Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
  • G06F30/20—Design optimisation, verification or simulation

Definitions

• the present invention relates to a method of optical and electrical simulation of a device, optoelectronic, implemented by computer, and a corresponding computer program product.
• an optoelectronic device intended to receive a luminous flux, such as a solar cell for example, it is customary to simulate the optical and electrical behavior of the device, in order to predict its performance.
• simulation methods have been developed which, based on a model of the optoelectronic device, represent, in particular, the materials constituting the device and their optical and electrical properties, their dimensions and the manufacturing process. the device, to simulate an illumination having a determined spectrum representative of the illumination to which the optoelectronic device will be subjected in operation, and to calculate the optical and electrical characteristics of the device.
• These methods can in particular be implemented by computer and there is software for making a digital model of the electronic device according to the materials used and the manufacturing method, and to simulate the application of a light beam with characteristics data on said digital model, in order to calculate optical and electrical characteristics of the device.
• This software is generally part of software TCAD (acronym for the term “Technology Computer Aided Design”).
• the simulated optical characteristics are typically the reflectivity of an incident beam, as a function of the wavelength, which is expressed as the ratio (in%) between the intensity of the reflected beam and the intensity of the incident beam.
• the simulated electrical characteristics are generally the external quantum efficiency, designated by the acronym EQE (the external equivalent efficiency word) or the characteristic of the current as a function of the voltage under illumination, denoted l (V) or IV.
• the light illuminating the device has a defined spectrum, for example the solar spectrum for a photovoltaic cell.
• the optoelectronic device is modeled as a structure having planar surfaces, including the surface for receiving illumination.
• the characteristics of the structure are defined according to the materials used, their arrangement and the manufacturing process of the device.
• the simulations are also performed by considering the normal incident beam on the surface of the structure.
• Figure 1 schematically illustrates a model conventionally used, being in the form of a structure S having a plane illuminated surface S s .
• Said surface S s is illuminated by an incident beam intensity I i.
• the beam I breaks down into an absorbed beam T of intensity t and a reflected beam R of intensity r, which are both normal to the plane surface S s .
• the optical simulation consists in applying to the structure an incident beam of a determined wavelength, for each wavelength for which it is desired to provide the reflectivity.
• the illumination conditions forming the input data of the simulation include, for a monochromatic beam, the intensity and the wavelength of said beam and, for a non-monochromatic beam, the intensity as a function of the length of the beam. wave.
• the result of the optical simulation is the calculation of the reflected part of the beam which, after normalization, provides the reflectivity of the optoelectronic device.
• the calculated reflectivity can be compared with experimental reflectivity measurements to validate the models and their parameters.
• FIG. 2 is a logic diagram showing the principle of a conventional simulation of the reflectivity of a solar cell.
• a structure S constituting a virtual model of the optoelectronic device is defined, this structure being defined according to the design and manufacturing characteristics of the device.
• Lighting conditions I * are also defined, comprising the properties (wavelength, intensity) of the incident beam.
• An optical simulation S1 of the structure S is implemented under illumination conditions I * .
• the reflectivity thus obtained can then be compared with the reflectivity of the device measured experimentally, in order to validate the models and their parameters.
• Electrical simulation includes a preliminary step of optical simulation consisting of calculating the fraction of the incident beam absorbed by the structure. This absorbed fraction is then converted into an electrical quantity, namely the concentration of excess carriers.
• This magnitude is itself used in an electrical simulation step to calculate the external quantum efficiency (EQE) or the characteristic of the current as a function of the voltage under illumination (IV).
• Figure 3 is a logic diagram showing the principle of a conventional electrical simulation of a solar cell.
• a structure S constituting a virtual model of the optoelectronic device is defined, this structure being defined according to the design and manufacturing characteristics of the device, as well as the illumination conditions I * comprising the properties (wavelength intensity) of the incident beam.
• the result Ts of this simulation is the part of the incident beam absorbed by the structure.
• the illuminated surface of the solar cells is not flat but textured, that is to say composed of a plurality of asperities comprising a succession of hollows and reliefs.
• This texturing is intended to reduce the reflections occurring on the surface of the cell and therefore to increase the yield thereof.
