Sub-Threshold transistors: 3 answers to find your way in this CMOS region

Why aren’t more companies using the sub-threshold region of CMOS transistors? In fact, why is the sub-threshold region not more popular? The idea of applying a voltage near or below a certain threshold is far from new since the earliest papers implicitly discuss it as the “parabolic region” in 1955¹. By using such a low voltage, transistors offer greater energy efficiency, thus enabling ultra-low-power applications.

Unfortunately, the side effects of using such a low voltage also limit the region’s usefulness. Put simply, the idea of using the sub-threshold operating region is excellent. Its usefulness in real-world devices, however, is far more nuanced. Yet, it hasn’t stopped some makers from selling devices that operate at the sub-threshold or near-threshold region. Let’s see why we all want it but why it’s so hard to deliver it.

What is the sub-threshold or weak inversion region?

The 3 regions of a transistor

Most understand a transistor as having three “regions”, meaning three relations between the voltage applied at the gate-source (V_GS) and the current measured between the drain and the source (I_DS).

1. When V_GS is below a certain threshold (V_T), many students are taught that I_DS is about zero, which textbooks traditionally refer to as the cut-off region.
2. Once V_GS exceeds V_T, I_DS experiences a sudden rise. As holes in the substrate of the transistor move deeper, a channel between the drain and the source allows for an electric field with a quadratic growth. This is often called the triode region.
3. Finally, after a certain level, an increase in V_DS only leads to a linear rise in I_DS, which textbooks often call the saturation region.

The sub-threshold region

This model explains the behavior of most transistors and is helpful in numerous situations, but it comes with caveats. For instance, in very small geometries, applying a V_GS below the threshold voltage can lead to sub-threshold conduction, which is why many refer to this region as the sub-threshold region. In the most simplistic terms, applying a V_GS below V_T generates an inversion layer under the gate oxide that enables a diffusion current as residual leakage current flows, making this a weak inversion. That’s why the sub-threshold region is also called weak inversion. When looking at the relation between V_GS and I_DS on a logarithmic scale, we notice exponential growth².

Understanding sub-threshold conduction helps dispel the misconception that V_T acts as a sort of switch. By this, we mean that in simplistic models, nothing happens below V_T, and then a strong inversion takes place immediately after exceeding this value. Reality is a lot more nuanced and complex. Indeed, weak inversion shows that conduction happens below V_T. Moreover, the threshold voltage itself is not a constant. As Reynders and Dehaeney show, when outlying the formula for the threshold voltage³, V_T varies according to the body effect, meaning the voltage between the source and the bulk (V_SB), the temperature, and a voltage barrier between the source and the drain (Drain-Induced Barrier Lowering or DIBL).

The 500 mV threshold

Looking at V_T from a practical standpoint, devices used in ultra-low-power systems today have a threshold voltage of 500 mV. However, as we saw, the exponential behavior that characterizes sub-threshold conduction is still observed a bit before and after that value. Moreover, the threshold itself may change depending on certain conditions. Hence, manufacturers will often apply a V_GS above 500 mV and still call it a sub-threshold design, even if it is technically a near-threshold operation. For instance, as we still observe weak inversion at 700 mV, many simplify their communication by only talking about sub-threshold operation, even if it is technically near-threshold, and it has become an accepted practice.

Why is sub-threshold a good thing?

A lower V_CORE

The benefits of the sub-threshold region are fairly evident. Thanks to the low V_GS and the exponential relationship with the current at the drain-source, it’s possible to go from a traditional voltage core (V_CORE) of 1.2 V to sub-one volt values. Furthermore, given that the power (in watts) is equal to the square of the voltage divided by the resistance, such a decrease in voltage dramatically affects the overall power consumption, which explains why we find engineers using sub-threshold transistors in ultra-low-power applications.

A lower dynamic consumption

The benefits of using the sub-threshold region become even more impressive when looking at the behavior of modern devices and their dynamic consumption. Indeed, when a system is in sleep or stop mode, the benefits of sub-threshold conduction don’t apply since the device is essentially off. However, as soon as it wakes up and the dynamic consumption takes over, the sub-threshold mode offers vastly more power savings thanks to the lower V_CORE and its relation to the power. However, since devices spend most of their time sleeping, some overlook those gains.

The problem is that many don’t realize that while an industrial machine, like a water-metering system, may have a duty cycle of only 0.1%, meaning that for every thousand cycles in STOP mode, it spends one cycle running, that one run represents about 80% of the overall power consumption. Indeed, savings in STOP modes are essential. However, the dynamic power required when running is so high that any efficiency improvements will have drastic effects, even if the device spends nearly all its time asleep. This is even more true in consumer systems, like wearables, where the duty cycle is between 5% and 20% since the system wakes up more often and spends more time running, meaning the dynamic power represents about 99% of the overall consumption.

Why are sub-threshold designs not more popular?

Greater voltage and temperature limitations

The most perceptive will have anticipated that while there are numerous efficiency advantages to sub-threshold conduction, the fact that weak inversion is a product of leakage current also comes with some significant drawbacks, the most direct being that it negatively affects STOP mode by increasing its power consumption. It also means that voltage and temperature ranges are much more restricted, as they exacerbate leakage currents, which are already substantial. It also explains why we rarely find sub-threshold designs in industrial applications. Niche systems and those living in harsh environments can’t afford the voltage and temperature limitations of today’s sub-threshold devices.

Slower performances

The other issue is performance. Both current leakage and the weak inversion taking place when applying a voltage below the threshold mean that operating frequencies are lower than when using the strong inversion region. As a result, a system will have a lower computational throughput. Over the decades, research has managed to mitigate this issue. Indeed, the first systems would only run at a few kilohertz. However, as we’ve now exceeded megahertz, manufacturers can obtain decent results even if we are still far from the requirements of high-performance systems.

More die variations

Finally, the exponential behavior of sub-threshold circuits means they are far more sensitive to die variations, which can be a particularly damaging issue as it severely affects yields. As a maker must deal with low voltages and leakage currents, the tiniest variations between dies on the same wafer can be complicated to manage. Consequently, it may result in more dies being rejected or needing complex manufacturing processes that may increase costs and lead time. Hence, while sub-threshold designs are very promising, those large stumbling blocks explain why they are not more popular. And it’s not until someone finds true solutions to those challenges that we should expect them to be mainstream.