范德堡法(翻译版).doc

=The van der Pauw Technique 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 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。）. 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 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。）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 densi