The die within integrated circuits are designed with signal integrity (SI) issues in mind and it is with a high degree of confidence that circuit designers commit to silicon and produce wafers. The wafers are sliced and diced to create die for ICs but it is here, at the packaging stage, that SI once again raises its head. In bonding out to the leadframe within the package we are effectively encasing our silicon die in a complex resistive, capacitive and inductive environment: this will change significantly the form of the signal leaving the package and hence affect the circuit's behaviour. Typically, most silicon vendors provide models of their circuits - models based on an accurate characterisation of the manufacturing process. These models can be simulated in SPICE to predict system-level behaviour. However, unless we also have models of the package, which forms the interconnection between die and the external circuit board, we do not really have a complete systems level description of the packaged IC. And without that we cannot be sure that the packaged chip will work as well as intended (if at all).

Thankfully, we can use electromagnetic (EM) analysis to quantify the effects of a package on the electrical performance of the circuit within. EM simulation tools (interfacing with the EDA tools used to design the circuit and its physical layout) extract a 3D solid model of the critical nets (or indeed the nets in the entire IC package) and analyse them to produce a SPICE-compatible model of their behaviour. It is of course necessary to add information not present in the original circuit layout data, such as details of the bond wires, the solder balls and the vias, but once we have that data we can characterise the entire package.

Consider the critical net traces shown in figure 1a: They have been analysed to predict their behaviour across the spectrum of frequencies shown in figure 1b. The frequency-dependant scattering parameter data can then be converted into a SPICE sub-circuit, so that SPICE simulations can predict the true characteristics of the packaged die. Traditional PCB tools can only analyse the structure in 2D without accounting for the true electrical performance of the via or other 3D structures. This is an acceptable approximation if the clock speeds are low, but with high clock speeds (>2GHz) the characterisation of the board or package in 3D is critical. For example, in the hundreds of MHz range, a via may be approximated as a simple inductor - but at 1GHz and above it is important to take into account the effects of high-frequency physics and the true 3D nature of the structure. When the SPICE nets have been generated from a true 3D analysis it is possible to characterise accurately ground bounce, under- and over-shoot, propagation delay, crosstalk, and simultaneous switching effects.

Seeing is believing EM simulation of a physical structure, such as an IC package, is done using finite element analysis (FEA). This works by taking a geometric model of the package and breaking it down into a number of small tetrahedra (the finite elements). Only by breaking down the structure into such small shapes can we accurately represent an arbitrary 3D geometry and assign realistic material properties to its component parts.

The electromagnetic behaviour of lossy and anisotropic materials in complex 3D structures is impossible to model using so-called 'closed' analytical methods. FEA however allows us to do detailed modelling by adopting a 'divide and conquer' approach. Rather than trying to get a single closed mathematical expression to represent the fields throughout a complex region, FEA uses simple (quadratic polynomial) expressions in all of the many tetrahedral finite elements that comprise the complex region under investigation.

A further advantage of FEA is that the 'mesh', in which we do our modelling, is independent of any particular coordinates system - so it can conform very closely to actual geometries and accommodate the large 'dynamic range' of dimensions - from very thin bondwires to large encapsulation structures. Some numerical techniques break down shapes into a series of rectangular brick-like elements. This means that approximations have to be used to map real geometries onto this artificial underlying structure - a risky process, which can lead to loss of electromagnetically significant information. Not only does EM simulation predict the macroscopic behaviour of a device, it also gives a detailed view of the actual electric and magnetic fields. Armed with this information, not attainable through traditional measurement techniques, the designer can develop a far greater insight into the behaviour of the device: and hence work more productively towards the final design.

Optimisation
Consider the simplified package model shown in figure 2a. It is based upon a high-speed optical communications package. If we view the package from above (2b) we can see where we will have mutual coupling. The leads on the outer edge of the leadframe are long and thin but far apart - therefore capacitance is low and inductance high. Within the package encapsulation however the gap between the leads reduces as the lead width increases - resulting in a higher capacitance and a lower inductance. Hence there is a transition in the impedance as signals enter the package: and this transition will give rise to reflections at high frequencies.

Figure 2c shows how the leadframe shapes can be optimised to improve signal integrity - and it is worth remembering that we have very little freedom when it comes to changing this geometry. We cannot for example change the package's pitch or the lead lengths if we still want to use the chip on a PCB; moreover, the attachment points of the bondwires at the chip are also fixed. We are however allowed to change the leadframe shape within the package - but only within reason: thermal and mechanical constraints restrict our design freedom.

Do such apparently minor changes make a difference? Yes. Figure 2d shows how an optimiser was able to improve the differential return loss of two such leads. Above 6GHz the return loss was significantly improved, by trading off low-frequency performance to extend the performance at desired high frequencies. This illustrates clearly how the combination of detailed electromagnetic analysis and optimisation allows us to meet the ever-increasing demands placed on electronic packaging.

Conclusion
EM simulation has reduced, if not removed entirely, the risks associated with the all-important 'packaging gamble' - a gamble which sees the stakes increasing with IC speed and performance. In addition, EM simulation is providing engineers (those planning to use the IC in their circuits) information regarding the performance and characteristics of the packaged IC even before it has been manufactured: affording a valuable time-to-market head start. Furthermore, as IC operating frequencies increase, modelling the die and the package as a whole will gain in importance.

Figure 1a:
Traces within the package design selected as critical nets for EM simulation

Figure 1b:
Differential transmission (blue) represents how much of the signal gets through; differential reflection (red) represents how much of the signal gets reflected back; and common-mode coupling (green)

Figure 2a
Example: A high-speed optical communications package

Figure 2b
The package design viewed from 'above' - showing the various cross sections which affect the local impedance

Figure 2c
How the lead frames can be optimised to improve signal integrity

Figure 2d
The differential return loss for the two leads, before (red) and after (purple) optimisation

Figure OPTIONAL 1
Frequency dependant scattering parameter data can be converted into a SPICE sub-circuit for inclusion in a wider circuit schematic. The graph at the bottom shows the voltage waveforms for over-shoot and propagation delay

Figure OPTIONAL 2
The advantages of FEA include a) the presence of a coordinate-independent mesh in which the structure can be modelled accurately and b) that the mesh can adapt to the greatly differing sizes of features within the geometry.