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 paper
presents a method to obtain precise RDS(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
(RDS(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 RDS(ON), gate charge (QG), and breakdown
voltage (BVDSS).
Wafer level RDS(ON) testing has been a challenge for test
engineers working with power MOSFETs. The most common method for
estimating the silicon contribution to RDS(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 RDS(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 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 level
RDS(ON) measurement methods
The typical approach used to measure RDS(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 RDS(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 RDS(ON)
measurement. Simply repositioning the wafer on the chuck will change
contact 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 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 RDS(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 RDS(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 RDS(ON). This section will describe how to
set 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. 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 RDS(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 RDS(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 RDS(ON) value calculated by VDC/IAB
is 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 the
RDS(ON) of the active area
Although the adjacent die method does yield precise measurements, it
does not yield an exact measurement of RDS(ON). This
difference is due to the geometries inherent in the measurement
setup. The adjacent-die method of measuring RDS(ON) is
somewhat sensitive to changes in die dimensions. To find the RDS(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 RDS(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 RDS(ON) values listed in the
datasheet. These are commonly listed for VGS = 4.5 V, and
VGS = 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 RDS(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
VGS. Let a2 be the active area resistance of
the model at low VGS. Let m1 be the simulated
resistance measurement of the model at high VGS. Let m2
be 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. 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 RDS(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 RDS(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
RDS(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
RDS(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 RDS(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
-
No references are used in this
paper.
