WO2017054730A1 - 一种薄层材料方块电阻测试方法 - Google Patents

一种薄层材料方块电阻测试方法 Download PDF

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Publication number
WO2017054730A1
WO2017054730A1 PCT/CN2016/100569 CN2016100569W WO2017054730A1 WO 2017054730 A1 WO2017054730 A1 WO 2017054730A1 CN 2016100569 W CN2016100569 W CN 2016100569W WO 2017054730 A1 WO2017054730 A1 WO 2017054730A1
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Prior art keywords
electrodes
electrode
thin layer
layer material
distance
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PCT/CN2016/100569
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English (en)
French (fr)
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张步法
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中国科学院上海硅酸盐研究所
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Priority to US15/763,961 priority Critical patent/US10495593B2/en
Publication of WO2017054730A1 publication Critical patent/WO2017054730A1/zh

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R27/00—Arrangements for measuring resistance, reactance, impedance, or electric characteristics derived therefrom
    • G01R27/02—Measuring real or complex resistance, reactance, impedance, or other two-pole characteristics derived therefrom, e.g. time constant
    • G01R27/14—Measuring resistance by measuring current or voltage obtained from a reference source
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N27/00—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means
    • G01N27/02—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance
    • G01N27/04—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance
    • G01N27/041—Investigating or analysing materials by the use of electric, electrochemical, or magnetic means by investigating impedance by investigating resistance of a solid body

Definitions

  • the present invention relates to a method for testing a sheet resistance of a conductive thin layer material, the thin layer material comprising a single layer or a plurality of layers of conductive materials, which may be metal materials, alloy materials, semiconductor materials, coating materials, and film materials, which may be It is independent or supported by a non-conductive substrate.
  • Piece resistance is one of the important electrical properties of thin-layer materials, and its accurate measurement is an important means of evaluating and monitoring semiconductor materials.
  • the same thin layer material is widely used in the manufacture of electronic devices, and its sheet resistance performance directly affects the quality of the device.
  • Thin layer metals, alloys, semiconductor materials, and conductive coating materials on substrates are used in semiconductor device fabrication and electronic circuit connections, as well as surface modification and protection of objects.
  • the probe tip is required to be hemispherical (radius 35 ⁇ - 250 ⁇ ) or flat circular section (radius 50 ⁇ - 125 ⁇ ) °
  • the potential field generated by the two end electrodes in the sample in the in-line four-probe method is inevitably affected by the two intermediate measuring electrodes.
  • This standard strictly requires a distance of 1.59 mm between adjacent probes, which limits the measurement range of the sample surface.
  • the probe current is required to be less than 100 mA. Since the shape of the probe indentation on the surface of the material to be tested is difficult to control, repeated tests are required to ensure the reliability of the measurement results. And improve measurement accuracy.
  • the in-line four-probe method is very complicated in measuring the sheet resistance of thin-layer materials, and it has high requirements on measuring instruments and operation skills, which limits its wider application.
  • the national standard "GB/T 1410-2006 solid insulating material volume resistivity and surface resistivity test method” specifies a measuring procedure and calculation method for measuring the surface resistivity of a flat material using a concentric ring electrode.
  • the technical problem to be solved by the present invention is to provide a thin
  • the layer material sheet resistance test method can improve the above-mentioned difficulties existing in the prior art, and has no limitation on the electrode diameter.
  • the larger diameter electrode can reduce the electrode/substrate interface contact resistance and the influence of electric heating on the sample surface.
  • a thin layer material sheet resistance test method of the present invention comprises: mounting two circular or circular electrodes on a surface of a thin layer material; resistance between the electrodes The measurement is performed; according to the theoretical model, the sheet resistance of the thin layer material is calculated from the measured electrical resistance between the electrodes, the diameter of each of the electrodes, and the distance between the electrodes.
  • the potential and current field distributions produced by a pair of circular or toroidal electrodes through a direct current enthalpy in a thin layer of material are calculated.
  • a method for calculating the electrical resistance in a thin layer of material between pairs of electrodes is provided, and then the sheet resistance of the thin layer material is determined by measuring this resistance.
