QUEST - Extraction of Frequency Dependent R, L, C, and G Transmission Line Models

 

1.0 Introduction

A primary use of QUEST is intended to be for extracting frequency dependent transmission line models for use in SPICE circuit simulations.

The generation of SPICE parameters for transmission line models is becoming increasingly important as clock speeds approach and exceed the 1 GHz frequency range. At these speeds many parts of a chip such as data buses, clock lines or power rails can no longer be modeled using simple RC networks. QUEST takes this one step further, as not only does it include inductance in the transmission line model but all the parameters in the generated models are frequency dependent.

One example of why this is so important is the physical phenomena called the "skin effect". This effect occurs at high frequencies in the interconnect layers and in the silicon substrate itself. In the interconnect layers at high frequencies the lines self-inductance of the lines may become significant and result in current conduction away from the centre of the interconnect thus changing its resistance. The "skin effect" in the silicon substrate can significantly alter the resistance and conductance. These effects will be illustrated by simulations performed by QUEST later in this article.

 

2.0 Major Features of QUEST

  1. The transmission line dimensions are extracted DIRECTLY from the chip layout, ie from GDSII or CIF format files using an in-built "Cut-Line" feature.


  2. The transmission line structure is built using Process information in combination with the "Cut-Line" feature described above.


  3. The cross-section of the conductors can be "trapezoidal" in shape, ie the side-walls do not have to be vertical, thus allowing for more realistic processing effects.


  4. The solver uses the "Fictitious Domain" method which has been demonstrated by independent users to be one of the highest speed solving methods around together with being very memory efficient.


  5. QUEST takes full account of the effects of substrate resistivity on the overlying conductors. This can have a significant effect on the RLCG results.

 

3.0 Description of Input and Output Formats

The input information for QUEST has three basic sets of inputs:

  1. The mask layout in GDSII, CIF or Silvaco's layout format from which a cutline will be taken defined by the user.


  2. Process description file, used in conjunction with the cutline to create the structure for analysis. An example of this syntax is shown in Figure 1.


  3. Command file to specify various user defined options as to what to do with the data. An example of this syntax is shown in Figure 2.

 


Figure 1. Command file of the process that
creates the two-dimensional structure.

 


Figure 2. Command file that controls which cutline to
operate on and the frequency range under study.



There are two basic outputs from QUEST:
  • transmission line model parameters

  • two-dimensional structure files


An example of the extracted transmission line parameters that are output from QUEST are shown in Figure 3. All the parameters, R, L, C and G, are frequency dependent. This file can be included into a spice simulation by, for instance, SmartSpice.



Figure 3. Sample transmission line model
that is generated by QUEST.



The internal quantities solved for by QUEST may also be saved to a two-dimensional structure file. This file may be viewed by the graphical tool TonyPlot for analysis. Figure 4 shows one example of which is a two-dimensional potential contour.



Figure 4. Two-dimensional plot of potential contours.





4.0 Effect of High Frequency and Substrate
Conductivity on R, L and C.


In this example the transmission line test structure shown in Figure 5 has been used to illustrate how the effect of the substrate changes as the frequency is increased. The structure consists of a single metal line over a substrate. The multi-insulator capability of QUEST is required as this structure contains six different insulators.


Figure 5. Example test structure of
the transmission line to be studied.



The structure is analyzed for the frequency range of 1 to 40 GHz. Figures 6, 7 and 8 illustrate the variation of resistance, capacitance and inductance as a function of frequency. In both experiments the substrate conductivity was varied from a Sigma of 0.1 Siemens/m to 10,000 Siemens/m.


Figure 6. Variation of resistance as the frequency is
increased for different substrate conductances.

 


Figure 7. Variation of capacitance with frequency
for different substrate conductivity.




Figure 8. Variation of inductance with frequency
for different substrate conductivity.




Different behavior is observed in the capacitance and inductance, for different substrate conductivities and for different frequencies (between 1GHz and 40 GHz). For the low conductivity substrate the inductance and the resistance are constant over the frequency range 1-40GHz. However the capacitance C, shows a sharp decrease at high frequencies. For high conductivity substrate two opposite behaviors are observed: the C is constant but the inductance decreases with the frequency. These phenomena could be explained as the following: at low frequencies and for low substrate conductivities, the substrate behave as a conductor, which results in a large value of the capacitance due to a decrease of the distance between the line and the ground (which is the oxide thickness). At higher frequencies the substrate behave as a dielectric, which results in a decrease of capacitance value due to the increase of the distance between the line and the ground. The resistance and the inductance however, remain nearly constant, since there is no skin effect inside the substrate at low frequencies.

In case of high substrate conductivity, the electrical field is mostly concentrated between the line and the top surface of the substrate, which results in a large value of the capacitance, almost constant over

the frequency range 1-40GHz. However due to the high substrate conductivity there is a significant skin effect inside the substrate. Currents are concentrated on a small region on top of the substrate. Therefore the resistance will increase and the inductance will decrease.

 

5.0 Conclusions

A unique new product QUEST has been introduced which allows a designer to investigate the high frequency behavior of lines within their layout such as clock, power, data lines, etc. With this product a designer may produce a frequency dependent transmission line model which may be used to investigate very accurately the operation of the chip through SPICE simulations. A future article in the Simulation Standard will address the application of models to SPICE design.