• the texture is in the form of a plurality of pyramids formed by etching the surface of the cell.
• pyramids generally have a geometry similar to each other but a random size distributed around a mean value.
• regular pyramids may be encountered, that is to say all of whose flanks have the same angle with respect to a flat average surface of the device.
• Figure 4 schematically illustrates this phenomenon of successive reflections on a device D shown in section, and whose illuminated surface S D consists of a plurality of inclined facets.
• the incident beam I is reflected a first time on a facet (radius R1) and partially absorbed in the device (radius T1), and the reflected ray R1 itself hits an adjacent facet and is reflected on this facet (radius R2 ), while a part is absorbed in the device (radius T2).
• an incident beam therefore interacts at least twice with the cell before being sent outward.
• the amount of light transmitted in the device is greater than in the case of a flat surface and the reflectivity is lower.
• the method of "ray tracing" does not take into account the presence of any antireflection layers, whose thickness is very thin, deposited on the surface of the device.
• the quantum efficiency is calculated from an analytic formula that is based only on optical considerations but does not take into account the results of the simulation.
• the FDTD method has the disadvantage of involving very long computation times, because of the number of pyramids to be taken into account (for example, for a model of 1000 ⁇ wide and pyramids whose base has a width of 10 ⁇ , it is necessary to perform the calculations for a hundred pyramids).
• An object of the invention is therefore to propose a method for simulating the optical and electrical properties of an optoelectronic device that makes it possible to take into account the texturing of the surface of said device.
• This method must be simple to implement and require calculation times that are not greater than the calculation time required for conventional simulations based on a flat surface of the device.
• This method must also be able to take into account different texturing geometries, according to the manufacturing method of the device.
• This method must also allow the simulation of any antireflection layers deposited on the surface of the device.
• a first light beam inclined with respect to the normal to said flat surface with a first non-zero angle simulating an angle of incidence of the incident beam the texture of the surface of the device, and whose intensity is equal to that of the incident beam, and by
• textured is meant that the illuminated surface is not smooth but has asperities, that is to say a succession of hollows and reliefs.
• the texture preferably comprises a plurality of facets arranged to form regular cones.
• a cone is defined as a volume delimited by a set of half-lines passing through the same point (the vertex) and based on a closed contour (the base).
• regular cone used in the present text thus covers the cones of revolution, whose base is circular and which are considered as having an infinity of facets, as well as the regular pyramids, whose base is polygonal (for example triangular, square, etc.) and thus have a finite number of facets.
• the facets are inclined relative to a planar mean surface of the device, which is a flat surface parallel to the other planar surfaces of the device, and parallel to the surface of the model.
• the average plane surface of the device is a horizontal surface, the normal to the surface being vertical.
• the incident light beam may be monochromatic (in which case its spectrum consists of a single line at the wavelength considered) or non-monochromatic, having a continuous or discontinuous spectrum over a range of wavelengths.
• each of said regular cones comprises a plurality (finite or infinite) of facets inclined at an identical angle with respect to a planar mean surface of the device surface; said first angle being equal to the angle between a facet and said flat average surface.
• said regular cones are regular pyramids.
• the second angle is defined as the angle of incidence of the reflected portion of the first beam on a facet adjacent to the facet struck by said first beam.
• the reflectivity of said first beam can be calculated.
• the reflectivity of said second beam can be calculated.
• the illumination of said planar surface of the structure is simulated by a third light beam inclined with respect to the normal to said surface with a third angle, said third angle being defined as being angle of incidence of the reflected portion of the second beam on a facet adjacent to the facet struck by said second beam.
• the illuminated surface of the device comprises an opaque zone.
• the first beam is modelized as a first half-beam directed towards the opaque zone and a second half-beam symmetrical with respect to the normal to the surface, each half-beam being inclined with respect to said normal with said first non-zero angle and having an intensity equal to half of that of the first beam and the second beam is modeled as a first half-beam directed to the opaque zone and a second half-beam symmetrical with respect to the normal to the surface, each half-beam being inclined with respect to said normal with said second angle and having an intensity equal to half that of the second beam.
• the reflectivity of an incident beam on the textured surface can then be calculated by taking the product of the reflectivities of the beams with which the illumination of the plane surface has been simulated.