  • the method of the present invention has no limitation on the electrode diameter, and the toroidal electrode has the same function as the circular electrode in the measurement, and the toroidal electrode may also improve the contact of the electrode edge with the thin layer material.
  • the thin layer material is a conductive material, including a metal material, an alloy material, a semiconductor material, a coating material or a film material.
  • the sheet material may comprise a single layer of material or a plurality of layers of material, and the sheet of material may be independent or supported by a non-conductive substrate.
  • the electrode may be connected between the thin layer material and the circuit, and the electrode may be connected to the surface by pressure contact, gluing, soldering, or electric welding of the surface of the electric conductor. Thin layer material.
  • the thickness of the thin layer material is uniform, preferably, the unevenness thereof is less than 1%; and the thickness of the thin layer material is much smaller than the diameter of the electrode, preferably, less than 1/10 of the minimum electrode diameter.
  • the potential and current field distribution by the circular electrode pair by the direct current ⁇ in the thin layer material is uniform in the material depth direction, and theoretical analysis can be performed in accordance with the two-dimensional field problem.
  • the planar size of the thin layer material is much larger than the distance between the electrodes, preferably greater than 10 times the distance between the electrodes, wherein the planar size includes the thin layer The length, width or diameter of the material.
  • the distance between the electrode and the edge of the thin layer material is much larger than the electrode The distance between them is preferably greater than 5 times the distance between the electrodes.
  • the planar size of the thin layer material is much larger than the distance between the electrodes, and the minimum distance between each electrode and the edge of the material is much larger than the distance between the electrodes, so that the potential and current distribution at the edge of the material are small. , the edge reflection effect can be ignored.
  • the point source model can be used to calculate the potential and current field distribution generated by the circular or circular shaped electrodes in the thin layer material.
  • the electrical conductivity of the electrode material is required to be much larger than the electrical conductivity of the thin layer material, so that the potential distribution of each electrode is uniformly the same, and the contact between the electrode and the thin layer material at the interface is required.
  • the resistance is small. That is, the contact resistance between the electrode and the electrode/thin material interface is small compared to the resistance in the thin layer material, which is negligible in the test.
  • the resistance of the electrode lead is considered to be known or small in the measurement. Therefore, the influence of the resistance in the electrode, the resistance of the electrode lead, and the contact resistance of the electrode/substrate interface is not considered in the theoretical analysis.
  • the present invention can improve the above-mentioned difficulties existing in the prior art, and there is no limitation on the electrode diameter, and the larger diameter electrode can reduce the electrode/substrate interface contact resistance and the influence of electric heating on the sample surface.
  • FIG. 1 is a schematic view showing a method for measuring the sheet resistance of a thin layer material by a circular electrode
  • FIG. 2 is a diagram showing the calculation of equipotential circles and current line distributions of two point electrodes generated by a direct current in a thin layer material using equations (1) and (4).
  • FIG. 1 is a schematic view showing a method of measuring the sheet resistance of a thin layer material by a circular electrode. Wherein the electrode as the first electrode 2
  • the radius of A and the electrode B as the second electrode 3 are r and r B ', respectively, and the distance between the centers of the two electrodes is
  • FIG. 2 is a graph showing the equipotential circle and current line distribution generated by a two-point electrode in a thin layer material by a direct current using equations (1) and (4).
  • the common points of the electrodes are calculated, and two point electrodes are assumed at the common points.
  • Select a suitable coordinate system so that the two electrodes have a common point symmetrically located on the c-axis (L 2- L ⁇ /2, 0) and ( L B I2- L ⁇ /2, 0).
  • L 4 and L s are the distances between the common points of the two electrodes and the center of the electrode A (see Equations (2) and (3) for the calculation of L n L j ).
  • Theoretical analysis found that the potential and current fields in the thin layer material outside the electrode are the same as the potential and current fields generated in the thin layer material by the two point electrodes (currently the same size) at the common point of the electrode.
  • the solid circles around the point electrodes represent equipotential lines, from large to small, their radii are 0.5 Lo, 0.25 Lo, 0.1 0.05 ⁇ and 0.01 L Q , respectively .
