A Unified Analog Design and Process Framework for Efficient Modeling and Synthesis

TechSynthesizer^TM, the second solution, is a completely autonomous software, easily integrable in all design environments. This tool allows the designers to automatically synthesize their devices, thus drastically reducing costs and time-to-market. The tool also offers the possibility to synthesize components taking into account the process variations.

Application: ST Microelectronics parameterized inductor

Aims of the survey

For this new generation STM technology, 11 variable parameters are considered: frequency, 6 design parameters (diameter, bump pitch, coil width,...) and 4 technological ones (metal thickness, core thickness,…). Figure 1 shows the inductor’s design for a given set of parameters.

The inductor frequency is over a broad range from 0.1 up to 20GHz. Design parameters have considerable range variations to tackle diverse design performances. Finally technological parameters have slighter variations but sufficient enough for the study of process variations.

Figure 1: STMicroelectronics BGA Inductor

The model outputs are electrical performances such as inductance value (Ldiff), quality factor (Qdiff) and resonance frequency – S/Y/Z parameters [8] have been also studied to help extracting equivalent electrical model (not detailed in this paper) –.

This survey presents:

• Inductor modeling: find an accurate analytical function linking the inductors geometrical and technological parameters to their performances.

• Inductors synthesizing: find a robust design that fulfills with the designer requirements, including design and process variation constraints.

Modeling framework

Experiment protocol

TechModeler^TM software generated 90 samples data points to cover optimally the input space parameters. For each sample, the electromagnetical simulator HFSS (from Ansoft [3]) simulated the BGA inductor for a frequency range from 0.1 to 20 GHz with a 0.1GHz increment.

In the following results of the study, 70 samples were sufficient to model efficiently the inductance. The last ones were kept for blind-validation of the models.

Checking out the design

As TechModelerTM allows an incremental generation of optimal parameters samples, we first generated 30 samples to check out the design.

The computed samples cover as well as possible the parameters space, by making all parameters independently variable for each sample. Thus, this unbiased exploration of parameters space enables a detection of design errors that is more efficient than user simulation trials. After four releases, the design has been fully corrected and is suitable for the studied range of parameters.

Refining the study

This analysis of the first data set of simulations allowed us to detect some strange simulation results (probably due to coarse grain of simulation far from the nominal frequency). We thus designed region of reliability of the simulator results by reducing the frequency range from 1 to 15 GHz. Furthermore we focus in this survey on inductor performances below the first resonance frequency.

Different output variables are modeled, such as performance values or electrical equivalent parameters. In this survey we focus on inductance value (Ldiff variable), quality factor (Qdiff variable), and resonance frequency models.

Furthermore, we limit modeling for frequency below the first resonance frequency. Some models tackle the performances strictly below the resonance, while others (as detailed in the next paragraph) take into account the first slope after resonance.

As the first resonance frequency defines the region of interest and is highly dependent on parameters, this model details are presented later in the paper.

Model performances

L and Q models including first resonance effect

The inductance value model is designed as a function of the 11 parameters (inputs) that compute the inductance value (output).

The TechModeler^TM software easily tackles L value function modeling from simulation data and gives a mean relative dispersion of 2.0% on modeling data and 2.6% on validation data.

Figure 2 shows data and modeling results of inductance value. The model in this figure is drawn for one given set of design and geometrical parameter over the frequency range.

Figure 2: model of inductance value (screenshots of TechModeler^TM software).
X-axis: frequency, Y-axis: Ldiff value (left and right line) with modeling data and validation data

In the same way, a quality factor model can be obtained (see Figure 3 for model curve and table 1 for dispersion results).

Figure 3: model of quality factor (screenshots of TechModeler^TM software)
X-axis: frequency, Y-axis: Qdiff value (left and right line) with modeling data and validation data

Resonance frequency model

The modeling of the resonance frequency gives a mean relative error of 1.5% on modeling data and 2.9% on validation data. This model was computed very quickly due to his low intrinsic complexity (about 1 hour of computing time on AMD Athlon 64 2.2 GHz, 1 GB RAM).

The visualization of models for a set of various parameters allows us to see graphically the dependence of resonance frequency on some parameters. For example, Figure 4 shows clearly the effect of diameter on resonance frequency.

Note that a rigorous detailed analysis of this model controlled by many parameters can be done thanks the other InfiniScale's software TechAnalyzerTM that includes sensibility analysis taking into account random variations of input parameters.

Figure 4: resonance frequency model
X-axis: diameter, Y-axis: resonance frequency

Summary of modeling results

Three models created with TechModelerTM were presented. Table 1 summarizes the goodness of fit of these models and computation time.

