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Optical properties of silicon at low temperatures J. Komma, G. Hofmann, C. Schwarz, D. Heinert, P. Pastrik, R. Nawrodt Institut für Festkörperphysik, Friedrich-Schiller-University Jena 04.10.2012 ELiTES meeting 2012 Friedrich-Schiller-Universität Jena Outline • motivation • absorption processes in semiconductors • electronic absorption • thermal heating • temperature dependence of the refractive index of silicon – measurement principle and experimental setup – acquired data – results Julius Komma Optical properties of silicon at low temperatures 2 / 14 Friedrich-Schiller-Universität Jena Motivation silicon is one material of interest for optical components for future detectors • dn/dT is needed for calculations of: – thermal lensing – thermo-refractive noise • for the design of the cryogenic parts of future detectors the optical absorption is needed (thermal equilibrium, cooling power,…) Julius Komma Optical properties of silicon at low temperatures 3 / 14 Friedrich-Schiller-Universität Jena Absorption processes inside a semiconductor conduction band valence band inter band absorption (band-band abs.) Julius Komma intra band absorption (free carrier abs.) Optical properties of silicon at low temperatures 4 / 14 Friedrich-Schiller-Universität Jena Phonon assisted band-band absorption • band band absorption conduction band phonon photon valence band 58 meV phonon dispersion and density of states for silicon [1] [1[ Phonon dispersion of silicon and germanium from first-principles calculations Wei and Chou Julius Komma Optical properties of silicon at low temperatures 5 / 14 Friedrich-Schiller-Universität Jena Electronic absorption due to phonons absorption below the energy gap is possible 2 10 1 absorption [1/cm] 10 0 10 silicon photodiode 1-phonon edge -1 10 -2 10 -3 10 2-phonon edge Gap -4 10 0.90 0.95 1.00 1.05 1.10 photon energy [eV] Julius Komma 1.15 1.20 photodiode inside a sample holder Optical properties of silicon at low temperatures 6 / 14 Friedrich-Schiller-Universität Jena Temperature dependent absorption • for lower temperatures phonons freezing out (beginning with the higher energy phonons) absorption below the gap is getting smaller 100 10 absorption [1/cm] 1 300 K 220 K 150 K 100 K 50 K 3K 0.1 0.01 1E-3 1E-4 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 photon energy [eV] Julius Komma Optical properties of silicon at low temperatures 7 / 14 Friedrich-Schiller-Universität Jena Absorption measurement in brewster angle • for p-polarised light there is no reflection on a surface if the angle of incident is the brewster angle • so all light can be used for the measurement without losses because of reflected light • scattered light causes problems inside a cryostat Julius Komma P0 Ptrans Optical properties of silicon at low temperatures 8 / 14 Friedrich-Schiller-Universität Jena Thermal absorption measurement • one sample of high purity to measure the absorption of silicon between 5 and 300 K • the upper sample is doped, so we expect a higher absorption due to free carriers. With lower temperatures the absorption is expect to become smaller, when the number of free carriers decreases doped sample pure silicon cover base setup to measure two samples inside a cryostat Julius Komma Optical properties of silicon at low temperatures 9 / 14 Friedrich-Schiller-Universität Jena Setup for dn/dT measurement • with the continuous helium flow cryostat it is possible to measure from <4 K up to 325 K • sample thickness: 0.3 … 14 mm Julius Komma Optical properties of silicon at low temperatures 10 / 14 Friedrich-Schiller-Universität Jena Extracting of dn/dT from exp data Ir = 𝐼0 , 1+ 𝜋2/ 4𝐹2sin2 𝜃 𝜃= 2𝜋𝑛𝑙 𝜆 interference maximum ↔ ∆𝜃= 𝜋 ∆𝜃= 𝜋 1.0 𝑑𝑛 𝑑𝑇 = 𝜆 2𝑙 Δ𝑇 0.8 − n T 𝛼(T) 110-4 1/K 110-6 1/K (𝑙 = 14 𝑚𝑚, 𝑇 = 300 𝐾) IR norm. 0.6 0.4 0.2 0.0 310.0 312.5 315.0 temperature [K] Julius Komma Optical properties of silicon at low temperatures 11 / 14 Friedrich-Schiller-Universität Jena Data at low temperatures 1.0 0.8 IR norm. 0.6 0.4 0.2 0.0 0 10 20 30 40 50 60 temperature [K] • problem: only a small change of n at low temperatures only a few fringes • dn/dT 0 for T 0 (3rd law of thermodynamics) Julius Komma Optical properties of silicon at low temperatures 12 / 14 Friedrich-Schiller-Universität Jena dn/dT (1/K) Results for dn/dT 10 -3 10 -4 10 -5 our data [1] Frey [2] 10 -6 10 -7 10 -8 10 -9 ET design study 20K: 3.5E-6 1/K [3] 0 50 100 150 200 250 300 temperature [K] [1] Thermo-optic coefficient of silicon at 1550 nm and cryogenic temperatures. Komma et al. [2] Temperature-dependent refractive index of silicon and germanium Bradley J. Frey et al. Julius Komma [3] The Einstein gravitational wave Telescope conceptual design study M. Abernathy et al. Optical properties of silicon at low temperatures 13 / 14 Friedrich-Schiller-Universität Jena Summary • The absorption inside a semiconductor consists of band-band and free carrier parts • band-band absorption can be measured with a photodiode – phonon assisted absorption below the gap energy • both processes together can be observed due to thermal heating • dn/dT was measured over a wide temperature range (5 … 300 K) 𝑑𝑛 𝑑𝑇 = 1.5𝑥10-6 1/K @20K and 8𝑥10-8 1/K @10K Acknowledgements: This work was supported by the German science foundation within the SFB TR7. Julius Komma Optical properties of silicon at low temperatures 14 / 14