  • L ⁇ L S-LA is the distance between the common points (or point electrodes) of the two electrodes.
  • the dashed line represents the current line in the thin layer material, representing the path from which the current is emitted 15° apart from the two point electrode positions.
  • the density of the dotted line represents the magnitude of the current intensity.
  • the vignette shows the potential and current field distribution near the right spot electrode, indicating that the closer to the point electrode, the smaller the center of the equipotential circle deviates from the spot electrode and the more uniform the current intensity distribution in the angular direction.
  • the position of the left equipotential center on the ⁇ is - A + L B ) 12
  • the right equipotential center is at L AS - ( L A + L B ) 12
  • L A is the distance between the centers of two equipotential circles, and the equipotential circle corresponds to the edge contour of the electrode.
  • the present invention provides a thin layer material sheet resistance test method, comprising: mounting two circular or circular electrodes on the surface of a thin layer material; The electrical resistance is measured; according to the theoretical model, the sheet resistance of the thin layer material is calculated from the measured electrical resistance between the electrodes, the diameter of each of the electrodes, and the distance between the electrodes.
  • the potential and current field distributions produced by a circular or circular electrode pair in a thin layer of material by a direct current enthalpy are calculated.
  • a method for calculating the electrical resistance in a thin layer of material between pairs of electrodes is provided, and then the sheet resistance of the thin layer material is determined by measuring this resistance.
  • Method of the invention for electrode diameter no limit.
  • the thin layer material in the present invention may be a single layer or a plurality of layers of metal materials, alloy materials, semiconductor materials, coating materials and film materials, and these thin layer materials may be independent or supported by a non-conductive substrate.
  • the thickness of the thin layer material in the present invention is much smaller than the diameter of the electrode, and therefore it is considered in the invention that the potential and current field distribution generated by the circular electrode pair by the direct current ⁇ in the thin layer material is uniform in the material depth direction.
  • Theoretical analysis can be handled according to two-dimensional field problems.
  • the planar dimension of the thin layer material is much larger than the distance between the electrodes, and the closest distance between each electrode and the edge of the material is much larger than the distance between the electrodes, so that the potential and current distribution at the edge of the material are small, and the edge reflection effect can be ignored.
  • the electrical conductivity of the electrode material is required to be much larger than the electrical conductivity of the thin layer material, and the potential distribution of each electrode is uniformly the same, and the contact resistance between the electrode and the thin layer material at the interface is required to be small. . That is, the contact resistance at the electrode and the electrode/thin material interface is small compared to the resistance in the thin layer material, which is negligible in the test. Similarly, the resistance of the electrode lead is considered to be known or small in the measurement (see Figure 1).
  • an electrode refers to a connection between a thin layer of material and a circuit, including a thin layer of material and a surface of a conductor that is pressure-bonded (e.g., a probe), glued, welded, welded, and otherwise connected.
  • the left electrode A ie, the first electrode 2 on the left side in FIG. 1
  • the right electrode B ie, the second right side in FIG. 1).
  • the electrode 3) is connected to the positive electrode, and the potential distribution V in the outer layer of the electrode is V (c, 3 see equation (1) in Fig. 3.
  • L n L s is the distance between the common points of the two electrodes and the center of the electrode, which is determined by the formula (2) in FIG. 3 and the formula (3) in FIG. 3.
  • L AS is the distance between the centers of the two electrodes (see Figures 1 and 2), and the centers of the two electrodes are respectively located on the c-axis - ( L A + L s )/2 and 2 ⁇ 5 - ( 2 ⁇ + 2 ⁇ )/2.
  • equation (1) is also the potential field generated by the two spot electrodes in the thin layer of material.
  • Figure 2 shows the potential distribution (formula (1)) and current (formula (4)) generated by a direct current in a thin layer of material from two point electrodes on the c-axis.
  • the two spot electrodes are located at ( / 2 / / 2,0) and ( /2- /2,0).
  • Theoretical analysis found that the potential and current fields in the outer layer of the electrode material and the two point electrodes at the common point of the electrode (through the same amount of current) produce the same potential and current fields in the thin layer of material.
