Nanophotonics: solar and thermal applications Shanhui Fan Ginzton Laboratory and Department of Electrical Engineering Stanford University http://www.stanford.edu/~shanhui
Nanophotonic Structures Photonic crystals Plasmonic Meta-materials Au SOI 2 m 1 m J. Pan et al, APL 97, 101102 (2010). L. Verslegers, Nano Letters 9, 235 (2009).
Photon as an important heat carrier From the sun On earth
Improving Solar Cell Efficiency P N V Sun Semiconductor PN junction
Light management Absorb sunlight using films as thin as possible 1. Reduce cost for expensive materials 2. Facilitate carriers extraction to improve efficiency
Challenges of light management for a-si cell Full absorption depth ~ 1000nm Carriers only travel for 200-300nm To facilitate carrier extraction, needs to absorb light with a layer thinner than the absorption length
Photocurrent Flat a-si cell (~280nm thick) Nanocone TCO a-si Ag 11.4 ma/cm 2 Total available: 20.5 ma/cm 2 17.5 ma/cm 2
Absorption spectra Nanocone Flat Broadband anti-reflection and effective light trapping
Broadband antireflection l = 450nm ITO a-si air a-si ITO Ag
Absorption spectra Nanocone Flat Broadband anti-reflection and effective light trapping
Light trapping l = 750nm air ITO a-si a-si ITO Ag
Combine theory with experiment Flat Nanocone J. Zhu, Z. Yu, G. Burkhard, C. Hsu, S. Connor, Y. Xu, Q. Wang, M. Mcgehee, S. Fan, and Y. Cui Nano Letters 9,279 (2009).
500nm
Significant efficiency enhancement Flat Nanocone Jsc= 11.4mA/cm 2 Jsc= 17.5mA/cm 2 Efficiency 4.7% Efficiency: 5.9% Most recent result: 9.7%
Absorption spectra Nanocone Flat Broadband anti-reflection and effective light trapping
An important theoretical question What is the fundamental limit of absorption enhancement using light trapping in solar cells? Classical Light Trapping Theory A. Goetzberger IEEE Photovoltaic Specialists Conference (1981). Optical confinement in thin Si-solar cells by diffuse back reflectors E. Yablonovitch J. Opt. Soc. Am. A (1982). Statistical ray optics P. Campbell & M. Green J. Appl. Phys. (1986). Light trapping properties of pyramidally textured surface
Absorption Weak absorption at semiconductor band edge 1.0 0.8 Si Mirror 0.6 0.4 0.2 0.0 50 m c-si Perfect AR Perfect back mirror 400 600 800 1000 Wavelength (nm)
The Conventional Limit Si Mirror sin 1 1 n Maximum absorption enhancement factor Derived with a ray tracing argument 4n 2 E. Yablonovitch, J. Opt. Soc. Am. 72, 899 (1982); Goetzberger, IEEE Photovoltaic Specialists Conference, p. 867 (1981); Campbell and Green, IEEE Trans. Electron. Devices 33, 234 (1986).
Absorption Maximum absorption enhancement occurs in the weak absorption limit 4n 2 with light trapping w/o light trapping Wavelength (nm)
From conventional to nanoscale light trapping M. Green (2001) J. Zhu, Z. Yu, et al, Nano Letters 9, 279 (2009). ~ 50 m Nanocone 500 nm Ray tracing Wave effect is important
Light Trapping With Grating Active layer mirror 500nm
Absorption enhanced by guided resonance Guided resonance peak. Narrow spectral width for each peak. Requires aggregate contribution of large number of resonances.
Statistical Temporal Coupled Mode Theory Instead of thinking about rays Think about many resonances Zongfu Yu, Aaswath Raman, and Shanhui Fan Proceedings of the National Academy of Sciences 107,17491 (2010).
absorption A single resonance Resonant frequency
A simple model of a single resonance Assume no diffraction in free space Incident plane wave External leakage rate e Resonator Intrinsic loss rate i i c n
Under, critical, and over coupling 100% 100% 100% under-coupling e i critical-coupling e i over-coupling e i Traditional use of resonance for absorption enhancement, such as resonance enhanced photodetectors, uses critical coupling
Spectral cross-section Incident spectral bandwidth Spectral cross-section A( )d Contribution of a single resonance to the average absorption over the bandwidth
Maximum spectral cross-section A( )d 100% 100% 100% under-coupling e i critical-coupling e i over-coupling e i MAX =2 i at the strong over-coupling limit, where the out-of-plane scattering dominates over the intrinsic absorption
Covering the broad solar spectrum with multiple resonances 88.5 MHz 97 MHz 106 MHz Radio a Radio b Radio c
Sum over multiple resonances M resonances m m
Multiple plane channels in free space Take into account diffraction in free space N channels M resonances max M N 2 i
Theory for nanophotonic light trapping Number of plane wave channels in free space: N Number of resonances in the structure: M = M N 2 i Maximum absorption over a particular bandwidth = M N 2 i Zongfu Yu, Aaswath Raman, and Shanhui Fan Proceedings of the National Academy of Sciences 107,17491 (2010).
