Title: Four Point Resistivity and Conductivity Type Measurements

Purpose:

To determine the resistivity of a substrate or a thin film by using the four point probe, current source, and digital multimeter (DMM). This SOP also determines the conductivity using the four point probe and a separate function generator and DMM.

General Instructions and Precautions:

The probe tips are a very critical part of the four point probe and great care should be taken when using the equipment. Two different materials are used for the probe tips. Tungsten Carbide is a crystalline material which is very hard and somewhat brittle. If the wafer is moved horizontally while the probe arm is down, the Tungsten Carbide tips tend to break off in little pieces. The second material, osmium, is also a hard material but does not chip. When mishandled, the entire tip can be broken. Osmium tips cost more than Tungsten Carbide and are the kind used in the four point probe system at U of L. [1]

Preparation:

1. Turn on the Keithley 220 current source and 196 DMM by pressing the red POWER switch, allowing 1-2 hours for warm up.
2. Place the test sample on the teflon disk and center the sample under the probe head. Centering the sample eliminates the need for correction factors other than that discussed below.
3. Lower the probe head by moving the top lever clockwise. If the probe tips do not make good contact with the sample then the probe arm must be adjusted. This is easily done by reaching up under the four point probe and rotating the adjustment knob. Lower the probe head until the probe tips contact the sample and depress about half way into the plastic head.
4. Raise the probe head by moving the top lever counterclockwise. [1]
5. Insure that the devices are connected as indicated in the resistivity column of the schematic (shown below and attached to the side of the four point probe). The schematic shows how the female banana plugs on the back of the four point probe are wired to the probe tips. The leads are labeled to match the schematic.

Resistivity Theory:

The four point probe is preferable over a two point probe because the contact and spreading resistances associated with the two point probe can't be measured. This means that the true sheet resistance can't be accurately separated from the measured resistance. The four point probe consists of two current carrying probes (1 and 4), and two voltage measuring probes (2 and 3) (refer to schematic). Since very little contact and spreading resistance is associated with the voltage probes, one can obtain a fairly accurate calculation of the sheet resistance which is then used to calculate the resistivity. The resistivity (p) of a semi-infinite wafer with equal probe spacing (s) is given by:

p=2*pi*s*V/I

Since wafers are not semi-infinite in extent, a combination of correction factors must be multiplied by the right hand side of this equation. By following the procedure below, the need for many of these factors is eliminated. The correction factors still needed, and the final forms of the formulas for sheet resistance and resistivity are given below in the procedure section. [2]

Resistivity Procedure:

1. Move the top lever fully clockwise noting that the probe tips are making contact with the sample.
2. The DMM should power in the DCV mode, if not press the DCV button on the Function panel.
3. The DMM should be in AUTO mode, if not press the AUTO button on the Range panel.
4. On the current source press SOURCE, enter the desired current by pressing the data buttons, EXPONENT, then press ENTER. The display should show the desired current. The current range is 20 µA to 101mA. A good starting amperage is 4.53 mA.
5. Apply this current to the sample by pressing OUTPUT/OPERATE.
6. Sometimes the V-LIMIT LED will flash, when this occurs the V-LIMIT needs to be increased. (The default V-LIMIT is 3 V.) To increase the voltage limit press V-LIMIT, enter a voltage (1 to 105 volts) by pressing the data keys, and press ENTER. Press SOURCE to have the current displayed. If the LED is still flashing, try reducing the current. Only set it as low as necessary because an excessively low current (low uA range) will give inaccurate readings
7. Read the voltage, shown on the DMM.
8. To stop the current flow press the OUTPUT/OPERATE button.
9. Raise the probe head by moving the top lever counterclockwise. Take the sample out of the four point probe stand.
10. Sheet resistance is given by:

    Sheet Resistance (R_s) = p/t= (V/I)*C.F.₁*C.F.₂

    where p is the resistivity,t is the thickness of the sample, and C.F.₁ is the sheet resistance correction factor which depends on the wafer diameter (d) and the probe tip spacing (s). For the UofL setup, s is equal to 62.5 mils. If the ratio of d/s is greater than 40, the sheet resistance correction factor levels off at 4.5324. If the ratio is less than 40, use the table below [3] to determine the appropriate correction factor. In the rectangle columns, the number refers to the length to width ratio, with the length being the longer of the two sides. The rectangle 4 column refers to a ratio greater than or equal to 4. Rectangular samples should be tested with the length paralell to the probe tips and the width should be taken as d when determining the correction factor. s is the spacing between the probe tips (62.5 mils for UofL setup and C.F.₂ is the resistivity correction factor. C.F.₂ is given in the table below. For the case when t is much less than s (less than 4/10 of s), C.F.₂ is simply equal to unity. [1] Note: the above equation and the table are only valid for junctions diffused on one side of the sample. A chemical source will diffuse both sides which means the back side must be removed to use these factors, or different factors must be used.

