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Resistance Structures
Diffused Resistor Modelling
Mask Layout
Below the words "Resistance Structures" are 5 "cross bridge" resistor structures
from diffusion #1 with widths varying from 2 to 20 μm. Below them are their diffusion
#2 counter parts and below those are metal versions. Cross bridge resistor structures
can be used to:
- Verify four point probe sheet resistance measurements.
- Measure effective line width.
To the right of the metal cross bridge resistors are two Van Der Pauw structures
which are also used for sheet resistance measurements.
In the right third of the "Resistance Structures" region there are eight diffused
resistors, four from diffusion #1 and four from diffusion #2.
- The diffusion #1 resistors and the diffusion #2 resistors are identical (except
that they were formed during different diffusions).
- The straight resistors are 20 μm wide with lengths of 400 and 800 μm.
- The serpentine resistor on the top has 38 corners, two end contacts, and the linear
portion measures 3000 x 20 μm.
- The second resistor has 64 corners, two end contacts, and the linear portion measures
2360 x 20 μm. Three metal lines go over the serpentine resistors numerous times.
Since metal lines can have difficulty with the height changes, this is a good structure
to test the integrity of the metal layer.
Theory
The resistance of a linear resistor obeys the simple equation
R = Rs (L / W)
However, resistors must include contacts and often include corners. When calculating
the total resistance of a resistor, the corners and contacts are often expressed
in the effectivenumber of squares.
Let Rs be the sheet resistance, Rc be the contact resistance,
Rk be the corner resistance, and nk be the number of corners.
Then the resistance of the resistor
Rtotal = Rs (L / W) + nk Rk + 2Rc
Expressed in the effective number of squares,
R = Rs (L/W + α nk + 2 β)
α = Rk / Rs,
β = Rc / Rs
where α and β are the effective number of squares for corners and contacts, respectively.
Therefore, using the given equations, sheet resistance, and two resistors of different
geometries, it is possible to determine alpha and beta.
Measurement
The dimensions of the diffused reisistors (in the right 1/3 of the "Resistance Structures"
area) are given above.
Measure the resistances of each of the eight resistors.
For Additional Information Consult
- R. W. Berry, P. M. Hall, and M. T. Harris, Thin Film Technology, (D. Van Nostrand,
Princeton, NJ, 1968).
- Arthur B. Glaser and Gerald E. Subak-Sharpe, Integrated Circuit Engineering, (Addison-Wesley,
Reading, MA, 1977).
- 1R. W. Berry, P. M. Hall, and M. T. Harris, Thin Film Technology, (D. Van Nostrand,
Princeton, NJ, 1968).
Sheet Resistance
Theory
The structures in the left 2/3 of the Resistance Structures area can be used to
measure the sheet resistance based on a method proposed by L. J. van der Pauw in
19581,2. Van der Pauw proved that the sheet resistance of an arbitrary shape
may be easily calculated if the following conditions are fulfilled:
- The contacts are at the circumference of the sample,
- The contacts are sufficiently small,
- The sample is of uniform thickness, and
- The surface of the sample does not have isolated holes.
The van der Pauw method involves forcing current through two adjacent points on
the perimeter of the shape and measuring the voltage across two other points on
the perimeter of the shape. If the structure is also symmetrical, as in the case
of the cross bridge resistors, the van der Pauw relation simplifies to
Rs = π (R34,12 + R13,24) / 2ln2
where
R34,12 = (V3 - V4)/I12
R13,24 = (V1 - V3)/I24,
and the numbering of contacts goes left to right, top to bottom:
Use the four contacts of in the upper two-thirds of each cross bridge resistor.
However, the cross bridge resistors common in industry are more susceptible to contact
effects. The clover-shaped structures were proposed by van der Pauw to reduce contact
effects.
Measurement
Drive current between the appropriate terminals and measure the voltage across the
other terminals. Determine the sheet resistance for each of the five diffusion 1
cross bridges, the five diffusion 2 cross bridges, the three aluminum cross bridges,
and the two cloverleafs. You may either fit a line to the voltage values as current
varies or measure voltage for a particular current.
Further Information
- Anner, George E. Planar Processing Primer. New York, NY: Van Nostrand Reinhold.
1990. pp. 79-82.
- L.J. van der Pauw, "A Method of Measuring Specific Resistivity and Hall Effect of
Discs of Arbitrary Shape," Philips Research Reports, 13 (February 1958): 1-9.
- Van der Pauw, L.J. "A Method of Measuring Specific Resistivity and Hall Coefficient
on Lamellae of Arbitrary Shape." Philips Technical Review, 20: 220-224.
Effective LineWidth
Theory
The line widths indicated on the mask are the line widths of the lines as designed.
the actual line width on a wafer will vary due to development, etching, diffusion,
the e-beam lithography which created the master (negligible), and the lithography
which copied the maser. Two cross bridge resistors can be used to measure the effective
line width (see Figure 1.) The bottom two-thirds of the structure will be used.
Let the
length between the inner arms (4 and 6) be L, and the design widths of two
lines be W1 and W2. Let ΔW be the process induced change of
W. We will assume that ΔW is the same for all of the lines. If the measured resistances
of the lines are R1 and R2, then
Rs = (W1 + ΔW) R1 / L (Ω/square)
Rs = (W2 + ΔW) R2 / L (Ω/square)
The two equations can be combined to yield:
ΔW = (R2 W2 - R1 W1) / (R1
- R2) (um)
and
Rs = R1 R2 (W2 - W1) / (L
(R1-R2))
Measurement
Measure the resistance of the resistor portion of each of the cross bridge resistors.
Force currentthrough pads 3 and 5 and measure the voltage across pads 4 and 6. The
resistance is determined by R = V/I.
This method, called the Kelvin measurement technique, eliminates contact resistance
effects. Since little current flows through pads 4 and 6, the voltage drop through
the arms and the contact should be negligible. You may either fit a line or use
a particular current value, but be consistent in whichever method you choose.
Measure the resistance for each of the five diffusion #1, diffusion #2, and three
aluminum resistors.
Questions
Using the equations above, determine values for ΔW and Rs. You may use
any combination of the structures you choose, but determine two values of ΔW and
Rs for each of the diffusion #1, diffusion #2, and aluminum layers.
Comment on the values of ΔW you found. Are they reasonable?
It is possible to compare results from three or four of the cross bridge resistors.
Are they consistent? Comment.
Compare the values for sheet resistance obtained here to those obtained with the
van der Pauw method and the four-point probe.
References
- Bahid El-Kareh and Richard J. Bombard, Introduction to VLSI Silicon Devices, Hingham,
Massachusetts: Kluwer Academic Publishers, 1986, pp. 41-42.
Further Information:
- Martin G. Buehler, S.D. Grant, and W.R. Turner, "Bridge and van der Pauw Sheet Resistors
for Characterizing the Linewidth of Conducting Layers," J. Electrochem. Soc., 125
(4), pp. 650-654,1978.
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Devices
LASI was used for mask layout.
The mask set is currently under revision 1998: Dane Sievers, which is a minor redesign
of revision 1994: Ron Stack. All revisions are based on the work of revision 1991: Kevin Tsurutome.
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