  • the solid circles surrounding the dot electrodes represent equipotential lines, which are 0.5 L from large to small. , 0.25 L. , 0.1L 0 , 0.05 LofP 0.01 Lo°
  • L 0 L B - L A .
  • the position of the center of the equipotential circle can be calculated according to equations (2) and (3).
  • the dashed line in Figure 2 represents the current line in the thin layer, representing the path from which the current is emitted 15° apart from the two point electrode position angles.
  • the dotted line density in Figure 2 represents the magnitude of the current intensity in the thin layer of material.
  • the vignette in the upper right corner of Figure 2 shows the potential and current field distribution near the right spot electrode, which indicates that the equipotential center of the circle near the spot electrode is at a small position away from the point electrode, and the current intensity near the point electrode is at an angle.
  • the distribution of directions is highly uniform.
  • the position of the left equipotential center on the _ is -( ⁇ + ⁇ )/2
  • the right equipotential center is at L AS -(L A +L s )/2
  • LA S is the distance between the centers of two equipotential circles, the equipotential circle corresponding to the edge contour of the electrode.
  • the present inventors have found that the potential and current field distribution of two circular electrodes in a thin layer of material (excluding the portion covered by the electrode) is the same as the potential and current field distribution produced by the two point electrodes through the same magnitude of direct current. .
  • the electrode on the left has a radius of 0.1 L.
  • the equipotential circle is the same size and in the same position, and the right electrode has a radius of 0.25 L.
  • the equipotential circles are the same size and in the same position.
  • the potential and current field distribution in a thin layer of material depends on the radius of the two circular electrodes, the distance between their centers, and the current passing through.
