Energy Transfer in Triple Semiconductor-Organic Hybrid Structures

With aim to increase set of modern commercial optoelectronic devices we investigate the optical properties of new triple semiconductor-organics-semiconductor nanostructure having two semiconductor layers with organic layer between. This will be development to majority of modern publications with investigations of only double hybrid nanostructures with one contacting semiconductor layer and one organic layer. It is supposed that the energy of exciton in the first layer is larger than the energy of exciton in organic layer and that the energy of exciton in organic layer is larger in comparison with energy of exciton in second semiconductor layer. It was shown that installation of organics leads to some frequencies at different parameters or to reflection increasing and transmission decrease or to reverted dependence. New recurrent method of inverted calculation for fields is proposed and using this method the frequency dependences of optical characteristics have been calculated. The role of second semiconductor layer in considered triple structure has been estimated.


Introduction
The majority of modern commercial optoelectronic devices such as LEDs, solar cells, and nonlinear-optical devices are built mainly on the basis of traditional inorganic semiconductors.Over the last couple of decades, however, a lot of progress has been made in producing devices based on organic electronic materials, which, for many applications, may become less expensive alternatives to inorganic counterparts.The development prospects of organic materials are however mostly limited in their scope to relatively low-performance areas.For this O. A. Dubovskiy, V. M. Agranovich DOI: 10.4236/snl.2017.71001 2 Soft Nanoscience Letters reason a qualitatively different way of using organic electronic compounds can be via exploiting resonant interactions in organic-inorganic hybrid two layer structures with the organic layer and very thin inorganic layer possessing nearly equal energies of neutral excitations (excitons) [1].Such approach was widely investigated and the results can be found in many review papers [2]- [11].Nonradiative energy transfer in a hybrid structure with organic overlayer has been experimentally studied in [2].The hybrid nanostructure with the InGaN quantum wells as a donor and a monolayer of quantum dots as an acceptor was first studied in [3].We also mention here investigating of structure, where the temperature dependence of exciton energy transfer was studied [4].It was shown that organic molecules can be overgrown with ZnO employing epitaxial methods without degradation of their electronic structure [5].It was investigated that Forster resonant coupling between the Wannier-Mott and Frenkel excitons in hybrid structures comprising single (Ga, In) N quantum wells spaced from FBDP polymer layers [6].Details of optical characteristics of hybrid films were investigated in [7].The results of first experimental observation of Dexter type energy transfer in organic/inorganic hybrid materials were published in [8] [9].However, in mentioned publications only the nanostructures with one contacting semiconductor thin layer and one organic layer were used.
In this paper we propose to investigate the possibilities which can be created by triple hybrid nanostructure.We investigate the optical properties of more complex triple semiconductor-organics-semiconductor nanostructure with two very thin semiconductor layers and organic layer between them.The thickness of each semiconductor layer must be small as in double semiconductor-organic structure, i.e., approximately 2 -4 nm.In contrast to previously published papers we take into account only external pumping wave assuming that thickness of organic layer is larger in comparison with exciton diffusion length in organics.
We suppose that in triple structure the energy of Wannier-Mott exciton in the first semiconductor layer is bigger than energy of Frenkel exciton in organic layer as it was assumed usually for double hybrid resonance structures [12] [13].
We assume also that external orthogonal to surfaces optical irradiation produces in the first semiconductor layer the Wannier-Mott excitons with the rather high energy.These excitons can create Frenkel excitons in the intermediate organic region of triple structure and we assume that their energy will be not less than the energy of the Wannier-Mott excitons in the last and lowest third layer of hybrid structure.The role of organics in this structure may be essential since its presence will increase energy flow to second semiconductor layer.The influence of organics may be interesting also in the case when the energies of used semiconductors are resonating with the energies of virtual modes of organic slab [14] [15].Main equations, new recurrent method of their solution and analytical frequency dependences of reflection and transmission coefficients are presented in Part 2. The influence of organic layer on the frequency of reflection and transmission is discussed and the comparison of spectra without and with in-Soft Nanoscience Letters stalled organics defines region of frequencies where organic layer gives positive effect.

