Friday, December 19, 2014



Autumn is a second Spring when every leaf is a flower. - Albert Camus

In many parts of the country - New England, the Atlantic alluvial plain westward into the Appalachians, the Pacific Northwest - the fall season brings a beautiful color combination of turning leaves in a soft autumn light. But the season is particularly distinct in Southern Utah. With the changes of landscape between mountain meadows at 10,000 feet in Cedar Breaks down to the desert country of the Vermilion Cliffs towards Arizona, there is a simply dazzling array of leaves in green, yellow, brown, red and orange shades lit in either desert or mountain sunlight. Throw in the many red, orange, white and pink cliff faces, canyons & rock formations of the area with stands of quaking aspen at the higher elevations and the autumn looks positively unreal in this region.

I actually used to hate the fall when I was a kid. Back then, autumn in New Jersey meant the end of summer's freedom with the start of school, weekends spent raking leaves out of the front and back yard and the approach of the cold and flu season. But just as one's taste for things like spinach, cheese and carrots goes from revulsion to happy acceptance and items such as whole milk, pasta and pizza become food which you simply can't get enough of to things that put inches on your waistline if you're just within 100 feet of them, everything changes with age. I now look at the fall as a time of warm fireplaces, cozy sweaters & blankets and urgently needed hats; of a final harvest from the garden and fruit trees, the approaching festivities and the closing of a busy and varied year.

If winter is slumber and spring is birth, and summer is life, then autumn rounds out to be reflection. It's a time of year when the leaves are down and the harvest is in and the perennials are gone. Mother Earth just closed up the drapes on another year and it's time to reflect on what's come before. - Mitchell Burgess

The cycle of the seasons and our own cycle of life is part of the rhythmic ordering of the natural world. There is, of course, an underlying structure supporting this order - one based on the 6th element of the periodic table: Carbon.

The intrinsic properties of carbon are such that it is magnificently suited for the formation of complex multi-atomic structures in the form of chains, arrays or other interesting geometries. Like almost all elements (boron being a particularly interesting exception), carbon is in its most stable state when it possesses 8 electrons in its outermost shell (this is known by chemists as the Octet Rule.) A single carbon atom only has 4 electrons in its outer shell, also called the Valence Shell. Thus, it can be said somewhat figuratively that carbon atoms 'hunger' for another 4 electrons, and are thus described as having a valence of 4. 

When an element forms a bond with another, it does so by sharing electrons from the valence shell. The closer to the atomic nucleus the valence shell is, the stronger the bonds. Here we see a major difference between carbon and its close cousin silicon, which also has a valence of 4 and is one row lower in the periodic table. Whereas carbon's valence stems from its second shell, silicon has a full complement of 8 electrons in the second shell and 4 electrons in its third. As a consequence, silicon can form very hard minerals such as quartz and granite, as well as chains of atoms that are hundreds long. However, carbon can form the hardest substance known to man - diamond. It can also form molecules many thousands of atoms long and can be found in millions of different chemical and geometric configurations. It is for this reason that Mother Nature chose carbon over silicon to express the incredible complexity and variety of organic life.

The flexibility of carbon is such that its structures contradict each other in the properties they manifest. For instance: diamond is the hardest substance known and is used in powerful industrial sanders and oil well drill bits, whereas graphite (which was the 'lead' in our pencils in grade school) is one of the softest materials and an excellent lubricant. One can see the same contrasts between diamond and graphite in terms of thermal or electrical conductivity.

Of all the configurations of carbon, one of the most amazing is the Aromatic Ring. The name describes a family of organic compounds that share a common structure and, interestingly, an often pleasant aroma. The geometry is rather basic - a planar hexagon. In its simplest form (that of benzene), each of the six carbon atoms bonds to its nearest neighbor and to a lone hydrogen atom. In order to complete the necessary electron octet of each carbon atom for stability, there are three double bonds interspersed in the carbon ring.


Naturally, the valence of the carbon atoms in the ring could be satisfied if the double bonds in the above diagram switched places with the single bonds. These bonds do, in fact, move around rather readily. Thus, for the sake of simplicity and to avoid truly silly arguments, the benzene molecule is often drawn simply as so:


If one were to remove one or more of the hydrogen atoms bound to each carbon, the ring can form an exquisite variety of molecules. The one of greatest interest to us for this discussion is a nearly miraculous material which holds tremendous promise for the future of the entire High Technology industry - Graphene.

Silicon has served wonderfully for the past 67 years as the underlying foundation of the second industrial revolution. At this point, however, it is undeniable that silicon has run its course as a material on which to base further major advances in High Technology. The ability of the vast collection of intellect and talent in technology circles to extract further value from silicon is reaching its end, based on the limitations inherent in the material. One can see this from the statements made by Broadcom's Henry Samueli this week regarding the utility of doing designs in silicon nodes deeper than 28nm:

What is it about graphene that suggests it could become the best way forward from silicon? There are indeed aspects of the material which are seemingly miraculous.

The Holy Grail


The Holy Thing is here again
Among us, brother, fast thou too and pray,
And tell thy brother knights to fast and pray,
That so perchance the vision may be seen
By thee and those, and all the world be healed. - Alfred, Lord Tennyson, "Idylls of the King"

The legends concerning King Arthur and his Knights of the Round Table are rooted in Dark Age tales and annals of highly disputed origin and authenticity which, nevertheless, gripped the minds of storytellers in England and France in the 12th and 13th centuries during Europe's High Middle Ages. Though the popularity of the legend waned in the Renaissance, it grew again in the 17th century and again in the 19th and 20th, a testament to the universal appeal of these tales to the fundamental hopes, aspirations and ideals of generations widely separated by time and circumstances.

