On Causation, Entropy, and Semiconductors: Friday Night Persnicketiness

Alexander,

Let us talk about a two things that interest me: causation and thermodynamics.1

I was reading a paper today that discusses the frontiers of current research in how charge transfer/separation in some two dimensional semiconductors/heterostructures works. The whole conversation in this micro-field is around the question of how we can build solar cells that are more efficient. To build these efficient solar cells we must be able to have electrons get ripped away from their happy positions in their material homes so that they can flow through wires. In reading this paper the following phrase caught my attention:

“Such an increase in DOS [density of states] with r [distance] provides an entropic driving force for charge separation.”

I would like to point out something a bit interesting in this sentence. The authors of this paper say that entropy is driving something to happen. Entropy is cast as the cause of an event. This type of language is ubiquitous in chemistry—especially in general chemistry type settings where we ask our students such questions as: “is this process entropy or enthalpy driven?”. There is something curious here, though. I made it very clear to my students when we discussed entropy that keeping track of the total entropy of the universe allows me to know if a process is possible, but it doesn’t tell me if the process will actually happen on any reasonable timescale. The common way of thinking of this goes something like: thermodynamics tells us what is not forbidden, but it doesn’t tell us if the things will actually happen.

So why were these authors so ok with saying that the entropy change of the process was driving the event? This is where the language (and thinking) of chemists (and maybe scientists/humans in general) becomes so weird. We oftentimes have a hard time correctly saying which things cause other things and which things are merely necessarily connected to the change.

I don’t think the authors are correct in saying that entropy drives charge separation. Rather there must be some sort of other physical mechanism(s) at play that cause electrons to get ripped from their positions when I shine light on a solar cell. This notion is because of something that I think is rather fundamental: thermodynamic state functions allow us to keep track of things and events, but they don’t force those things to happen. Now let us cast this statement in an analogy.

Let us think of my bank account. It is currently populated with some amount of currency. If we wanted to we could track the time evolution of my bank account by monitoring the amount of currency. Now, my paying of rent is necessarily connected with a decrease of the amount of money in my bank account. Additionally, if I have no money in my bank account I cannot pay my rent. In this way, the money in my bank account is kind of like the thermodynamic entropy change with respect to a process. I hope we can both agree that my rent being paid is not caused by or driven by the fact that my bank account has money in it. The cause of me paying my rent has its very start at my desire to continue living in my house next month. This desire won’t be fulfilled if I don’t have money in my account (that is if the entropy increase is not positive then the reaction won’t happen), but it is not caused by money being in my account! Rather the money being in the account is a necessary condition for the event to happen, but it is not a sufficient condition to be the cause of my rent check getting written.

The very notion of a cause now comes into play. How do I know when one event causes another? The hardcore Humean/empiricist will of course say that we can never ever know for sure that one event causes another, all we can know is that one event always (to our best knowledge) directly follows another event. But us pragmatic chemists that actually desire to help humanity probably shouldn’t spend all of our time thinking in this way. We want to be able to build semiconductors that make good solar cells after all. So we should probably be okay with saying some things cause other things (like billiard balls smacking into each other) because we want to be able to use these causes to inform our decision in solar cell fabrication.

To say it again, the pure empiricist doesn’t want to ever say anything causes something else. They are much happier saying that events are correlated in some way. But we humans want to 1) build concrete associations between events and 2) build solar cells. We could just build solar cells based on massive amounts of known correlations. But this makes us sad, we like thinking that we are making solar cells informed by our proposed mechanisms concerning how charge transfer happens at an interface.

It is now apparent that we scientists are all screwed up. We want to build things, but we aren’t quite absolutely sure how to build the perfect solar cell. Moreover, using our current method of inquiry we can never be sure of how to build the perfect solar cell. We can’t even know if a solar cell connected to my battery is really the reason my battery is charging… oh dear. I guess we are stuck using words like ’cause’ and ‘drive’ in an informal and imprecise way. We must be very careful with these words, though. As always, we should never confuse cause and correlation; we should never confuse the fact that a room always gets messier with the actual cause of the room getting messier—the toddler writing on the wall.2

-Darien

And now the footnotes:

  1. For those that have not taken a chemistry class in a while, the carefully defined notion of a ‘spontaneous process’ is important to have in one’s back-pocket for this post. Please see the possibly esoteric Wikipedia page on spontaneous processes. I apologize for this post going against the originally stated rules of AlkynesofPi, but it seems like we violated those within a few weeks of inception.
  2. Now, Alexander, after the above rant about causation in semiconductors I assume you have now found a little flaw in my dislike of the authors’ usage of the notion of an entropy driven process. You should be saying to me: “But Darien, maybe entropy IS actually a cause. You don’t know. It seems to be really well correlated to lots of events.” To this I sheepishly respond, the notion of entropy causing anything is rather messy. It seems like a universal truth that any change that occurs is accompanied by an increase in the total entropy of the universe. So, the authors’ noting of the entropy increase of the system and the event happening being correlated is nothing new. This is such a not-new thing that we have a universally accepted name for it — the Second Law of Thermodynamics. This not-newness maybe makes it useless in rational design of solar cells. But the flaw in my original peeve is still evident, this entropy change may indeed be the cause, I simply don’t (can’t?) know.