Conductivity Type Theory:

A four point robe can be used to determine conductivity type through use of the rectification method. With this method, "the sign of the conductivity is determined by the polarity of a rectified ac signal at a point contact to the semiconductor. When two probes are used, one should be rectifying and the other should be ohmic. Current flows through a rectifying contact to n-type material if the metal is positive and for p-type if it is negative. Rectifying and ohmic contacts are difficult to implement with two-point contacts. Fortunately, four-point probes can be used with appropriate connections not requiring ohmic contacts. An ac voltage is applied between probes 1 and 2, and the resulting potential is measured between probes 4 and 2. The voltage drop V₄₂ is small when the ac voltage at probe 2 is positive because the metal-semiconductor junction is forward biased. But for negative voltage at probe 2, the junction is reverse biased; V₄₂ is large and positive. The large positive and small negative ac V₄₂ result in a dc component with the polarity of the semiconductor-metal junction voltage necessary to reverse bias the junction. For n-type V₄₂ is greater than 0, and for p-type V₄₂ is less than 0." [2]

Conductivity Type Procedure:

1. Disconnect the leads between the Keithley units and the probe from the back of the four point probe unit.
2. Connect the leads from the function generator and DMM as shown in the conductivity type column of the schematic.
3. Turn on the function generator and DMM and set up a signal on the function generator. A 1 kHz sinusoid with the amplitude knob set at the midpoint should be fine. The DMM should be set to measure DC voltage.
4. Set up the sample in the same manner as described in the resistivity procedure.
5. If the DMM displays a positive voltage, the sample is n-type, and a negative voltage indicates p-type regardless of the magnitude of the voltage.
6. Because this station will more commonly be used for resistivity testing, all connections should be restored according to the resistivity column of the schematic before leaving it.

   Four Point Probe Schematic

   

References:
[1] B. Dickson, F.M. Smits, "Operation Manual for the SYS-301 Resistivity 
    Probing System."
[2] D.K.Schroder,Semiconductor Material and Device Characterization,
    Arizona State University, Tempe, Arizona.
[3] S.M. Sze, VLSI Technology, AT&T Bell Laboratories, Murray Hill, 
    New Jersey.

Bibliography:
[1]  Am. Soc. Test. Mater., ASTM Standard, F84, Part 43.
[2]  Am. Soc. Test. Mater., ASTM Standard, F723, Part 43.
[3]  W.E. Beadle, J.C.C. Tsai, and R.D. Plummer, Quick Reference
     Manual for Silicon Integrated Circuit Technology, Wiley, New
     York, 1985.
[4]  F.M. Smits, "Measurement of Sheet Resistivities with the Four Point
     Probe," Bell Syst. Tech. J. 37, 711 (1958).
[5]  F. Wenner,"A Method of Measuring Earth Resistivity,"Bulletin of
     the Bureau of Standards 12, 469-478, 1915.
[6]  L.B. Valdes, "Resistivity Measurements on Germanium for Transistors,"
     Proc. IRE 42, 420-427, Feb. 1954.
[7]  H.H. Wieder, "Four Terminal Nondestructive Electrical and Galvanomagnetic
     Measurements," in Nondestructive Evaluation of Semiconductor Materials
     and Devices (J.N. Zemel, ed.), Plenum Press, New York, NY, 1979, 67-104.
[8]  R. Hall, "Minimizing Errors of Four-Point Probe Measurements on Circular 
     Wafers," J. Sci. Instrum. 44, 53-54, Jan. 1967.
[9]  A. Uhlir Jr., "The Potentials of Infinite Systems of Sources and Numerical 
     Solutions of Problems in Semiconductor Engineering," Bell Sys. Tech. J.
     34, 105-128, Jan. 1955.
[10] M.G. Buehler, "A Hall Four Point Probe on Thin Plates," Solid State 
     Electron. 10, 801-812, Aug. 1967.

created by Ziyi Dai
modified by Thomas Mooney 8/18/97
modified by Thomas Mooney 10/28/97


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