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Photoconductivity and photoconversion at a photorefractive thin crystal plate
Optical Materials xxx (2016) xxx–xxx
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Optical Materials journal homepage: www.elsevier.com/locate/optmat
Photoconductivity and photoconversion at a photorefractive thin crystal plate Jaime Frejlich a, Ivan de Oliveira b,⇑, William R. de Araujo c, Jesiel F. Carvalho d, Renata Montenegro d, Marc Georges e, Karl Fleury-Frenette e a
Instituto de Física ‘‘Gleb Wataghin”/UNICAMP, Campinas, Brazil Laboratório de Óptica, Faculdade de Tecnologia/UNICAMP, Limeira, SP, Brazil Laboratório Nacional de Luz Síncrotron, Campinas, SP, Brazil d Instituto de Física, Universidade Federal de Goiás, Goiânia, GO, Brazil e Centre Spatial de Liège, Université de Liège, Belgium b c
a r t i c l e
i n f o
Article history: Received 8 December 2015 Received in revised form 23 February 2016 Accepted 24 February 2016 Available online xxxx Keywords: Photoconductivity Photorefractive materials Optoelectronics
a b s t r a c t We report on the photoconductivity and the photoelectric conversion measured on a thin photorefractive sillenite crystal plate, between transparent electrodes, in the longitudinal configuration where the current is measured along the same direction of the light beam through the sample. Its behavior is based on the already reported light-induced Schottky effect. The wavelength for optimal photoconductivity is determined. A specific parameter is formulated here for quantitatively determining the photoelectric conversion efficiency of the sandwiched material. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Photorefractive materials are photoconductive and electrooptics and are particularly suited for almost real-time reversible optical recording by transforming a spatially modulated illumination into a corresponding volume index-of-refraction modulation that can be read using an auxiliary probe beam [1–3]. These materials are also useful as high capacity volume memories [4–7], optical components fabrication [8] and for mechanical vibration modes detection in 2D [9,10] and various nondestructive metrology applications [11]. In this paper we shall focus only on the photoconductive properties and photoelectric conversion performance of photorefractive Bi12TiO20 crystal. Light-induced Schottky effect at a transparent conductive electrode-bulk photorefractive crystal interface was already reported [12] before and shown to be due to the large density of electron-filled Localized States in most photorefractive materials [13] that allow to produce a large density of free electrons in the conduction band (CB), close to the illuminated transparent conductive electrode, by the action of light of adequate wavelength. Free electrons in the CB diffuse to the electrode until a sufficiently large depletion layer and associated electric barrier is build up to ⇑ Corresponding author.
stabilize the process. The same barrier but of opposite polarization is build up at the rear photorefractive-electrode interface. As light is strongly absorbed while going through the photorefractive plate thickness, the electric potential barrier is much weaker at the less illuminated rear interface than at the more illuminated front one, as schematically illustrated in Fig. 1. Such an unbalanced voltage difference produces an overall drift of photoelectrons through the ITO-sandwiched photorefractive slab. Photorefractive materials of the Sillenite familly are known to have a large forbidden bandgap (BG) in the range of 3.2 eV (corresponding to a light of k 388 nm) that makes them quite transparent in almost the whole visible range. The action of light on nominally undoped sillenites excites mainly electrons from Localized States in the BG to the CB. The energy gap between the Fermi level and the bottom of the CB in these materials being about 2.2 eV [13–15] (corresponding to k 564 nm), this one should obviously be the minimum photonic energy for photoelectron generation in the sample’s volume, at least in thermally relaxed conditions. Most materials however, and particularly sillenites, have plenty of empty Localized States in between the Fermi level and the CB [15], that may be filled by optical pumping (with light of photonic energy equal to or higher than 2.2 eV, for sillenites) thus allowing light of photonic energy lower (or even much lower) than 2.2 eV to effectively participate in the photoelectric process too. On the other hand, such large number of empty centers makes
E-mail address: [email protected] (I. de Oliveira). http://dx.doi.org/10.1016/j.optmat.2016.02.046 0925-3467/Ó 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: J. Frejlich et al., Opt. Mater. (2016), http://dx.doi.org/10.1016/j.optmat.2016.02.046
2
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Fig. 2. Undoped photorefractive Bi12TiO20 crystal sample with H being its height, d its thickness, and ‘ its width. In the longitudinal configuration the front and rear surfaces are coated with transparent conductive ITO electrodes that are separated by the crystal thickness d. In the transverse configuration instead, silver ink glue electrodes are painted on the opposite lateral (1 0 0) surfaces and their separation is the width ‘. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 1. Schematic representation of the device operation under illumination, in the longitudinal configuration, including a schematic voltage diagram along the device’s thickness, without externally applied voltage. The arrows represent the light intensity.
