The present invention relates generally to the field of optics and in particular discloses a mechanism for improved light trapping in thin optical and photoelectronic structures.

Background

A thermodynamic limit of 4« ² times actual thickness (n is refractive index), applies for both coherent' and incoherent light ² . For high index materials (e.g. silicon), 4n ² enhancement can be substantial (50-60 times), additionally impacting performance of related devices such as light emitting diodes (LEDs). For lower index material, potential pathlength gains by conventional approaches are less dramatic, detrimental for devices like organic solar cells, where short excitonic transport distances dictate extreme thinness. Summary

An optical device is provided comprising an functional layer of less than a wavelength of light in thickness and a layer of transparent material having a thickness greater than a wavelength of light, the transparent material forming an optical interface with the material of the functional layer and the transparent material having a refractive index nj which is higher than the refractive index n ₂ of the material of the functional layer.

The functional layer could be an active layer of a photovoltaic device an LED, a thin low index layer doped with rare earths or with other optically active material such as in a device for frequency upconversion of incident light or other optical devices that might be formed in a low index material. This structure is particularly useful in the design of organic LED devices and organic photovoltaic devices.

The active layer will desirably have a thickness which is at least less than the shortest wave length to which the device is sensitive and preferably at least one third of that wavelength. It is anticipated that the functional layer will generally be less than lOOnm and more likely 50nm or less. The thickness of the transparent layer will desirably have a thickness greater than a wavelength of the longest wave length to which the device is sensitive and preferably at least two wavelengths. In a further embodiment, a plurality of functional regions may be provided, adjacent pairs of functional layers separated by transparent layers. The separating transparent layers will preferably have a thickness in the range of 0 to 1 wavelength and ideally about 0.5 wavelengths of light at the peak sensitivity of the functional layers.

Preferably such layers of transparent material will be located on either side of the functional layer to form optical interfaces, with each of the transparent material layers forming an optical interface with a respective functional layer or layers.

The layer or layers of transparent material may only be transparent at wavelengths to which the device is sensitive or at least may not be transparent at least at some other wavelengths.

The layer or layers of transparent material are preferably textured on their surfaces distal from the functional layer. The texturing may have feature sizes of 100- 200nm or less. The interface between the transparent layer or layers and respective functional layers will preferably be non-textured.

A scattering layer may be provided on the side of the device distal to the light receiving surface (or a light emitting surface in the case of a LED device or a light receiving or emitting surface in the case of an upconversion device). Alternatively a reflective surface may be provided on the side of the device distal to the light receiving surface (light emitting surface in the case of a LED device or a light receiving or emitting surface in the case of an upconversion device) and preferably separated from the adjacent transparent layer such as by an air gap or dielectric layer to optimise reflection.

Brief description of the drawings

Embodiments of the invention will now be described with reference to the accompany drawings in which:

Figure 1 schematically shows a nominal solar cell or Light Emitting Diode

(LED) geometry in which low the index active layer is inserted between higher index transparent cladding layers;

Figure 2 graphically illustrates calculated light-trapping boost for the scheme of

Figure 1 as a function of active layer thickness for different active layer extinction coefficients; and

Figure 3 schematically shows a double active layer geometry with planar surfaces and a rear scattering layer such as formed by diffraction gratings, plasmonic nanoparticles, photonic crystals or combinations of these. Detailed description of embodiments

The higher internal than external optical density of states for solar cells and related optoelectronic devices gives potential for substantial increases in internal optical absorption (or emission) pathlengths. It is found that, for schemes based on propagating evanescent modes, such as in frustrated total internal reflection, limits can be enhanced over those previously thought possible. This enhancement is particularly relevant for low index materials such as not only organics in the very thin planar devices often of most interest, but also other materials such as polar inorganic semiconductors (e.g. CdTe). An embodiment of the invention will be described by way of example with generally reference to a photovoltaic device but it will be recognized that the invention is also applicable to other optical or optoelectronic devices such as LEDs and optical converters in which case the direction of travel of light in the devices will (in some instances) be reversed.