  • the current in the thin layer material is generated by the rounded edge of the electrode, the central portion of the circular electrode does not participate in the transfer of current, and the properties of the thin layer under the electrode cover do not affect the measurement results.
  • a circular electrode can be used to cover the area of individual defects (including voids, contamination, uneven thickness, etc.) present in the thin layer of material.
  • the toroidal electrode has the same function as the circular electrode in the measurement, and the use of the toroidal electrode makes it possible to improve the contact of the electrode edge with the thin layer material.
  • the thin layer material sheet resistance test method of the present invention can improve the above-mentioned difficulties existing in the prior art, and there is no limitation on the electrode diameter, and the larger diameter electrode can reduce the electrode/substrate interface contact. The effect of electrical resistance and electrical heating on the surface of the sample.

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Abstract

一种薄层材料(1)方块电阻测试方法，包括：在薄层材料(1)的表面安装二个圆形或圆环形的电极A，B；对所述电极A，B之间的电阻进行测量；根据理论模型，从测量的所述电极A，B之间的电阻、各所述电极A，B的直径和所述电极A，B之间的距离计算所述薄层材料(1)的方块电阻。该方法对电极A，B直径没有限制，且圆环形电极A，B和圆形电极A，B有相同的功能，圆环形电极A，B还可改善电极A，B边缘与薄层材料的接触。

Description

一种薄层材料方块电阻测试方法 技术领域
[0001] 本发明涉及一种导电薄层材料方块电阻测试方法， 薄层材料包括单层或多层导 电材料， 可能是金属材料、 合金材料、 半导体材料、 涂料和薄膜材料， 这些薄 层材料可能是独立的或受到非导电基片支撑的。
背景技术
[0002] 方块电阻是薄层材料的重要电性能之一， 它的精确测量是评估和监测半导体材 料的重要手段。 同吋薄层材料在电子器件制作中得到广泛应用， 它的方块电阻 性能直接影响器件的质量。 薄层金属、 合金、 半导体材料和基片上的导电涂层 材料应用于半导体器件制造和电子线路连接， 还有物体表面改性和防护。
[0003] 目前的国家标准" GB/T 14141-2009硅外延层、 扩散层和离子注入层薄层电阻的 测定直排四探针法"对测试半导体材料薄层电阻的四探针法作了详细规定， 要求 探针针尖为半球形 （半径为 35 μηι - 250 μιη) 或平的圆截面 （半径为 50 μηι - 125 μηι) °
[0004] 直排四探针法中两端电极在样品中产生的电势场不可避免地受到中间两个测量 电极的影响。 这个标准严格要求相邻探针之间距离为 1.59 mm， 限定了样品表面 的测量范围。 为了避免小探针接触点电加热对测量表面的影响， 要求探针电流 小于 100 mA, 同吋由于被测材料表面的探针压痕形状难以控制， 需要进行重复 测试以保证测量结果的可靠性和提高测量精度。 总之直排四探针法测量薄层材 料的方块电阻过程繁复， 对测量仪器及操作技能要求很高， 限制了它的更广泛 应用。