Main Equations and Recurrent Procedure of Their Solution for Triple Hybrid
We investigate triple hybrid structure using set of planes orthogonal to z-direction with electric fields polarized in x-direction and magnetic fields polarized in y-direction.Structure of triple hybrid semiconductor-organic-semiconductor is shown schematically by Figure 1.This structure includes upper plane of first semiconductor with Wannier-Mott exciton of high energy (WMH).Intermediate organic slab of finite thickness L with Frenkel exciton (FR) is disposed be- Usual procedure of solution with appropriated determinants for this system of linear equations for , 2,3, ,9 with fixed 1 E is well known.But for hy- brid structures with increasing number of planes rank of determinants drastically increases and using of standard procedure is embarrassing.
We use below inverted procedure considering as known last transmitting wave.In this case for Figure 1 it is the field 9 E .Then simple recurrent proce- dure without any determinants of high rank defines in inverted order all amplitudes , , E E near shady WML in inverted order and all functions , 8, 7, , 2 i E i =  are defined as functions of field 9 E .Linear dependence of really fixed external field 1 E is defined on the final stage as function of field 9 E .Inversion of this function defines coefficient of transmission E E .Inversion of all other de- pendences defines all fields including field 2 E of reflected wave and coefficient of reflection Advantage of this reverted procedure with start from WML side is stipulated by possibility to define pair of amplitudes over plane or border as linear functions of known functions under plane or border.Analogous procedure is impossible for start in equations from pumping side because for first plane WMH from two equations must be defined three unknown fields 2 3 4 , , E E E and the same in following steps.Only the last step of defining pair of fields under plane as functions of two fields over plane in this direct approach closes procedure by solution of two equations only for 2 E and 9 E .On the contrary proposed pro- cedure allows simplify analytical calculations for triple structure.Found recurrent relations allow investigating more complex hybrid structures-super lattices with big amount of planes and organic slabs with any order of physical parameters.Calculations below are performed in the same system of non dimensional units that were used in [12] [13]-frequency and oscillators strengths in units of main frequency WMH and length in organic slab thickness L. We subsequently define frequency dependences of successive introduced functions , 9 8,9 9 Corresponding continuity equations for electric and magnetic fields on lower border of FR slab have the following forms E E E E + = + , ( ) Frequency dependence of dielectric permeability ( ) ε ω for FR has the stan- dard form ( ) where 0 ω is frequency of exciton transition in FR, 0 ε -constant part of dielec- tric permeability ( ) Due to increasing complexity of analytical forms of functions Solutions of Equations ( 9) have the following forms , .
The exact analytical dependences of functions , , Equations for WMH at the distance 1 d from upper border of FR have the following form ) (12) has the following frequency dependence ( ) with own frequency 1 ω и oscillator strength 1 Γ .The solutions of these equa- tions have the following forms , .
The exact analytical dependences of functions , , , .
So used recurrent procedure allows to find in ( 5), ( 8), ( 10), ( 14) and (15) all functions ,9 , 1, 2, ,8 as linear functions of the field 9 E .Solutions for system of dynamic equations in standard direct ap- proach with pumping field 1 E have the following forms after inverting All frequency dependences for fields and flows of energy are defined by relations (16) for any region of hybrid.It is evident that function Ψ reveal de- terminant for system of eight equations.If the external pumping is absent with ( ) j j j j j j j j j j j j j j j j j and quantum outlet LED (8%) [16].

Frequency Dependences of Reflection and Transmission Coefficients for Separate Components of Triple Hybrid
Investigation of detailed forms of frequency dependence for reflection coefficient and transmission coefficient was done with numerical parameters used in [12] [13] for semiconductors ZnO or GaAs and anthracene as organic material with 1.5 eV Ω   and ( ) e e e e e e 1 Solutions of Equation (18) defining dependences 1 2 , E E from 3 E have the following forms The exact analytical dependences of functions T ω are defined as In correspondence with energy conservation the balance equation ( ) ( ) For second simple case when only organics is absent at 0 0 Γ = for corres- ponding fields numeration analogous to Figure 1 The exact analytical dependences of functions e e e e e e e 1 e 1 Solutions of (23) have the following forms The exact analytical dependences of functions , , Then the coefficients of reflection and refraction are defined by following finale relations ( ) At last it is interesting to consider isolated organics without WMH and WML at 1 2 0, 0 Γ = Γ = .For this case from ( 16) at 8 0 E = the following relations de- fine dependences 5 6 , E E from 7 E 5 5,7 7 Then relations (20) define 3 4 , E E and with (14) reflection coefficient ( ) demonstrate "virtual modes" defined by FR slab thickness, that where investigated in [14] [15].It was shown in [14] [15] that frequencies of these "virtual modes" are condensing near low frequency side of frequency 0 ω .These "virtual modes" are presenting the set of points for finite in z direction 3D organics that will form dispersion dependence of frequencies for infinite in z direction crystal.It was found that increasing of intrinsic absorption γ leads to decreasing am- plitudes and increasing widths of all resonances.

