Lecture 7 Optical Characterization of Inorganic Semiconductors

1. Lecture 7 Optical Characterization of Inorganic Semiconductors Dr Tim Veal, Stephenson Institute for Renewable Energy and Department of Physics, University of Liverpool Nov 3, 2016

2. L7 Lecture Outline Lecture 7:Optical properties of semiconductors • Optical spectroscopy in PV research • Optical spectroscopies, methods and proceses • Transmission, reflection, absorption, photoluminescence • Phenomena/properties determined by optical spectroscopy • Band gap type and energy determination: methods and pitfalls • Some case studies

3. L7 Renewable Energy Mix Max Birkett, PhD thesis, UoL (2016) Note the complementary nature of wind and PV technologies

4. L7 Optical Spectroscopy in PV Need to measure optical properties of new and sustainable materials to determine Suitability for PV applications What band structure properties do we want from a PV absorber? Band gap size, type? Free carriers? Max Birkett, PhD thesis, UoL (2016)

5. Conversion efficiency cb Eg hn Energy EF vb

6. Conversion efficiency • One electron per photon • Eg = energy available from each cb Eg hn EF hn vb p-type n-type

7. Power at ground level is about 1000 W/m2

8. L7 Solar spectrum Max Birkett, PhD thesis, UoL (2016)

9. Shockley – Queisser efficiency limit L M Peter

10. L7 Optical absorption Absorption is expressed in terms of a coefficient, α(hν), which is defined as the relative rate of decrease of light intensity L(hν) along its propagation path: Every initial state Ei is associate with a final state Ef such that: Ef= hv – Ei For parabolic bands, Ef – Eg= ℏ2k2/2me* and Ei = ℏ2k2/2mh* Absorption coeff is proportional to the transition probability from Ei to Ef and also the density of electrons in the initial state ni and the number of empty final states nf J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.

11. L7 Optical absorption Therefore It can be shown that the density of states is: Therefore plot of α2 versus hν for a direct gap gives straight line for absorption edge (see later) J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.

12. L7 Optical absorption How thick does an absorber layer need to be so that the majority of photons are absorbed? I(hv) = I0exp(-α(hv)z), z is the depth in the material, I0 is unattenuated light intensity The higher the absorption coefficient, the thinner the layer can be. (Si needs to be thick. CdTe can be thin.) J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.

13. L7 Optical absorption For indirect absorption, a phonon is required for momentum conservation. For absorption of a phonon of energy, Ep, the absorption coefficient is given by and for phonon emission is: Therefore plot of α1/2 versus hν for an indirect gap gives straight line for absorption edge (see later) J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.

14. L7 Optical absorption Both phonon emission and absorption are possible for hv > Eg +Ep, so the absorption coefficient is given by J. I. Pankove, Optical Processes in Semiconductors, Dover Publications, Inc., 1971.

15. L7 Optical absorption

16. L7 Absorption spectrometers Two types of spectrometer are used for absorption: Fourier Transform infrared (FTIR) UV-vis-near IR spectrophotometer Max Birkett, PhD thesis, UoL (2016)

17. L7 How to measure absorption? But how do we measure light absorbed by a material? We can only measure what is not absorbed. We can measure what is transmitted, T and what is reflected, R Then, with knowledge of the film thickness, we convert T and R to absorption coefficient, , somehow...

18. L7  from d, T and R?

19. reflection/transmission introduction  from d, T and R? • the reflectivity and transmissivity are respectively • the ratios of reflected and transmitted to incident power • the Fresnel coefficients at each boundary are written • in the refractive indexes of the materials, N=n+iK. • a simple approximation gives the reflectivity and • transmissivityfor a single incoherent optical layer • more complicated models consider oscillations in the • spectra due to interference from internal reflections • generally, it may not be possible to solve R and T for N Max Birkett, PhD thesis, UoL (2016)

20. reflection/transmission spectroscopy Power reflection coefficient Power transmission coefficient Max Birkett, PhD thesis, UoL (2016)