free electrons to be easily retrapped thus reducing the overall photoelectric conversion efficiency. 2. Wavelength-Resolved Photoconductivity Wavelength-Resolved Photoconductivity measurements [16] were first carried out in the transverse configuration where the light is perpendicularly incident on the input crystal face and the photocurrent is collected in the transverse direction (along crystal axis [1 0 0] in the sample of Fig. 2) with silver glue electrodes painted on the lateral opposite faces. This configuration was already shown [14,15] to be adequate for studying the position of the photoactive centers inside the material bandgap even using discrete wavelength illumination. The longitudinal configuration instead, where a thin photorefractive crystal slice is sandwiched between transparent conductive ITO electrodes and the photocurrent is measured along the same direction of the incident light, is here shown to be adequate for studying the photoconductivity and photoelectric conversion performance. 2.1. Photoconductivity measurement Both transverse and longitudinal configurations will be here mathematically described and compared to each other in terms of their interest for studying the material and its performance. 2.1.1. Transverse configuration Transverse configuration leads us to a convenient specific photonic energy dependent specific photoconductivity parameter rt that was already defined as [16]:
rt ðhmÞ ¼
iph ‘ hm ad ; Hd V Ið0Þ 1 ead
where V is the applied voltage through the sample’s width ‘ with H being the height and d the thickness of the crystal as represented in Fig. 2. Ið0Þ is the irradiance of photonic energy hm as measured inside the crystal at its input face of surface H‘. The overall optical absorption coefficient including light-induced effects if ever present is a with Ua representing the fraction of absorption coefficient giving rise to electrons excited to the CB. The parameter in Eq. (1) can be also written, in terms of material properties, as:
X ðUaÞi ;
rt ðhmÞ ¼ qls
ð2Þ
i
where q, l and s are the electric charge value, mobility and lifetime of the photoexcited charge carriers (electrons in the CB for sillenite crystals) in the extended state. The summation at the right-hand side in the equation above is carried out on all Localized States (photoactive centers in the Band Gap) found at an energy gap of hm from the bottom of the CB and its representation as a function of hm is characterized by discrete steps each one of them indicating the position of a filled Localized State in the BG, as reported elsewhere [15]. 2.1.2. Longitudinal configuration Experimental results in this paper for this configuration are all referred to the crystal sample described in Fig. 2 with H ¼ 9:75 mm, ‘ ¼ 5:10 mm and d ¼ 0:81 mm. In this configuration the photoelectric current iph and the light irradiance Ið0Þ are both flowing parallel to each other along the coordinate z and perpendicularly to the input crystal surface. We should therefore write
iph ¼ rðzÞEðzÞH‘; IðzÞ rðzÞ ¼ qlsUa ; hm IðzÞ ¼ Ið0Þeaz :
ð3Þ ð4Þ ð5Þ
Because of the continuity of the current (iph independent of z) it is
ð1Þ
EðzÞrðzÞ / EðzÞIðzÞ ¼ Eð0ÞIð0Þ;
Please cite this article in press as: J. Frejlich et al., Opt. Mater. (2016), http://dx.doi.org/10.1016/j.optmat.2016.02.046
ð6Þ
J. Frejlich et al. / Optical Materials xxx (2016) xxx–xxx
From Eqs. (6) and (5) we deduce that az
EðzÞ ¼ Eð0Þe :
ð7Þ
In the absence of light-induced potential barriers the relation between the applied voltage V and the electric field Eð0Þ at the input plane inside the material is
Z
ead 1 V¼ EðzÞdz ¼ Eð0Þ d; ad 0 ad Eð0Þ ¼ ðV=dÞ ad ; e 1
crystal volume and photoelectron generation on the other side. This trade-off for our 0.81 mm thick plate results in a maximum photoconductivity efficiency (g‘ ) at k 2:5 eV. For a thicker plate of the same material we should expect the peak to shift to lower hm. 3. Photoelectric conversion
d
ð8Þ ð9Þ
and Eq. (3) therefore becomes
iph ¼ qlsUa
