Paper: Method to Accurately Measure the On-Resistance of a Power MOSFET in Wafer Form

This is a paper I had published back in 2008. It's a simple measurement technique that uses a variation of the Kelvin measurement method (where the voltage sensing probes are separate from the current forcing probes). This is for precision low resistance measurements. I'm re-posting it here because the publisher deleted the images. 

John Andrews

Abstract— Obtaining an accurate measurement of the on resistance (R_DS(ON)) of a large die power MOSFET in wafer form is challenging. This paper presents a method to obtain precise R_DS(ON) measurements by using equipment commonly found in any wafer test lab. The accuracy of these measurements can be greatly improved by incorporating correction factors obtained by finite element analysis (FEA) simulation of the device under test (DUT).

I.INTRODUCTION

_MOST power MOSFETs are built on a silicon wafer with a highly doped, ultra-low resistivity silicon substrate. Since these are vertical devices, the back of the wafer is used for the drain connection, whereas the top metal is used for the source and gate connections. A typical large die covers 0.1 cm² and can conduct 30 amps in packaged form. The on-resistance between drain and source (R_DS(ON)) for a large die, 30V power MOSFET can be one milliohm in silicon. The package adds some resistance, but its resistance is much lower than trying to connect to a bare MOSFET with probes.

A typical application for a power MOSFET is in a DC-DC converter. The most important characteristics of the MOSFET in this application are R_DS(ON), gate charge (Q_G), and breakdown voltage (BV_DSS).

Wafer level R_DS(ON) testing has been a challenge for test engineers working with power MOSFETs. The most common method for estimating the silicon contribution to R_DS(ON) uses a small test die to measure specific resistance in mΩ·cm². This value is assumed to be fairly consistent across the wafer. The resistance of a product die can be calculated by dividing the specific resistance by the active area. One shortcoming of this method is that a wafer map of R_DS(ON) can not be generated without sacrificing a significant amount of wafer area.

In situations where the small test die is affected by etch loading effects, the test die does not accurately represent the R_DS(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 level R_DS(ON) measurement methods

The typical approach used to measure R_DS(ON) is to force current between the chuck and the probes contacting the top of the wafer.

For accuracy in a Kelvin resistance measurement, there are several important 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 R_DS(ON) measurement setup. One source of error is the contact between the wafer and the chuck. Because there is roughness on the chuck and on the back of the wafer, electrical contact is made in discrete areas. The contact resistance between the wafer and the chuck is large enough to introduce significant error in the R_DS(ON) measurement. Simply repositioning the wafer on the chuck will change contact areas and change the R_DS(ON) measurement results.

Other sources of measurement variation are probe contact resistance, and probe placement. When more than one probe is used to force current, then probe contact resistance can introduce variation into the measurement because it will change the current density at different locations. This will affect the measurement at the voltage sensing probe.

III.The adjacent-die method

Because the wafer to chuck connection was a major source of error, and could not be fixed without investing in new equipment, I needed to find a way to measure R_DS(ON) without using the contact on the back side of the wafer. Even if I used the chuck only to measure drain voltage, the measurement error was unacceptably high.

This method measures R_DS(ON) without using the connection on the back of the wafer. The connections to the drain are achieved using the adjacent dies on either side of the device under test (DUT). The internal wafer structure is much more consistent than the connection between a wafer and a chuck. For this reason, the adjacent-die method is much more precise than the conventional method of measuring R_DS(ON). This section will describe how to set up a probe station to precisely measure R_DS(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. If the wafer contacts the chuck, then it allows current to flow in parallel with the substrate, changing the measurement results. A sheet of paper may be used to insulate the wafer from the chuck. It will not interfere with the vacuum used to hold the wafer on the chuck.
Referring to Fig. 2, the adjacent dies along the long edges of the DUT will be used to measure R_DS(ON). Use probe A to force current into the die to the left of the DUT. Three or four hundred milliamps is a sufficient current. A gate probe is not required on this die because the current will forward bias the body diode. The die to the right of the DUT will be used to measure drain voltage.
 Fig. 2 illustrates the adjacent-die R_DS(ON) measurement method. 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 current flowing from drain to source, the drain and source are at the same voltage. This method takes advantage of that principle to measure the drain voltage on probe D. The volt meter connected between probes C and 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-source current. The gate bias voltage is connected between probes C and E. If it were connected between probes B and E, then the voltage drop between probe B and the source pad would decrease the actual gate voltage applied to the DUT.

