Monday, July 08, 2013

Contacts III: The search for measurements

In the last two posts I've talked a bit about contact resistances, but I haven't said much of anything about how to infer these experimentally. 

In some sense, the best, most general way to understand contact voltages is through scanning potentiometry.  For example, this paper (pdf - sorry for the long URL) in Fig. 10 uses a conductive AFM tip to look at the local electrostatic potential as a function of position along an organic transistor under bias.  When done properly, this allows the direct measurement of the potential difference between, e.g., the source electrode and the adjacent channel material.  If you know the potential difference and the current flowing, you can calculate the contact resistance.  Even better, this method lets you determine the \( I-V \) characteristic of the contact even if it is non-Ohmic, because you directly measure \(V\) while knowing \(I\).   The downside, of course, is that not every device (particularly really small ones) has a geometry amenable to this kind of scanned probe characterization.

A more common approach used by many is the transmission line method.  In the traditional version of this, you have a whole series of (otherwise identical) devices of differing channel lengths.  You can then plot the resistance of the device as a function of \(L\).  For Ohmic contacts and an Ohmic device, the slope of the \(R-L\) plot gives the channel resistance per unit length, while the intercept at \(L \rightarrow 0\) is the total contact contribution.  This does not tell you how the contact resistance is apportioned between source/channel and channel/drain interfaces (this can be nontrivial - see the figure I mentioned above, where most of the voltage is dropped at the injecting contact, and a smaller fraction is dropped at the collecting contact).  Related to the transmission line approach is the comparison between two- and four-terminal measurements of the same device.   The four-terminal measurement, assuming that no current flows in the voltage contacts and that the voltage probes are ideal, should tell you the contribution of the channel.  Comparison with the two-terminal resistance measurement should then let you get some total contact resistance.  I should also note that, if you know that the channel is Ohmic and that one contact dominates the resistance, you can still use length scaling to infer the \( I-V \) characteristic of the contact even if it is non-Ohmic.

The length scaling argument to infer contact resistances has also been used to great effect in molecular junctions.  There, for non-resonant transport, the usual assumption is that the bulk of the molecule (whatever that means) acts as an effective tunneling barrier, so that conductance should fall exponentially with increasing molecular length (assuming the barrier height does not change with molecular length, an approximation most likely to be true in saturated as opposed to conjugated molecules).  Thus, one can plot \(log G\) as a function of molecular length, and expect a straight line, with an intercept that tells you something about the contact between the molecule and the metal electrodes.  This has been done in molecular layers (see here, for example), and in single molecule junctions (see here, for example).  These kinds of contact resistances can then be related, ideally, to realistic electronic structure calculations looking at overlap between electronic states in the metal and those of the linking group of the molecule.

Hopefully these three posts have clarified a little the issue of contact effects in electronic devices - why they are not trivial to characterize, and how they may actually tell you interesting things.


Anonymous said...

in your next post you chastise your readers for not commenting on this post. This spurred me to action. There is a probe of transport in thermopower that seems to be slightly more immune to contacts. I would love to know if you have had any experience/thoughts or know about work using thermopower versus resistance to characterize contacts.

For instance often in organics I worked on - before I learnt that pure gold makes better contact than Cr/AU or Ti/Au - seemingly activated 2 probe(or even 4 probe) "resistances" have metallic thermopower behaviour (fall proportional to T with cooling and have magnitudes in the range of compensated metals.

I am a grad student who was once made to do thermopower and I always wished more people did it or talked about it.

Douglas Natelson said...

Hi, Anon - Thanks for commenting. (I was really looking at the page views, by the way - I had been surprised by how few people had read the posts.)

Thermopower is a very neat technique, and I was thinking of doing a separate post on it. On the molecular scale it's getting a lot of play these days because it can tell you a lot about whether it's smart to think about transport via holes (that is, through a mostly filled level) or electrons (through a mostly empty level). I really don't know much about thermopower as a means of characterizing contacts except in the crudest sense. Do you have a reference?

Unknown said...

Hi Doug,

I read all your contact posts. Perhaps my feed reader doesn't contribute to your page view count. I consider myself well informed regarding the topic, but the average reader probably could not follow the discussion without some figures or sketches. I understand that including figures would increase your work time significantly, but that might increase your readership and the number of links to your blog.

I don't understand Anon's point about T dependence. This predicted trend applies to any conducting platform (metals, organics, and semiconductors). This is clearly demonstrated here: arXiv:1307.0249.

I have been measuring thermopower in nanowires for a few years now. I would say that the contact resistance is only as important as the resistance of the active region. Afterall, a thermoelectric device is like a battery with an internal resistance (the contact resistance can be lumped into this). To measure its thermopower, the thermoelectric device is connected to a voltage amplifier, which has in input impedance and acts as a load resistance in a battery circuit. The relative size of the load resistance and the internal resistance will effect the voltage drops (thermovoltage), current, and electric power in such a circuit. This is also shown here: arXiv:1307.0249 and here: arXiv:1109.1009. The internal resistance can also change as a function of temperature, while the load resistance does not. Therefore, temperature-dependent thermopower measurements can be difficult to interpret.

When the contacts form Schottky barriers and induce Coulomb blockade, their effect on thermopower is obvious (even if the Coulomb blockade is weak). Similarily, I have seen unpublished data demonstrating that crystal disorder in nanowires can produce localized states as identified by thermopower measurements. This type of effect is predicted here: doi: 10.1186/1556-276X-6-286.

Anonymous said...

Hi, Doug

Interesting three posts.

Do you think contacts or the area around them may be important for resistive switching that is observed in some (many?) oxides?


Horace said...

This is cool!

jim smith said...

This spurred me to action. There is a probe of transport in thermopower that seems to be slightly more immune to contacts.
Transmission Hollywood FL

Major Neo said...

Hi Natelson,
It was really a treat to read your "Contacts" series, i have some basic query regarding "contact resistance", is the -ve contact resistance (as observed by some groups in graphene FETs)have any physical significance/what does -ve means; does it implies deduction from the channel contribution !!!