Ið0Þ ad ðV=dÞ ad H‘: hm e 1
ð10Þ
iph d hm ead 1 ¼ : H‘ V Ið0Þ ad
Photoelectric conversion, that is to say, photocurrent flowing without any externally applied electric field, is expected to arise in an ITO-sandwiched photoconductive photorefractive crystal plate in the longitudinal configuration because of the unbalanced front-to rear potential barrier difference produced by the light. In fact in the absence of an externally applied field a photocurrent
iph ¼ qls 0
Following the same procedure as for the transverse configuration we should write a specific photoconductivity:
r‘
ð11Þ
iph hm ; q Ið0ÞH‘
i =q hm g ¼ ph ; V=d Ið0ÞH‘
g0 ¼ ls
that represents the ‘‘number of photoelectrons drifted per unit externally applied electric field and per unit incident photon”. Preliminary results for undoped Bi12TiO20 are reported in Fig. 3. Note that, differently than for the transverse configuration, there are no steps here but a rather wide peak centered at hm 2:5 eV. Note also that the curve arising from the positively polarized rear electrode is larger than for the reverse polarization, in good qualitative agreement with what should be expected from the schema in Fig. 1. The position of the peaks in Fig. 3 is certainly the result of a trade-off between the higher hm required for exciting as much electrons to the CB as possible with an associated higher ad (a thickness) that should positively increase the front-to-rear potential barrier difference on one side but would reduce the illuminated
Fig. 3. Plotting of g‘ on the right-hand ordinate axis with positive polarization (ranging from 0 to 500 V) both at the front () and at the rear () electrode, as measured on the undoped Bi12TiO20 crystal plate (labeled BTOJ18L and represented in Fig. 2) with d ¼ 0:81 mm and ITO electrodes on the front and rear H‘ 50 mm2 surfaces. The dashed curves are the fitting of both efficiencies near their maximum using a second order polynomial. The overall optical absorption coefficient a is shown (filled M) at the left-hand ordinate axis.
ð13Þ
0
g0
ð12Þ
Ið0Þ H‘UahEi; hm
should arise where hEi stays for the effective light-induced electric field. A specific phenomenological photoelectric conversion efficiency should be defined from Eq. (13) as
However, because of the building up of potential barriers in the ITOcrystal interfaces, the electric field distribution inside the crystal volume is differently than formulated in Eq. (7) and therefore Eq. (11) is not useful. Instead we should better reformulate it to describe a kind of photoconductivity efficiency ‘
3
ð14Þ
representing the number of electrons flowing per unit photon incident inside the crystal, with g0 being also described by
X ðUaÞi hEi;
ð15Þ
i
where as for the transverse configuration, the summation is over all Localized States in the energy gap hm below the bottom of the CB. Preliminary experimental results displayed in Fig. 4 show that there are no steps but peaks at the position where filled photoactive centers are expected, mainly a big one at 2.2 eV where the Fermi level is expected and a sensibly smaller one close to 2.5 eV. Much smaller peaks are also visible before and after these two ones. The term hEi in Eq. (13) is certainly affected by the light intensity and its photonic energy hm. Therefore, differently than for the transverse configuration, it is not easy to correlate the size of the peaks with the density of charge carriers in the corresponding Localized States. These peaks may therefore hardly give information about the photoactive centers themselves but are useful to point out at which photonic energy hm maximum photoelectric conversion occurs. Comparative results in Fig. 5 do confirm that peaks arising from the longitudinal configuration experiment without applied electric
Fig. 4. Photoelectric conversion efficiency (g0 ) measured in the longitudinal configuration on the same crystal sample as in Fig. 3 but without any externally applied electric field. The parameter ad is also plotted here.