This adjacent-die method does require the die on the right (under probes D and F) to be functional. Not every die on the wafer is good, so the gate current should be watched while taking measurements. If the gate and source are shorted on this die, then the measurement result may not be correct.

 The R_DS(ON) value calculated by V_DC/I_AB is useable, but an even more accurate value of the R_DS(ON) of the active area can be obtained.

IV.Using finite element analysis to find the R_DS(ON) of the active area

Although the adjacent die method does yield precise measurements, it does not yield an exact measurement of R_DS(ON). This difference is due to the geometries inherent in the measurement setup. The adjacent-die method of measuring R_DS(ON) is somewhat sensitive to changes in die dimensions. To find the R_DS(ON) contribution due to the MOSFET’s active area alone, we can compare the measurement results to the simulations.

FEA software can be used to simulate the measurement setup shown in Fig. 2. These simulations will allow us to predict what the measurement result will be, given the resistances of the individual components in the model. Once this relationship is established, we can predict the resistance of the active area, given the measurement result.

The simulation model is a three dimensional representation of the three MOSFETs. Fig. 3 shows a cross-section of the model with the bulk resistances of each region labeled.  

In the simulation model, the active area contribution to R_DS(ON) can be approximated by the familiar formula,

In this formula, length is the thickness of the active area region in the simulation model. R is the resistance; ρ is the bulk resistance; and area is the active area of the die.

The simulation is run twice to obtain results using two different active area resistance values. It is convenient to simulate it using both the high and low R_DS(ON) values listed in the datasheet. These are commonly listed for V_GS = 4.5 V, and V_GS = 10 V, depending on the product. The simulations only need to be performed once for each die size, as long as the rest of the simulation parameters remain valid.

Using the difference between the simulated measurement result and the actual active area contribution, we can derive a formula to find the active area resistance, given the measurement values from the adjacent-die method.

A.Simulation Model Parameters

 In the simulation model, for simplicity, the resistance of the active area of the MOSFET on the left was adjusted to result in a voltage drop across it of approximately 0.7 V at the given current forcing conditions.  

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 R_DS(ON) model can be approximated by block shapes. Because of current spreading in the substrate, the simulation model should include enough wafer area beyond the edges of the DUT to account for this with minimal error. This radius is approximately six times the die width.

C.Model Calulations

Let a₁ be the active area resistance of the model at high V_GS. Let a₂ be the active area resistance of the model at low V_GS. Let m₁ be the simulated resistance measurement of the model at high V_GS. Let m₂ be the simulated resistance measurement of the model at low V_GS.

 We can plot this data using the active area resistance as the x axis, and the simulated R_DS(ON) measurement as the y axis. The two points are (a₁,m₁), and (a₂,m₂). The formula for the line through these two points may be used to predict the active area resistance, given the measured R_DS(ON) using the adjacent die method.

  

V.Sources of measurement variation using the adjacent-die method

 According to the simulation results, some factors have very little effect on the measurement. The substrate thickness is typically 200 μm. Varying the thickness from 175 to 225 μm only results in a 1% error in R_DS(ON) (simulated measurement). Also, variations in the back metal sheet resistance will not change the results more than 1%. A surprising result from simulations is that variations in top metal thickness and resistivity also have negligible effects on results.  

Several factors introduce variation into the measurements. The most significant are probe placement, and substrate resistivity.

 Variations in substrate resistivity result in a linear response in R_DS(ON) measurement. The graph in Fig. 7 shows results from substrate resistivities that are well beyond the normal distribution of actual product. This was done to show that the response is linear.  

The probe placement on the DUT must be consistent. Variations in probe placement will result in changes in measurement. Probe placement on the dies to the left and the right of the DUT (labeled A and D in Fig. 2) also affect measurements, but not to the same degree. The cause of this measurement variation is the fact that the sheet resistance of the top metal is greater than zero.

 Moving either probe B or C from the center to an edge of the source pad can result in a significant error. Fig. 7 shows the error from moving either probe B or C. Each line represents a 2% error in R_DS(ON). A 5x5 grid of probe placements was used to create the 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 to measure the R_DS(ON) of the active area of a MOSFET in wafer form. This expedites the technology development process because the data can be obtained before the products are packaged and tested.

Acknowledgment

J.T. Andrews thanks his supervisor Bruce Marchant for his support.

References

1. No references are used in this paper.