Thermal Emission in the Near Field from Polar Semiconductors and the Prospects for Energy Conversion

Transcription

1 Thermal Emission in the Near Field from Polar Semiconductors and the Prospects for Energy Conversion R.J. Trew, K.W. Kim, V. Sokolov, and B.D Kong Electrical and Computer Engineering North Carolina State University

2 Fundamental Questions: Can incoherent thermal energy be converted to coherent radiation? Is it possible to harvest this energy and convert it to useable dc energy?

3 Thermal Radiation Generally, thermal radiation has been considered ISOTROPIC BROAD BAND INCOHERENT => Similar to the WHITE NOISE due to the uncorrelated process of photon spontaneous emission Planck s Black Body Radiation: I B ( ω T ), = 3 π c 3 ω [ exp( ω k T ) 1] B

4 Near-Field Spectra of Thermal Emission Thermal sources can show partially coherent spectra in the near-field Evanescent surface wave plays an important role for near-field spectra Evanescent surface wave carries sub-wavelength spatial information since it decays exponentially

5 Near-Field vs. Far-Field Near-Field Partially coherent: quasimonochromatic Strong intensity Evanescent mode: decays exponentially away from the source Far-Field Incoherent: nearly white noise Weak Intensity Propagating mode What makes the differences in the near-field spectra? => Thermal excitation of surface polaritons leading to a resonant (monochromatic) behavior

6 Phonon Polariton Polaritons: Quasi-particles resulting from strong coupling of electromagnetic waves with an electric or magnetic dipole-carrying excitation Phonon-Polaritons: Polaritons resulting from the coupling of an infrared photon with a polar phonon Polar solid (dielectric/semiconductor) can cause strong polar phonon-photon coupling

7 Surface Electromagnetic Waves Surface EM waves: A particular type of waves that exists at the interface between two different media - propagates along the interface - decays exponentially in the perpendicular direction Surface waves due to coupling between the EM field and resonant polarization oscillation in the material => Surface polaritons Surface plasmon polariton: coupling with the surface charge density wave Surface phonon polariton: coupling with the surface infrared optical phonon

8 Surface EM Waves Vacuum (ε 1, z > 0) z H y E k x Dielectric [ε(ω) =ε' (ω) + i ε" (ω), z < 0] k ω c = εω ( ) : Dispersion relation of surface EM wave Approximated ε(ω) for real ω when εω ( ) + 1 ωlo ω iγ LOω ωlo ω ε ( ω) = ε ε ω iγ Surface EM wave: Only TM (Transverse Magnetic) modes exists in the non-magnetic media Available frequency range for surface phonon polariton wave excitation: ω TO ~ ω [ε(ω) S < - ε 1 for real k ] ω TO TO ω ω TO ω

9 Dispersion Relation for Surface Waves Range of surface wave frequency and wave numbers: where k c = ω TO /c Approximated limiting frequency: ω ω = ω s ω 0 s < ω <, < k <, TO ω s TO ε 0 ε when The large density of states at ω s causes quasimonochromatic radiation of near-field thermal emission k c ε ω ω ω ω LO ( ω) ε TO

10 Calculated Dispersion Relations ω, 10 1 s -1 ω, 10 1 s -1 ω, 10 1 s -1 ω, 10 1 s ω 0 s = InP ω 0 s = GaAs ω 0 s = ω 0 s = SiC k, 10 4 cm -1 GaN Dispersion relation for surface phonon polaritons: k ω c = εω ( ) εω ( ) + 1 Dielectric function for an isotropic material: ω ω iγ ω TO i TO εω LO LO ( ) = ε ω ω γ ω

