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Resistance Structures

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.

Devices

BJTs

Capacitors

Contact Resistance

Control Structures

Diodes

Inverters

Integrated Circuit Cells

Misalignment Structures

Miscellaneous FETs

nMOSFETs

pMOSFETs

Resistors


Device Cell


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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