John Andrews
Abstract—Obtaining an accurate measurement of the on resistance (RDS(ON))of a large die power MOSFET in wafer form is challenging. This paperpresents a method to obtain precise RDS(ON) measurementsby using equipment commonly found in any wafer test lab. The accuracyof these measurements can be greatly improved by incorporatingcorrection factors obtained by finite element analysis (FEA)simulation of the device under test (DUT).I.INTRODUCTION
MOSTpower MOSFETs are built on a silicon wafer with a highly doped,ultra-low resistivity silicon substrate. Since these are verticaldevices, the back of the wafer is used for the drain connection,whereas the top metal is used for the source and gate connections. Atypical large die covers 0.1 cm2 and can conduct 30 ampsin packaged form. The on-resistance between drain and source(RDS(ON)) for a large die, 30V power MOSFET can be onemilliohm in silicon. The package adds some resistance, but itsresistance is much lower than trying to connect to a bare MOSFET withprobes.
A typical application for a power MOSFET is in a DC-DC converter. The most important characteristics of the MOSFET in this applicationare RDS(ON), gate charge (QG), and breakdownvoltage (BVDSS).
Wafer level RDS(ON) testing has been a challenge for testengineers working with power MOSFETs. The most common method forestimating the silicon contribution to RDS(ON) uses asmall test die to measure specific resistance in mΩ·cm2.This value is assumed to be fairly consistent across the wafer. Theresistance of a product die can be calculated by dividing thespecific resistance by the active area. One shortcoming of thismethod is that a wafer map of RDS(ON) can not be generatedwithout sacrificing a significant amount of wafer area.
In situations where the small test die is affected by etch loadingeffects, the test die does not accurately represent the RDS(ON)of the prime die.
The method presented in this paper can be used in both bench testing,and in automated testing.
II.Problems associated with typical wafer levelRDS(ON) measurement methods
The typical approach used to measure RDS(ON) is to forcecurrent between the chuck and the probes contacting the top of thewafer.
For accuracy in a Kelvin resistance measurement, there are severalimportant factors to consider.
the geometry of the device under test (DUT), and the connections to that device
the material boundaries
the bulk resistivity of the various materials in the test
There are several sources of error in a typical RDS(ON)measurement setup. One source of error is the contact between thewafer and the chuck. Because there is roughness on the chuck and onthe back of the wafer, electrical contact is made in discrete areas.The contact resistance between the wafer and the chuck is largeenough to introduce significant error in the RDS(ON)measurement. Simply repositioning the wafer on the chuck will changecontact areas and change the RDS(ON) measurement results.
Other sources of measurement variation are probe contact resistance,and probe placement. When more than one probe is used to forcecurrent, then probe contact resistance can introduce variation intothe measurement because it will change the current density atdifferent locations. This will affect the measurement at the voltagesensing probe.
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Because the wafer to chuck connection was a major source of error,and could not be fixed without investing in new equipment, I neededto find a way to measure RDS(ON) without using the contacton the back side of the wafer. Even if I used the chuck only tomeasure drain voltage, the measurement error was unacceptably high.
This method measures RDS(ON) without using the connectionon the back of the wafer. The connections to the drain are achievedusing the adjacent dies on either side of the device under test(DUT). The internal wafer structure is much more consistent than theconnection between a wafer and a chuck. For this reason, theadjacent-die method is much more precise than the conventional methodof measuring RDS(ON). This section will describe how toset up a probe station to precisely measure RDS(ON).
List of required equipment
Probe station with six available probes
- Volt meter
- Current source
It is important to insulate the wafer from the conductive chuck. Ifthe wafer contacts the chuck, then it allows current to flow inparallel with the substrate, changing the measurement results. Asheet of paper may be used to insulate the wafer from the chuck. Itwill not interfere with the vacuum used to hold the wafer on thechuck.
Referring to Fig. 2, the adjacent dies along the long edges of theDUT will be used to measure RDS(ON). Use probe A to forcecurrent into the die to the left of the DUT. Three or four hundredmilliamps is a sufficient current. A gate probe is not required onthis die because the current will forward bias the body diode.Thedie to the right of the DUT will be used to measure drain voltage.
Fig. 2 illustrates the adjacent-die RDS(ON) measurementmethod.The three MOSFETs and six probes are shown graphically,while the electrical connections are shown schematically.

In a MOSFET, when the gate is turned on, and there is no currentflowing from drain to source, the drain and source are at the samevoltage. This method takes advantage of that principle to measure thedrain voltage on probe D. The volt meter connected between probes Cand D measures the voltage between drain and source of the DUT.
Three probes connect to The DUT; probe C to measure source voltage,probe E to force gate voltage, and probe B to conduct drain-sourcecurrent. The gate bias voltage is connected between probes C and E.If it were connected between probes B and E, then the voltage dropbetween probe B and the source pad would decrease the actual gatevoltage applied to the DUT.