As illustrated in Figure 1, an optoelectronic device device might employ a relatively symmetrical arrangement, where the thin active photovoltaic layer 11 again having a ref active index n ₂ is inserted between non-absorbing cladding layers 12, 13, each of which is assumed to have a higher refractive index n ₁ . The complex index n ₂ = n ₂ - ik ₂ accommodates active layer absorption [exp(+iωt) convention for radial frequency and time convention]. Initially, cladding layers are assumed macroscopic in thickness with Lambertian scattering surfaces 14, 15. Zero reflection for light incident on the top cladding is assumed and a perfect, displaced mirror 16 is assumed for the rear (k ₄ →∞). Related geometries (excluding the intervening layer) have been analysed, with the present analysis readily extended to these and to less ideal front and rear reflectance.

The geometry schematically illustrated in Figure 1 can apply to a Solar cell or

Light Emitting Diode (LED). In the case of LEDs, directionality can be imparted to the emitted light by geometrical or other means known to the art, further enhancing the optical gain provided by the new light trapping scheme. The drawings illustrate devices that absorb/emit in all directions. If the emission direction is restricted to a half-angle theta, as might be desirable for some LED applications, the output can be further boosted by an amount up to [1/sin(θ)] ² .

The Lambertian front surface scatters incident light into all available optical modes (directions). A scattered ray impinging on the active layer generally will have portions reflected, transmitted and absorbed. Relative amounts depend on incident angle, and layer thickness, Fresnel coefficients for the first cladding/active layer interface determining this are for (s and p polarisation):

where

The active layer extinction coefficient, fa, is assumed finite but much smaller than «2 in some of the following so that n. ₂ can be regarded as real when non-critical.

As a baseline, consider the case of thick active layer with incoherent reflections at its two interfaces. For incident angles on this layer above the critical angle all light is reflected. For Lambertian distributions, the fraction reflected in this way equals: where φ is azimuthal angle. Integrating gives (fa small):

This leaves a fraction not so reflected. Some of this is also reflected. The rest is refracted into the active layer at a more oblique angle than (Snell's law). To determine limiting performance, additional features (i.e. interfacial antireflection coatings or texture) are assumed to reduce the reflection to zero. Then the average light pathlength in the active layer is twice the layer thickness for weak absorption. Cladding layers will trap such light for a pathlength enhancement of of this ₁ similarly ² enhanced, in the active layer. This gives the expected enhanced active layer of 4n ² .

Assuming now coherent reflection from the two active layer interfaces, reflected and transmitted amplitudes, incorporating multiple reflections are:

where r is the appropriate Fresnel (s or p) coefficient at the cladding/active layer interface and δ ₂ is a generally complex phase/attenuation factor: λ is vacuum wavelength and d ₂ is active layer thickness. Assuming k ₂ << n ₂ , n ₂ cosθ ₂ simplifies to, forθ ₁ << θ _c :

Note the sign changes as θ _c is exceeded and associated change in δ ₂ from being largely real to largely imaginary. The product of real and imaginary parts ofn ₂ cosθ ₂ is constant at -n ₂ k ₂ (when one is large, the other is small).

The fractional energy absorption for the ray incident on the active layer is:

From Eqs. (5) and (6): Subscripts r and i designate real and imaginary parts. The r variables have maximum magnitude around unity with r _i and δ _2i vanishingly small well below θ _c and δ _2r vanishingly small well above θ _c , for small k ₂ . This allows simplifications, ie. for θ ₁ <θ _c :

Expected maximum absorption per pass is -2δ _2i , showing possibilities for surpassing this when sin(2δ _2r ) and cos(2δ _2r ) have appropriate sign. Light-trapping marginally 4n ² is possible. This essentially arises from modification of the wavelength distribution of the density of optical states ⁷ similar to boosts in resonant cavity photodetectors ⁸ . Agrawal ² establishes this must always be at the expense of response for otherθ ₁ .

For θ ₁ > θ _c , simplification of Eq. (12) depends upon active layer thickness. For δ _2i >> 1 , exponential terms are relatively small, giving:

For g [ ] giving weak absorption that becomes insignificant compared to that for angles <θ _c . Absorption approaches a constant value given by, θ ₁ >>θ _c :

The conclusion is, for thick layers, light trapping limits are similar to the incoherent case, although values can be higher over a limited wavelength or angular range.