[0005] 而对于固体绝缘材料， 国家标准" GB/T 1410-2006固体绝缘材料体积电阻率和 表面电阻率试验方法 "规定了采用同心环形电极测量平板材料表面电阻率的测定 程序和计算方法。
技术问题
[0006] 鉴于现有技术中存在的上述缺陷， 本发明所要解决的技术问题在于提供一种薄 层材料方块电阻测试方法， 能够改善现有技术中存在的上述困难， 对电极直径 没有限制， 较大直径电极可以减小电极 /基片界面接触电阻及电加热对样品表面 的影响。
问题的解决方案
技术解决方案
[0007] 为了解决上述技术问题， 本发明的一种薄层材料方块电阻测试方法， 包括： 在 薄层材料的表面安装二个圆形或圆环形的电极； 对所述电极之间的电阻进行测 量； 根据理论模型， 从测量的所述电极之间的电阻、 各所述电极的直径和所述 电极之间的距离计算所述薄层材料的方块电阻。
[0008] 根据本发明， 计算由圆形或圆环形电极对通过直流电流吋在薄层材料中产生的 电势和电流场分布。 同吋提供一种计算电极对之间薄层材料中电阻的计算方法 ， 然后通过测量这个电阻测定薄层材料的方块电阻。 本发明的方法对电极直径 没有限制， 且圆环形电极在测量中和圆形电极有相同的功能， 圆环形电极还有 可能改善电极边缘与薄层材料的接触。
[0009] 又， 在本发明中， 所述薄层材料为导电材料， 包括金属材料、 合金材料、 半导 体材料、 涂料或薄膜材料。 此外， 所述薄层材料可包括单层材料或多层材料， 且所述薄层材料可以是独立的或者由非导电基片支撑。
[0010] 又， 在本发明中， 所述电极可连接于所述薄层材料和电路之间， 所述电极可通 过导电体表面受压接触、 胶粘、 焊接、 电焊的方式连接于所述薄层材料。
[0011] 又， 在本发明中， 所述薄层材料的厚度均匀， 优选地， 其不均匀度小于 1 %; 且所述薄层材料的厚度远小于所述电极的直径， 优选地， 小于最小电极直径的 1/ 10。
[0012] 根据本发明， 薄层材料中由圆形电极对通过直流电流吋产生的电势和电流场分 布在材料深度方向是均匀的，理论分析上可以按照二维场问题处理。
[0013] 又， 在本发明中， 所述薄层材料的平面尺寸远大于所述电极之间的距离， 优选 地， 大于 10倍电极之间的距离， 其中所述平面尺寸包括所述薄层材料的长、 宽 或直径。
[0014] 又， 在本发明中， 所述电极与所述薄层材料的边缘之间的距离远大于所述电极 之间的距离， 优选地， 大于 5倍电极之间的距离。
[0015] 根据本发明， 薄层材料的平面尺寸远大于电极之间的距离， 且每个电极与材料 边缘的最小距离远大于电极之间的距离， 这样在材料边缘电势和电流分布均很 小， 可以忽略边缘反射效应。
[0016] 又， 在本发明中， 可利用点源模型计算圆形或圆环形的所述电极在所述薄层材 料中产生的电势和电流场分布。
[0017] 又， 在本发明中， 要求电极材料的电导率远大于薄层材料的电导率， 所以对每 个电极它的电势分布是均匀相同的， 且要求电极和薄层材料在界面的接触电阻 很小。 即相比薄层材料中的电阻,电极中电阻和电极 /薄层材料界面的接触电阻很 小,在测试中可以忽略不计。 类似地， 测量中认为电极引线的电阻已知或很小。 所以理论分析中不考虑电极中电阻、 电极引线的电阻和电极 /基片界面接触电阻 的影响。
发明的有益效果
有益效果
[0018] 本发明能够改善现有技术中存在的上述困难， 对电极直径没有限制， 较大直径 电极可以减小电极 /基片界面接触电阻及电加热对样品表面的影响。
[0019] 根据下述具体实施方式并参考附图， 将更好地理解本发明的上述内容及其它目 的、 特征和优点。
对附图的简要说明
附图说明
[0020] 图 1为圆形电极测量薄层材料方块电阻方法示意图；
[0021] 图 2是显示利用公式 （1) 和 （4) 计算二个点电极通过直流电流在薄层材料中 产生的等势圆和电流线分布的示意图。
[0022] 符号标记：
[0023] 1， 薄层材料； 2， 电极 A (第一电极） ； 3， 电极 B (第二电极） ； 4， 电极引 线。 本发明的实施方式
[0024] 以下结合附图和下述实施方式进一步说明本发明， 应理解， 附图及下述实施方 式仅用于说明本发明， 而非限制本发明。
[0025] 图 1为圆形电极测量薄层材料方块电阻方法示意图。 其中作为第一电极 2的电极
A和作为第二电极 3的电极 B的半径分别是 r 和 r B' 二个电极中心之间的距离是
L 。
