Introduction:
Images of emerging Transparent Conducting (TC) Technologies
As technology penetration increases, people are demanding more out of their devices, both in terms of performance and aesthetics. A good junction of the two is transparent conduction: consider wearable electronics that people can’t see or a clear flexible display. In the 1930’s people only imagined the power of devices that could happen: literally today we have made them a reality.
Critical to the function of these devices are transparent conductors that can power these devices. In reality, transparent conductors already exist as critical components for many devices: the iPhone, the Kindle, the Nintendo DS and Solar Panels already use transparent conducting technology. Transparent conductors, as their name suggest, must at a basic level meet two requirements: high conductivity (sigma) and high optical transparency (transmittivity in the optical range of > 80% or even higher). Unfortunately, most standard materials for making PCB’s do not have these characteristics. Transparent conductors were discovered by accident by Corning in the 1930’s and oxides of tin and indium began their experimentation. Further along in the 70s organic polymers began to look promising with the discovery of polyacetylene.
Why a second look?
While transparent conducting oxides (TCO’s) and organic polymers have a relatively long history, there are a couple of reasons to look at the technology again. Physically, new technologies are emerging that may create better options transparent conductors. Economically, the rise in demand for LCD’s has created huge volatility in the price of Indium, a rare earth by-product of Zinc mining found predominantly in China and Canada. While not of physical interest, the fact that 83% of Indium is consumed by LCD’s creates an issue of looking for alternatives.
(Indium Prices have been highly volatile over
the past decade)
Goal
The goal of this presentation has been limited in scope. Simply, we will broadly review transparent conducting technology, explaining where possible the physical reasons behind the transparency. In particular we will focus on one key aspect: the dielectric function using the Drude-Lorentz model. We will then have an overview of criteria for transparent semi-conductors as well as which ones look most promising.
One lesson during the course of this project was that in order to truly understand the optical and conductive properties of different materials, a significant expertise in both mathematics and physics is required, which this author does not claim to possess. For those looking for an introduction to some of the key aspects, an introductory solid state physics text has proven highly useful.
Some initial thoughts:
Before diving into transparent conductors, it makes sense to ask transparent to what and how conductive? If that sounds like a stupid question, in fact a majority of the current research for industrial application centers around those questions. Some of the limitations of the predominant standard TC, indium tin oxide, have to do with the fact that although it has high optical transparency, it has very high IR (heat) reflectivity. In many applications, this feature is not desirable. It comes as no surprise that different TC’s will have different applications.
Criteria for selecting Transparent Conductors:
Gordon (2000) suggests the figure of merit for transparent conductors should be its electrical conductivity divided by its visible absorption coefficient alpha: putting these two together, we see:
This equation tends to be a good indicator of the performance of TC’s, and we will see that the industry dominant ITO is not the best in this metric. However, for a given application, there are a wide range of other criteria that are important depending on the engineering task. These include the following:
· Plasma frequency (seen above)
· Work function (energy need to remove an electron from the conduction band)
· Thermal Stability (how well the material performs under heat)
· Deposition Temperature (used for applying films, see appendix)
· Diffusion Barriers between substrates
· Ease of etching
· Mechanical and Chemical Durability
· Toxicity
It is no surprise that different materials then are used in different applications.
Physics: Dielectric Function, Plasma Frequency and the Drude / Lorentz Model
So how do transparent conductors become transparent?
In order to understand transparency, we will now attempt to understand the physics behind the phenomenon. As we know all light act as waves. When light ‘hits’ an object, one of three things can happen” it is either absorbed, reflected or transmitted, leading to the equation: Io = Ia + Ir + It. For example, when light is absorbed, it means that it’s wavelength provides the quantum energy for electrons at the surface to ‘jump’ to the next level of energy. How can we understand this phenomenon at a deeper level?
First consider that all matter is made up of moving atoms, which themselves are made up of moving particles. In solids, the atoms form regular, long-ordered crystal lattices, which determine part of the optical properties. Another part is the interaction of light at the boundary of these materials with ‘electron clouds’, or plasma. One way of understanding this interaction is through the Drude-Lorentz model, which assumes that electrons are ‘harmonic oscillators’ (ie attached by springs) to the nucleus.