For very thin layers, both δ _2i and δ _2r << 1. Expanding Eq. (12) to first order in these gives for all Φ ₁ :

For s and p polarizations, this reduces to the following d ₂ small):

These remarkable equations hold for all θ ₁ . The s polarisation is absorbed as if of energy densityn ₂ /n ₁ lower in the active layer but travelling the same direction as in the cladding (no refraction), p polarisation is absorbed even more strongly. Absorption increases as θ _c is exceeded. Since Lambertian surfaces randomise direction and polarisation, Lambertian pathlength enhancement is found by inserting the average into the integrand on the numerator of Eq. (4) and integrating over all angles giving:

The first expression shows the boost compared to the baseline 4n ₂ d ₂ derived earlier. The structure of Figure 1 substantially increases pathlength over what have been called thermodynamic limits. If the cladding index is twice the active layer index, the relative boost is 12. The second expression shows the boost relative to the cladding. Surprisingly, pathlength enhancement is even higher in the active layer than in the cladding. For a cladding index twice that of the active layer, enhancement is 3 times higher than possible in the cladding. This is attributed to the high evanescent local photon density of states (LPDOS) in the active region and their high occupancy by propagating evanescent modes. The effect is related to the increased luminescence from emitters close to interfaces. In Figure 2 a calculated light-trapping boost is illustrated for the scheme of Figure 1 as a function of active layer thickness for different active layer extinction coefficients.

As d ₂ increases, the situation reverts to the less desirable case previously referenced. This transition can be delayed by splitting the active layer into multiple layers 21, 22 (refer to Figure 3 discussed below). Compared to a single layer 11 of thickness 2d ₂ , the gain increases as the thickness D of the intervening layer 22 increases from zero to about half a wavelength. The situation resembles double barrier tunnelling with angle the energy analogue. For large <¾, resonances occur at angles corresponding to propagating modes of the intermediate dielectric slab. Splitting into more than two active regions, the situation eventually resembles a ID crystal with resonant angles splitting into bands.

Referring to Figure 3, a double active layer geometry is shown in this case with planar surfaces 24, 25 and a rear scattering layer 26 such as formed by diffraction gratings, plasmonic nanoparticles, photonic crystals or combinations of these.

Layer absorption with increasing <¾ and the effect of finite is explored for a specific case ofn ₁ =3.5,n ₂ =2.0-ik ₂ and 600nm wavelength in Figure 4, which graphically illustrates calculated absorptance for the solar cell geometry of Figures 1 & 3 as a function of the total thickness of the active layer (i.e. both when the active layer is a single layer and when split into two layers). .

Cladding layers requirement, if not an active cell region, must have small absorption over wavelengths of active layer response. Thin cladding layers can help. Although microstructured random scatterers of 100-200 nm feature size give good experimental and modelled performance, even thinner cladding may be desirable. Coherent scattering from metallic plasmonic particles, photonic crystals or diffraction gratings (Figure 3) would be consistent with scattering incident light into trapped waveguide modes of thin planar devices. Without the active layer (or layers), light trapping with such coherent scattering is bounded by the incoherent limits, with some falloff as available modes reduce. Pathlength enhancement possible in the cladding layer may be less than 4n ² with d ₂ zero. It is concluded the planar structure of Figure 3 could at best match the case with scattering surface texture.

The higher the index contrast between cladding and active layers, the more effective is light trapping. Constraints arise from Moss's Rule (n ⁴ E _g approximately constant with bandgap E _g ). High index materials generally have small bandgap, hence high absorption. However, some materials strongly violate Moss's Rule with scope for synthesising nanomaterials in this category. Materials giving high side violations are ideal cladding candidates.

Organic semiconductors have low index relative to inorganics of similar effective E _g so are ideal for this scheme. Inorganic cladding layers could also serve as ultraviolet, oxygen and moisture barriers.

For inorganic tetrahedral semiconductors, high covalency and small atomic spacing gives high index, suggesting combinations where high polarity, loosely packed semiconductors (e.g. CdTe) form the active layer with less polar, more tightly packed claddings.

Similar advantages apply to related optoelectronic devices such as LEDs. It will be appreciated by persons skilled in the art that numerous variations and/or modifications may be made to the invention as shown in the specific embodiments without departing from the scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.