 11 Probes 11a to 11f Electrode probe 12 Excitation circuit 13 Switching circuit 14 Keyboard (input means)
15, 16 Amplifier circuit 17 Negative feedback circuit 18 Computer (calculation means)
19 Display circuit (display means)
20 Power supply circuit

Claims (2)

A resistivity measurement method for measuring an in-plane resistivity ρ _ip and a thickness direction resistivity ρ _{z of} an in-plane isotropic material,
Six electrode probes comprising a pair of energizing electrode probes and two pairs of first and second measuring electrode probes are brought into contact with the surface of the in-plane isotropic material to thereby provide the energizing electrodes. When a current is passed between the probe tips, a ratio V _EF / V _BC between a potential difference V _BC generated between the first measurement electrode probes and a potential difference V _EF generated between the second measurement electrode probes is obtained. As P, the resistivity ρ _{ip in the in-} plane direction and the resistivity ρ _z in the thickness direction are

(T is the thickness of the in-plane isotropic material, q (P), g _BC (P), and g _EF (P) are functions determined by the dimensions of the in-plane isotropic material and the coordinates of the electrode probe)
The resistivity measurement method characterized by calculating by this. An intrinsic resistivity meter that measures the resistivity ρ _ip in the in-plane direction and the resistivity ρ _{z in the} thickness direction of the in-plane isotropic material,
A probe having six electrode probes each composed of a pair of energizing electrode probes and two pairs of first and second measuring electrode probes, and contacting the surface of the in-plane isotropic material; ,
An excitation circuit for supplying a current between the energizing electrode probes;
Respective potential differences V _BC and V _EF between the first and second measurement electrode probes are detected, and the ratio V _EF / V _BC is P, and the in-plane resistivity ρ _ip and the thickness direction The resistivity ρ _z of

(T is the thickness of the in-plane isotropic material, q (P), g _BC (P), and g _EF (P) are functions determined by the dimensions of the in-plane isotropic material and the coordinates of the electrode probe)
Computing means for calculating by
Input means for inputting the functions q (P), g _BC (P), g _EF (P) (a function determined by the dimensions of the in-plane isotropic material and the coordinates of the electrode probe) and a current value to the arithmetic means; ,
A specific resistivity meter comprising: a display means for displaying the calculated resistivity ρ _ip in the in-plane direction and resistivity ρ _z in the thickness direction.

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