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6СОЛНЕЧНАЯ ЭНЕРГЕТИКА
Солнечные электростанции
SOLAR ENERGY
Solar thermal plants
I SELF-ORDERED Ge/Si QUANTUM DOT INTERMEDIATE BAND I PHOTOVOLTAIC SOLAR CELLS
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1 A.M. Kechiantz, K. W. Sun*, H. M. Kechiyants**, L. M. Kocharyan***
CD II Department of Applied Chemistry, National Chiao Tung University, Hsinchu, Taiwan ^ E-mail: arakech@mail.nctu.edu.tw
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0 * Department of Applied Chemistry, National Chiao Tung University, Hsinchu, Taiwan
E-mail: kwsun@mail.nctu.edu.tw
** Scientific Research Division, State Engineering University of Armenia, Yerevan, Armenia
E-mail: hovkechi@yahoo.com
*** Department of Physics, State University of Armenia, Yerevan, Armenia
E-mail: lkocharyan@ysu.am
Self-ordered super-lattice of Ge quantum dots creates intermediate band within energy gap of n-doped Si host material. Investigation has shown that already 100 times concentrated solar illumination allows Ge quantum dots to transfer electrons from valence band via intermediate states (confined ground electronic states of quantum dots) into conduction band, and to increase by about 30 % both photocurrent and conversion efficiency of Ge/Si quantum dot solar cells in respect to those of conventional Si solar cells.
Introduction
For the last decade the importance of efficient and environmental friendly conversion of nuclear and solar energy into electricity has been becoming more apparent [1—3]. It is reflected in the world's production of solar photovoltaic cells and modules. Production has been increasing at a rate of 25 % per annum since 1997 and was as high as 512 Mw/yr in 2003 [4].
As production cost is reducing, solar electrical energy is surely becoming favorable and profitable in many fields of energy consumption. Now the cost is as low as 0.10-0.12 USD per kWh [5]. Further reducing of it is expected in the next decade. Due to newly developed technologies, next generation of photovoltaic solar cells is expected to reduce the cost of solar electricity by 2-3 times. Such reducing of the cost will make solar electrical energy competitive with conventional energy sources and involve solar energy into global energy production [1].
First of all the next generation of photovoltaic solar cells must be based on low-cost production technologies, however, it may contain also expen-
sive elements. Low-cost chemical technologies have already demonstrated their ability in production of thin film solar cells [6]. Low-cost concentrators of solar energy have also exhibited their efficiency. Conjugated with highly efficient but expensive semiconductor cells, concentrators are able to reduce the net cost of produced solar electricity [7]. Such solar cells gain from high quality materials and from technologies already used in industry. Silicon is the most cheap semiconductor material traditionally used in industry. It is 4-5 times cheaper than germanium. Photovoltaic cells produced on the base of silicon are compatible with silicon IC technology and therefore incur low-cost of launching into industrial production.
The next generation of photovoltaic solar cells must have high efficiency of conversion solar energy into electrical energy. Efficiency of conversion, h, is given by n = FFVocJsc/Pm, where Voc and Jsc are the open circuit voltage Voc = (nkT/e)ln(1 + Jsc/Jd) and the short circuit current; n and Jd are the ideality factor and the dark current of p-n-junc-tion; FF is the fill-factor and PiU is the intensity of concentrated solar energy [8]. Assuming that all photons would have the same energy s. so that
* Доклад на Второй конференции по возобновляемой энергетике «Энергия будущего» (Ереван, июнь 2005 г.). The report on the Second Renewable Energy Conference "Energy for Future" (Yerevan, 2005)
Статья поступила в редакцию 17.10.2005. The article has entered in publishing office 17.10.2005.
