Relative Permittivity of PCB Substrates: High-k or low-k dielectrics?

The relative permittivity of water makes this pencil appear bent

If you’ve paid attention to refraction, then you know something about the physics of relative permittivity. The semiconductor industry has managed to continue scaling to smaller technology nodes by using materials with high dielectric constant (so-called high-k dielectrics), but can you see similar benefits in your PCB with similar substrate materials? What about the use of low-k dielectrics?

The answer is not so simple, and you’ll need to weigh tradeoffs involved in using materials with different dielectric constant. There are other properties of the substrate to consider as well, and these properties are unrelated to the substrate’s relative permittivity.

Relative Permittivity of PCB Substrate Materials

With most boards, designers have been able to get away with designing on FR4 thanks to some creative design decisions. These days, there are many more options for PCB substrates that provide a number of benefits in specific applications. If you’re looking for ease of thermal management in a harsh environment, ceramic substrates may be your best bet for heat dissipation without additional active cooling measures. If your focus is on reducing losses on long transmission lines, there are many high speed laminates available that are specialized for low loss in particular frequency ranges.

The frequency dependence of relative permittivity and loss tangent are important points to consider as you should aim to optimize the behavior of your board over the relevant frequency range. Relative permittivity can vary widely from ~2 to above ~10 over a range of frequencies. The same applies to the imaginary part of the relative permittivity. If you look at data on these quantities in a variety of materials, you’ll find that most manufacturers only quote a value at specific frequencies, or they don’t even specify a frequency. In this case, you’ll have to look to the research literature, take your own measurements with your proposed substrate material, or use a model like the wideband Debye model or Kramers-Kronig relations to model the real and imaginary relative permittivity.

Schematic showing changes in the relative permittivity with frequency

In general, dielectric loss, which is proportional to the imaginary part of the relative permittivity, is also proportional to the frequency of an electromagnetic wave propagating in a material. This is why attenuation is normally plotted as a linear function of frequency, although this is technically incorrect as the imaginary permittivity is also a function of frequency as shown above. Peaks in the imaginary relative permittivity spectrum arise due to different polarization mechanisms that occur in different frequency ranges. These mechanisms form the basis for calculating the refractive index of a material in different frequency ranges.

The table below shows some representative values that can be taken as objectively accurate somewhere in the 100 MHz to 1 GHz range. One should note that the value for typical FR4 varies by up to ~15%, depending on the fiberglass weave pattern and fill factor. The routing direction across the fiberglass also affects the effective dielectric constant a signal would see as it travels on a trace.

Source: Intel PCB Stackup Guidelines for FPGAs

The relative permittivity of your PCB substrate material will also vary with humidity and temperature. Some FR4 weaves have high adsorptivity toward water as they can be very porous. As water has a high relative permittivity (~80) and conductivity, any PCB on FR4 that operates in a very humid environment will have greater losses at higher speed/higher frequency. A higher ambient temperature also increases losses in general as it increases the polarization dephasing in any material. This is quantified using a thermal coefficient of Dk (TCDk); lower TCDk values are preferred over the widest range of operating temperature as possible.

Crosstalk Through Capacitive Coupling

Changes to the relative permittivity will affect a board’s parasitic capacitance between a trace and its reference conductor, or between a trace/power bus and any other nearby conductors. It will also affect the natural frequency and impedance of a transmission line on a substrate. The geometry of your transmission lines must be precisely controlled to ensure consistent impedance.

The substrate’s relative permittivity is an important determinant of capacitive crosstalk. If we consider two traces running in parallel along a substrate, a potential difference between the two traces will induce a similar (albeit distorted) pulse in each trace. The two pulses then spread and propagate towards the lower potential ends of the respective traces.

The magnitude of the capacitively coupled current is proportional to the mutual (or parasitic) capacitance between the two traces, thus a board with a lower relative permittivity is desirable if you want to reduce the magnitude of any induced current. From an impedance perspective, this increases the impedance seen by a stream of digital pulses, which decreases the capacitively induced current. This can help you keep crosstalk signals in single ended traces within your noise margin.

You’ll notice from the above table that the loss tangent tends to scale downwards with lower relative permittivity, so you stand to gain the benefits of lower dielectric loss (be careful to note the frequency range!). However, a lower relative permittivity increases the critical link length that corresponds to a transition to transmission line behavior. Be sure to keep this in mind alongside impedance during routing. There is one benefit in that using a substrate with lower relative permittivity requires using a trace geometry with lower mutual inductance in order to maintain constant characteristic impedance. This then decreases the magnitude of inductive crosstalk alongside capacitive crosstalk.

Theoretical overdamped near-end response induced in a trace through strong inductive and capacitive crosstalk

In contrast, a substrate with higher relative permittivity will have a shorter critical trace length due to the slower propagation velocity. Using a board with higher capacitance requires arranging traces with higher inductance to yield consistent impedance throughout an interconnect. This will increase the damping constant seen by transient response, which could bring an interconnect closer to the perfectly damped or overdamped case, depending on the termination network one uses. In the author’s opinion, it is a good idea to simulate critical interconnects for a range of relative permittivity values in order to determine the best substrate for your particular application.

Whether you’re designing a high speed or high frequency PCB, your design software needs to include a complete materials library for defining the material properties of your substrate. Altium Designer provides these important multilayer design tools alongside layout, MCAD/ECAD collaboration, and simulation features in a unified design interface.

Now you can download a free trial of Altium Designer to learn more about the layout, layer stack management, and simulation tools. You’ll also have access to the industry’s best documentation and production planning features in a single program. Talk to an Altium expert today to learn more.