In voltage reference circuit design, the bandgap curvature problem affects circuit structure and part count. It sets the bar on temperature coefficient, i.e. the reference voltage's stability over varying temperatures. But why should material scientists concern themselves with an analog IC designer's problem? This article explains why I think this niche needs attention from material scientists to further make improvements in designing voltage reference circuits. 



The Bandgap Curvature Problem

The bandgap curvature problem is a trivial consequence of nonlinearity. Due to the absence of a device that exhibits linearly decreasing voltage drop with rising temperature, commonly known as the "complementary-to-absolute-temperature" or CTAT component, engineers have settled with the voltage drop of a P-N junction (i.e. a diode), which is non-linear. Ergo, the summation of the CTAT and PTAT (proportional-to-absolute-temperature) has a non-zero offset. This offset, when measured across a temperature range, is not constant and varies like a curve. This curvature is the bandgap curvature problem, and leads to inaccuracies as the reference voltage changes too with temperature. The term bandgap is used because the bandgap voltage of the material (1.2 for Silicon) is a preponderating part of the equation that determines CTAT. It is occasionally mistaken for the reference voltage as remaining factors that determine CTAT are negligible in value.

There are established methods in addressing this non-linearity at the cost of additional components. Common techniques include squared PTAT correction, using a VBE loop, and nonlinear cancellation. These solutions, the parallel version of the nonlinear cancellation technique being most popular, implement series/parallel combinations of current sources/mirrors that add to the layout area of the circuit, increasing cost.

A Solution at the Physical Level

Because of the absence of a realizable CMOS component with a temperature characteristic stipulated by the previous paragraphs, it is natural to seek a solution at a different level/layer of the design process. It is challenging to attempt an avant-garde train of thought at the physical level because methods are customarily inveterate with respect to the design rules of a process. However, if material scientists could find a material that can undergo deposition, turning silicon into a doped material that decreases its voltage drop with respect to temperature, then the bandgap curvature problem is solved with savings on components and area.

More seasoned designers may see the idea as pure hogwash, finding it nearly impossible to synthesize such a material. They would argue to just stop wasting time on wishful thinking and pipe dreams. But how about tunnel or Esaki diodes? The idea of a negative resistance region in the I-V curve is counter-intuitive. Yet such a component allowed microwave applications that mandate oscillators, amplifiers and switching circuits. Why should designers have a closed mind on the bandgap curvature problem when it comes to a change in the physical process?

After all, implied advantages of such a material don't end at reduced cost and area. The power rail can be reduced further due to an extremely stable reference. A linear CTAT has the potential of  perfectly cancelling out the PTAT, perhaps yielding temperature coefficients in the ppb (parts per billion). With lower reference voltages, logic high and low voltage levels (VIH, VIL, VOH, VOL) could be lowered too resulting in higher efficiency. 

Thus, wouldn't it be nice if material scientists could come up with such a breakthrough?