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A SPICE resistor model has no stray capacitance, nor does it recognize any possible effects from surrounding layers. There are some cases where such a simple model is inadequate. For example, the frequency and phase response of large-value (50 kΩ and above) resistors can be significant enough to bring about oscillation in a feedback path.
An error is also introduced in a divider if the resistors are diffused and placed in the same pocket or “tub.” Each resistor is at a different DC potential, and their voltage dependence will result in slightly different values. This error becomes large with ion-implanted resistors.
Some simulation programs have the capability to extract stray capacitances from the layout, but few pay heed to voltage dependence. If you want the complete behavior before the layout is done, here is a subcircuit model:
.SUBCKT RCV 1 2
R1 1 4 RB {m/3}
R2 4 5 RB {m/3}
R3 5 6 RB {m/3}
V1 6 2 0
B1 6 1 I=I(V1)*(0.0033*((V(3)–(V(1)+V(2))/2))^0.6)
D1 1 3 DRSUB {m/2}
D2 4 3 DRSUB {m}
D3 5 3 DRSUB {m}
D4 6 3 DRSUB {m/2}
.ENDS
.MODEL DRSUB D IS=1E-16 RS=50 CJO=2.7E-14 M=0.38 VJ=0.6
This is, again, a subcircuit. As we see in Figure 3-15, the resistor is divided into three equal sections. Assuming that the resistor is P-type, the stray capacitance is represented by four diodes to the surrounding N-type material.
Figure 3-15. Equivalent circuit for a 3-segment resistor in an IC process.
To model the voltage dependence, the current is measured in the dummy (0 V) voltage source, V1. From it, a current (I1) is created and subtracted from the total current through the resistor. The value of this current is:
$$I_1 ~=~ I (V_1) ~\times~ \bigg( 0.0033 \, ~\times~ \bigg( V3 ~-~ \frac {V1~+~V2}{2} \bigg) \bigg) ^{0.6}$$
where 0.0033 and 0.6 are values that determine the amount and shape of voltage dependence, respectively. Note that the bias voltage is applied from Terminal 3 to the midpoint of the resistor. The B device is, in Simetrix, an arbitrary function that serves as a current-controlled current source.
Contrary to common belief, a three-section lumped model is remarkably accurate. Compare the frequency response of such a model with one that has 160 sections (Figure 3-16).
Figure 3-16. Comparison of the frequency response for lumped resistor models. [click to enlarge]
Models for Capacitors
There are only two cases where a simple, ideal capacitor model is inadequate:
- There is a requirement for unusual precision. If one plate of an oxide capacitor is a diffused layer—or a poly layer with a high sheet resistance—the capacitance will decrease slightly as the potential across the plates is increased. A competent model will reflect this nonlinearity.
- The capacitor is used at the high-frequency end. In this case, it’s not of great importance for the model to show the nonlinearity. Instead, it should reflect any series resistance and stray capacitances from both the lower and the upper plate to neighboring regions.