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J. Frejlich et al. / Optical Materials xxx (2016) xxx–xxx
its performance is still much lower than that one (about 0.7 electrons/photon at 2 eV) for a typical commercial semiconductorbased device. Acknowledgements We acknowledge partial financial support from the Conselho de Desenvolvimento Científico e Tecnológico (CNPq), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Fundo de Apoio ao Ensino, Pesquisa e Extensão (FAEPEX/UNICAMP), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Fundação de Amparo à Pesquisa do Estado de Goiás (FAPEG) all from Brazil. Fig. 5. Comparative results for the same sample showing the degrees arising from a the transverse configuration experiment (rt ) under applied electric field () and the peaks appearing at each one of the steps measured in the longitudinal configuration (g0 ) without any applied field ().
field do appear at the step from one degree to the other. Note also that there are steps and peaks below 2.2 eV in Fig. 5 showing that the sample here is, at least, less relaxed than in Fig. 3 and therefore we should expect sensibly different values for the peaks at 2.2 and 2.5 eV too. It is worth pointing out that the strong apparent lowering in a value as the photonic energy approaches the bandgap limit at 3.2 eV in Figs. 3 and 4 is not actually due to a reduction in a (in fact a strongly increases) but to the occurrence of luminescence-based emission of lower photonic energy radiation from the sample, that is measured by the non wavelength-selective detector just behind the sample. Such an apparent lowering in a also depends on the intensity of the incident light so that it is not surprising to see sensibly different values for a in both figures referred to above. 4. Conclusions It becomes clear that while Wavelength-Resolved Photoconductivity measurement in the transverse configuration is useful for studying the Localized States in the material Band Gap even using discrete wavelength illumination, longitudinal configuration is better suited for studying the photoconductivity and photoconversion performance of the material. Because of the nature of data produced using a longitudinal configuration, a continuous wavelength spectrum source of light would be better suited than the discrete one in this paper, differently than for the transverse configuration experiments. The relevant result here reported is that it is possible to produce a very simple structure (ITO-sandwiched photorefractive slab) performing as a photoelectric conversion device using a non-photovoltaic photorefractive material even if
References [1] L. Solymar, D.J. Webb, A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials, Clarendon Press, Oxford, 1996. [2] P. Günter, J.P. Huignard, Topics in Applied Physics: Photorefractive Materials and their Applications I, Springer Verlag, 1987. [3] P. Günter, in: P. Günter, J.-P. Huignard (Eds.), Photorefractive Effects and Materials – Topics in Applied Physics: Photorefractive Materials and Their Applications I and II, vols. 61 and 62, Springer, Berlin, Heidelberg, 1988. [4] Fai H. Mok, Angle-multiplexed storage of 500 holograms in Lithium Niobate, Opt. Lett. 18 (1993) 915–917. [5] K. Buse, A. Adibi, D. Psaltis, Non-volatile holographic storage in doubly doped lithium niobate crystals, Nature 393 (1998) 665–668. [6] Lambertus Hesselink, Sergei S. Orlov, Alice Liu, Annapoorna Akella, David Lande, Ratnakar R. Neurgaonkar, Photorefractive materials for nonvolatile volume holographic data storage, Science 282 (1998) 1089–1094. [7] Wei-Chia Su, Ching-Cherng Sun, Nicholai Kukhtarev, Arthur E.T. Chiou, Polarization-multiplexed volume holograms in LiNbO3 with 90-deg geometry, Opt. Eng. 42 (2003) 9–10. [8] R. Müller, M.T. Santos, L. Arizmendi, J.M. Cabrera, A narrow-band interference filter with photorefractive LiNbO3, J. Phys. D: Appl. Phys. 27 (1994) 241–246. [9] J.P. Huignard, J.P. Herriau, T. Valentin, Time average holographic interferometry with photoconductive electrooptic Bi12 SiO20 crystals, Appl. Opt. 16 (1977) 2796–2798. [10] J. Frejlich, P.M. Garcia, Advances in real-time holographic interferometry for the measurement of vibrations and deformations, Optics Lasers Eng. 32 (1999) 515–527. [11] P. Lemaire, M. Georges, Dynamic holographic interferometry: devices and applications, in: P. Gunter, J.