Reproducing the conventional limit (the math) d L Random texture can be understood in terms of grating with large periodicity Conventional limit Large Periodicity L >> l Large Thickness d >> l Maximum absorption = M N 2 i Maximum enhancement factor F / d =4n 2
The intuition about the conventional limit from the wave picture Number of resonance in the film F M Nd Thickness of the film When the thickness d l Double the thickness doubles the number of the resonances
The key in overcoming the conventional limit Number of resonance in the film F M Nd Thickness of the film Nanoscale modal confinement over broad-bandwidth
Light confinement in nanoscale layers Light Scattering Layer e = 12.5, t = 80nm Light Confining Layer e = 12.5, t = 60nm Light Absorption Layer e = 2.5, = 400 cm -1, t = 5nm Mirror
Enhancement: 15 times the conventional limit Light intensity distribution 5nm thick 60n 2 15 times of the classical limit
Simulated Absorption Spectrum Enhancement Factor Angular Response 4n 2 Red: 4n 2 limit Zongfu Yu, Aaswath Raman, and Shanhui Fan Proceedings of the National Academy of Sciences 107,17491 (2010).
Statistical Temporal Coupled Mode Theory Instead of thinking about rays Think about many resonances Zongfu Yu, Aaswath Raman, and Shanhui Fan Proceedings of the National Academy of Sciences 107,17491 (2010).
Guidance for grating design Assuming isotropic emission (obtained when the grating period is much larger than the wavelength) 2D 1D ~ l/2n Maximum enhancement factor F 4n 2 n Zongfu Yu, Aaswath Raman, and Shanhui Fan, Optics Express 18, A366 (2010).
z Grating with periodicity on the wavelength scale y x L Enhancement factor over 4n 2 with grating Counting number of channels in free space k y 2 /l 2 /L k x Zongfu Yu, Aaswath Raman, and Shanhui Fan, Optics Express 18, A366 (2010).
Angular sum rule of the enhancement factor Conventional case Arbitrary spatial emission pattern Uniform emissivity with the cone Zero emissivity outside the cone F max 4n2 sin 2 d d F, cos sin 4 n 2 P. Campbell and M. A. Green, IEEE Transactions on Electron Devices 33, 234 (1986). Zongfu Yu, Shanhui Fan, Applied Physics Letters 98, 011106 (2011).
Nanophotonics for solar cells With Y. Cui s group at Stanford Dr. Zongfu Yu, Aaswath Raman J. Zhu et al, Nano Letters 9, 279 (2009). J. Zhu, C. M. Hsu, Z. Yu, S. Fan, and Y. Cui, Nano Letters 10, 1979 (2010). Z. Yu, A. Raman and S. Fan, Proceedings of the National Academy of Sciences 107,17491 (2010). Z. Yu, A. Raman and S. Fan, Optics Express 18, A366 (2010). Z. Yu and S. Fan, Applied Physics Letters 98, 011106 (2011). A. Raman, Z. Yu, and S. Fan, Optics Express 19, 19015 (2011).
Photon as an important heat carrier From the sun On earth
Improving Solar Cell Efficiency P N V Sun Semiconductor PN junction
Photon Energy Electron Energy Basic Semiconductor Physics Conductance band Power Valence band k Solar Spectrum Semiconductor Bandstructure
Photon Energy Electron Energy Photons with energy below the band gap Conductance band E g Power E g Valence band k Solar Spectrum Semiconductor Bandstructure They do not contribute.
Photon Energy Electron Energy Photons with energy above the band gap Conductance band E g Power E g Valence band k Solar Spectrum Semiconductor Bandstructure They do contribute, but only partially. After absorption, each photon contributes to approximately E g worth of the energy, the rest is lost due to thermalization.