[0026] 图 2是显示利用公式 （1 ) 和 （4) 计算二个点电极通过直流电流在薄层材料中 产生的等势圆和电流线分布的图。 在二个电极中心的连线上， 计算电极的公共 点， 在公共点处假设二个点电极。 选择合适的坐标系,使得二个电极公共点对称 地位于 ;c轴上（ L 2- L Β/2, 0)和（ L BI2- L Α/2, 0)处。 这里 L 4和 L s是二个电极公 共点与电极 A中心之间的距离 （L n L j勺计算见公式 （2) 和 （3) ) 。 理论分 析发现， 电极外薄层材料中的电势和电流场与二个位于电极公共点的点电极 （ 通过同样大小的电流） 在所述的薄层材料中产生的电势和电流场相同。 环绕点 电极的实线圆圈代表等势线， 由大到小它们的半径分别是 0.5 Lo, 0.25 Lo, 0.1 0.05 ^和 0.01 LQ。 这里 L^ L S- L A是二个电极公共点 （或点电极） 之间的距离。 虚线代表薄层材料中的电流线， 代表从两个点电极位置角度相隔 15°发出电流的 路径。 虚线的密度代表电流强度的大小。 小插图显示的是右边点电极附近的电 势和电流场分布情况， 表明越靠近点电极， 等势圆圆心偏离点电极位置越小和 电流强度在角度方向的分布越均匀。 根据公式 (2)和 (3)计算， 左边等势圆圆心在 ■ 由上的位置是- A+ L B) 12, 右边等势圆圆心在 L AS- ( L A+ L B) 12, 这里 L A 是二个等势圆圆心之间的距离， 等势圆对应于电极的边缘轮廓。
[0027] 针对现有技术中的问题， 本发明提供了一种薄层材料方块电阻测试方法， 包括 ： 在薄层材料的表面安装二个圆形或圆环形的电极； 对所述电极之间的电阻进 行测量； 根据理论模型， 从测量的所述电极之间的电阻、 各所述电极的直径和 所述电极之间的距离计算所述薄层材料的方块电阻。
[0028] 根据本发明， 计算由圆形或圆环形电极对通过直流电流吋在薄层材料中产生的 电势和电流场分布。 同吋提供一种计算电极对之间薄层材料中电阻的计算方法 ， 然后通过测量这个电阻测定薄层材料的方块电阻。 本发明的方法对电极直径 没有限制。 本发明中薄层材料可以是单层或多层金属材料、 合金材料、 半导体 材料、 涂料和薄膜材料， 这些薄层材料可能是独立的或受到非导电基片支撑的
[0029] 本发明中薄层材料的厚度远小于电极的直径， 因此在此发明中认为薄层材料中 由圆形电极对通过直流电流吋产生的电势和电流场分布在材料深度方向是均匀 的， 理论分析上可以按照二维场问题处理。 薄层材料的平面尺寸远大于电极之 间的距离， 且每个电极与材料边缘的最近距离远大于电极之间的距离， 这样在 材料边缘电势和电流分布均很小， 可以忽略边缘反射效应。
[0030] 又， 本发明中要求电极材料的电导率远大于薄层材料的电导率， 对每个电极它 的电势分布是均匀相同的， 且要求电极和薄层材料在界面的接触电阻很小。 即 相比薄层材料中的电阻， 电极中电阻和电极 /薄层材料界面的接触电阻很小， 在 测试中可以忽略不计。 类似地， 测量中认为电极引线的电阻已知或很小 （见图 1
) 。 因此理论分析中不考虑电极中电阻、 电极引线的电阻和电极 /基片界面接触 电阻的影响。
[0031] 本发明中电极是指薄层材料和电路之间的连接方式， 包括薄层材料和导电体表 面受压连接 （例如探针） 、 胶粘、 焊接、 电焊和其它连接方式。
[0032] 研究发现， 当取二个电极中心连线为 c轴， 左边电极 A (即图 1中左边的第一电 极 2) 接直流电源负极， 右边电极 B (即图 1中右边的第二电极 3) 接正极吋， 电 极外面薄层材料中的电势分布 V( c，3参见图 3中的式 ( 1)。
[0033] 这里 /。是二个电极在薄层材料中通过的直流电流， ρΙ是薄层材料的方块 电阻， ρ和 分别是薄层材料的电阻率和厚度。 π=3.1416是圆周率常数。
[0034] L n L s是二个电极公共点与电极 Α中心之间的距离， 由图 3中的式 (2)和图 3中 的式 (3)决定。
[0035] 这里 Γ ^Π Γ β分别是电极 A和电极 B的半径， L AS是二个电极中心之间的距离 （ 见图 1和图 2) ， 二个电极中心分别位于; c轴上 - ( L A+ L s)/2和 2^5 - ( 2^+ 2^)/2 处。
[0036] 通过计算得到薄层材料中相对应的电流密度矢量为图 3中的式 (4)。