-P. Huignard (Eds.), Photorefractive Materials and Their Applications 3, Springer Series in Optical Sciences, vol. 3, Springer, New York, USA, 2007, pp. 223–253 (chapter 8). [12] Jaime Frejlich, Christophe Longeaud, Jesiel F. Carvalho, Photoinduced Schottky barrier in photorefractive materials, Phys. Rev. Lett. 104 (2010) 116601. [13] J. Frejlich, Photorefractive Materials: Fundamental Concepts, Holographic Recording, and Materials Characterization, Wiley-Interscience, New York, 2006. [14] J. Frejlich, R. Montenegro, T.O. dos Santos, J.F. Carvalho, Characterization of photorefractive undoped and doped sillenite crystals using holographic and photoconductivity techniques, J. Opt. A: Pure Appl. Opt. 10 (2008) 104005. [15] J. Frejlich, R. Montenegro, N.R. Inocente Jr., P.V. dos Santos, J.C. Launay, C. Longeaud, J.F. Carvalho, Phenomenological characterization of photoactive centers in Bi12TiO20 crystals, J. Appl. Phys. 101 (2007) 043101-1–043101-12. [16] R. Montenegro, N.R. Inocente Junior, J. Frejlich, New possibilities for the measurement of wavelength-resolved photoconductivity, Rev. Sci. Inst. 77 (2006) 043905-1–043905-6.
Please cite this article in press as: J. Frejlich et al., Opt. Mater. (2016), http://dx.doi.org/10.1016/j.optmat.2016.02.046
Contents lists available at ScienceDirect
Optical Materials journal homepage: www.elsevier.com/locate/optmat
Photoconductivity and photoconversion at a photorefractive thin crystal plate Jaime Frejlich a, Ivan de Oliveira b,⇑, William R. de Araujo c, Jesiel F. Carvalho d, Renata Montenegro d, Marc Georges e, Karl Fleury-Frenette e a
Instituto de Física ‘‘Gleb Wataghin”/UNICAMP, Campinas, Brazil Laboratório de Óptica, Faculdade de Tecnologia/UNICAMP, Limeira, SP, Brazil Laboratório Nacional de Luz Síncrotron, Campinas, SP, Brazil d Instituto de Física, Universidade Federal de Goiás, Goiânia, GO, Brazil e Centre Spatial de Liège, Université de Liège, Belgium b c
a r t i c l e
i n f o
Article history: Received 8 December 2015 Received in revised form 23 February 2016 Accepted 24 February 2016 Available online xxxx Keywords: Photoconductivity Photorefractive materials Optoelectronics
a b s t r a c t We report on the photoconductivity and the photoelectric conversion measured on a thin photorefractive sillenite crystal plate, between transparent electrodes, in the longitudinal configuration where the current is measured along the same direction of the light beam through the sample. Its behavior is based on the already reported light-induced Schottky effect. The wavelength for optimal photoconductivity is determined. A specific parameter is formulated here for quantitatively determining the photoelectric conversion efficiency of the sandwiched material. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Photorefractive materials are photoconductive and electrooptics and are particularly suited for almost real-time reversible optical recording by transforming a spatially modulated illumination into a corresponding volume index-of-refraction modulation that can be read using an auxiliary probe beam [1–3]. These materials are also useful as high capacity volume memories [4–7], optical components fabrication [8] and for mechanical vibration modes detection in 2D [9,10] and various nondestructive metrology applications [11]. In this paper we shall focus only on the photoconductive properties and photoelectric conversion performance of photorefractive Bi12TiO20 crystal. Light-induced Schottky effect at a transparent conductive electrode-bulk photorefractive crystal interface was already reported [12] before and shown to be due to the large density of electron-filled Localized States in most photorefractive materials [13] that allow to produce a large density of free electrons in the conduction band (CB), close to the illuminated transparent conductive electrode, by the action of light of adequate wavelength. Free electrons in the CB diffuse to the electrode until a sufficiently large depletion layer and associated electric barrier is build up to ⇑ Corresponding author.
