### Should Material Scientists Care About the Bandgap Curvature Problem?

When designing a reference voltage, the bandgap curvature problem is considered as it affects the structure of the circuit and the number of components that come into play. It sets the bar on the reference voltage's temperature coefficient, i.e. its stability over varying temperatures. But why should material scientists be concerned with a problem that solely concerns the analog IC designer?

#### The Bandgap Curvature Problem

The bandgap curvature problem may sound unfamiliar to the uninitiated in CMOS design, but its premise is simple. Due to the absence of a device that exhibits a 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 diode, which is non-linear. Ergo, the summation of the CTAT and PTAT (proportional-to-absolute-temperature) has an offset. This offset is the bandgap curvature problem, and leads to inaccuracies in the reference voltage over a range of temperatures. 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 the CTAT. It is occasionally mistaken for the reference voltage as the remaining factors that determine the 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. It is challenging to attempt a train of thought at the physical level because the 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 exclaim indignantly  - "Hogwash! Its nearly impossible to synthesize such a material! Stop wasting your time on wishful thinking!" Well, I would persistently argue "How about the Schottky diode then?" The idea of a negative resistance region in the I-V curve is certainly counter-intuitive to the Physics-oriented mind. We were able to come up with such a component, resulting in superior switching and reverse-recovery times. Why should we have a closed mind on the bandgap curvature problem when it comes to a change in the physical process?

After all, the positive implications 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, 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?

### Calculator Techniques for the Casio FX-991ES and FX-991EX Unraveled

In solving engineering problems, one may not have the luxury of time. Most situations demand immediate results. The price of falling behind schedule is costly and demeaning to one's reputation. Therefore, every bit of precaution must be taken to expedite calculations. The following introduces methods to tackle these problems speedily using a Casio calculator FX-991ES and FX-991EX.

►For algebraic problems where you need to find the exact value of a dependent or independent variable, just use the CALC or [ES] Mode 5 functions or [EX] MENU A functions.

►For definite differentiation and integration problems, simply use the d/dx and integral operators in the COMP mode.

►For models that follow the differential equation: dP/dx=kt and models that follow a geometric function(i.e. A*B^x).

[ES]
-Simply go to Mode 3 (STAT) (5)      e^x
-For geometric functions Mode 3 (STAT) 6 A*B^x
-(Why? Because the solution to the D.E. dP/dx=kt is an exponential function e^x.
When we know the boundary con…

### Common Difficulties and Mishaps in 6.004 Computation Structures (by MITx)

Updated:
May 6, 2018
VLSI Project: The Beta Layout [help needed]Current Tasks: ►Complete 32-bit ALU layout [unpipelined] in a 3-metal-layer C5 process. ►Extend Excel VBA macro to generate code for sequential instructions (machine language to actual electrical signals).
Current Obstacles/Unresolved Decisions:
►Use of complementary CMOS or pass transistor logic (do both? time expensive, will depend on sched.
►Adder selection: Brent-Kung; Kogge Stone; Ladner Fischer (brent takes up most space but seems to be fastest, consider fan-out) [do all? time expensive, will depend on sched.)
►layout requirements and DRC errors