[0037] 这里 /和 > /分别是 ;c和 y轴单位方向。 [0038] 本发明发现公式 （1) 同样是二个点电极在薄层材料中产生的电势场。 图 2显示 由 c轴上二个点电极通过直流电流在薄层材料中产生的电势 （公式 （1) ) 和电 流 （公式 （4) ) 场分布， 二个点电极分别位于（ /2- /2,0)和（ /2- /2,0) 。 理论分析发现， 电极外薄层材料中的电势和电流场与二个位于电极公共点的 点电极 （通过同样大小的电流） 在所述的薄层材料中产生的电势和电流场相同 。 环绕点电极的实线圆圈代表等势线， 由大到小它们的半径分别是 0.5 L。, 0.25 L。 ,0.1L0, 0.05 LofP 0.01 Lo° 这里 L。是二个点电极 (即二个电极公共点) 之间的距 离， L0=LB-LA。 等势圆越大， 其圆心位置偏离点电极位置越远。 等势圆圆心的 位置可以根据公式 (2)和 (3)计算。 图 2中虚线代表薄层中的电流线， 代表从两个 点电极位置角度相隔 15°发出电流的路径。 图 2中虚线密度代表薄层材料中电流强 度的大小。 图 2右上角的小插图显示的是右边点电极附近的电势和电流场分布情 况， 它表明在点电极附近的等势圆圆心偏离点电极位置很小， 且在点电极附近 的电流强度在角度方向的分布高度均匀。 根据公式 (2)和 (3)计算， 左边等势圆圆 心在_ 由上的位置是-( ^+ ^)/2， 右边等势圆圆心在 LAS-(LA+Ls)/2， 这里 L AS是二个等势圆圆心之间的距离， 等势圆对应于电极的边缘轮廓。
[0039] 本发明发现两个圆形电极在薄层材料中 (不包括电极覆盖的部分)产生的电势和 电流场分布与两个点电极通过同样大小的直流电流产生的电势和电流场分布相 同。 例如当左边的电极与半径为 0.1 L。的等势圆同样尺寸且处于相同位置， 右边 的电极与半径为 0.25 L。的等势圆同样尺寸且处于相同位置， 当这个电极对通过与 点电极对相同的电流吋， 它将在薄层材料中 （不包括电极覆盖的部分） 产生同 样的电势和电流场分布。
[0040] 本发明发现圆形电极之间材料中电流路径是通过二个点电极的圆弧， 这些圆弧 由下面方程描述： 参见图 3中的式 (5)。
[0041] 这里 0是电流线经过左边点电极位置与 c轴之间的交角。 圆弧的圆心在 )轴上-
L。/(2to«e)处， 圆弧的半径为
Figure imgf000008_0001
[0042] 从前面的理论发现可以计算出二个电极之间薄层材料中的电阻为： 参见图 3中 的式 (6)。
[0043] 通过实验测量二个电极之间材料中的电阻 /? AS， 利用上面公式可以从测量的电 阻计算出薄层材料的方块电阻： 参见图 3中的式 (7)。
[0044] 薄层材料中的电势和电流场分布取决于二个圆形电极的半径、 它们圆心之间的 距离和通过的电流。 在理想情形下， 薄层材料中的电流由电极的圆形边缘产生 ， 圆形电极的中心部分不参与传输电流， 电极覆盖下的薄层材料性质不影响测 量结果。 因而可以利用圆形电极覆盖薄层材料存在的个别瑕疵 （包括空洞、 污 染、 厚度不均匀等） 区域。 由此进一步推断， 圆环形电极在测量中和圆形电极 有相同的功能， 且使用圆环形电极有可能改善电极边缘与薄层材料的接触。 工业实用性
[0045] 综上所述， 采用本发明的薄层材料方块电阻测试方法， 能够改善现有技术中存 在的上述困难， 对电极直径没有限制， 较大直径电极可以减小电极 /基片界面接 触电阻及电加热对样品表面的影响。
[0046] 在不脱离本发明的基本特征的宗旨下， 本发明可体现为多种形式， 因此本发明 中的实施形态是用于说明而非限制， 由于本发明的范围由权利要求限定而非由 说明书限定， 而且落在权利要求界定的范围， 或其界定的范围的等价范围内的 所有变化都应理解为包括在权利要求书中。

Claims

权利要求书
一种薄层材料方块电阻圆测试方法， 包括：
在薄层材料的表面安装二个圆形或圆环形的电极；
对所述电极之间的电阻进行测量；
根据理论模型，从测量的所述电极之间的电阻、 各所述电极的直径和 所述电极之间的距离计算所述薄层材料的方块电阻。
根据权利要求 1所述的方法， 所述薄层材料为导电材料， 包括金属材 料、 合金材料、 半导体材料、 涂料或薄膜材料。
根据权利要求 1或 2所述的方法， 所述薄层材料包括单层材料或多层材 料， 且所述薄层材料是独立的或由非导电基片支撑。
根据权利要求 1至 3中任一项所述的方法， 所述电极连接于薄层材料和 电路之间， 所述电极通过导电体表面受压接触、 胶粘、 焊接、 电焊的 方式连接于所述薄层材料。
根据权利要求 1至 4中任一项所述的方法， 所述薄层材料的厚度均匀， 优选地， 其不均匀度小于 1 %; 且所述薄层材料厚度远小于所述电极 直径， 优选地， 小于最小电极直径的 1/10。
根据权利要求 1至 5中任一项所述的方法， 所述薄层材料的平面尺寸远 大于电极之间距离， 优选地， 大于 10倍电极之间的最大距离， 其中所 述平面尺寸包括所述薄层材料的长、 宽或直径。
根据权利要求 1至 6中任一项所述的方法， 所述电极与薄层材料边缘之 间的距离远大于电极之间的距离， 优选地， 大于 5倍电极之间的最大 距离。
根据权利要求 1至 7中任一项所述的方法， 利用点源模型计算圆形或圆 环形的所述电极在所述薄层材料中产生的电势和电流场分布。
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