The quest for the Holy Grail is perhaps the greatest of the stories associated with Arthur and his Knights. Thru this quest, Arthur sought to end the conflicts between his faithful yet competitive and ambitious servants - all eager to please their liege and elbow each other aside to win the king's favor - by providing them a cause towards which they could direct all their energies. Each and every knight failed in this great quest except for Sir Galahad, who proved the only one with a heart pure and true to deserve the honor of recovering the Grail. No matter the writer or era in which variations of the story have been produced, it is always implied that the quest for the Holy Grail is a way for Men to renew a spiritual proximity with the Divine and bringing about a Golden Age for humanity.

Yet the grail itself is supposedly a very ordinary thing - a simple cup or bowl, humble of composition and design in either stone or clay, from which Jesus is alleged to have drunk at the Last Supper. A scientific/engineering analogue for this basic item exists in the form of the aromatic ring, which in its most mundane form belies its potential significance for the future of High Tech.

In 1962, it was discovered that a simple benzene molecule stripped of its hydrogen atoms could bond with other aromatic rings in the same condition to form sheets of material one carbon atom in thickness in a honeycomb or chicken wire pattern. The resultant sheet, first isolated in the lab in 2004, demonstrated incredible properties. 

From a purely mechanical point of view, graphene is the strongest material known to science. By point of comparison: graphene has more tensile strength than the strongest steel by more than two orders of magnitude (let that sink in for a moment.) Its resistance to sudden shock is also quite stunning - though the material is vulnerable to fracturing, it nevertheless demonstrates an ability to distribute the force of a violent impact that is 10x greater than that shown by steel for the same unit weight.

The thermal conductivity of graphene is far superior to any other form of carbon. The regularity of the matrix permits thermal energy to be conducted with high efficiency in all directions. The implications to heat dissipation and long term reliability of complex circuit designs implemented in graphene are thus very positive.

The key capability for any material that hopes to replace silicon will be its electrical properties. Once again, graphene proves itself to be highly unusual in this regard as well as fantastically promising. (Note: for this portion of the discussion, you may want to keep a bottle of tylenol handy.)

The key to understanding the different conducting capabilities of a conventional silicon lattice and a 2D sheet of graphene lies in the structure of the materials. While pure silicon forms the same hard and dense crystalline cube as carbon does when it is in its diamond form, the flat hexagon building block of graphene is starkly different - remember, it has those three double bonds floating around within its form. An interconnected grid of these rings could thus be said to be 'soaked' in a bath of electrons. This leads to a much greater ease of electron flow thru the structure and provokes materials scientists to view graphene as having the nature of a metal. 

There are other pecularities that are being researched intensely. One of these is how graphene conducts electricity. In most materials, making a molecule conduct requires moving an electron from its valence band to a conduction band, as described in quantum mechanics. There is an energy expenditure associated with this, commonly described as a band gap. In graphene, however, this band gap is zero. Once again we can see how the ease with which an aromatic ring moves electrons around its hexagon translates to an extreme ease of movement of electrons throughout an array of rings in graphene.

Since graphene does not behave like other materials when it comes to conducting electrons, the mathematics that describe it are also starkly different. Electron behavior in silicon can be captured with the classic Schrodinger formulation of quantum states for particles small enough to clearly exhibit the wave-particle duality that predicates quantum mechanics. However, Schrodinger's approach does not work effectively for graphene. Instead, it has been discovered that a simplified version of Dirac's more complex equations describe electron behavior in graphene extremely well. This has fascinated solid state physicists and materials scientists for some years now, as the Dirac theorems were the first to unify quantum mechanical theory with Einsteinian relativity. In other words, graphene's electrons seem to manifest relativistic behavior. (Feel free to pop open that bottle of Tylenol now.)

Graphene electrons are not actually moving at the speed of light - they are in fact 300x slower (though that's still pretty fast.) Nevertheless, the relativistic characteristics of current flow are such that electrons in graphene appear to be massless. Even at room temperature, graphene conducts so well that it seems to support superconducting current levels. 

This does not mean that graphene is not without its problems. The material, as noted before, is highly reactive. Placing various conducting or semiconducting materials (including other graphene sheets) in close proximity has a notable effect on graphene's behavior. The fact that single sheet graphene is what shows the greatest promise is also, at the moment, an Achille's Heel of the material, as it is subject to small mechanical defects and irregularities induced by heat or vibration which also profoundly affect its properties. Much research is underway to determine ways of controlling graphene as predictably and meticulously as can currently be achieved with silicon. 

For man, autumn is a time of harvest, of gathering together. For nature, it is a time of sowing, of scattering abroad. - Edwin Way Teale

Like nature in Autumn, researchers are using the approaching winter of silicon to sew the seeds for a new technological Spring based on graphene. There are a great variety of things engineers and scientists are trying to do with graphene to make it amenable to IC applications. We'll talk about that in the next installment.

1 comment:

  1. Great article. I read your blog and come away more intelligent every time. thank you.


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