范德堡法(翻译版)

精品文档 1欢迎下载 TheThe vanvan derder PauwPauw TechniqueTechnique In order to determine both the relaxation time mean free path and the carrier density Fermi parameters a combination of a resistivity measurement and a Hall measurement is needed We discuss here the van der Pauw technique which due to its convenience is widely used in research and industry to determine the resistivity of uniform samples As originally devised by van der Pauw 5 one uses an arbitrarily shaped but simply connected i e no holes or nonconducting islands or inclusions thin plate sample containing four very small contacts placed on the periphery preferably in the corners of the plate A schematic of a rectangular van der Pauw configuration is shown in Fig 2 van der Pauw 法 精品文档 2欢迎下载 为了确定两个弛豫时间 平均自由路径 和载流子密 度 费米参数 电阻率测量和霍尔测量的组合是必 要的 我们在这里讨论的 van der Pauw 法 由于其 方便性 被广泛用于研究和行业确定均匀样品的电阻 率 最初设计由 van der Pauw 法 5 一个使用一 个任意形状的 但简单的连接 即无孔或不导电的岛 屿或夹杂物 薄板样品中含有四的非常小的接触放 在外围 最好在角落 的板 一个长方形的 van der Pauw 配置示意图如图 2 所示 The objective of the resistivity measurement is to determine the sheet resistance Van 精品文档 3欢迎下载 der Pauw demonstrated that there are actually two characteristic resistances and associated with the corresponding terminals shown in Fig 2 and are related to the sheet resistance through the van der Pauw equation 电阻率测量的目的是确定薄层电阻 van der Pauw 证实其实有两个特性电阻 如图 2 所示 与相应的终 端相关的 并通过 van der Pauw 法方程的薄层电阻 有关 2 which can be solved numerically for 这可以解 决数字 The bulk electrical resistivity can be calculated using 的体积电 阻率可以计算使用 精品文档 4欢迎下载 To obtain the two characteristic resistances one applies a dc current into contact 1 and out of contact 2 and measures the voltage 要 获得这 2 个特性电阻 一个适用于直流电流为接触 1 和接触 2 和测量电压从接触 4 接触 3 如图 2 所示 from contact 4 to contact 3 as shown in Fig 2 Next one applies the current into contact 2 and out of contact 3 while measuring the voltage 接下来 一个适用于电流接触 2 和接触 3 from contact 1 to contact 4 同时测量电 压从接触 1 接触 4 and are then The objective of the Hall measurement in the van der Pauw technique is to determine the sheet carrier density 在 van der Pauw 法霍尔 测量的目的是确定载流子密度 by measuring the Hall voltage 通过测量霍尔电压 The Hall 精品文档 5欢迎下载 voltage measurement consists of a series of voltage measurements with a constant current 霍尔电压测量由一系列的电压测量与一个 恒定电流 and a constant magnetic field 和 恒定磁场 applied perpendicular to the plane of the sample Conveniently the same sample shown again in Fig 3 can also be used for the Hall measurement 应用于样品平 面垂直 方便 同样的样品 如图 3 所示 也可用于 霍尔测量 精品文档 6欢迎下载 To measure the Hall voltage a current is forced through the opposing pair of contacts 1 and 3 and the Hall voltage 要测量霍尔电压 电流通过相对的 1 和 3 和霍尔电压来强制通过 is measured across the remaining pair of contacts 2 and 4 Once the Hall voltage is acquired the sheet carrier density can be calculated via 测量的其余两个接触 2 和 4 一旦 获得霍尔电压 可通过计算表载流子密度 The bulk