A comparison of two van-der-Pauw measurement configurations of resistivity

Based on the solution of an electrostatics boundary-value problem, this paper compares two van-der-Pauw-type measurement configurations of resistivity, with respect to the movement of the point-like voltage and current contacts away from the periphery of a thin, square sample. The movement involves both a reduction in the size of the contact array, without any change in its shape or orientation, and a displacement of its center. The formulas derived are applicable to any rigid displacement such that all contacts remain within the boundary of the sample, but only displacements parallel to the edges of the sample or along its diagonal are examined. Both arrays are square, with the first initially coinciding with the corners of the sample and the second initially having its corners centered on the edges of the sample. The solution indicates that the deviation from the ideal van der Pauw resistivity measurement is less sensitive to a reduction in the size of the undisplaced contact array when the first configuration is used. However, under displacements, the situation is complicated markedly by boundary effects, with the results depending on the direction of displacement and the size of the array.     

Generalization of the van der Pauw relationship derived from electrostatics

In an earlier paper, this author, along with two others Weiss et al. (2008) [1], demonstrated that the original van der Pauw relationship could be derived from three-dimensional electrostatics, as opposed to van der Pauw’s use of conformal mapping. The earlier derivation was done for a conducting material of rectangular cross section with contacts placed at the corners. Presented here is a generalization of the previous work involving a square sample and a square array of electrodes that are not confined to the corners, since this measurement configuration could be a more convenient one. As in the previous work, the effects of non-zero sample thickness and contact size have been investigated. Buehler and Thurber derived a similar relationship using an infinite series of current images on a large and thin conducting sheet to satisfy the conditions at the boundary of the sample. The results presented here agree with theirs numerically, but analytic agreement could not be shown using any of the perused mathematical literature. By simply equating the two solutions, it appears that, as a byproduct of this work, a new mathematical relationship has been uncovered. Finally, the application of this methodology to the Hall Effect is discussed.     

应用神经计算范德堡函数无需加权向量调整学习率的半导体电阻率测量方法

范德堡函数通常用于测量半导体的电阻率,但是很难得到电压测量值。如果把它表示为一个多项式,就可以获得半导体的电阻。 通常情况下,五个样本的横坐标可以为任何非线性函数提供足够的精度。因此,关键是要确定多项式的系数。我们通过用神经计算,采取五个系数作为权数,构造一个神经网络解决这个问题。最后,我们得到了范德堡函数的多项式表达。     

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.     

High field activation of micropipes in high resistivity silicon carbide

Micropipes in high resistivity (p≥5 kΩcm) SiC are highly activated in parallel electric fields (vertical devices) at room temperature starting at very low fields of 5-10 kV/cm, especially in the doped material. No activation of micropipes is observed in high fields (>100 kV/cm) perpendicular to their orientation (lateral devices). In the last case, the high field limitation is due to surface flashover phenomena taking place at 100-175 kV/cm in vacuum ambient and depending strongly on the material growth technology and the gap length. Non-ohmic behavior was not observed in lateral devices up to high applied fields. The high field characterization method is proposed as a powerful tool for the evaluation of the quality of SiC material for next-generation high voltage/high power devices.     

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 ,加快了计算速度     

斜置式方形探针测量单晶断面电阻率分布mapping技术

介绍了一种应用斜置式方形探针测量单晶断面电阻率的测试方法 ,将Rymaszewski直线探针测试方法引入到方形探针测试 ,并对测试过程中产生的游移以及图像监控问题进行了讨论 .应用此测试方法得到了 75mm的全片电阻率分布的mapping图 ,测试结果表明该方法可以在测量区域明显减小的同时保证测量的精确性 ,是一种行之有效的测量方法     

HIGH EFFICIENCY NUMERICAL SIMULATION OF RESISTIVITY TOOLS WITH DIFFERENT ELECTRODE RADII IN COMPLEX MEDIA

The Numerical Mode-Matching(NMM) method is far more efficient than the integral equation method and the finite element method, but it could not be applied to problems such as low frequency electrode-type resistivity tool with different electrode radii. In this paper, this problem is dealt with using an approximate NMM method, and the simulation of hybrid laterolog-3 tool gives very good results and the computer time is only 1% more than the traditional NMM. It is an extension of the application of NMM method.     