This adjacent-die method does require the die on the right (underprobes D and F) to be functional. Not every die on the wafer is good,so the gate current should be watched while taking measurements. Ifthe gate and source are shorted on this die, then the measurementresult may not be correct.
The RDS(ON) value calculated by VDC/IABis useable, but an even more accurate value of the RDS(ON)of the active area can be obtained.
IV.Using finite element analysis to find theRDS(ON) of the active area
Although the adjacent die method does yield precise measurements, itdoes not yield an exact measurement of RDS(ON). Thisdifference is due to the geometries inherent in the measurementsetup. The adjacent-die method of measuring RDS(ON) issomewhat sensitive to changes in die dimensions. To find the RDS(ON)contribution due to the MOSFET’s active area alone, we can comparethe measurement results to the simulations.
FEA software can be used to simulate the measurement setup shown inFig. 2. These simulations will allow us to predict what themeasurement result will be, given the resistances of the individualcomponents in the model. Once this relationship is established, wecan predict the resistance of the active area, given the measurementresult.
The simulation model is a three dimensional representation of thethree MOSFETs. Fig. 3 shows a cross-section of the model with thebulk resistances of each region labeled.
In the simulation model, the active area contribution to RDS(ON)can be approximated by the familiar formula,
In this formula, length is the thickness of the active arearegion in the simulation model. R is the resistance; ρis the bulk resistance; and area is the active area of thedie.
The simulation is run twice to obtain results using two differentactive area resistance values. It is convenient to simulate it usingboth the high and low RDS(ON) values listed in thedatasheet. These are commonly listed for VGS = 4.5 V, andVGS = 10 V, depending on the product. The simulations onlyneed to be performed once for each die size, as long as the rest ofthe simulation parameters remain valid.
Using the difference between the simulated measurement result and theactual active area contribution, we can derive a formula to find theactive area resistance, given the measurement values from theadjacent-die method.
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In the simulation model, for simplicity, the resistance of the activearea of the MOSFET on the left was adjusted to result in a voltagedrop across it of approximately 0.7 V at the given current forcingconditions.
Table 1
Regions in the simulation model
Material | Resistivity | Thickness |
Top metal | 0.03 Ω·μm | 5 μm |
Substrate | 30 Ω·μm | 200 μm |
Back metal | 0.16 Ω·μm | 0.7 μm |
Active area | 1000 Ω·μm | 10 μm |
Fwd diode | 1,280,000 Ω·μm | 10 μm |
B.Simulation Geometry
The structures in the RDS(ON) model can be approximated byblock shapes. Because of current spreading in the substrate, thesimulation model should include enough wafer area beyond the edges ofthe DUT to account for this with minimal error. This radius isapproximately six times the die width.
C.Model Calulations
Let a1 be the active area resistance of the model at highVGS. Let a2 be the active area resistance ofthe model at low VGS. Let m1 be the simulatedresistance measurement of the model at high VGS. Let m2be the simulated resistance measurement of the model at low VGS.
We can plot this data using the active area resistance as the x axis,and the simulated RDS(ON) measurement as the y axis. Thetwo points are (a1,m1), and (a2,m2).The formula for the line through these two points may be used topredict the active area resistance, given the measured RDS(ON)using the adjacent die method.
V.Sources of measurement variation using theadjacent-die method
According to the simulation results, some factors have very littleeffect on the measurement. The substrate thickness is typically 200μm. Varying the thickness from 175 to 225 μm only results in a 1%error in RDS(ON) (simulated measurement). Also, variationsin the back metal sheet resistance will not change the results morethan 1%. A surprising result from simulations is that variations intop metal thickness and resistivity also have negligible effects onresults.
Several factors introduce variation into the measurements. The mostsignificant are probe placement, and substrate resistivity.
Variations in substrate resistivity result in a linear response inRDS(ON) measurement. The graph in Fig. 7 shows resultsfrom substrate resistivities that are well beyond the normaldistribution of actual product. This was done to show that theresponse is linear.
The probe placement on the DUT must be consistent. Variations inprobe placement will result in changes in measurement. Probeplacement on the dies to the left and the right of the DUT (labeled Aand D in Fig. 2) also affect measurements, but not to the samedegree. The cause of this measurement variation is the fact that thesheet resistance of the top metal is greater than zero.
Moving either probe B or C from the center to an edge of the sourcepad can result in a significant error. Fig. 7 shows the error frommoving either probe B or C. Each line represents a 2% error inRDS(ON). A 5x5 grid of probe placements was used to createthe plot. Only one probe was moved out of position at a time.
VI.Conclusion
The adjacent die method is a cost-effective and precise method tomeasure the RDS(ON) of the active area of a MOSFET inwafer form. This expedites the technology development process becausethe data can be obtained before the products are packaged and tested.
Acknowledgment
J.T. Andrews thanks his supervisor Bruce Marchant for his support.
References
No references are used in this paper.