EN Van der Pauw method 范德堡法Wiki.docx

1、EN Van der Pauw method 范德堡法 WikiVan der Pauw method 范德堡法From Wikipedia, the free encyclopediaThe van der Pauw Method is a technique commonly used to measure the resistivity and the Hall coefficient of a sample. Its power lies in its ability to accurately measure the properties of a sample of any arb

2、itrary shape, so long as the sample is approximately two-dimensional (i.e. it is much thinner than it is wide), solid (no holes), and the electrodes are placed on its perimeter. The van der Pauw Method employs a four-point probe placed around the perimeter of the sample, in contrast to the linear fo

3、ur point probe: this allows the van der Pauw method to provide an average resistivity of the sample, whereas a linear array provides the resistivity in the sensing direction.1 This difference becomes important for anisotropic materials, which can be properly measured using the Montgomery Method, an

4、extension of the van der Pauw Method.From the measurements made, the following properties of the material can be calculated: The resistivity of the material The doping type (i.e. whether it is a P-type or N-type material) The sheet carrier density of the majority carrier (the number of majority carr

5、iers per unit area). From this the charge density and doping level can be found The mobility of the majority carrierThe method was first propounded by Leo J. van der Pauw in 1958.2Contents 1 Conditions 2 Sample preparation 3 Measurement definitions 4 Resistivity measurementso 4.1 Basic measurementso

6、 4.2 Reciprocal measurementso 4.3 Reversed polarity measurementso 4.4 Measurement accuracyo 4.5 Calculating sheet resistance 5 Hall measurementso 5.1 Backgroundo 5.2 Making the measurementso 5.3 Calculations 6 Other calculationso 6.1 Mobility 7 Footnotes 8 ReferencesConditionsThere are five conditio

7、ns that must be satisfied to use this technique:31. The sample must have a flat shape of uniform thickness2. The sample must not have any isolated holes3. The sample must be homogeneous and isotropic4. All four contacts must be located at the edges of the sample5. The area of contact of any individu

8、al contact should be at least an order of magnitude smaller than the area of the entire sample.Sample preparationIn order to use the van der Pauw method, the sample thickness must be much less than the width and length of the sample. In order to reduce errors in the calculations, it is preferable th

9、at the sample is symmetrical. There must also be no isolated holes within the sample.Some possible contact placementsThe measurements require that four ohmic contacts be placed on the sample. Certain conditions for their placement need to be met: They must be on the boundary of the sample (or as clo

10、se to it as possible). They must be infinitely small. Practically, they must be as small as possible; any errors given by their non-zero size will be of the order D/L, where D is the average diameter of the contact and L is the distance between the contacts.In addition to this, any leads from the co

11、ntacts should be constructed from the same batch of wire to minimise thermoelectric effects. For the same reason, all four contacts should be of the same material.Measurement definitions The contacts are numbered from 1 to 4 in a counter-clockwise order, beginning at the top-left contact. The curren

12、t I12 is a positive DC current injected into contact 1 and taken out of contact 2, and is measured inamperes (A). The voltage V34 is a DC voltage measured between contacts 3 and 4 (i.e. V4 - V3) with no externally applied magnetic field, measured in volts (V). The resistivity is measured in ohmsmetr

13、es (m). The thickness of the sample t is measured in metres (m). The sheet resistance RS is measured in ohms per square (/sq or ).Resistivity measurementsThe average resistivity of a sample is given by = RSt, where the sheet resistance RS is determined as follows. For an anisotropic material, the in

14、dividual resistivity components, e.g. x or y, can be calculated using the Montgomery method.Basic measurementsTo make a measurement, a current is caused to flow along one edge of the sample (for instance, I12) and the voltage across the opposite edge (in this case, V34) is measured. From these two v

15、alues, a resistance (for this example, R12,34) can be found using Ohms law:In his paper, van der Pauw showed that the sheet resistance of samples with arbitrary shapes can be determined from two of these resistances - one measured along a vertical edge, such as R12,34, and a corresponding one measur

16、ed along a horizontal edge, such as R23,41. The actual sheet resistance is related to these resistances by the van der Pauw formulaReciprocal measurementsThe reciprocity theorem 1 tells us thatTherefore, it is possible to obtain a more precise value for the resistances and by making two additional measurements of their reciprocal