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,...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.展开更多
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...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.展开更多
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...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.展开更多
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 a...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.展开更多
For plane singly-connected domains with insulating boundary and four point-sized contacts, C<sub>0</sub> …C<sub>3</sub>, van der Pauw derived a famous equation relating the two trans-...For plane singly-connected domains with insulating boundary and four point-sized contacts, C<sub>0</sub> …C<sub>3</sub>, van der Pauw derived a famous equation relating the two trans-resistances R<sub>01,23</sub>, R<sub>12,30</sub> 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.展开更多
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 perform...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.展开更多
经由磁控溅射生长的金属薄膜,其电阻率是反映所选取薄膜材料性和性能评估的重要依据。为得到高精度的薄膜电阻率,采用由Pt制备的薄膜电阻进行测试研究,通过范德堡(Van der Pauw)函数的反演优化四线法设计了测试系统,采用交/直流四线方...经由磁控溅射生长的金属薄膜,其电阻率是反映所选取薄膜材料性和性能评估的重要依据。为得到高精度的薄膜电阻率,采用由Pt制备的薄膜电阻进行测试研究,通过范德堡(Van der Pauw)函数的反演优化四线法设计了测试系统,采用交/直流四线方式在该系统上进行实验数据采集。实验结果表明:范德堡修正因子f可以匹配0.7以下的值,增大了系统测试的适用范围;直流四线法更容易受到失调电压和测试电流大小的影响,交流四线法的抗干扰能力优于直流四线法。为了评定系统测试的准确性,将交流四线法测量的结果与美国吉时利生产的Keithley-2400源表和Keithley-2182A纳伏表测量的结果进行对比,其相对误差小于1.92%,为精密薄膜制备的均匀性检测领域提供重要参考,具有实际的应用价值。展开更多
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 express...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.展开更多
After Cornelius de Pauw,one of the most eminent representatives of the European Enlightenment,had published the second volume of his Recherches philosophiques sur les Américains,which in many ways was even more p...After Cornelius de Pauw,one of the most eminent representatives of the European Enlightenment,had published the second volume of his Recherches philosophiques sur les Américains,which in many ways was even more provocative than the first,a violent debate arose in Berlin,spreading quickly to a number of European countries and especially overseas.There is good reason to identify the first phase of this dispute as the Berlin Debate about the New World,especially when considering that Brandenburg and Prussia had been active colonists and had attempted to secure their share in the European move towards expansion.Was it a coincidence that,in 1769,of all places,this debate entered the heated phase of international dispute about the New World in the Prussian capital,which—after all—was a tranquil and idyllic spot compared to Paris,Amsterdam,or London?Certainly,as King of Prussia,Frederick II was the type of leader who made it clear that he was planning to write new music for the symphony of great political powers.From the beginning,the Prussian King was aware of the far-ranging political dimensions of his most-famous operatic project Montezuma.As he told Francesco Algarotti as early as October 1753,he was aiming to send a precise and memorable political message.Is it possible to understand the libretto from Frederick’s royal hands,the performance of“his”opera with Carl Heinrich Graun’s music,Giuseppe Galli Bibiena’s stage architecture,Giovanna Astrua’s arias,and hundreds of other people involved as a prelude to the Berlin Debate about the New World,which had led to heated discussion in the worldwide République des Lettres since the late 1760s?展开更多
文摘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.
基金supported by the Science Fund from the Ministry of Science and Technology of China(Grant No.2013CBA01600)the National Key Research&Development Project of China(Grant No.2016YFA0202300)+1 种基金the National Natural Science Foundation of China(Grant Nos.61474141,61674170,61335006,61390501,51325204,and 51210003)the Chinese Academy of Sciences(CAS) and Youth Innovation Promotion Association of CAS(Grant No.20150005)
文摘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.
文摘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.
文摘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.
文摘For plane singly-connected domains with insulating boundary and four point-sized contacts, C<sub>0</sub> …C<sub>3</sub>, van der Pauw derived a famous equation relating the two trans-resistances R<sub>01,23</sub>, R<sub>12,30</sub> 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.
基金supported by the National Natural Science Foundation of China (51772043 and 51802036)the Open Foundation of National Engineering Research Center of Electromagnetic Radiation Control Materials (ZYGX2017K003-3)+2 种基金Sichuan Science and Technology Program (2018GZ0434)the support from the Shenzhen Peacock Plan (1208040050847074)the Office of Naval Research (ONR) support Grant (NAVY N00014-17-1-2973)
文摘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.
文摘经由磁控溅射生长的金属薄膜,其电阻率是反映所选取薄膜材料性和性能评估的重要依据。为得到高精度的薄膜电阻率,采用由Pt制备的薄膜电阻进行测试研究,通过范德堡(Van der Pauw)函数的反演优化四线法设计了测试系统,采用交/直流四线方式在该系统上进行实验数据采集。实验结果表明:范德堡修正因子f可以匹配0.7以下的值,增大了系统测试的适用范围;直流四线法更容易受到失调电压和测试电流大小的影响,交流四线法的抗干扰能力优于直流四线法。为了评定系统测试的准确性,将交流四线法测量的结果与美国吉时利生产的Keithley-2400源表和Keithley-2182A纳伏表测量的结果进行对比,其相对误差小于1.92%,为精密薄膜制备的均匀性检测领域提供重要参考,具有实际的应用价值。
文摘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.
文摘After Cornelius de Pauw,one of the most eminent representatives of the European Enlightenment,had published the second volume of his Recherches philosophiques sur les Américains,which in many ways was even more provocative than the first,a violent debate arose in Berlin,spreading quickly to a number of European countries and especially overseas.There is good reason to identify the first phase of this dispute as the Berlin Debate about the New World,especially when considering that Brandenburg and Prussia had been active colonists and had attempted to secure their share in the European move towards expansion.Was it a coincidence that,in 1769,of all places,this debate entered the heated phase of international dispute about the New World in the Prussian capital,which—after all—was a tranquil and idyllic spot compared to Paris,Amsterdam,or London?Certainly,as King of Prussia,Frederick II was the type of leader who made it clear that he was planning to write new music for the symphony of great political powers.From the beginning,the Prussian King was aware of the far-ranging political dimensions of his most-famous operatic project Montezuma.As he told Francesco Algarotti as early as October 1753,he was aiming to send a precise and memorable political message.Is it possible to understand the libretto from Frederick’s royal hands,the performance of“his”opera with Carl Heinrich Graun’s music,Giuseppe Galli Bibiena’s stage architecture,Giovanna Astrua’s arias,and hundreds of other people involved as a prelude to the Berlin Debate about the New World,which had led to heated discussion in the worldwide République des Lettres since the late 1760s?
