基于Van Der Pauw原理的溶液电导率计

为实现对于电导率的准确测量,研究Van Der Pauw原理及其应用于电导率绝对测量的理论依据,设计径轴二维可调的四电极结构.分析电极的对称性、电导池的封闭性对测量结果的影响,实验结果证明对称性好、结构封闭的Van Der Pauw法电导率计,对溶液电导率具有较高的测量精度,并能够实现绝对测量.基于Van Der Pauw法的电导池常数κ仅与电极长度有关的原则,设计几种不同电极长度的电极,开展多种不同电导率溶液的测量实验,得出不同电导池常数κ的最佳测量范围.运用电导池常数为0.1cm-1的电极,对电导率为20~500μS/cm内的多个实际水样进行测量,相对误差小于1.0%.结果表明该新型电导率测量方法具有很好的应用前景和推广价值.

Direct measurements of conductivity and mobility in millimeter-sized single-crystalline graphene via van der Pauw geometry

We report the direct measurements of conductivity and mobility in millimeter-sized single-crystalline graphene on SiO2/Si via van der Pauw geometry by using a home-designed four-probe scanning tunneling microscope（4P-STM）. The gate-tunable conductivity and mobility are extracted from standard van der Pauw resistance measurements where the four STM probes contact the four peripheries of hexagonal graphene flakes, respectively. The high homogeneity of transport properties of the single-crystalline graphene flake is confirmed by comparing the extracted conductivities and mobilities from three setups with different geometry factors. Our studies provide a reliable solution for directly evaluating the entire electrical properties of graphene in a non-invasive way and could be extended to characterizing other two-dimensional materials.

Simple Proofs of Upper and Lower Envelopes of Van Der Pauw’s Equation for Hall-Plates with an Insulated Hole and Four Peripheral Point-Contacts

For plane singly-connected domains with insulating boundary and four point-sized contacts, C0 …C3, van der Pauw derived a famous equation relating the two trans-resistances R01,23, R12,30 with the sheet resistance without any other parameters. If the domain has one hole van der Pauw’s equation becomes an inequality with upper and lower bounds, the envelopes. This was conjectured by Szymański et al. in 2013, and only recently it was proven by Miyoshi et al. with elaborate mathematical tools. The present article gives new proofs closer to physical intuition and partly with simpler mathematics. It relies heavily on conformal transformation and it expresses for the first time the trans-resistances and the lower envelope in terms of Jacobi functions, elliptic integrals, and the modular lambda elliptic function. New simple formulae for the asymptotic limit of a very large hole are also given.

Study of Copper Thin Films Resistivity by Using Van der Pauw Method at Low Frequencies

The objective of this work research is the use of four-point measurements and so-called Van Der Pauw methods in measuring the resistivity of copper thin films widely used in the manufacture of planar components such as inductor and others. Aligned configuration and square configuration are commonly used to measure thin films resistivity before use. But differences in values between the two configurations according to frequency and thickness were observed according to the authors. Measurements with both configurations on the same thin films must make it possible to know measurements evolution as a function of frequency and thickness. The observation of measuring frequency ranges of each configuration and the minimum thicknesses to have solid copper resistivity are the main contributions of the paper. This electrical characterization is carried out on copper thin films deposited on alumina substrates (50 mm × 20 mm × 635 μm) using RF sputtering technique. Copper thin films with various thicknesses (3.3 μm, 3.6 μm and 5.2 μm) were characterized. Low-frequency electrical characterization of these thin films was performed by four-point measurement method and using an HP 4284A type LCRmeter over the frequency range of 20 Hz to 1 MHz. Van der Pauw’s method was used to calculate resistivity. These studies allowed us to know influence of measurement configurations and influence of parameters such as frequency and thickness of the copper thin films on resistivity.

A Theoretical Study on Van Der Pauw Measurement Values of Inhomogeneous Compound Semiconductor Thin Films

The influence of intermixing heterogeneous regions that have different electrical properties from the base materials on van der Pauw measurement values was theoretically studied by computer simulation using the finite-element method. The measurement samples selected were thin films of inhomogeneous semiconductors. Calculated electrical properties, such as resistivity, carrier density, and mobility of the thin films, varied in predictable ways when heterogeneous regions were dispersed in wide ranges over the samples. On the other hand, the mobility of the thin films showed a different change when heterogeneous regions were locally concentrated in the measurement samples.

Neurocomputing van der Pauw function for the measurement of a semiconductor's resistivity without use of the learning rate of weight vector regulation

Van der Pauw＇s function is often used in the measurement of a semiconductor＇s resistivity. However, it is difficult to obtain its value from voltage measurements because it has an implicit form. If it can be expressed as a polynomial, a semiconductor＇s resistivity can be obtained from such measurements. Normally, five orders of the abscissa can provide sufficient precision during the expression of any non-linear function. Therefore, the key is to determine the coefficients of the polynomial. By taking five coefficients as weights to construct a neuronetwork, neurocomputing has been used to solve this problem. Finally, the polynomial expression for van der Pauw＇s function is obtained.

