Experiment 3 -
IC Resistors

W.T. Yeung, Y. Shin, W.Y. Leung and R.T. Howe

UC Berkeley EE 105

This lab introduces the Micro Linear Lab Chips, with measurements of IC resistors and a distributed delay line. From the layout of the resistors, you will interpret the measured resistance as a sheet resistance of the layer from which the resistor is fabricated. The Micro Linear chips are "tile arrays" that consist of standard devices in fixed locations. The polysilicon resistors on Lab Chip 1 consist of 15 and 36 series-connected resistors, with aluminum (metal 1) being used as an interconnect layer. A long metal runner is measured from which you can measure the sheet resistance of the metal 1 layer. Using this value, you can make an improvement in your estimate of the polysilicon sheet resistance and attempt to estimate the metal-polysilicon contact resistance. A diffused "base resistor" is included that will enable you to measure the effect of depletion width on resistance. Finally, you will examine the delay of a distributed RC delay line.

The HP-4145 Semiconductor Parameter Analyzer will be used and its results compared to those obtained from the digital multimeter. The key concepts introduced in this lab are:

Calculation of the sheet resistance given the layout of a resistor and the measured resistance

The non-ideal behavior of IC resistors

Measurement errors and the resulting uncertainty in calculated parameters

The variation of resistance in junction-isolated diffusion resistors as a function of the reverse bias on the isolation diode.

Delay of distributed RC delay line

Reading: H&S Chapter 2 (especially section 2.6) for sheet resistance
Chapter 3.5 (see Example 3.6 for a similar structure to the base diffusion resistor).

From the layout (1.5 m between grid points) in Fig. 1, find the number of squares for the polysilicon resistor M3520 on Lab Chip 1. Assume that the contact regions at the ends of the resistor count as one square and use the effective number of square for right-angle bends from the Appendix at the end of this lab.You will note that in some cases, you will have to make a rough estimate in regards to geometry that is not mentioned in literature. In any case, state your assumptions and justify your choice for the "effective" square.)

1. Using the digital multimeter, measure the resistance of the polysilicon resistor RP3-RP4 (PINS #21-22) on Lab Chip 1. This resistor consists of 15 M3520 polysilicon resistors in series, as shown in Fig. 2.

2. The M3520 resistor is nominally 3450 . Assuming your measurement is 15 times the resistance of one M3520, how close are your resistors to the nominal value.

3. Neglecting the contribution of the aluminum metal 1 interconnects and the polysilicon-aluminum ohmic contacts (we will consider these later), calculate the sheet resistance R_o of the polysilicon film.

4. If we assume that the polysilicon thickness is t_POLY = 0.35 m (a typical value) and that the doping concentration is N_d = 10¹⁹ cm^-3, estimate the mobility of electrons in the polysilicon film. Note that the grain boundaries in polysilicon greatly affect the mobility.

FIGURE 1.

FIGURE 2.

1. Figure 3 shows a very long metal 1 aluminum runner connecting to two bonding pads (Metal Runner I and Metal Runner II, PINS 13-15) on Lab Chip 1. Note that Fig. 3 is not to scale. The metal runner has a small but non-zero resistance. Use the HP-4145 to find the resistance of this metal runner. Since metal is very conductive, the 4145 will reach its current compliance limit. This is not a problem; for small voltages, the 4145 will still give accurate results.

2. From the layout in Fig. 3, determine R_o of metal 1. The width of the runner is 3 m. Assume that the large "chunks" at the pad of PIN #15 and the small one at the pad of PIN #13 together contribute about one square and that the five turns have approximately the same length for simplicity.

FIGURE 3.

1. Using the digital multimeter, measure the resistances of the 36 series-connected wide poly resistors (M3524) shown in Fig. 4. The layout and cross section of M3524 is given in Fig. 5.

2. Using the effective number of squares for the contact regions at the ends of each M3524 resistor from the Appendix and neglecting the contributions of the metal connections, estimate the sheet resistance of polysilicon and compare your result with what you found in 3.1. Which calculation would you place more confidence in? Why?

3. A more accurate value for the sheet resistance of polysilicon and potentially, an estimate of the resistance of the many polysilicon-aluminum ohmic contacts can be made using the measurements on both resistors (RP1-RP2 and RP3-RP4). The resistance of either resistor can be expressed as the sum of three contributions:

(EQ 1)

where N_poly is the number of poly resistor segments (15 or 36), R_p is the resistance of each segment (found from the product of the polysilicon sheet resistance and the number of squares), the second term (in parentheses) is the total resistance of the metal 1 interconnections (both horizontal and vertical straps), and the final term is the total resistance due to the ohmic contacts between the polysilicon and the aluminum (N_poly-Al is the number of contacts and R_poly-Al is the contact resistance in .)

