Semiconductor Shade (10 September 2024)

If money were no object an amenity I’d install is a garden-house. Harbouring this dream an accompanying technical feat to brood about was how to protect selective areas within the shelter from bright sunlight when conducting certain activities.

Wouldn’t it be beautiful if such a system were automated with solar tracking to constantly target the designated areas against a changing orientation of the sun? In view of such a requirement I’d lean towards the actuator being electronically controlled. In my day dreaming that narrowed down the means to accomplish the task. Since light has an electromagnetic wave nature I imagined a system that could interact with incident light in a way that would cancel it out by destructive interference through superposition with waves somehow generated by the system. 

Consulting an electromagnetism book I changed my position slightly, being reminded that electromagnetic waves are attenuated by the medium in which they propagate by an attenuation, 𝛂, given by ,

where 𝛚 is the angular frequency of the waves, 𝛍 and 𝛆 are, respectively, the permeability and permittivity of the medium. 𝛔 is the electrical conductivity of the medium. I wondered if we could manipulate the value of 𝛔 in a material in a manner that would allow us to change this attenuation and in so doing alter the transparency of the material. So searching through the electromagnetism book I found the equations for electrical conductivity. I took particular interest in semiconductors since these would serve the application I was looking into as they are partially conducting media. Hence an appropriate epithet for this proposition might be “semiconductor shade”.

For semiconductors 𝛔 is given by,

where n_i is the number density of charge carriers, i.e. electron-hole pairs, q is elementary charge, 𝛇_e and 𝛇_h are, respectively, the mobilities of the electrons and holes in the semiconductor. I thought I remembered these parameters being temperature dependent. So I had the idea - if we could control the parameters by tuning the temperature of the semiconductor we’d consequently modify the conductivity and hence the transparency of the semiconductor. So I recoursed to a book on semiconductor physics for insight into these parameters. In the relevant chapter I came to see that n_i does indeed have a temperature dependence and it’s given by,

where T is temperature, whereas W_g is the energy gap of the semiconductor and k is the Boltzmann constant. I learnt that in doped semiconductors, above room temperature n_i increases rapidly with temperature upto a given critical temperature which can be as high as 500 Kelvins in degenerate semiconductors i.e. heavily doped semiconductors. This seemed encouraging. So I created a spreadsheet to experiment with the above given equations using data on intrinsic silicon for W_g, 𝛇_e and 𝛇_h. I discovered attenuation for a wave of frequency 5.5∙10¹⁴Hz began at 93.8°C (i.e. 366.95 Kelvins). 

I googled to see if there were transparent semiconductors that could behave as my application needed and encountered the transparent oxide semiconductors Indium Tin Oxide (ITO) and Aluminium Zinc Oxide (AZO). Data on the parameters 𝛇_e, 𝛇_h, and W_g for various doping concentrations of these semiconductors isn’t at my disposal to calculate the exact temperatures we’d need to attain to observe transition from transparency to opacity or even translucence. 

Anyhow, if a low-priced  transparent oxide semiconductor could exhibit this optical transition at reasonable temperatures, the garden-house I imagined could be constructed with discrete cells of this material each with an individually controlled heating element embedded in it to raise the semiconductor’s temperature to that required for opacity. The house could target the appropriate areas within the shelter at each instant to protect them from the sun merely by tracking the sun and heating only those cells in the sun rays’ path to the target area. 

Energy to heat these cells could be harnessed from the sun photo-voltaically as well as through thermoelectricity; specifically the Seebeck effect. Not only would this be a sustainable and green source but there’d be a symbiotic relationship since brighter sunlight to shield the target space from would also mean more energy available to effect the shade.