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2605 Inst & Techniques


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                                      A   G R E AT E R      M E A S U R E   O F   C O N F I D E N C E
                                                                                                                             Current
                                                                                                                             Source


                                                                                                                           Voltmeter




                                                                                                         Figure 1. Four-Point Collinear Probe


Instrumentation and
                                                                                                         Configuration

                                                                                                          = [/ln2] * [V/I] * t * k

Techniques for Measuring                                                                                 where:  =     volume resistivity (ohm-cm)


High Resistivity and Hall
                                                                                                                V=     measured voltage (volts)
                                                                                                                I =    source current (amperes)
                                                                                                                t =    sample thickness (cm)

Voltage of Semiconducting                                                                                       k =    a correction factor based on the
                                                                                                                       ratio of the probe to wafer di-


Materials
                                                                                                                       ameter and on the ratio of wafer
                                                                                                                       thickness to probe separation1.

                                                                                                         van der Pauw Resistivity
                                                                                                         Measurements
Mary Anne Tupta, Keithley Instruments, Inc.                                                                  The van der Pauw method involves ap-
                                                                                                         plying a current and measuring voltage us-




T
                                                                                                         ing four small contacts on the periphery of
          HE resistivity and Hall mobility of           conductor measurements are the four-point        a flat, arbitrarily shaped sample of uniform
          semiconducting materials are fun-             collinear probe method and the van der           thickness. This method is particularly useful
          damental properties investigated              Pauw method. There are variations in the         for measuring very small samples because
          during product and process devel-             instrumentation depending on whether the         geometric spacing of the contacts is unim-
          opment. For example, the resistiv-            material has high or low resistivity. The fo-    portant. Effects due to a sample's size, which
ity of a semiconductor device is primarily              cus of this article is on instrumentation and    is the approximate probe spacing, are irrel-
dependent on bulk doping and can affect                 measurement techniques for high resistivity      evant.
capacitance, series resistance, and threshold           semiconductor material.                              Resistivity derivation. Using this meth-
voltage. Therefore, accurate measurements                                                                od, the resistivity can be derived from a total
of these properties are essential. Measure-             Four-Point Collinear Probe Method                of eight measurements that are made around
ment techniques and instrumentation affect              for Resistivity                                  the periphery of the sample with the configu-
the level of accuracy and difficulty in con-                The most common way of measuring the         rations shown in Figure 2. Once all the volt-
ducting these tests.                                    resistivity of a semiconductor material is by    age measurements are taken, two values of
                                                        using a four-point collinear probe. This tech-   resistivity, A and B, are derived as follows:
Instrumentation Issues                                  nique involves bringing four equally spaced      A = [/ln2] * [fAt] * [(V1



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