By solving the two equations simultaneously, find the sheet resistance R_o of polysilicon and the contact resistance R_poly-Al by using the results from 3.3 for the sheet resistance of metal 1. Given the uncertainty in your measurements, estimate the uncertainly in your values for R_o and R_poly-Al.

Note: due to the small value for R_poly-Al and uncertainties in the measurements, the calculation may lead to a negative answer, which is obviously not possible. Note that we have assumed that the polysilicon has a uniform sheet resistance for the two areas of Lab Chip 1 where the two resistors are fabricated, which may not be correct. There are other contributions to the total measured resistance which haven't been accounted for; can you identify any of these? Would they affect your results?

FIGURE 4.

FIGURE 5. .

We will repeat the above experiment using the HP-4145. In Exp. 1, you found the resistance of a carbon resistor by taking the slope the resistor's I-V characteristics. You will again use the same method to find the resistance of an IC resistor.

1. Load the program with the following keystrokes: [GET] PR [EXE].

2. Place the Lab Chip 1 into the test fixture.

3. Connect SMU1 to the connection dedicated to pin 23 and SMU2 to pin 24.

4. Use the cursor and marker to find the resistances of the resistors. (refer to Exp. 1 if you had forgotten how to do this). Use the "append" feature so that only one 4145 plot is needed.

5. Compare the results with the results obtained from the digital multimeter. Which do you think is more accurate?

Figure 6 shows the cross section and layout of the base diffusion resistor on Lab Chip 1. Note from the cross section that the well contact (PIN 20, RBW) is connected to the n type epitaxial (epi) layer that underlies the p-type base diffusion. If the reverse bias on the pn junction between the epi and the base diffusion is changed, then the depletion width will change, as calculated in Example 3.6 of H&S. As a result, the effective undepleted thickness of the base diffusion will change and the resistance between RB2 and RB1 (PINS 16 and 17) will increase. This effect is not as pronounced since the epi layer is more lightly doped than the base diffusion. Finally, note that even with RB2 and RBW shorted together and grounded, a large voltage on RB1 will cause an increase in the depletion width at that end of the resistor, which will cause deviations from a linear resistor.

Connect PINS 17 and 20 to GND and measure the I-V characteristic by changing the voltage of PIN 16 from 0 V to - 5 V. Note that a negative voltage is required to avoid forward-biasing the p-base-to-n-epi junction. Find the value of the resistor as the inverse of the slope of the I-V plot over the range 0 V to -1 V.

Now connect the power supply in series with a 100 k resistor to RBW, PIN 20. Repeat the resistor I-V measurements over the range 0 to -1 V for voltages of 2.5 and 5 V applied to RBW. Defining the resistance R_B to be the inverse of the straight-line fit to I-V over the range 0 -> -1 V, plot R_B as a function of V_RBW.

FIGURE 6. Base Diffusion Resistor on Lab Chip 1. Pin 20 controls the resistor RB.

The circuit for distributed RC delay is shown below. The MOS transistor is configured as a "source follower" and minimizes the effect of the large parasitic capacitance attached to PIN 27 from the breadboard and cabling.

Apply a small sinusoidal input(10 kHz) with a DC bias of 3V at v_in. Connect v_in to Channel A and connect v_out to Channel B of the gain/phase meter. Set the gain/phase meter to B/A mode and start increasing the frequency of the signal generator. Measure the -3 dB frequency and make a Bode Plot. Apply a pulse train of amplitude =1V and frequency=10 kHz at the input and measure the delay time(0-50%) of the distributed RC network.

FIGURE 7.

Assuming that there is a single -3dB frequency,

Applying a unit step input u(t) gives

or

So the time delay(0-50%) is given by

Compare the relationship between your -3 dB frequency and time delay (0-50%) with the relationship above. What is the disadvantage of using very long metal runners in an IC chip? (explain) (hint-very long metal runners can be modeled as a distributed RC network.)

For IC layout, it is convenient to work with a parameter called sheet resistance R_{o Fo}r a region of length L and width W the sheet resistance is found from

_{where L/W is the number of squares. Non-rectangular regions can be modeled by an effective number of squares, as shown in Fig. 8.}

FIGURE 8.