stabilize the process. The same barrier but of opposite polarization is build up at the rear photorefractive-electrode interface. As light is strongly absorbed while going through the photorefractive plate thickness, the electric potential barrier is much weaker at the less illuminated rear interface than at the more illuminated front one, as schematically illustrated in Fig. 1. Such an unbalanced voltage difference produces an overall drift of photoelectrons through the ITO-sandwiched photorefractive slab. Photorefractive materials of the Sillenite familly are known to have a large forbidden bandgap (BG) in the range of 3.2 eV (corresponding to a light of k 388 nm) that makes them quite transparent in almost the whole visible range. The action of light on nominally undoped sillenites excites mainly electrons from Localized States in the BG to the CB. The energy gap between the Fermi level and the bottom of the CB in these materials being about 2.2 eV [13–15] (corresponding to k 564 nm), this one should obviously be the minimum photonic energy for photoelectron generation in the sample’s volume, at least in thermally relaxed conditions. Most materials however, and particularly sillenites, have plenty of empty Localized States in between the Fermi level and the CB [15], that may be filled by optical pumping (with light of photonic energy equal to or higher than 2.2 eV, for sillenites) thus allowing light of photonic energy lower (or even much lower) than 2.2 eV to effectively participate in the photoelectric process too. On the other hand, such large number of empty centers makes
E-mail address: [email protected] (I. de Oliveira). http://dx.doi.org/10.1016/j.optmat.2016.02.046 0925-3467/Ó 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: J. Frejlich et al., Opt. Mater. (2016), http://dx.doi.org/10.1016/j.optmat.2016.02.046
2
J. Frejlich et al. / Optical Materials xxx (2016) xxx–xxx
Fig. 2. Undoped photorefractive Bi12TiO20 crystal sample with H being its height, d its thickness, and ‘ its width. In the longitudinal configuration the front and rear surfaces are coated with transparent conductive ITO electrodes that are separated by the crystal thickness d. In the transverse configuration instead, silver ink glue electrodes are painted on the opposite lateral (1 0 0) surfaces and their separation is the width ‘. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 1. Schematic representation of the device operation under illumination, in the longitudinal configuration, including a schematic voltage diagram along the device’s thickness, without externally applied voltage. The arrows represent the light intensity.
free electrons to be easily retrapped thus reducing the overall photoelectric conversion efficiency. 2. Wavelength-Resolved Photoconductivity Wavelength-Resolved Photoconductivity measurements [16] were first carried out in the transverse configuration where the light is perpendicularly incident on the input crystal face and the photocurrent is collected in the transverse direction (along crystal axis [1 0 0] in the sample of Fig. 2) with silver glue electrodes painted on the lateral opposite faces. This configuration was already shown [14,15] to be adequate for studying the position of the photoactive centers inside the material bandgap even using discrete wavelength illumination. The longitudinal configuration instead, where a thin photorefractive crystal slice is sandwiched between transparent conductive ITO electrodes and the photocurrent is measured along the same direction of the incident light, is here shown to be adequate for studying the photoconductivity and photoelectric conversion performance. 2.1. Photoconductivity measurement Both transverse and longitudinal configurations will be here mathematically described and compared to each other in terms of their interest for studying the material and its performance. 2.1.1. Transverse configuration Transverse configuration leads us to a convenient specific photonic energy dependent specific photoconductivity parameter rt that was already defined as [16]:
rt ðhmÞ ¼
iph ‘ hm ad ; Hd V Ið0Þ 1 ead