11 Near-Field Spectra Supported by Surface Waves Classical Spectral Energy Density (Plank s Black-body Radiation) 3 ω I B ( ω, T ) = θ ( ω, T ) N( ω) = 3 π c exp ω k T 1 Thermal emission from a semi-infinite slab (z < 0) of homogeneous and isotropic polar solid into vacuum/air (z>0) including the near-field spectra I(, z ω, T) = θω (, T) N(, z ω, T) ω dk N(, z ω, T) = 8 π ε ( ω) dz g (, ω z, z ) c k ' '' ε ( ω) = ε ( ω) + iε ( ω) ' g (, ω z, z ) αβ Mean energy of a quantum oscillator θ ( ω, T ) = ω exp( ω k T ) 1 B : dielectric function [ ( ) ] B Density of oscillation modes per unit volume ω π c ( ω ) = '' ' ' 4 αβ αβ, = ( π ) xyz,, k : -D Fourier transform of the electromagnetic Green tensor (, rr, ' ω) N G αβ

12 Fluctuation Dissipation Theorem The total energy is the summation of electric and magnetic energy such as u ω, z = u ω, z + u ω, z, z > 0 ( ) prop ( ) evan ( ) E E E where 1 1 kdk ( ) ( ) ( ω, = ) 0 ω, 1 1 u z u T r r prop s p E 0 γ1 and 1 kdk u z u T r k r k z ( ω, ) = ( ω, ) Im( ) + ( 1) Im( ) exp[ Im( γ ) ] evan s p E γ 1 ( ) 1 i( k ) 1 k ( ε k ) 1 γ 1 = 1 k γ = γ 1 1 = 0 Wave vector component for z- direction of each region and propagating and evanescent mode r s 1 r p 1 = = ( γ1 γ ) ( γ1+ γ ) ( εγ1 γ) ( εγ + γ ) 1 Fresnel reflection factors for s- and p-polarization

13 Relevant Material Parameters Material ω LO, 10 1 s -1 ω TO,10 1 s -1 γ LO,10 1 s -1 γ TO,10 1 s -1 ε ε InP GaAs E E E Al O 3 E A A GaN [9] 1.508[9] 5.3 SiC

14 Near-Field Thermal Emission SiC 1.5x x10-7 z=100µm u(ω,z) (ev s/cm 3 ) 5.0x x x10-7.0x x10-3.0x10-3 z=µm z=100nm 1.0x ω (10 1 s -1 ) Thermal emission spectra of a semi-infinite SiC sample at three different locations from the surface (z = 1000 µm, µm, and 0.1 µm) with T=300K

15 Near-field Thermal Emission Cubic GaN u(ω,z) (ev s/cm 3 ).0x x10-7 z=100µm 1.0x x x x x10-7.0x x x x10-3.0x ω (10 1 s -1 ) z=µm z=100nm Thermal emission spectra of a semi-infinite cubic GaN sample at three different locations from the surface (z = 1000 µm, µm, and 0.1 µm) with T=300K

16 Near-field Thermal Emission Al O 3.0x x10-7 z=100µm u(ω,z) (ev s/cm 3 ) 1.0x x x x x x x x10-3.0x10-3 z=µm z=100nm ω (10 1 s -1 ) Thermal emission spectra of a semi-infinite Al O 3 sample at three different locations from the surface (z = 1000 µm, µm, and 0.1 µm) with T=300K

17 Near-Field Thermal Emission GaAs 1.5x10-7 z=100µ m 1.0x x10-8 u(ω,z) (ev s/cm 3 ) 3.0x10-6.0x x10-6.0x10-1.5x10-1.0x10-5.0x ω (10 1 s -1 ) z=µ m z=100nm Thermal emission spectra of a semi-infinite GaAs sample at three different locations from the surface (z = 1000 µm, µm, and 0.1 µm) with T=300K.

18 Near-Field Thermal Emission InP u(ω,z) (ev s/cm 3 ) 1.5x10-7 z=100µm 1.0x x x10-6.0x x10-3.0x10 -.0x10-1.0x ω (10 1 s -1 ) z=µm z=100nm Thermal emission spectra of a semi-infinite InP sample at three different locations from the surface (z = 1000 µm, µm, and 0.1 µm) with T=300K.