Frequency Dependences of Reflection and Transmission
The frequency dependences ( ) R ω and ( ) T ω (17) of fully combined triple hybrid with interacting components are shown on Figure 3 This difference that is up to 10 percent in order has negative sign in region of frequency 2 ω and positive sign in other regions including region of frequency 1 ω .It is seen that near these frequencies function

( )
Rd ω has oscillations.Rd ω < in the same region of frequencies.It means that at this frequency installation of organics in contrary decreases reflection and increases transmission.
We have investigated also spectra of reflection and transmission for different distances 2 d between FR and WML including case when WML is absent.It was found that WML is working as reflector turning light back to organics that is important for transformation current to light.

Conclusion
It was shown that installation of organics at external pumping with frequency near own frequency WMH leads to some frequencies at different parameters or to reflection increasing and transmission decrease and vice versa to reflection decreasing and transmission increase.The results of this article allow defining regions of parameters and frequency where technological effectiveness may be increased.The proposed new inverted method of calculation allows quick effective defining of optical characteristics for investigated triple hybrid and for super lattices of arbitrary sequence of planes and their parameters.It was found also by comparison spectra of triple hybrid with and without WML that works as reflector turning light back to organics.The proposed new inverted method of calculation may be useful also for reverse technology of transformation light to current by super lattices with arbitrary sequence of planes and their parameters.
6,9 7,9 8,9 The exact analytical dependences of functions  The exact analytical dependences of functions =  of all pairs for planes and borders.Start begins from fields 7 8 of hybrid with interacting components are defined from this equation.The frequency dependences of reflection coefficient ( ) R ω and transmission coefficient ( ) T ω have as result the following analytical forms O. A. Dubovskiy, V. M. Agranovich DOI: 10.4236/snl.2017.710017 Soft Nanoscience Letters that non dimensional own frequencies WMH, FR and WML are quite near and are decreasing in succession do not take into account unimportant non resonant factors.Organics has oscillator strength exceeding oscillator strength of semiconductors.It was taken into account for used set of parameters frequency dependences of reflection and transmission coefficients.Two equations of continuity for electric and magnetic field in plane WMH at 1 are shown in relations (A5) of Appendix.Equations for WMH have the following forms

Figure 2 .
Figure 2. (a) Reflection spectrum of one isolated semiconductor plane with WMH; (b) Reflection spectrum of two semiconductor planes with WMH and WML without organics; (c) Thin structure of virtual modes in reflection spectrum of isolated organics without semiconductors.

Figure 2
seen thin multi resonance structure below 0 ω in narrow compared with Figure 2(a), Figure 2(b) interval of frequency.Two arrows from Figure 2(c) to Figure 2(b) show this interval.Detailed calculations with increasing high precision have shown that at frequency approaching to 0 ω from left side continuously appears sequences of new resonances.These resonances are condensing below frequency 0 ω .These additional resonances on Figure 2(c) (a) and Figure 3(b).It was taken into account only one own FR frequency with 0 1 ε = .It is seen that due to relation ( ) ( ) following from Part 2 exactly Figure 3(b) is mirror copy of Figure 3(a).There are seen on Figure 2(a) two outside quasi Lorenz type curves modified by interaction between components with resonances at frequencies 1 ω and 2 ω corresponding to WMH and WML.Spec- trum of FR on Figure 3(a) is seen in the center between these frequencies.It is seen that at one own frequency of FR below frequency 0 ω appears developed set of few resonances.

Fig.4b demonstratesat 1 L
Fig.4b demonstrates mirror curve for difference of transmission coefficient.Positive sign of

Figure 3 .
Figure 3. (a) Frequency dependence of reflection coefficient for triple hybrid structure; (b) Frequency dependence of transmission coefficient for triple hybrid structure.

Figure 4 .
Figure 4. (a) Difference of reflection coefficients of triple hybrid structure with organics and without organics; (b) Difference of transmission coefficients of triple hybrid structure with organics and without organics.
two equations for plane