21. reflection/transmission spectroscopy Phase shift average out for an incoherent system so can be ignored giving: We are trying to find . We can do this by solving the quadratic in exp(- d) given by the Ttot expression: Except we don’t measure R0, we measure Rtot... Max Birkett, PhD thesis, UoL (2016)

22. reflection/transmission spectroscopy 0 R=0 Self-consistent, iterative approach Rtot =R0 Ignoring internal reflections results in greater inaccuracies when the absorption coefficient is low <104 cm-1, so exactly where we are most interested where the absorption edge begins. Max Birkett, PhD thesis, UoL (2016)

23. complexities in reflection/transmission spectroscopy • no unique solution may exist; noise further complicates. • solutions: • Rexpr-R(n)=0 • Texpr-T(n)=0 T R Max Birkett, PhD thesis, UoL (2016)

24. complexities in reflection/transmission spectroscopy • no unique solution may exist; noise further complicates. • solutions: • Rexpr-R(n)=0 • Texpr-T(n)=0 • EXAMPLE: 1. consider a material with some known complex refractive index Max Birkett, PhD thesis, UoL (2016)

25. complexities in reflection/transmission spectroscopy • no unique solution may exist; noise further complicates. • solutions: • Rexpr-R(n)=0 • Texpr-T(n)=0 • 2. calculate the reflectivity Rsim and transmission Tsim which will be found experimentally Max Birkett, PhD thesis, UoL (2016)

26. complexities in reflection/transmission spectroscopy • no unique solution may exist; noise further complicates. • 3. now explore solution domain: separately eval. R and T over complex refractive mesh, plot contours of residuals Rsim-R(n) • solutions: • Rsim-R(n)=0 • Tsim-T(n)=0 T R Max Birkett, PhD thesis, UoL (2016)

27. complexities in reflection/transmission spectroscopy • no unique solution may exist; noise further complicates. • solutions: • Rexpr-R(n)=0 • Texpr-T(n)=0 T R • 4 solutions consistent with simulated R/T spectra Max Birkett, PhD thesis, UoL (2016)

28. complexities in reflection/transmission spectroscopy • no unique solution may exist; noise further complicates. • solutions: • Rexpr-R(n)=0 • Texpr-T(n)=0 T R • simulated R/T spectra used this refractive index Max Birkett, PhD thesis, UoL (2016)

29. vulnerabilities of typical absorption relations • typically used relations to evaluate optical absorption • use approximations which introduce inaccuracies • if we assume no internal reflections, then we can • solve the second equation for the absorption coefficient • (by ignoring the denominator and assuming R0=Rtot), • giving absorption spectra: α=1/d * log[(1-Rtot)²/Ttot] • the accuracy of such approximations may be evaluated • for a simulated system: by computing Rtot & Ttot, and • plotting the ratio of the evaluated to realabsorption Max Birkett, PhD thesis, UoL (2016)

30. vulnerabilities of typical absorption relations • typical relations findabsorption strength inaccurately. • evaluated/actual absorption Max Birkett, PhD thesis, UoL (2016)

31. vulnerabilities of typical absorption relations • typical relations findabsorption strength inaccurately. • evaluated/actual absorption • very poor accuracy here Max Birkett, PhD thesis, UoL (2016)

32. L7 SLME Shockley-Quiesser assumes step function 100% absorption for E>Eg and 0% for E<Eg Spectrally limited maximum efficiency (SLME) uses absorptivity of a(E) = 1-exp(-2(E)d) with R = 0 for front surface and R = 1 for back surface. Better approx., but still far from reality. Yu and Zunger, Phys. Rev. Lett. 108, 068701 (2012) SLME efficiency versus minimum band gap for I-III-VI materials for film thickness of 0.5 microns.