高纯半绝缘SiC电阻率影响因素

采用物理气相传输(PVT)法进行高纯半绝缘SiC晶体生长,利用高温真空解吸附以及在系统中通入HCl和H2的方法,有效降低了系统中N、B和Al等杂质的背景浓度。使用二次离子质谱(SIMS)对晶体中杂质浓度测试,N、B和Al浓度分别小于1×1016、1×1015和2×1014 cm-3。对加工得到的晶片进行测试,全片的电阻率均在1×1010Ω·cm以上,微管密度小于0.02 cm-2,(004)衍射面的X射线摇摆曲线半高宽为34″。结果表明,该方法可以有效降低SiC晶体中N、B和Al等杂质浓度,提升SiC晶片的电阻率。使用该方法成功制备了4英寸(1英寸=2.54 cm)高纯半绝缘4H-SiC晶体。     

In Situ Study of Nanostructure and Electrical Resistance of Nanocluster Films Irradiated with Ion Beams

An in situ study is reported on the structural evolution in nanocluster films under He⁺ ion irradiation using an advanced helium ion microscope. The films consist of loosely interconnected nanoclusters of magnetite or iron‐magnetite (Fe‐Fe₃O₄) core‐shells. The nanostructure is observed to undergo dramatic changes under ion‐beam irradiation, featuring grain growth, phase transition, particle aggregation, and formation of nanowire‐like network and nanopores. Studies based on ion irradiation, thermal annealing and electron irradiation have indicated that the major structural evolution is activated by elastic nuclear collisions, while both electronic and thermal processes can play a significant role once the evolution starts. The electrical resistance of the Fe‐Fe₃O₄ films measured in situ exhibits a super‐exponential decay with dose. The behavior suggests that the nanocluster films possess an intrinsic merit for development of an advanced online monitor for fast neutron radiation with both high detection sensitivity and long‐term applicability, which can enhance safety measures in many nuclear operations.     

钒注入制备半绝缘SiC的退火效应

对钒离子注入P型和n型4H-SiC制备半绝缘层的方法和特性进行了研究.注入层电阻率随退火温度的升高而增加,经过1 650℃退火后,钒注入p型和n型SiC的电阻率分别为1.6×1010Ω·cm和7.6×106Ω·cm.借助原子力显微镜对样品表面形貌进行分析,发现碳保护膜可以有效减小高温退火产生的表面粗糙,抑制沟槽的形成.二次离子质谱分析结果表明退火没有导致明显的钒在SiC中的再扩散.即使经过1 650℃高温退火,也没有发现钒离子向SiC表面外扩散的现象.     

Towards van der Waals Epitaxial Growth of GaAs on Si using a Graphene Buffer Layer

Van der Waals growth of GaAs on silicon using a two‐dimensional layered material, graphene, as a lattice mismatch/thermal expansion coefficient mismatch relieving buffer layer is presented. Two‐dimensional growth of GaAs thin films on graphene is a potential route towards heteroepitaxial integration of GaAs on silicon in the developing field of silicon photonics. Hetero‐layered GaAs is deposited by molecular beam epitaxy on graphene/silicon at growth temperatures ranging from 350 °C to 600 °C under a constant arsenic flux. Samples are characterized by plan‐view scanning electron microscopy, atomic force microscopy, Raman microscopy, and X‐ray diffraction. The low energy of the graphene surface and the GaAs/graphene interface is overcome through an optimized growth technique to obtain an atomically smooth low­ temperature GaAs nucleation layer. However, the low adsorption and migration energies of gallium and arsenic atoms on graphene result in cluster‐growth mode during crystallization of GaAs films at an elevated temperature. In this paper, we present the first example of an ultrasmooth morphology for GaAs films with a strong (111) oriented fiber‐texture on graphene/silicon using quasi van der Waals epitaxy, making it a remarkable step towards an eventual demonstration of the epitaxial growth of GaAs by this approach for heterogeneous integration.     