where V is the applied voltage through the sample’s width ‘ with H being the height and d the thickness of the crystal as represented in Fig. 2. Ið0Þ is the irradiance of photonic energy hm as measured inside the crystal at its input face of surface H‘. The overall optical absorption coefficient including light-induced effects if ever present is a with Ua representing the fraction of absorption coefficient giving rise to electrons excited to the CB. The parameter in Eq. (1) can be also written, in terms of material properties, as:
X ðUaÞi ;
rt ðhmÞ ¼ qls
ð2Þ
i
where q, l and s are the electric charge value, mobility and lifetime of the photoexcited charge carriers (electrons in the CB for sillenite crystals) in the extended state. The summation at the right-hand side in the equation above is carried out on all Localized States (photoactive centers in the Band Gap) found at an energy gap of hm from the bottom of the CB and its representation as a function of hm is characterized by discrete steps each one of them indicating the position of a filled Localized State in the BG, as reported elsewhere [15]. 2.1.2. Longitudinal configuration Experimental results in this paper for this configuration are all referred to the crystal sample described in Fig. 2 with H ¼ 9:75 mm, ‘ ¼ 5:10 mm and d ¼ 0:81 mm. In this configuration the photoelectric current iph and the light irradiance Ið0Þ are both flowing parallel to each other along the coordinate z and perpendicularly to the input crystal surface. We should therefore write
iph ¼ rðzÞEðzÞH‘; IðzÞ rðzÞ ¼ qlsUa ; hm IðzÞ ¼ Ið0Þeaz :
ð3Þ ð4Þ ð5Þ
Because of the continuity of the current (iph independent of z) it is
ð1Þ
EðzÞrðzÞ / EðzÞIðzÞ ¼ Eð0ÞIð0Þ;
Please cite this article in press as: J. Frejlich et al., Opt. Mater. (2016), http://dx.doi.org/10.1016/j.optmat.2016.02.046
ð6Þ
J. Frejlich et al. / Optical Materials xxx (2016) xxx–xxx
From Eqs. (6) and (5) we deduce that az
EðzÞ ¼ Eð0Þe :
ð7Þ
In the absence of light-induced potential barriers the relation between the applied voltage V and the electric field Eð0Þ at the input plane inside the material is
Z
ead 1 V¼ EðzÞdz ¼ Eð0Þ d; ad 0 ad Eð0Þ ¼ ðV=dÞ ad ; e 1
crystal volume and photoelectron generation on the other side. This trade-off for our 0.81 mm thick plate results in a maximum photoconductivity efficiency (g‘ ) at k 2:5 eV. For a thicker plate of the same material we should expect the peak to shift to lower hm. 3. Photoelectric conversion
d
ð8Þ ð9Þ
and Eq. (3) therefore becomes
iph ¼ qlsUa
Ið0Þ ad ðV=dÞ ad H‘: hm e 1
ð10Þ
iph d hm ead 1 ¼ : H‘ V Ið0Þ ad
Photoelectric conversion, that is to say, photocurrent flowing without any externally applied electric field, is expected to arise in an ITO-sandwiched photoconductive photorefractive crystal plate in the longitudinal configuration because of the unbalanced front-to rear potential barrier difference produced by the light. In fact in the absence of an externally applied field a photocurrent
iph ¼ qls 0
Following the same procedure as for the transverse configuration we should write a specific photoconductivity:
r‘
ð11Þ
iph hm ; q Ið0ÞH‘
i =q hm g ¼ ph ; V=d Ið0ÞH‘
g0 ¼ ls
that represents the ‘‘number of photoelectrons drifted per unit externally applied electric field and per unit incident photon”. Preliminary results for undoped Bi12TiO20 are reported in Fig. 3. Note that, differently than for the transverse configuration, there are no steps here but a rather wide peak centered at hm 2:5 eV. Note also that the curve arising from the positively polarized rear electrode is larger than for the reverse polarization, in good qualitative agreement with what should be expected from the schema in Fig. 1. The position of the peaks in Fig. 3 is certainly the result of a trade-off between the higher hm required for exciting as much electrons to the CB as possible with an associated higher ad (a thickness) that should positively increase the front-to-rear potential barrier difference on one side but would reduce the illuminated
Fig. 3. Plotting of g‘ on the right-hand ordinate axis with positive polarization (ranging from 0 to 500 V) both at the front () and at the rear () electrode, as measured on the undoped Bi12TiO20 crystal plate (labeled BTOJ18L and represented in Fig. 2) with d ¼ 0:81 mm and ITO electrodes on the front and rear H‘ 50 mm2 surfaces. The dashed curves are the fitting of both efficiencies near their maximum using a second order polynomial. The overall optical absorption coefficient a is shown (filled M) at the left-hand ordinate axis.
