**Hello dears,**

_Continuing with the electrical characterization, I will give a brief summary on the electrical resistivity measurements, with the help of the ASTM (American Society of Testing Materials) which are the standards to characterize materials, and in turn an advanced guide for laboratory. As mentioned in the previous article, knowing the electrical resistivity of a semiconductor compound is very important, since by means of this technique it is possible to verify what behavior the material has, that is, whether it is conductive, semiconductor or insulating. Important for future technological applications._

_Now I will explain the bar method of 2 probes and 4 probes, in summary form, to finally develop the equations that are needed to determine the electrical resistivity of a material._

## _**Two contact method:**_

The sample to be characterized must have a bar or strip shape, the ratio between the length and the largest transverse dimension of the sample should not be less than 3 to 1 cm. The cross section of the sample must be clean, homogeneous and uniform, so that it is easier to take the measurements, and not that there are errors in the results. Before measuring, you should check if the contacts are ohmic [see here](https://steemit.com/steemstem/@carloserp-2000/electrical-characterization-of-a-semiconductor-compound-part-2-electrical-resistivity-as-function-of-the-temperature-four-probe).

<center> https://steemitimages.com/DQmXKD7icSBZzosYfTJp9hVrtHYbrRDQ6RKjXoPmWNiZip9/image.png
_Figure 1. Experimental disposition of the sample for the two-contact method [1]._ </center>

_**In Figure 1 we can see how is the sample of the material, and how to place the contacts on the surface of the sample (the contacts should be very thin copper wire). Where _V_ is the voltage and _I_ the current.**_

## _**Four contact method:**_

In this case a flat sample surface is required, for the contacts in the sample can be of any size or shape that approximates a semi-infinite solid. The conditions for a semi-infinite solid approximate 2% when the thickness of the sample and the distance from any probe to the nearest edge are at least four times the spacing of the probe.

<center> https://steemitimages.com/DQmcAXCEfgmAYpnkas7a4ux7EuVA4radgkPTf9upLQRdfR8/image.png
_Figure 2. Experimental disposition of the sample for the method of four contacts [1]._ </center>

_**In Figure 2 we can see how is the sample of the material and how to place the contacts on the surface of the sample (the contacts should be very thin copper wires). Where _V_ is the voltage, _I_ the current, _H_ the height, _L_ distance between the contacts and finally _W_ width of the sample.**_

_**It should be noted that in [the previous publication](https://steemit.com/steemstem/@carloserp-2000/electrical-characterization-of-a-semiconductor-compound-part-2-electrical-resistivity-as-function-of-the-temperature-four-probe). explain how to determine the electrical resistivity as a function of temperature, and also show the equation that should be used for this method.**_

_If the sample has a circular cross section and has a thickness greater than one, but less than four, multiplied by the spacing of the probe, measure the thickness and diameter as follows:_

* Measure and record five thickness values, https://steemitimages.com/DQmPxHhXM3vkLrpwCo4vMFikCt62uNoBWPkHth5rrShfcVE/image.png, at several points near the center of the sample, then calculate and record the average thickness, _w_ :

<center> https://steemitimages.com/DQmR91ifzWMfBQbGPSjyTY1f9AhxtrGBcwE5vhZQ2Ydo1Qw/image.png </center>

* Measure and record three values of the diameter of the sample, https://steemitimages.com/DQmZzMeX2FfHpjqvJoiNm295Cj5pSpPeqjgbcscX6SGz9gP/image.png, calculate and record the average diameter, _D_ :

<center> https://steemitimages.com/DQmPvTrP1jhLaJTi9aXHzdPwwVAcxY5y4ATPp3QtMxbxCu9/image.png </center>

* The surface on which the electrical resistivity is determined for any of the 2 methods will be cleaned or polished with a liquid called "alumina", this liquid is special to make the materials shine so that they look cleaner and their measurements are accurate. Then the measurement will be made thereafter without unnecessary delays. The sample should not show surface cracks or other observable defects with normal vision and should be free of rust on the surface

## **Process:**

Then to perform the experiment you must first measure and record the ambient temperature, then keep the sample at this temperature for a sufficient time to reach equilibrium.

_" The time required for the balance of a sample depends on the mass of the sample. For small samples, 30 minutes to 1 hour should be enough. For large ingots, 1 to 2 days may be required. "_

### _**For the method of two contacts or probes:**_

* Measure the cross-sectional area of the sample.

* Connect the power cables of the electrical circuit, and measure the ends of the sample, place the contacts on the eroded surface, and adjust the current so that the electric field in the sample does not exceed 1 V / cm.

* Measure the potential, first through the standard resistance, then through the potential contacts, and again through the standard resistance. During the measurement, the potential through the standard resistance will not change by more than 0.5%.

* Reverse the direction of the current and repeat the previous procedure, in this case if you want to move the contacts to a new location and repeat the measurements, this is done in order to verify that at all points the same current is circulating.

### _**For the method of four contacts or probes:**_

* Place the contacts on the surface of the sample in a location such that the distance from each contact to the nearest edge is at least four times the contact spacing, pass a known current through the external contacts and measure the drop of the contact. potential through internal contacts.

_" The current must be of sufficient magnitude so that the potential drop can be measured with the required precision.If the current is chosen equal to 2 times the contact spacing, the potential drop through the internal contacts for measurements in semi-solid -infinites is numerically equal to resistivity and calculations can be avoided "._

* Reverse the direction of the current and repeat the measurement.

_**To calculate the electrical resistivity of a semiconductor material the following equations are needed:**_

_Calculate the resistivity for direct and reverse current directions:_

### _**For the test method of two contacts or probes:**_

<center> https://steemitimages.com/DQmT5MXodHwisqA2JCnVmBfr5xWPKVxhkv1VdV5xZmzNLR7/image.png </center>

and

<center> https://steemitimages.com/DQmY2p4u6avQ3uFuHuaZWsuNTLauZqLBX6s6agCvGT1C5W1/image.png </center>

Where,

<center> https://steemitimages.com/DQmQsV6qw252icG1EBUuDicumJyhAz1o11XDzfKgXbAuFsU/image.png </center>

### _**For the test method of four contacts or probes:**_

<center> https://steemitimages.com/DQmSFyRGDEaiGakdVberEDToxPPWavVcBqotAY9qDLwAhr6/image.png </center>

and

<center> https://steemitimages.com/DQmPWqpCKMy9o9pBCRvj96udhiEV5Y3AKQ8CyV9Pin3rpzi/image.png </center>

Where,

<center> https://steemitimages.com/DQmcSZVCjCV6uVbbt1RzjQVotnYdWZknRqBHgCGHYDMjckj/image.png </center>

**And in this way we can determine the electrical resistivity in a material.**
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**References**

* [1] ASTMF43-99. Standard Test Methods for Resistivity of Semiconductor Materials. Vol 10

* ASTMF 84-99 Standard Test Method for Measuring Resistivity of Silicon Wafers With an In-Line Four-Point Probe. Vol 10-05.

* Smith, W; Hashemi. (2006) Fundamentos de la ciencia e ingeniería de los materiales. Cuarta Edición. México. Editorial McGraw Hill.

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<center> _**If you have any questions regarding the published topic, do not hesitate to ask your questions, my person will gladly try to clarify your concerns.**_ </center>

<center> _**Carlos Pagnini**_ </center>

<center> @carloserp-2000 </center>
______________________________________________________

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