• the intensity of the second beam can be calculated by multiplying the intensity of the first beam by the reflectivity of said first beam.
• the intensity of the third beam can be calculated by multiplying the intensity of the second beam by the reflectivity of said second beam.
• the intensity of the third beam can be weighted by a probability coefficient depending on the angle of the facet.
• the incident beam is non-monochromatic and the reflectivity of the first, the second and, where appropriate, the third beam for each of a plurality of sampled wavelengths of the spectrum of the incident beam is calculated. and the reflectivity of said incident beam is calculated by performing the product of the reflectivities of said beams for each of said wavelengths.
• it is possible to calculate an intensity spectrum of the second beam by multiplying the intensity of the first beam by the reflectivity of said first beam for each of said wavelengths.
• the concentration of excess carriers in the structure under the effect of said illumination is deduced from said absorbed intensity.
• the external quantum efficiency and / or the current characteristic as a function of the voltage of the optoelectronic device are calculated.
• the part of the first, the second and / or, where appropriate, the third beam transmitted in the structure is calculated during the simulation, and the inclination of said beam is corrected. part transmitted by deviating.
• the invention also relates to a computer program product comprising a set of instructions which, once loaded on a computer, allow the implementation of the method as described above.
• Said product can be on any computer medium, such as a memory or a CD-ROM.
• FIG. 1 is a diagram of a known type of model used to simulate the optical and electrical properties of an optoelectronic device
• FIG. 2 is a logic diagram showing the principle of a conventional simulation of the reflectivity of a solar cell
• FIG. 3 is a logic diagram showing the principle of a conventional electrical simulation of a solar cell
• FIG. 4 schematically illustrates the effect of the texturing of the surface on the interaction between an incident beam and the optoelectronic device
• FIG. 5 schematically illustrates the simulation principle according to the invention
• FIG. 6 is a sectional diagram of an optoelectronic device that can be simulated in accordance with the invention.
• FIG. 7 is a logic diagram showing the principle of an optical simulation according to the invention
• FIG. 8 is a logic diagram showing the principle of an electrical simulation according to the invention
• FIGS. 9A and 9B respectively show the reflectivity curves as a function of the wavelength obtained with a method according to the prior art that does not take into account the texture of the illuminated surface and with the method according to the invention
• FIGS. 10A and 10B respectively show the external quantum efficiency (EQE) curves as a function of the wavelength obtained with a method according to the prior art that does not take into account the texture of the illuminated surface and with the method according to FIG. 'invention,
• FIG. 12 is a sectional diagram of a variant of an optoelectronic device that can be simulated according to the invention, comprising an opaque zone on the textured surface,
• FIG. 13 schematically illustrates a variant of the simulation principle according to the invention, in which the textured surface of the device is partly covered with an opaque zone.
• FIG. 5 illustrates the general principle of optical and electrical simulation of an optoelectronic device whose surface to be illuminated is textured.
• Said simulation is implemented by computer.
• the device is modeled in the form of a structure S whose illuminated surface is modeled by a plane surface S s .
• the incident light beam is not modeled by a single normal beam at the surface, but by two incident beams and l 2 inclined relative to the normal N at the surface. S, whose angles of incidence are chosen according to the texture of the surface of the device.
• a first light beam is inclined relative to the normal N to said surface with a first angle ⁇ non-zero.
• the first beam thus simulates an angle of incidence of the incident beam on the texture of the surface of the device, and its intensity is equal to that of the incident beam I.
• a second light beam l 2 is inclined with respect to the normal N to the surface S with a second angle ⁇ 2 , simulating an angle of incidence of the reflected part of the incident beam on the texture of the surface of the device.
• the device D has, as illustrated in FIG. 6, an illuminated surface S D whose texture consists of an alternation of plane facets F inclined with respect to a flat average surface Sm.
• said facets are arranged relative to each other to form regular cones.
• Said cones have a regular shape, that is to say that each of the facets constituting their flanks has an identical angle with respect to their base, considered to be in a horizontal plane, and this angle is identical for all the cones.
• the cones may have different sizes distributed randomly on the surface S D.
• the cones obtained are generally pyramids with a square base.