表面粗糙度的激光及相关在线测量方法

随着机械加工自动化程度的提高 ,对表面粗糙度在线测量提出了越来越高的要求。目前 ,为了提高生产效率和实现生产的自动化 ,生产过程中实时检测愈加受到重视。传统的触针测量法 ,由于测量速度和测量条件的原因 ,不适于在线检测。光学测量方法近年发展很快 ,它是一种非接触测量法。根据测量原理可以归纳为干涉测量法、聚焦测量法、散射测量法、散斑测量法四种。本文重点介绍了这些技术进行表面粗糙度在线测量的原理和目前的研究结果。并对这些方法发展前景进行了分析和预测     

大尺寸碳化硅单晶生长环境研究

针对基于物理气相输运法的碳化硅(SiC)单晶生长系统,考虑对流换热的影响建立了传热与传质数学模型,并采用数值模拟的方法研究了其生长系统内的温度场与气相流场.研究表明:坩埚内温度、温度梯度以及加热效率随线圈匝间距与线圈直径的增加而逐渐降低.旋转坩埚可有效解决因线圈螺旋形状而导致的温度场不均匀性.通过不断调整线圈与坩埚之间的相对高度,可保证高品质晶体生长所需的最优温度场环境.此外,坩埚内径尺寸的增加,会加剧其内部自然对流效应.     

Imaging of contamination on wafers using a scanning surface potential difference measurement technique

The sensitivity of the ChemetriQ^® method toward various contaminants was evaluated. Offering high resolution mapping without edge exclusion, the method based on surface work function lateral non-uniformities, i.e. the so called surface potential difference imaging (SPDI), appears to be very sensitive to traces of metals on Si wafers with native oxide. Using intentional contamination protocols and comparative methods such as total-reflection X-ray fluorescence (TXRF), different dynamics have been seen element to element. As an example, the signal for Fe and Cu contamination on Si is very strong, offering the capability to detect levels in the 10¹⁰ at/cm² range, while it is in the 10¹² at/cm² range for Al. This does not obviously agree with work function differences between Si and the metals; and the exact reason for signal variations must be further investigated. Practical results show that the method can be applied indifferently to CZ wafer front side or backside, whatever the polish finish; can be applied to silicon on insulator (SOI) wafers; and can be very useful for the control of wafer edge contamination left after deposition and further bevel and edge etch steps.     

探针尺寸对四探针法测量薄膜电阻率精度的影响

The four-probe technique is widely used in the characterization of electrical properties of solids and thin films. To investigate the influence of finite size probes with non-planar contact on the standard four-probe method, we have proposed an image method to simulate the potential distribution within the specimen. The numerical results show that for infinitely thick samples, the standard method can only provide accurate determination of resistivity （relative error below 1%） when the ratio of the average inter-electrode spacing to the diameter of the probe is greater than 3. We have also found that disregarding the probe size brings a less dominate error than that introduced by the approximate formula, when the sample＇s thickness is close to the inter-electrode spacing.     

基于双探头的新型液晶显示器响应时间测量方法的研究

为了消除背光源亮度波动对液晶显示器(LCD)响应时间测量准确性的影响,并抑制测量电路的噪声,提出了一种新的响应时间测量方法.采用双探头对LCD屏幕进行同步接触式亮度测量,其中一个探头用于监测背光源亮度的波动,通过2个探头测量结果的对比,消除背光源亮度波动对测量结果的影响.利用5点三次平滑和分段多项式拟合去除电路噪声.结果表明,使用此测量方法能够明显消除液晶背光源亮度波动对测量精度的影响,同时可以有效抑制测量中的噪声,响应时间测量误差小于±0.02 ms.     

激光冲击强化靶背面自由表面速度的全光纤光子多普勒测速法测量

用现有的光纤通信器件,搭建了全光纤光子多普勒速度测量(Photonic Doppler Velocimetry,PDV)系统;用PDV系统测量了激光冲击强化(Laser Shocking Peening,LSP)靶背面自由表面速度。提出了一种称为微分法的新的PDV数据处理方法,并证明了与传统条纹法相比,在相同的硬件条件下,不但提高了测量精度,而且扩大了测量范围。用微分法对LSP实验中的测量数据进行了处理,实现了运动初始阶段自由表面瞬时速度的精确测量,因此微分法对冲击波与轰爆波中瞬态加速过程的数据处理特别适用。