CN5216 – Problem Set #2 Structure, Electronic, and Optical Properties
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CN5216 – Problem Set #2
Structure, Electronic, and Optical Properties (Through Lecture 6)
2022
1. Energy Materials Crystals and Symmetry (10 Points) The year is 2027, and you are having a reunion with two friends of yours (Frankie and Robin) from NUS. They tell you that they are now being employed at Solar Cell Corp, where they make solar cells.
Robin specializes in developing new TCO layers, specifically hydrogen-doped indium oxide (H:In2O3 ). Robin mentions casually that it is cubic, and Frankie responds, “Oh, that is simple then?” Robin says, “No! It has like 80 atoms in its unit cell! The future of Solar Cell Corp depends on figuring out how to grow In2O3 better.” Frankie says, “No, lah! AZO is good enough to be profitable, we will be fine!” You remember something about AZO being easy to grow.
Since you want to rejoin the conversation, you quickly try to google about In2O3 and AZO (aluminum-doped Zinc Oxide).
You find the unit cell of In2O3 (cubic) and ZnO (hexagonal) upon which H:In2O3 and AZO are based:
Answer the following questions related to crystallography, conductivity, and mobility based on your understanding of these energy materials.
a. Unit cells. Which plane/direction/family of planes is highlighted in the cubic cell below?
Hint: Be careful of the axes!!!
(2 points)
b. For H:In2O3 and AZO, explain how do you expect their mobility and conductivity to vary in three dimensions (ie. along a, b, c axes)? Explain what is your expectation based on. State and explain to what extent are H:In2O3 and AZO isotropic or anisotropic. Hint: Assume the structure of H:In2O3 and AZO are identical to the structures provided for In2O3 and ZnO.
(4 points)
c. For In2O3, consider the reciprocal space lattice. In your own words, explain what is the meaning of a lattice point in the reciprocal lattice? In your own words and based on your understanding of the topics we introduced in lecture, describe two kinds of information about properties of In2O3 that can be gained from examination of the reciprocal lattice of In2O3 ?
Hint: This question is purposely open-ended, and there are many potential answers. We strongly do not recommend to google some fancy concepts that we did not touch upon in course. If you look something up, stick to concepts and derivatives of concepts that we discussed previously. Overall, tell us what you think.
(4 points)
2. Optical and Electronic properties. (10 Points) One afternoon one of your friends is telling you about their research into halide perovskite CsPbBr3, which is a direct band gap semiconductor. Your friend Sparky shows you a paper about the interesting structural evolution of CsPbBr3 based on temperature (from DOI: 10.1016/j.matlet.2020.128458): (Hint: Strongly not recommended to read this paper during your assignment preparation)
(a) Your friend Sparky thinks they can measure the conductivity of CsPbBr3 crystals,
but they also ask for your help to calculate it from known values. The intrinsic carrier concentration of CsPbBr3 is reported to be 108 cm-3 at room temperature with a mobility of roughly 600 cm2 V−1 s−1 . Calculate the conductivity of CsPbBr3 assuming that the mobility is isotropic.
(3 Points)
(b) For the CsPbBr3 light emission in a photoluminescence experiment (shine short
wavelength light on CsPbBr3 ), your friend notices that there are small changes in the emission wavelength as the laser irradiation heats up the sample. Your friend believes that they can understand the data using the Varshni relation (introduced briefly in lecture 6) from 20°C to 160°C. Explain why is or why is not this a good idea?
(4 points)
(c) Your friend tried to measure the band gap of the CsPbBr3 material by photoluminescence, but they did not get their thin film of CsPbBr3 film (deposited on Ag foil) to emit any light. Luckily, your friend noticed that a piece of CsPbBr3 that fell off the Ag foil emits light strongly under photoexcitation. Fully explain what role could the Ag foil likely play in preventing radiative recombination?
(3 points)
2022-09-14