A general and simple method for evaluating the electrical transport performance of graphene by the van der Pauw–Hall measurement

Expected for many promising applications in the field of electronics and optoelectronics, a reliable method for the characterization of graphene electrical transport properties is desired to predict its device performance or provide feedback for its synthesis.However, the commonly used methods of extracting carrier mobility from graphene field effect transistor or Hall-bar is time consuming, expensive, and significantly affected by the device fabrication process other than graphene itself.Here we reported a general and simple method to evaluate the electrical transport performance of graphene by the van der Pauw–Hall measurement.By annealing graphene in vacuum to remove the adsorbed dopants and then exposing it in ambient surroundings, carrier mobility as a function of density can be measured with the increase of carrier density due to the dopant re-adsorption from the surroundings.Further, the relationship between the carrier mobility and density can be simply fitted with a power equation to the first level approximation, with which any pair of measured carrier mobility and density can be normalized to an arbitrary carrier density for comparison.We experimentally demonstrated the reliability of the method, which is much simpler than making devices and may promote the standard making for graphene characterization.

交/直流薄膜方块电阻测试系统设计与分析

四探针法测量薄膜方块电阻具有测量精度高、稳定性好等优点,被广泛应用于薄膜器件制备、半导体微区掺杂等领域。为了提高薄膜方块电阻的测试速度及精度,以改进的范德堡法原理为基础,采用压控电流源方式输出稳定的电流,利用LabVIEW软件搭建了一套能使用交/直流测量薄膜方块电阻的测试系统。为了验证该测试系统的合理性及测试速度,选取Pt金属薄膜作为被测样品进行方块电阻的测量。测试结果表明,直流法和交流法都能精确测量薄膜方块电阻,直流法和交流法的单次测试时间分别为0378 s和0317 s,系统的测试速度优于商用280SI半导体设备。交流法测试Pt金属薄膜方块电阻的抗干扰能力比直流法强。该系统为被测样品选取合适的测试电流和测试方法提供了参考,对薄膜样品进行变温电阻率连续测量具有重要意义。

范德堡方法在ZnO薄膜测试中的应用

近年来 ,随着对宽禁带半导体材料 ,氧化锌薄膜研究的快速发展 ,对其电学性质的研究也显得尤为重要。主要介绍范德堡方法在ZnO薄膜电学性质测量中的应用 。

利用多项式拟合规范化方法实现范德堡函数的高精度反演

薄层电阻是IC生产过程中在线工艺监控测试的项目之一 ,其中经常使用范德堡法和Rymaszewski法作为普通四探针法的补充方法 .应用这两种测试方法时必须要用到范德堡函数 ,而已知的范德堡公式是隐函数 ,只见报道其显函数的近似表达式 ,精度低 ,未见到有精确的多项式拟合公式 .为此 ,本文利用非线性反演和规范化拟合的办法给出了范德堡函数的多项式形式 ,其精度可达到± 0 19% 。

基于范德堡法的非饱和土电阻率测试方法

电阻率法是实现无干扰土体压实度及水分迁移测试的一种有效方法。范德堡法(vdP法)广泛应用于半导体等材料的电阻率测量领域,有较高的精度,将该方法引入非饱和土电阻率测试,研发了一种只接触土体表面而不破坏土体结构的土体电阻率测试装置及方法,装置由钛电极片、交流恒流源、电压采集及数据处理系统4部分组成。采用此装置对某粉黏土的电阻率进行了测试研究,验证了电极尺寸、试样高度以及温度对于测试精度的影响;测试了不同含水率、压实度下土体电阻率的变化规律,试验表明所提供的测试方法具有精度高、测试稳定、对土样无干扰等优点。

非饱和粉土路基内水分迁移规律试验研究

动载作用下非饱和粉土路基内部的水分迁移规律,对研究重载铁路在浸水状态下的路基稳定具有重要意义。基于范德堡原理,利用土样的电阻率特性,研制出一套基于GDS动三轴仪的非饱和土样含水率分布规律测试系统。利用该系统开展浸水动三轴试验,并对试验过程中非饱和试样的分层含水率进行连续测试,探究土样的初始压实度、动载的动应力幅值对非饱和土样内部水分迁移的影响规律。结果表明:该测试系统可在动三轴试验过程中对非饱和试样的分层含水率进行实时、无损、连续地测定,测试结果的最大误差为0.7%;非饱和土样在动载作用下随其含水率逐渐增大,土样的初始压实度对电阻率的影响程度减弱,接近饱和含水率时可忽略;土样初始压实度、含水率与土体电阻率具有确定的函数表达式,并具有良好的相关性及唯一性。结合试验结果分析认为:降雨及动荷载共同作用下,路基内水分在某一深度土体积聚,该区域孔隙水压力增大,强度降低,导致翻浆冒泥病害的发生;路基压实度及列车轴重增大,均会抑制路基内水分向下部迁移,有助于路基的稳定,但轴重增加,可能导致路基的失稳,当轴重大于临界动应力时,路基将发生破坏。