• the technique usually used to perform the surface texturing forms regular pyramids with a square base, whose minimum width of the base is preferably greater than 1 ⁇ .
• the invention is not limited to this particular texture but, as indicated above, applies to any texture consisting of regular cones.
• the angle ⁇ 1 of the beam is defined as being equal to the angle between a facet of the regular cone and a horizontal plane coinciding with the base of said cone.
• the beam 1 2 it is considered to correspond to the part of the beam reflected on a facet of a cone and arriving on a facet of an adjacent cone.
• the beams and l 2 also have the same wavelengths as the incident beam whose illumination is desired to simulate.
• the beams 1 and 2 will have the same wavelength as this one.
• the beams and l 2 will have the same wavelengths as this one.
• the respective intensities of each of the said wavelengths for the beams and l 2 are not necessarily equal to that of the incident beam.
• two optical simulations are successively carried out under different lighting conditions, that is to say respectively with the beam and the beam 1 2 with their respective angles of incidence.
• the reflectivity for the corresponding wavelength is simulated.
• the reflectivity for a sample of wavelengths of said spectrum is calculated.
• the logic diagram of FIG. 7 illustrates the principle of this optical simulation.
• the S-structure is used with a planar surface that models the optoelectronic device whose surface is textured.
• a first optical simulation SOI consists in illuminating the surface S s of the structure in the first illumination conditions 11 * , namely those of the first beam.
• a second optical simulation S02 consists in illuminating the surface S s of the structure in the second illumination conditions 12 * , namely those of the second beam 1 2 .
• the result Rs2 of this second simulation is the reflectivity of the beam reflected by a first facet for the wave length (s) considered (s).
• the reflectivity being a normalized quantity, it is sufficient to work for this simulation with relative intensities and it is not necessary, in this context, to calculate the intensity of the part of the incident beam transmitted through the surface of the structure.
• the final reflectivity Rn of the incident beam on the textured surface is obtained by performing the product of the two reflectivities simulated above (calculation step C).
• the product of the reflectivities obtained by the first and the second simulation thus constitutes a relevant representation of the reflectivity of the textured surface illuminated by a normal incident beam.
• the transmitted light is the sum of the part transmitted by the incident beam during its first interaction with a facet and the part transmitted by the beam once reflected during its interaction with a second facet.
• the simulation is thus carried out on a structure having a plane surface on which the first beam inclined at an angle ⁇ 1 (illumination conditions 11 * ) is made with respect to the normal and the second beam 1 2 inclined by a angle a 2 (lighting conditions 12 * ).
• the intensity of this second beam is calculated by the intensity and reflectivity of the first beam.
• the structure S is used with a plane surface which models the optoelectronic device whose surface is textured.
• a first SOI optical simulation aims to build the second beam as described above.
• This first SOI simulation is performed in the first illumination conditions 11 * and consists in simulating the reflectivity Rs1 of the first incident beam.
• the intensity of the second beam l 2 is then calculated (step C) for each wavelength (as indicated above, a single wavelength is considered if the monochromatic beam, a sampling is considered if the beam is non monochromatic. ) by multiplying the intensity of the first beam by its reflectivity Rs1.
• a second optical simulation S02 is then carried out, in which the illumination of the structure S is simulated simultaneously with the first illumination conditions 11 * (beam with the intensity of the real beam and the angle of incidence ⁇ - ⁇ ). and the second illumination conditions 12 * (beam 1 2 with the intensity calculated in step C and the angle of incidence a 2 ).
• the result J of the electrical simulation SE1 is either the quantum efficiency (EQE) or the characteristic of the current as a function of the voltage under illumination (IV).
• the result obtained is more precise since it takes into account the concentration of excess carriers which is different, because of the texturing of the surface, that of a device having a flat surface, and that is itself determined from the two optical simulations SOI and SO2 that take into account the texture of the surface.
• FIGS. 9A and 9B thus present the comparative results of the reflectivity Rn as a function of the wavelength ⁇ obtained by simulation (SIMUL curve) and experimentally (EXP curve), for an AM1.5G solar spectrum and an optoelectronic device consisting of a solar cell whose surface is textured.
