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The term Ohms-cm ("Ohms centimeter") refers to the measurement of the "bulk" or "volume" resistivity of a semi-conductive material. The value in ohms-cm is the inherent resistance of a given material. Ohms-cm is used for measuring the conductivity of a three dimensional material such as a silicon ingot or a thick layer of a material. The term "Ohms-per-square" is the expression for sheet resistance and it is used when measuring the resistance value of a thin layer of a semi-conductive material. The sheet resistance of a given material will change depending on the thickness of the layer. This article briefly explains the relationship between Ohms-cm and Ohms-per-square, and how to convert from Ohms-per-square to Ohms-cm. To calculate Ohms-cm using the Jandel RM3 Test Unit, one needs to know the thickness of the wafer (if it is a homogeneous material) or the thickness of the top layer that's being measured, to be able to calculate Ohms-cm.
A.When the thickness exceeds 5/8 (62.5%) of the spacing between two needles - after which sheet resistance needs more than 1% correction. So, 0.625mm (625 microns) for a probe head with 1mm needle spacing. If the thickness is equal or greater than five times the probe spacing, the correction factor to be applied to the formula resistivity(rho) = 2 x pi x s x V/I is less than 0.1% Q.I have heard that the calculations for sheets resistance still apply at sample thicknesses of up to 40% of the tip spacing between two pins, however, this information is saying that it is okay up to 62.5%, which means wafers up to 625 microns thick can be measured using sheet resistance calculations. Don't most companies use volume resistance measurements when measuring bare silicon wafers, most of which are about 550 microns thick? A.It is a question of what you consider to be okay. From the graph at http://www.fourpointprobes.com/page16.pdf we can see that at t/s = 0.625 the correction is 0.9898 - effectively 0.99 and within 1%. Less than 40% of the tip spacing and the measurements need no correction. I think most companies measure volume resistance of their wafers, but not by using a volume resistance equation - this is why it is necessary to know the thickness of the wafers - if they were using the volume resistance equation they would not need to know the wafer thickness. If one has a unit that assumes wafer thickness of 550 microns it can measure sheet resistance and multiply its result by 0.055 to give volume resistance. From the graph at http://www.fourpointprobes.com/page14.pdf it would appear that if you measure bulk on a 550 micron wafer with a 1.591mm probe head then t/s = 0.34 and a correction of 0.25 would need to be applied. ======================================================== Q.What is the range of bulk resistivity (Ohms-cm) that the Jandel RM3 Test Unit can measure in Ohms-cm? A. The RM3 Test Unit can measure sheet resistance in the range from 1 milliohm-per-square up to 5 x 108 ohms-per-square and volume resistivity in the measurement range from 10-3 to 106 ohms-cm. The following is the answer for the question "What is the range of bulk resistivity (Ohms-cm) that the Jandel RM3 Test Unit can measure in Ohms-cm?": This crops up regularly, and it is hard to answer - let me give you an example to show the problem. [Please note that the RM3 Test Unit is now supplied with PC software that simplifies the task of calculating volume resistivity for wafers and bulk materials such as ingots] The normal range of sheet resistance which the (now discontinued) Jandel RM2 Test Unit could measure was between 1 and 107 ohms per square. The volume resistivity would be numerically equal to the sheet resistance if the specimen was 1 cm thick and made from the same material from which the sheet resistance figure was derived. It is difficult to define the limits of volume resistivity that the RTU can measure - for example we could not measure the volume resistivity of a block of platinum 1 cm thick because it is too highly conducting for the RTU to obtain a reading. If it was a platinum film 200 Angstroms thick then we could measure the sheet resistance easily and it would be approx 100 ohms per square. Let's consider a specific wafer sample: Let us assume that the wafer is 0.5mm thick and its resistivity is 0.005 Ohms-cm. By pressing the ohm/sq button, we can set the RM3 to deliver 4.5324 mA so the mV displayed is numerically equal to the sheet resistance in ohms/square. In this situation we can say that: bulk resistivity = sheet resistance x thickness in cm.
This would be the displayed reading. Of course, if it was a thin film, the thickness would be much less than 0.5mm and the sheet resistance correspondingly more so it would be possible to calculate the bulk resistivity more accurately. It is the eternal problem of low resistivity materials, where a supplementary voltmeter able to read a microvolt or less, is desirable. Such a voltmeter would be useful for the 0.005 Ohm-cm material -essential if it was thicker than 0.5mm. If we were to assume that we were talking about the bulk resistivity of silicon wafers, then, using the formula rest=2 x pi x s x V/I we calculate that with a probe tip spacing of 1.00mm, V=2V, I=10 nanoamperes the MAXIMUM value of resistivity would be about 10^8 ohm.cm. Using V=10 x 10^-6V and I=10x10^-3 amperes the MINIMUM value would be about 6 x 10^-4 ohm.cm. There are limitations on these values - in practice it may not be possible to drive the minimum current in the high resistivity material owing to contact resistance, and equally for the low resistivity material we are only looking at a single digit at the end of the voltage display. So, for the now discontinued RM2 Test Unit we quoted something a little less ambitious say 10^-2 up to 10^6 ohms.cm. However, for the RM3 Test Unit (the current version) we quote the volume resistivity measurement range from 10^-3 to 10^6 ohms-cm. System accuracy is within 0.3% The equation for calculating Ohms-cm without converting from sheet resistance is:  ) x V/IWhere s is the spacing between each of the four point probe tips in cm. If one uses a probe head with tip spacing of 1.591mm (62.6 mils), since 1.591mm is 1/(2 x pi)cm, it cancels out to V/I Q. I understand that the RM3 Test Unit can read out directly in ohms-per-square for use when measuring thin films (sheet resistance), but how do I measure thick materials that are measured in ohms-cm (volume resistivity)? What current level do I select for a particular material? A. When making an ohm-cm measurement, ideally you will want to use a current which will simplify the math. The formula is 2 x pi x s x V/I where s is the spacing between each of the needles in cm. If you use a probe with tip spacing of 1.591mm (~same as 62.6 mils), it makes the math easier since 0.1591 is 1/(2 x pi). Therefore we would have: Resistivity = V/I This means that if 1mA current is used, then the measured voltage value (in millivolts) = the resistivity of the sample in ohms-cm. If you want to measure on the 'High' range it may be that the voltage will be too high to measure. In this case you could try 100uA and the mV result would need multiplying by 10. If the voltage value is quite low (maybe 9mV or so) you could increase the current to 10mA and then the mV result could be divided by 10 to give the resistivity (higher currents can sometimes offer more stable results). |
| Four-Point-Probes is a division of Bridge Technology. To request further information please call Bridge Technology at (480) 988-2256 or send e-mail to Larry Bridge at: sales@bridgetec.com |
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