19 Monochromatic Emission vs. Distance I(ω, z = 0.1µm ) 10-4 ev s / cm InP GaAs Al O 3 GaN SiC Z = 0.1μm I(ω, z =.0µm ) 10-8 ev s / cm InP GaAs Al O 3 GaN SiC Z =.0μm I(ω, z = 4.0µm ) 10-9 ev s / cm InP GaAs Al O 3 GaN SiC Z = 4.0μm ω, 10 1 s ω, 10 1 s ω, 10 1 s -1 I(ω, z = 7.0µm ) 10-9 ev s / cm InP GaAs Al O 3 GaN SiC Z = 7.0μm I(ω, z = 8.0µm ) 10-9 ev s / cm InP GaAs Al O 3 GaN SiC Z = 8.0μm I(ω, z = 1µm ) 10-9 ev s / cm InP GaAs Al O 3 GaN SiC Z = 10μm ω, 10 1 s ω, 10 1 s ω, 10 1 s -1 GaAs maintains monochromatic properties for the longest distance from the surface ( i.e. z ~ 7.95 μm)

20 Comparison of Near-Field Peak Intensity Materials ω peak,10 1 s -1 I(ω,z), 10-5 ev s / cm (ω = ω z = 0.1μm ) peak, 3 λ, μm ω s0, 10 1 s -1 InP GaAs Al O 3 E GaN SiC Semiconductors with smaller surface phonon energies (e.g., InP, GaAs) exhibit stronger near-field emission peaks.

21 Peak Spectral Energy Density vs. Distance u(ω,z) ev s/cm InP GaAs Al O 3 SiC GaN z (µm) Spectral energy density of thermal emission as a function of the distance z from the surface calculated at ω = ω peak and T = 300 K Emission with a shorter wavelength tends to decay faster.

22 Temperature Dependence u(ω p,z) (ev s/cm 3 ) InP SiC GaAs GaN (a) Al O z (µm) (b) 300 o K 600 o K InP GaAs SiC Al O 3 GaN The difference in the spectral energy density between the materials with large vs. small surface phonon energies decreases as the temperature goes up.

23 Comparison Between Candidate Materials All materials show near-field quasi-monochromatic thermal emission spectra. The height of the emission peaks varies significantly from material to material. ω θ ( ω, T ) = exp( is the main determining factor for the ω kbt ) 1 peak intensity height. => larger intensity for a smaller ω peak (i.e., surface phonons with a longer wavelength). The peak intensity exponentially decrease and disappear within the distance of one wavelength evanescent mode. The materials with a smaller ω peak tend to maintain monochromatic emission for a longer distance from the surface.

24 Electric Energy Density The total radiation energy can be found by integrating with respect to ω: d U z = ω u ω, z 0 π ( ) ( )

25 Electric Energy Density 10-7 U(z) mj/cm z, µm 3.0x10-3.0x x ω, 10 1 s -1 Electromagnetic energy density U(z) near a semi-infinite GaAs interface as a function of z (T = 300 K): curve 1 - Δ is centered at ω p ; curve - Δ is centered at ω max (z), corresponding to the maximum value of u(ω,z), that shifts as a function of z; dashed curve - blackbody radiation. (Δ is integration period; full width half maximum) Surface wave energy is several orders of magnitude larger than blackbody radiation

26 Proposed Energy Conversion Device Near-field thermal emission supported by the surface phonon polariton shows coherence in a corresponding frequency domain => Quasi-monochromatic; Spectral Coherence Spatial coherence can be achieved by using microstructures such as gratings, micro cavity or photonic crystal, etc..

27 Summary The polar semiconductor/insulator materials, InP, GaAs, GaN, SiC, and Al O 3, demonstrate a quasi-monochromatic thermal emission in the near-field zone. The electric energy intensity for the quasi-monochromatic thermal emission is several orders of magnitude greater than black body radiation. (GaAs at z= 100nm and T=300K: 1.46 x 10-7 mj/cm 3, Black body radiation: 1.6x10-1 mj/cm 3 ) The thermal coefficient for nanoscale radiation heat transfer is calculated and the results shows that heat transfer is drastically enhanced by surface phonon coupling. (GaAs T=300K, h c = mj/cm at z=10nm, h c = mj/cm at z=100μm) The angular emissivity pattern shows that the thermal emission can be controlled to have directionality