ð13Þ
0
g0
ð12Þ
Ið0Þ H‘UahEi; hm
should arise where hEi stays for the effective light-induced electric field. A specific phenomenological photoelectric conversion efficiency should be defined from Eq. (13) as
However, because of the building up of potential barriers in the ITOcrystal interfaces, the electric field distribution inside the crystal volume is differently than formulated in Eq. (7) and therefore Eq. (11) is not useful. Instead we should better reformulate it to describe a kind of photoconductivity efficiency ‘
3
ð14Þ
representing the number of electrons flowing per unit photon incident inside the crystal, with g0 being also described by
X ðUaÞi hEi;
ð15Þ
i
where as for the transverse configuration, the summation is over all Localized States in the energy gap hm below the bottom of the CB. Preliminary experimental results displayed in Fig. 4 show that there are no steps but peaks at the position where filled photoactive centers are expected, mainly a big one at 2.2 eV where the Fermi level is expected and a sensibly smaller one close to 2.5 eV. Much smaller peaks are also visible before and after these two ones. The term hEi in Eq. (13) is certainly affected by the light intensity and its photonic energy hm. Therefore, differently than for the transverse configuration, it is not easy to correlate the size of the peaks with the density of charge carriers in the corresponding Localized States. These peaks may therefore hardly give information about the photoactive centers themselves but are useful to point out at which photonic energy hm maximum photoelectric conversion occurs. Comparative results in Fig. 5 do confirm that peaks arising from the longitudinal configuration experiment without applied electric
Fig. 4. Photoelectric conversion efficiency (g0 ) measured in the longitudinal configuration on the same crystal sample as in Fig. 3 but without any externally applied electric field. The parameter ad is also plotted here.
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its performance is still much lower than that one (about 0.7 electrons/photon at 2 eV) for a typical commercial semiconductorbased device. Acknowledgements We acknowledge partial financial support from the Conselho de Desenvolvimento Científico e Tecnológico (CNPq), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Fundo de Apoio ao Ensino, Pesquisa e Extensão (FAEPEX/UNICAMP), Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and Fundação de Amparo à Pesquisa do Estado de Goiás (FAPEG) all from Brazil. Fig. 5. Comparative results for the same sample showing the degrees arising from a the transverse configuration experiment (rt ) under applied electric field () and the peaks appearing at each one of the steps measured in the longitudinal configuration (g0 ) without any applied field ().
field do appear at the step from one degree to the other. Note also that there are steps and peaks below 2.2 eV in Fig. 5 showing that the sample here is, at least, less relaxed than in Fig. 3 and therefore we should expect sensibly different values for the peaks at 2.2 and 2.5 eV too. It is worth pointing out that the strong apparent lowering in a value as the photonic energy approaches the bandgap limit at 3.2 eV in Figs. 3 and 4 is not actually due to a reduction in a (in fact a strongly increases) but to the occurrence of luminescence-based emission of lower photonic energy radiation from the sample, that is measured by the non wavelength-selective detector just behind the sample. Such an apparent lowering in a also depends on the intensity of the incident light so that it is not surprising to see sensibly different values for a in both figures referred to above. 4. Conclusions It becomes clear that while Wavelength-Resolved Photoconductivity measurement in the transverse configuration is useful for studying the Localized States in the material Band Gap even using discrete wavelength illumination, longitudinal configuration is better suited for studying the photoconductivity and photoconversion performance of the material. Because of the nature of data produced using a longitudinal configuration, a continuous wavelength spectrum source of light would be better suited than the discrete one in this paper, differently than for the transverse configuration experiments. The relevant result here reported is that it is possible to produce a very simple structure (ITO-sandwiched photorefractive slab) performing as a photoelectric conversion device using a non-photovoltaic photorefractive material even if
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Please cite this article in press as: J. Frejlich et al., Opt. Mater. (2016), http://dx.doi.org/10.1016/j.optmat.2016.02.046