Photon Energy Electron Energy Shockley-Queisser Limit Conductance band E g Power E g Valence band k Solar Spectrum Semiconductor Bandstructure A single-junction cell: maximal efficiency 41%. n Junction Solar Cells - Detailed Balance Limit of Efficiency of p 1961)( 32, 510.Phys.Appl.Queisser, J. William Shockley and Hans J
Photon Energy Electron Energy What if the sun was a narrow-band emitter? Conductance band E g +de E g Power E g Valence band k Solar Spectrum (T s =6000K) Semiconductor Bandstructure (T e =300K) Approach Thermodynamic Limit
Solar Thermo-Photovoltaics (STPV) P N Sun (T s = 6000K) Intermediate Absorber and Emitter (T i = 2544K) Solar Cell (T e = 300K) The sun to the intermediate The intermediate to the cell R. Swasnson, Proc. IEEE 67, 446 (1979); P. Harder and P. Wurfel, Semicond. Sci. Technol. 18, S151 (2003).
6000K STPV: The Challenge 2544K 300K P N Design requirement for the intermediate Broad-band wide-angle absorber Narrow-band emitter Material requirement for the intermediate Need to have large optical loss. Need to withstand high temperature. Tungsten is a natural choice of material.
Dielectric Function of Tungsten Tungsten is a very lossy material in the solar wavelength range.
Absorptivity of a semi-infinite slab of Tungsten W Neither a good absorber or a good emitter.
Nanostructured Tungsten Photonic Crystals Broad-band absorber Narrow-band Emitter 250nm
Tungsten Broad-Band Wide-Angle Absorber E. Rephaeli and S. Fan, Applied Physics Letters 92, 211107 (2008).
Towards ideal solar thermal absorber An ideal solar thermal absorber a near-unity absorption in the optical wavelength a near-zero absorption in the thermal wavelength range
Thermal Emitter Vacuum Lamp: 1800-2700K Gas Filled Lamp: Up to 3200K www.intl-lighttech.com/applications/appl-tungsten.pdf
Emissivity Narrow-band Tungsten emitter tuned to band gap of 0.7eV Blackbody 2100K W Si SiO2 Energy (ev) E. Rephaeli and S. Fan, Optics Express 17, 15145 (2009).
Schematic Incorporating both Absorber and Emitter
System Efficiency Beating Shockley-Queisser Limit 6000K ~2000K 0.7eV cell P N Solar TPV (0.7eV cell) Direct PV (1.1eV cell) Direct PV (0.7eV cell) # of Suns E. Rephaeli and S. Fan, Optics Express 17, 15145 (2009).
Photon as an important heat carrier From the sun On earth
Active control of thermal transport Electronic integrated circuit Can we provide more active control of thermal transport? http://www.aztex.biz/wpcontent/uploads/2009/01/ic-chipexample.jpg
Thermal Rectification (Thermal Diode) Body 1 Body 2 Forward Bias T H S 12 T L T H >T L Backward Bias T L S 21 T H Rectification occurs when S 12 S 21 Previous experiments on phonon and electrons. Relies upon phonon-phonon or electron-electron interactions. Novel capability for thermal management Here, we aim to create thermal rectification for photons
Our construction Photon mediated Heat conducting channel is linear (vacuum) The nonlinearity is in the dependency of the refractive index with respect to temperature d=100nm SiC (3C) SiC (6H) C. Otey, W. Lau, and S. Fan, Physical Review Letters 104, 153401 (2010).
Sharp thermal features in the near field d = 1000 m d d = 2 m SiC (300K) d = 0.1 m Narrow-band resonance Greffet et al, PRL 85, 1548 (2000).
Mechanism for thermal rectification Body 1 Body 2 1 T 2 T 1 T 2 T Two different objects, both support narrowband resonances The resonant frequencies have different temperature dependence.
Forward bias Body 1 Body 2 Body 1 500K 300K Body 2 1 T 2 T Resonances overlap, large thermal transfer
Backward bias Body 1 Body 2 Body 1 300K 500K Body 2 1 T 2 T Resonances do not overlap, small thermal transfer
Our scheme Narrow-band electromagnetic resonances with temperature dependent resonant frequency. orward everse C. Otey, W. Lau, and S. Fan, Physical Review Letters 104, 153401 (2010).
A simple rectifier design Use surface phonon polaritons as our temperature dependent resonances SiC has TO phonons that give clean dielectric resonances in infrared that dominates the near field SiC-3C and SiC-6H have different TO phonon frequency temperature dependence d=100nm SiC (3C) SiC (6H) 3C 6H
Spectral heat flux SiC 3C SiC 6H SiC 3C SiC 6H Forward Reverse
Overall heat flux T l 300K Rectification S 12 S 21 S 21 C. Otey, W. Lau, and S. Fan, Physical Review Letters 104, 153401 (2010).
Summary Nanophotonic light trapping Solar Thermophotovoltaic Thermal Diode SiC (3C) SiC (6H) Dr. Zongfu Yu Aaswath Raman Eden Rephaeli Clayton Otey Dr. Wah Tung Lau Acknowledging support from GCEP, DOE, AFOSR