International Scientific Journal for Alternative Energy and Ecology ISJAEE №12(32) (2005) QC
Международный научный журнал «Альтернативная энергетика и экология» АЭЭ №12(32) (2005) О J
Солнечная энергетика Солнечные электростанции
Pill = sggpS> where sg is the semiconductor energy band gap, gp is the effective intensity of solar photon flux and S is the level that harvested solar light is concentrated, the short circuit current Jsc and the conversion efficiency n can be written as
Jsc = eitgpS, (1)
n = FF (nkTT Sg ) x^n (1 + eX^gpS/Jd ), (2)
where x is the quantum efficiency of cell, and is the harvested part of solar energy.
Dependences of conversion efficiency (2) on the quantum efficiency x and on the harvested part of solar energy are rather linear. Dependences on the dark current Jd and on the concentrating of harvested light S are logarithmical. The concentrating of light relatively slow increases conversion efficiency. Nevertheless concentrating is very important because it reduces a share of expensive semiconductor cells in total cost of solar modules [7].
For many of semiconductor solar cells and even in some of thin film solar cells the quantum efficiency x is about one [6]. On the other hand because sub-band photons never contribute into photocurrent, the harvested part of solar energy is never reach to 100 %. For example, it is about 60 % in silicon and 40 % in GaAs solar cells [8].
The expression (2) reveals key problems that must be solved for constructing the next generation of photovoltaic solar cells: producing by low-cost technology; reducing of dark current Jd; increasing the level of concentrating S; involving subband photons into generating of photocurrent [7].
Sub-band absorption of infrared photons in quantum dots may be used for two-step excitation of electrons from valence band into conduction band [9]. The two-step excitation through intermediate band allows to use otherwise wasted energy of sub-band photons for generating photocur-rent and increasing conversion efficiency without degrading the open-circuit voltage. Limiting efficiency as high as 63 % has been calculated for such solar cells [10]. This value is even greater than efficiency of two-junction solar cells.
The purpose of this paper is to fit the concept of "Intermediate Band" [9] to Si solar cells. The efficiency of two-step transferring of electrons from valence band into conduction band strongly depends on intensity of irradiation. In this paper we analyze silicon solar cell conjugated with n-doped Ge/Si quantum dot absorber and calculate the level of concentrating needed for utilizing two-step excitation of photocurrent in silicon.
Silicon solar cell with Ge/Si quantum dot absorber
It is used to suggest that "intermediate band" absorber must be sandwiched between p- and n-type semiconductors layers, e. g. for InAs/GaAs quantum dot solar cells it must be within depletion layer of GaAs p-n-junction [11]. However, the sandwiching of semiconductor with lower band gap within depletion layer increases generation-recombination current in p-n-junctions [12]. It reduces open circuit voltage in solar cells that like
conventional Si cells have dark current limited with recombination of carriers in depletion layer.
We offer to use as absorber self-ordered superlattice of Ge quantum dots introduced in n-doped Si host material. Because Ge creates only valence intermediate band within energy gap of Si, the two-step absorption of sub-band photons may be removed off from depletion layer of p-n-junction into diffusion-length thick layer near the junction. No additional dark current is induced then. Another gain is that now two-step absorption is performed within layer as thick as diffusion length of minority carriers. This layer is much thicker than the depletion layer in Si based solar cells. The simplified energy-band diagram of silicon solar cell conjugated with Ge/Si quantum dot absorber is given in Fig. 1.
ЙЮ2 = S g
ftfflj = S gl - -t "t
•
я-type
p-type
VB edge
Growth direction
Fig. 2
Fig. 1
In fact no abrupt shaped offsets must be in valence band and no flat edge must be in conduction band at the interface between Si and Ge. The real diagram is more complex. Grown dots are tensile strained due to the lattice and thermal mismatch of Si and Ge. Elastic strain transfers into silicon and material mixing occurs at the interface. It trends to minimize the energy of mismatch and to degrade the interface sharpness of energy bands [13]. Conduction band becomes wave-shaped and energy band gap becomes smoothly narrowed around the dot, Fig. 2 [14]. However, it never reduces mobility of carriers in conduction band of silicon [15]. Tensile strain shifts light-hole band up in energy with respect to heavy-hole band, reducing direct band gap in Ge quantum dots. Strained Ge even shows absorption spectrum "red" shift of 30-nm [16].