33. L7 SLME CuSbS2 and CuBiS2 have stronger absorption onsets and so will (just considering this property) give greater efficiency for thinner films. They will get closer to the SQ limit. Kumar and Persson, J. Renewable Sustainable Energy 5, 031616 (2013)

34. L7 SnS2 optical absorption L. Burton, T. J. Whittles, T. D. Veal, V. R. Dhanak, A. Walsh, et al., J. Mater. Chem. A (2015)

35. L7 SnS2 optical absorption L. Burton, T. J. Whittles, T. D. Veal, V. R. Dhanak, A. Walsh, et al., J. Mater. Chem. A (2015)

36. L7 SnS2 optical absorption L. Burton, T. J. Whittles, T. D. Veal, V. R. Dhanak, A. Walsh, et al., J. Mater. Chem. A (2015)

37. L7 Temperature dependence • Temperature dependence of band gap of semiconductors is due to: • Dilation of the lattice due to increasing temperature • T-dependent electron phonon interactions • Most commonly used and simple parameterization of T dependence of semiconductor band gaps is that of Varshni (Physica34 (1967)149) but many more detailed treatments exist. • where α and β are experimental determined parameters.

38. CuSbS2: T dependent absorption spectra Clear trend of increasing absorption edge as T is reduced Feature at 1.83 eV is unidentified, but reduces in intensity as T is increased. Max Birkett, PhD thesis, UoL (2016)

39. CuSbS2: T dependent absorption spectra Max Birkett, PhD thesis, UoL (2016)

40. CuSbS2: absorption indirect band gap α=A(hν-Eg)2 Eg = 1.56 eV Max Birkett, PhD thesis, UoL (2016)

41. CuSbS2: absorption direct band gap α=A(hν-Eg)1/2 Eg = 1.69 eV Max Birkett, PhD thesis, UoL (2016)

42. CuSbS2: T dependent direct band gap Max Birkett, PhD thesis, UoL (2016)

43. L7 Temperature dependence • Why does the temperature dependence of the band gap matter for new and sustainable photovoltaic absorbers? • Solar cells operate over a significant range of temperatures due to: • range of ambient temperatures they are subjected to • heating by solar radiation • Range of temperatures could be 0 to 60°C

44. L7 Temp. effects on solar cells Temperature increase results in: Short circuit current JSCslightly increasing due to increased light absorption due to decrease in band gap Open circuit voltage and fill factor decrease with increase temp. due to decrease in band gap Fall in VOC dominates T dependence As an example, for Si, VOC falls by about 2.3 mV per °C temp. increase* So about 115 mV fall in VOC for 50°C temp. Increase, leading to significant fall in device efficiency *Martin Green, Solar Cells. Operating Principles, Technology and System Applications (Prentice Hall, 1982)

45. L7 T dependence of cell efficiency Singh and Ravindra, Sol. Energy Mat. Sol. Cells 101 (2012) 36 0.4-7.8% absolute change in efficiency for 10K temperature change, depending on material

46. L7 Low T absorption and DFT First principles computational methods (density functional theory) are increasingly being used to understand existing materials and design ones for photovoltaics. Density functional theory has traditionally been really bad at predicting band gaps. But now with hybrid functional it is generally reasonably good  However, DFT calculated properties at 0 K, so we need experimental data at low temp to compare with the calculations. J. Furthmueller, F. Fuchs and F. Bechstedt, in T. D. Veal (Ed.) Indium Nitride and Related Alloys (CRC Press, 2009)

47. CuSbS2: DFT band structure (HSE06) DFT HSE06 Indirect Eg = 1.67 eV Direct Eg = 1.82 eV 4 K exp values: Indirect Eg = 1.56 eV Direct Eg = 1.69 eV C. Savoury and D. O. Scanlon, UCL

48. L7 FTIR FTIR combined transmission and reflection for optical absorption

49. L7 FTIR FTIR variable angle specular reflectivity for plasma and phonon measurements

50. L7 Photoluminescence Photoluminescence can be powerful for investigating defect related transitions.