Electromagnetic absorption in transparent conducting films

Abstract

In this article we calculate the skin depth of indium tin oxide (ITO) films (and related materials) as a result of free electron absorption within the visible spectrum using the simple Drude model. We also discuss the consequences of finite skin depth for the transparency of current spreading layers for light emitting diode (LED) applications. Low sheet resistances are highly desirable for these layers, but the free electron density n in ITO cannot be increased much beyond 2×1021 cm−3 without pulling the plasma frequency into the red end of the visible spectrum (thus making it highly reflective); furthermore, any increases in the film thickness cause reduced transparency due to the finite skin depth δ. However, above the plasma frequency for n≈1021 cm−3 we find that increases in the electron mobility μe cause increases in δ, since then approximately δ∝μe. Therefore, if μe in ITO can be increased above present state-of-the-art values around 50 cm2 V−1 s−1 to intrinsic limiting values around 100 cm2 V−1 s−1 by improved film processing, then substantial increases in transparency are possible whilst not sacrificing the high conductivity. The output optical power of a LED using an ITO current spreading layer with high n is also approximately proportional to μe, so mobility increases also have a direct impact on the external power efficiency of these devices.