 

When Lower Quality Is Better: The Splendidly Sneaky Art Of Q-Switching

Good afternoon, Darien. 

As you know, I work with a Ti-Sapphire ultrafast laser system.  I suppose that to be precise I should say that I work with two such systems: one for each of my projects.  While we are being precise, though, one might call into question my usage of the term “work” here.  I shall move on quickly without addressing this, and hope that nobody notices.  Anyway, my point is that my lasers generate femtosecond pulses using a cool process called mode locking.  You are familiar with this, I am quite sure.  We are both also aware that there are other lasing mechanisms that are capable of producing pulses.  One of these is the Q-switch, which produces very high power pulses that are not nearly as short as the pulses we use in our research.  Shortly after joining the Dlott group, I was given an introductory book on lasers, which provided a brief overview of the mechanism of laser action various pulsed lasers.  This book contained a brief explanation of various types of pulsed lasers, but I found myself quite confused by it.  I asked Will Shaw (alias “Old Will”) to explain this material to me, and he kindly obliged.  What follows is my attempt to reproduce his excellent explanation of Q-switching.  He actually uses a Q-switched laser, by the way.  The high power apparently comes in handy for blasting aluminum foil pellets at panes of glass.

As you know, lasers have three important parts.  The crystal which produces the light, the pump which energizes the crystal so that it can produce light, and the cavity, which stores the light so that it passes through the crystal repeatedly.  the “Q” in “Q-switching” stands for “Quality”, and the quality being referred to is the quality of the cavity.  In this context, a high quality cavity is one that stores light very efficiently, while a low quality cavity is one that either absorbs the emitted light or lets it escape without being reflected back through the crystal.  For most types of lasers, it is uber important to have a high quality factor, since you need the beam to pass through the crystal many times before population inversion is achieved.  In Q-switching, though, you want your laser quality to be very low most of the time, and only become good occasionally.  This could be easily accomplished by sticking an aluminum block in front of one of the cavity end-mirrors, in order to absorb any light that came from the crystal.  When the block is in place, the quality factor would be low, but it would “SWITCH” to high quality the moment you removed the block.  Thus the term “Q-switching”.  In practice, there are more sophisticated ways of doing this, but the idea is the same.

If I was reading this, I would have become confused and given up during the past paragraph, because it kept going on about Q-switching, but never explained how a low quality factor can allow for lasing to happen.  I will try to remedy that here.  It turns out that Q-switching works by achieving a VERY inverted population in the crystal.  Not some wimpy, ordinary population inversion where you barely have more excited state species than ground state species.  I’m talking about the vast majority of the species being excited.  Most lasing mechanisms don’t allow for such a state to be achieved, because as soon as you get a little bit of population inversion, you start building up an increasingly powerful pulse train that “sweeps out” the excited state species from the crystal via stimulated emission.  In Q-switching, though, you don’t have any pulse train, because you have made the quality super low.  You are pumping your crystal, and some of the excited species in the crystal undergo spontaneous emission, but the fluorescence generated this way gets absorbed once it leaves the crystal, rather than reflecting back to be amplified by stimulated emission.  Sure, a photon spontaneously emitted in the center of the crystal might cause a little stimulated emission in the process of exiting the crystal, but spontaneous emission is rare enough that the population inversion isn’t substantially depleted by this process.  With no way to leave (other than rare spontaneous emission events), the energy pumped into the crystal just builds up.  The population inversion gets more and more extreme.  When it finally approaches a maximum, you are ready to fire your pulse!  You remove the aluminum block (or activate your sophisticated mechanism for switching the quality) and PRESTO! Nothing happens.  At first.  It takes a bit for the stimulated emission to start building up.  Once it does, though, you get a rapid, exponential growth of the pulse power in the cavity.  All that energy stored in the form of an inverted population gets swept out as a tremendously powerful pulse, which you release from the cavity as soon as the population inversion is depleted.  Then you start all over again.  I find it terribly cool that you can store up energy in a crystal this way!  The idea of a nearly complete inversion of population is enough to plaster a sloppy grin on my face.  I hope you find this as cool as I do.  If you don’t, I’ve clearly communicated it poorly.

If you wanted to generate high power pulses using another method, you would run into trouble.  If I remember correctly, maintaining a really powerful pulse train in the cavity ends up damaging it… or something like that.  I think that the advantage of Q-switching here is that the pulse is only very powerful for a brief instant (a few trips through the cavity) before it is released.  I’m not certain of this, though.  I should probably read up on it some more.  But then, there are many things that I should read up on, and I should be reading some of them right now.  I’m afraid I have dashed this off rather quickly, so please enquire concerning anything which is unclear. 

Have a fabulous afternoon!

-Alexander