微区薄层电阻四探针测试仪及其应用

用斜置的四探针方法 ,依靠显微镜观察 ,将针尖置于微区图形的四个角区 ,用改进的范德堡公式可以得到微区的薄层电阻。文中对测准条件作了分析。并用该仪器测定了硼扩散片的薄层电阻分布。在测试过程中应用微处理器 。

MOCVD生长GaN:Si单晶膜的研究

获得高质量的ｎ型ＧａＮ单晶膜是制作ＧａＮ基光电子器件的关键之一。采用立式ＭＯＣＶＤ系统生长ＧａＮ：Ｓｉ单晶膜，通过优化生长工艺，获得了电子载流于浓度高达２ ×１０１９ｃｍ－３，迁移率达１２０ｃｍ２／Ｖ·ｓ的ｎ型ＧａＮ：Ｓｉ单晶膜；并有效地抑制了ＧａＮ中由深能级引起的黄带发射，大大提高带边发光强度。研究结果还表明：随着Ｓ掺杂量的增大，ＧａＮ：Ｓｉ单晶膜的电子载流于浓度增加，迁移率下降，Ｘ光双晶衍射峰半高宽增大。首次报道了随掺Ｓ量增大，ＧａＮ：Ｓｉ单晶膜的生长速率显著下降的现象。

基于范德堡法的溶液电导率绝对测量方法

将范德堡电阻率测量方法用于溶液电导率的测量中，设计了封闭式四电极电导池；测量系统采用交流微电流源提供激励信号，对响应信号进行放大与处理，通过微机系统实现与上位机的通信与控制。研究了范德堡法电导率测量的影响因素，通过对标准溶液的测量，验证了该方法测量范围可达0～40 mS／cm、测量误差控制在±1％，可以作为电导率基准测量方法。

绝对法纯水电导率测量系统研究

为实现对于纯水电导率的准确测量,研究了基于范德堡原理的电导率绝对测量方法,设计了封闭式四电极电导池,构建了一套封闭恒温的纯水电导率测量系统。通过实验进行测量精度分析,并评定了该测量系统的不确定度,证明该方法在纯水电导率测量领域能作为基准方法使用,具有较高的精度以及可溯源性。

基于虚拟仪器的薄膜电阻率测量系统设计

基于虚拟仪器技术及Rymaszewski四探针双电测组合法设计了薄膜电阻率自动化测量系统.在虚拟仪器软件LabVIEW和数字量输出模块NI 9401的控制下,利用基于CD4052芯片的接口电路实现电流探针、电压探针的自动切换,并通过LabVIEW程序控制Keithley 2400数字源表实现两次电压测量;同时根据两次电压测量结果由LabVIEW程序完成范德堡修正因子和方块电阻的计算;最终实现薄膜电阻率自动测量、记录和显示.试验结果表明,所设计的自动测量系统不仅可以满足多种薄膜电阻率测量要求,而且提高了测量精度和自动化程度,同时精简了薄膜电阻率测量过程.

热退火对电子束蒸镀方法制备的ZnO:Al薄膜光电性质的影响

采用电子束蒸镀方法在Si(100)衬底上沉积了ZnO:Al(ZAO)薄膜.在氧气气氛下对ZnO:Al薄膜进行了退火处理,退火温度的范围为400～800℃.X射线衍射(XRD)图样表明所制备的ZnO:Al薄膜具有六方结构,为c轴(002)择优取向的多晶薄膜.用Van der Pauw法测量了ZAO薄膜的电学特性,结果显示其电导率在500℃达到最大值.测量了ZAO薄膜的室温微区光致发光和变温发光光谱,观测到了ZnO自由激子、束缚在中性施主中心(D0)上的束缚激子以及束缚在离化施主中心(D+0)上的束缚激子发射.

无学习率权值调整神经计算法拟合范德堡多项式

提出了一种新的神经计算的方法,其最大的特点是在进行特定的权值调整时无须加入学习率。计算开始时先给出一组随机的权值作为被拟合多项式的系数,由这组权值得到的拟合点上被拟合多项式值与期望值的各误差绝对值之和。依据其小分数的负值直接来调整权值,使各误差之绝对值不断减小,通过反复迭代计算,最终当各误差都在规定范围内时便得到期望的权值。在实际的计算中利用这种方法进行曲线拟合能方便地求出拟合多项式的系数,便于编程,简化了计算过程。将这种方法应用到范德堡函数的多项式拟合中,得到了范德堡函数f=1+0.03237714η-0.04037678η2+0.00857881η3-0.00077693η4+0.00002604η5并画出了曲线。

利用范德堡法在金刚石对顶砧中精确测量样品电阻率

利用有限元分析方法(FEA)对金刚石对顶砧(DAC)中范德堡法测量极微小样品电阻率的误差进行数值模拟与分析,结果表明,对于极微小样品,电极与样品的接触面积是影响电阻率精确测量的重要因素,测量误差随接触面积的增大而增大,对半导体材料尤其明显.当样品厚度与直径的比值小于0.45,且电极和样品的接触面边长与样品直径的比值小于0.1时,测量电极是否满足点接触条件,范德堡法均能给出精确的测量结果.