• said textured surface consists of regular pyramids with a square base and whose flank angle with respect to the base is 54.74 °; the average width of one side of the base being 5 ⁇ .
• the optical simulation was carried out according to a method of the prior art, by modeling the cell in the form of a structure having a flat surface and with a normal illumination at the surface.
• the optical simulation was performed in accordance with the invention, by modeling the cell in the form of a structure having a flat surface and with the illumination conditions 11 * , 12 * as defined above.
• FIGS. 10A and 10B for their part show the comparative results of the quantum efficiency EQE as a function of the wavelength ⁇ obtained by simulation (SIMUL curve) and experimentally (EXP curve), for a solar spectrum AM1.5G and a optoelectronic device identical to that forming the subject of FIGS. 9A and 9B.
• the electrical simulation was carried out according to a method of the prior art, by modeling the cell in the form of a structure having a flat surface and with a normal illumination at the surface.
• FIG. 10B the electrical simulation was carried out in accordance with the invention, modeling the cell in the form of a structure having a flat surface and with the illumination conditions 11 * , 12 * as defined above.
• FIGS. 11A and 11B present the comparative results of the current density I as a function of the voltage V obtained by simulation (SIMUL curve) and experimentally (EXP curve), for an AM1.5G solar spectrum and an optoelectronic device identical to that forming the subject of FIGS. 9A, 9B, 10A and 10B.
• the electrical simulation was carried out according to a method of the prior art, by modeling the cell in the form of a structure having a flat surface and with a normal illumination at the surface.
• FIG. 11B the electrical simulation was carried out in accordance with the invention, by modeling the cell in the form of a structure having a flat surface and with the illumination conditions 11 * , 12 * as defined above. high.
• optical and electrical simulation method which has just been described can be used for different purposes.
• this optimization may comprise the optimization of the thicknesses of the anti-reflection layers for a given material, or the selection of a material intended to form one of these layers according to its optical properties.
• This method can also make it possible to evaluate the effect of a surface texturing on the optical and electrical behavior of a non-textured optoelectronic device, or conversely the evaluation of the performance of a textured device if it is removed. texturing.
• the optoelectronic device D has, on its illuminated textured surface S D , an opaque zone O partially covering said surface.
• Said opaque zone may be, for example, an electrical contact deposited on the surface of the device.
• the incident light is either totally directed to this opaque region - leading to overestimate the effect of light in this region), wholly directed outside this area - leading to an underestimation of the effect of light in the region below the opaque zone.
• a variant of the method described above comprises modeling the first beam in the form of a first half-beam read towards the opaque zone and a second half-beam 2 symmetrical relative to to the normal N at the surface S s (see Figure 13).
• Each half-beam read, 2 is inclined relative to said normal N with the angle ⁇ defined above and has an intensity equal to half that of the first beam h.
• the second beam 1 2 is modeled as a first half-beam 1 2 directed towards the opaque zone and a second half-beam 22 symmetrical with respect to the normal N, each half beam l 2 i, l 22 being inclined relative to said normal N with the angle a 2 defined above and having an intensity equal to half that of the second beam l 2 .
• a variant of the simulation method makes it possible to take this third reflection into account in order to improve the accuracy of the results.
• the rays reflected twice on adjacent facets have a non-zero probability but not equal to 1, which depends on the angle of the facets, to hit a third facet.
• a variant of the simulation method makes it possible to take into account this possible third reflection, with the corresponding probability, to improve the accuracy of the results.
• the rays are artificially deflected after their transmission in the device, in order to give them the real angle with respect to the geometry of the device.
• This actual angle is calculated as a function of the angle of the facets of the cones relative to the average surface S m of the device.
• This deviation can be implemented by different numerical methods within the reach of those skilled in the art, and can be programmed at any distance from the surface.

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• 2012
  • 2012-06-29 FR FR1256235A patent/FR2992753A1/fr not_active Withdrawn
• 2013
  • 2013-06-28 EP EP13732525.4A patent/EP2867807A2/de not_active Withdrawn
  • 2013-06-28 WO PCT/EP2013/063692 patent/WO2014001532A2/fr not_active Ceased
  • 2013-06-28 US US14/411,662 patent/US20150169799A1/en not_active Abandoned

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