Table 1: modeling results

InfiniScale technology allowed us to perform a very fast and accurate modeling even in high dimensional parameter space (4 design parameters and 6 technological ones) and over a broad frequency range. Furthermore these modeling needed only a small number of simulations (only 70).

All the models will then be used for synthesis presented in the next section.

Table 2: copied/pasted OP1 synthesis point

Synthesizing

Classical multi-objective resizing

The TechSynthesizer^TM software gives the optimal inductor parameter set to reach the desired performance.

One inductor has been synthesized according to the following specifications (see table 3).

Table 3: copied/pasted specifications of the synthesis

This specifications example shows the different kinds of constraints TechSynthesizerTM can support:

Fixed value constraints: the freq parameter has been constrained to the 3.6 GHz fixed value.

Interval constraints: the diameter parameter has been constrained to a value between 0.4 and 0.45 mm.

Gauge constraints: the Ldiff criterion is constrained for three different frequency points (3.3, 3.6 and 3.9 GHz) to a value between 0.9 and 1.1 nH.

Multi-objectives: specifications ask to minimize the diameter, and maximize the Qdiff quality factor.

TechSynthesizer^TM synthesis calculation lasts a few minutes, and produces a report at the end of the process that gives the resulting synthesis point with a remind section holding the specifications attached with the given result.

The resulting synthesis point can be copied/pasted inside a document, like this article for instance (see table 2).

A rapid analysis of the resulting synthesis point can be done inside TechSynthesizer^TM, plotting the output parameters as a function of one input parameter.

In the figure 5 and figure 6, the Ldiff output parameter is plotted as a function of the frequency parameter. In figure 5, input parameters of the OP1 synthesis point are given by the synthesis result. In figure 6, input parameters are the same as OP1, except for the m1_thick parameter that is increased of 10%.

Figure 5: Ldiff(freq) @ OP1

Figure 6: Ldiff(freq) @ OP1/m1_thick+10%

Synthesizing with process variations

Analyzing figure 6 shows that the resulting synthesis point is not robust regarding the metal thickness: Ldiff is out of the defined gauge when m1_thick varies of 10%.

In order to get a more robust design taking into account the process variations, it is possible to add a tolerance constraint inside the synthesis specifications:

Tolerance constraints: Ldiff and m1_thick parameters are constrained to have a tolerance of 10%.

With these two supplementary tolerance constraints, the resulting synthesis point is slightly different (see table 5):

Table 5: OP2 toleranced synthesis result

We can notice that with this OP2 synthesis point, the quality factor is slightly lowered, and the Ldiff value remains quasi the same.

The tolerance analysis on m1_thick parameter gives the following results:

This analysis shows that the resulting toleranced synthesis point OP2 is now robust regarding the metal thickness: Ldiff stays inside the defined gauge when m1_thick varies of 10% (see figure 8).

To validate our synthesis results we simulated the inductor with parameters resulting from the synthesis and then compare the simulation performance with the user performance goal.

Figure 7: Ldiff(freq) @ OP2 (with process variation)

Figure 8: Ldiff(freq) @ OP2/m1_thick+10%

Synthesis results validation

Three designs have been synthesized through TechSynthesizerTM, respecting three different specific specifications. Simulations have been launched by the STMicroelectronics team for each one of these designs. The obtained Ldiff and Qdiff performances presented less than 3% dispersion between the synthesized designs and the simulated ones. This error is logically the same as the predicted mean relative error as computed with validation data during modeling step (see table 4).

Table 4: Tolerance constraints

Conclusion

In this article the InfiniScale flow for an efficient modeling and synthesis of analog devices is described, and successfully applied to the validation survey leaded by STMicroelectronics onto its new BGA inductor technology. Accurate models have been obtained using TechModelerTM software, and a robust design has been synthesized mixing both design and technological/process parameters, using TechSynthesizerTM.

Finally, the ability of this flow has been industrially approved on many analog circuits and MEMS.

References

[1]    InfiniScale web site: www.infiniscale.com

[2]    STMicroelectronics web site: www.st.com

[3]    Ansoft corporation HFSS web site: www.ansoft.com/products/hf/hfss

[4]    The spice page: bwrc.eecs.berkeley.edu/Classes/IcBook/SPICE

[5]    Empirical model-building and response surfaces, G. E.P. Box, N. R. Draper, Ed. John Wiley & Sons – 1987.

[6]    Plans d’expériences : construction et analyse, D. Benoist and Y. Tourbier, Ed. Lavoisier – Tec & Doc – 1994.

[7]    Plan d’expériences pour surfaces de réponse, J. Goupy, Ed. Dunod – 1999.

[8]    S-Parameter techniques, Test & Measurement application notes 95-1, Hewlett Packard