Rather than reproduce the mathematical derivation myself, I will point the reader to one I have found, which will do a far better job explaining the physics and its effect on optical and electrical properties. If we take the effect of an electric field, we can use the Lorentzian model which uses Newton’s equation as its basis The thorough look can be taken here than we have time for, but explains the model and its implications on EM very thoroughly.
Basically the Lorentz model assumes that electrons are held to the nucleus by a spring, which has a damping term that reduces its movement. Determining the driving force and using euler’s formula we get a complex exponential which describe the periodic oscillation. We find that the force on the electron depends on its electron susceptibility (Xi) and the permittivity of vacuum (epsilon 0). Free electrons are defined by the fact that they do not have a spring force (no nucleus to ‘revert’ to). It is these free electrons that are most interesting to us from a conduction and optical standpoint. These electrons act as if they are an electron gas surrounding the metal (or a plasma). This plasma frequency determines part of the optical properties, as do the electric susceptibility and the frequency of the incoming radiation.
Metals: a first look
A natural first look for transparent conductors would be metals, since they have a high conductance and are very well understood. Their high conductance comes from their high free electron density. In fact, thin films of metals are used frequently in electronics. Unfortunately however, in order to achieve transparency, the metal films used would need to be incredibly thin. In many instances this is not an issue and in fact gold and other thin film metals are used in LCD’s and other electronics currently. However, we know that resistance is a function of both the resistivity (or conductance) the length of the wire and its area. By reducing the thickness of the wires, we might expect the resistivity to increase. In fact we see that this is the case: for metals, at the threshold that they approach complete optical transparency their resistivity goes up enormously. Below we see a picture of different metals and their sheet resistance plotted against thickness:
(source: Applied Physics Letters, Transparent and conductive electrodes based on unpatterned, thin metal films)
Physically, the increase in resistivity as thickness decreases is predicted by the Fuchs-Sonderheim model, which has the form:
We don’t need to go through the math to understand the resistivity will increase as the thickness decreases. In metals, this happens around 20nm, which we will see shortly poses a major trade-off for optical transparency.
In metals, optical transparency falls off very quickly as thickness increases. Below we plot transmittance against thickness at 600nm for 3 common conducting metals.
(Source: refractiveindex.info)
Additionally, metals thin enough to be transparent also suffer from higher sheet resistance due to electron scattering at the surface and grain boundaries.
Current Transparent Conduction: TCO’s
Metals as we see are not transparent in a thickness that makes them workable for electronics—so is the idea of transparent conductors a fantasy? It turns out that a different type of materials, named transparent conducting oxides, has the properties required for the task. These are doped semiconductors that have high optical transparency (due to their large band gap) and high conductivity due to n-type doping. Transparent conducting oxides are basically n-type semiconductors which can be doped to change their conductivity. In terms of physical parameters, transparent conduction can be achieved if the ceramic material has EG > ≈ 3eV, a free carrier concentration (N) above ≈1019−20 cm−3 and a mobility μ larger than ≈ 1 cm2 V−1 s−1, which can be verified for metallic oxides such as ZnO, In2O3 and SnO2 (Transparent Oxide Electronics: From Materials to Devices).
In many cases, there is a tradeoff between transparency and resistance based on the optical and dc conductivities of the materials. The formula used to calculate these is below:
Indium Tin Oxide and other Transparent Conducting Oxides:
Transparent conductive oxides have been around as we have seen for decades, and are currently the TC of choice for most industrial applications. The reason is because their fabrication has been to large degree understood and variables, such as the doping concentration, can be manipulated for various uses. However, there are other transparent conducting oxides and many of them exhibit better optical and conductive properties: as ITO’s cost increases these are and will be continued to be substitutes for ITO. Below is a table comparing the sheet resistance and absorptive coefficient for transparent conductive oxides at thicknesses used in industrial applications:
As we can see, ITO is not the best in either resistance or absorption; however, we find in many other criteria of merit it falls near the middle, making it a good ‘average’ choice that is well understood by industry.