Then Ge/Si quantum dot solar cells will have absorption spectrum corresponding to the 0.8 eV
CB edge
International Scientific Journal for Alternative Energy and Ecology ISJAEE № 12(32) (2005) Международный научный журнал «Альтернативная энергетика и экология» АЭЭ №12(32) (2005)
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A. M. Кечиянц, К. У. Сун, X. M. Кечиянц, Л. M. Кочарян
Фотовольтаические солнечные элементы с промежуточной зоной, созданной Ge/Si самоорганизующимися квантовыми точками
wide direct band gap of tensile strained Ge and the dark current still corresponding to current induced by generation-recombination in depletion layer of Si p-n-junction. Another gain from the strain and material mixing is that no recombination centers exist at the interface between silicon and quantum dots. Due to absorption in germanium, Ge/Si quantum dot solar cells may have reduced thickness of base in p-n-junction and gain from reduced resistance of base compare to Si solar cells. Because both Si and Ge are indirect band gap semiconductors, minority carrier lifetime t is relatively large in these materials. It is about 1 |is in Ge/Si quantum dots [17], which is enough large for carriers induced within the base to arrive to p-n-junction.
Concentrating of solar light for two-step excitation of carriers
The intermediate band is filled with electrons in n-doped Si base of Ge/Si quantum dot solar cells. When the Ge/Si quantum dot absorber is exposed on solar light, infrared photons, that have hrn < ESi, transfer those electrons with the rate of a1g1S from intermediate band into conduction band of n-doped Si and release pd electronic states in quantum dots, where a1 is the absorption coefficient for this transition, a = PNc (Nd - pd ), while Nd is the bulk density of confined intermediate electronic states, Nc is the density of electronic states in conduction band, P1 is the coefficient of electron transferring. By the same time infrared photons transfer electrons with the rate of a2g2S also from valence band into released electronic states in quantum dots and create holes in valence band of n-doped Si. Absorption coefficient of this transition is a2 = P2Nypd.
The density of confined holes is pd = a1g1T1S. Here t1 is the characteristic time of electron-hole recombination from conduction band into released electronic states in quantum dots. For given level of concentrating, S, the density of released electronic states pd has to be so large that both transitions have to occur with the same rate, a1g1S = a2g2S. This makes efficiency of two-step electron transferring dependant on intensity of irradiation because only for t1 time the confined intermediate electronic states are empty for electron transferring from valence band. Then S = (N^ ad )(Ng2Tl), where ad is the absorption coefficient for electron transition from valence band into released electronic states in quantum dots.
Absorption coefficient ad of transition into confined electronic states in quantum dots has been calculated in [18] for InAs/GaAs quantum dots. The value of Nd/ad = 1013 cm-2 is revealed from those calculations. The carrier lifetime limited by interband recombination in Ge/Si quantum dots is as large as Tj = 1 |s [17].The sub-band solar radiation intensity is about g2 = 1017cm-2 • s-1 [8]. Then concentrating of S = 102 suns is needed for two step excitation of minority carriers in Ge/Si quantum dot solar cells. In this case the inter-band absorption spectrum will show 0.2 eV "red" shift with
respect to absorption spectrum of conventional silicon solar cells. Then the photocurrent and the efficiency of conversion are increased by about 30 % while the dark current has no any change.
Conclusions
The two-step excitation of minority carriers is increased in tensile strained Ge/Si quantum dot solar cells along with concentrating the solar radiation. Already concentrating of S = 102 suns makes able to put in use sub-band photons of solar radiation and to increase by about 30 % both photo-current and conversion efficiency of tensile strained Ge/Si quantum dot solar cells in respect to conventional Si solar cells.
Acknowledgment
This work was supported by the National Science Council of Republic of China under contract No. NSC 93-2112-M-259-009.
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International Scientific Journal for Alternative Energy and Ecology ISJAEE № 12(32) (2005) Международный научный журнал «Альтернативная энергетика и экология» АЭЭ № 12(32) (2005)