Part of the high viability of ITO is that doped it has a
very high number of electron carriers. If we recall that electrical
conductivity is driven by the number of charge carriers and their mobility, 
,
ITO shows high promise due to its high (~10^20/cm^3) number of carriers.
However, TCO’s have numerous problems, which have been well documented in the literature. First they are brittle which means they can crack and break severely limiting their conductivity and their application to flexible products. Secondly, the current process for creating TCO’s requires high heat environment and vacuum, which is an expensive fabrication process.
Carbon Nanontubes:
Carbon Nanotubes have emerged as one of the most promising challengers to ITO; they are optically transparent and have high conductivity and flexibility. While they have a lower charge carrier density than ITO (10^17 / cm^3) they can have higher electron mobility.
More importantly, they have not yet achieved the thin nature and low resistance required of commercial applications:
Graphene:
Graphene is still an early stage research technology, but it shows some promise. Initially modeling shows that based on a number of layers, it can achieve very low resistivity and high transparency based on the number of layers (100 – 2.3N % transmittance and 62.4 / N Ohms square). The problem is that currently technologies do not exist to grow a large uniform sheet of graphene which will have these properties. Graphene also suffers the same problem as metals in that transmittance goes down as the the number of layers go up. We should consider graphene to be a very early technology, with promise if cheap fabrication methods are found.
Thin Metal Sheets / Films and Nano-wires
Despite the properties listed above, thin metal films have been investigated again more recently. Many experiments have used silver films and shown that they compare favorably in conductivity to ITO, and additionally are more malleable. Thin metal films are subject to the same fabrication constraints as TCO’s (namely high temperature vacuum deposition), and as we’ve seen above quickly use their desirable optical properties as thickness increases.
(here we see again transmittance quickly falls
off as thickness increases)
Other technologies include creating a ‘grid’ of wires, which allows for increased transparency in between the
PEDOT:PSS
Conducting polymers have been around since the 80’s when polyacetylene was shown to have conductivity when doped. Unfortunately many of these polymers were unstable in air, and only recent with the addition of polystyrenesulfonic acid (PSS) have polymer conductors began to see more promise. PEDOT: PSS seems to be the most well used and is currently commercially available under the name Clevios. The value of these formulations is that they are stable in water and can be easily applied to any material you can put liquid on. The optical transparency compares favorably (see table below) with indium tin oxide, however, the sheet resistance is an order of magnitude higher and varies highly with temperature, making it not ready for primetime yet. This is caused by the instability of the doped state, where chemical and thermal reactions can cause changes in electrical conductivity. However, the materials have the upside of having significant flexibility mechanically.
Comparing some transparent conductors:
(Source: Journal of Applied Physics 2009, Sangeeth, Jaiswal and Menon)
We can see first off that competing technologies begin at a disadvantage vs. ITO with respect to their sheet resistance. Their resistivity also varies much more with respect to heat due to the physical structure (called hopping transport).
Source (Advanced Materials)
(Source: Gordon, 2000)
(Some comparisons)
Sources:
[To Be Completed]
Appendix:
Non-Transparent “Skinny Wires”
Other technological solutions don’t value transparency as much as flexibility or other properties. John Rogers at the University of Illinois has shown that IC’s can be integrated into the skin as ‘tattoos’.
More information can be seen here:
Preparation of TCO’s
Transparent conductors can be prepared in many ways. Among the commercially prevalent transparent conductive oxides, preparation usually takes 3 forms: physical sputtering, chemical vapor deposition, and spraying. Of the 3, CVD has taken over. An overview of the technologies follows.
For physical sputtering, an ion beam bombards accelerates particles of the dopant, and by momentum transfer these particles are put into the TCO. This happens in a low pressure, high temperature condition with the ambient environment filled with a noble gas (eg argon). The deposition rate will vary based on the temperature of the substrate, the applied voltage of the beam, and the partial pressure.
For chemical vapor deposition, gases of the conducting oxide are mixed with oxygen gas to create the oxide which is then condensed onto a substrate.
For spraying, the basic chemicals are mixed in water or alcohol and sprayed onto a high temperature substrate. This requires high temperatures otherwise incomplete vaporization may occur.
Basic figures of the engineering processes are below:
