The Features of Impurity Thermal-Photovoltaic and thermal-Voltaic Effect of Polycrystalline Structures

A model of a p-n junction in the area of the grain boundaries in polycrystalline p-n structures is proposed. Shown mechanism of formation of impurity thermal-voltaic and impurity thermal-photovoltaic effects in IGB.A concept of creating highly effective comparatively inexpensive solar energy converters will be justified by the results we obtained during the study of the ITPV and ITV effects. Proposed theoretical model and experimentally obtained results can be useful in study of poly-Si n+-p structures, for example during external treatment. They allow explaining why in certain temperature ranges, an additional local heating, or applied potential, or a local illumination of pre-heated surface of poly-Si n+-p structure containing deep level impurities, can dramatically change the flow of current. In other words, such external treatment become trigger mechanism for discharge of charges accumulated in IGB due to impurity related thermal voltaic or thermal and photo-voltaic effects.


Introduction
A new phenomenon we have recently discovered by experiments in the inter-grain boundaries (IGB) of polycrystalline silicon (PS) solar cell (SC). It is the so-called impurity photovoltaic effect, as well as the impurity thermal-voltaic effect (ITV) and the impurity thermal-photovoltaic Effect (ITPV) [1,2]. The impurity photovoltaic effect leads to increasing the photocurrent owing to absorption of sub-zone photons, which allows significant increase in the single junction solar cell efficiency; the ITPV and ITV effects lead to formation and separation of additional electron-hole (eh) pairs with participation of impurities while increasing temperature of a semi-conductive structure [1,2], Down-converter and Up-converter changing photon energy with impurity participation [3][4][5][6][7][8]. Therefore, this field of studies is a perspective direction of photo-voltaics and thermal-photovoltaics.
A concept of creating highly effective comparatively inexpensive solar energy converters will be justified by the results we obtained during the study of the ITPV and ITV effects [1,2].

Charged Inter-Grain Boundary Model
It is known that the inter-grain boundaries in the polycrystalline silicon solar cell are the centers where the defects are accumulated decreasing the solar cell efficiency, as well as the doping and residual impurities from an initial material which create localized charged states [1][2][3]. Filling of charged states in IGB results in changing the height of the potential barriers, which significantly influences the transfer of charge carriers (CC).
Several methods are commonly used to determine electronic properties of IGB, and a number of models are introduced in the literature to explain charge carrier transport within and between the grains. One of well studied, applicable to poly-Si elemental semiconductors is a model of thermoionic emission (see [3] and references therein). The model allows obtaining information on wide range of charge carrier energies and can be used for p-and n-type materials. Figure 1 shows energy diagram of charged IGB in poly-Si suggested by the thermoionic emission model, where (a) and (b) represent p-type and n-type conductivity cases, respectively. The model predicts the existence of total electrical current th J generated by main carriers flowing from left to right [3]: where kT e = β is an inverse thermal difference of potentials, е is an electron, k is the Boltzmann's constant,  As shown in Fig. 1a), the holes are captured by the states on the boundary surface which locate above the Fermi level Е р . A corresponding positive charge is compensated by negatively charged acceptors in the region of the spatial charge. Thermoelectron emission creates current In this formula ss Y is the characteristic total conductivity of traps dependent on their energy distribution in space and on capture cross section. The current ss J is identically equal to the derivative in time with respect to charge bound on the boundary surface; it is caused by changes in the barrier depth δϕ . On IGB the following striking phenomenon ought to arise. According to the process of hole capture and emission on the boundary surface, the width of the spatial charge region should vary in order for total electroneutrality to be kept. This, in turn, influences the whole zone diagram in

Results and Discussion
Wafers having p-type electrical resistivity ρ∼1 Ω⋅  cm were made from molten secondary poly-Si [9]. Samples obtained from these wafers had thickness of ~300 mkm and area of 1×1 sm 2 and are schematically depicted in Fig. 2(a). Similarly, n + -p structures were formed on same wafers by means of diffusion of phosphor at 1100 °С into the bulk down to the depth of ~1.5 mkm (Fig. 2(b)). The conductivity, surface and bulk resistivity measurements were carried out using modified and Van der Pauw four probe methods. Data were recorded in semi-automatic mode as samples were heated from 20 to 300 ºC. In Fig. 2 grains are denoted P and shown as the rectangles separated by the grain boundaries, i.e. regions marked 4. The dots within IGB in Fig. 2 illustrate recombination centers, concentration of which depends upon the diffusion of impurities into this region that takes place during crystallization of poly-Si in a graphite melting pot. A precursor mixture for poly-Si in this study was composed of silicon scrap and materials containing deep-level impurities. Similar composite material but without deep-level impurities has been used in fabrication of solar cells with efficiency of > 12% at electrical current of 1.5 A [2,9]. To describe charge carriers transport between two neighbor grains (Fig. 2(a)) one needs to determine the height Advances in Energy and Power 1(2): 51-55, 2013 53 of potential barrier in IGB region. The following equation was used in this study to calculate the barrier height based on experimental data that included temperature dependency of the conductivity and both surface and bulk resistivity ρ [3]: Where a is a grain size. Figure 3 shows results of calculation which suggest that the barrier grew exponentially from 0.3 eV to 0.8 eV as temperature risen from 20 up to 300 ºC. It is evident that the data points recorded during sample heating and cooling overlap quite well. Data reported here for poly-Si formed from molten silicon precursor in graphite pot ( ) [9] agree with the data on samples fabricated using other techniques, such as the Chokralsky method of pulling crystal from the molten precursor containing up to 10% of technical silicon ( ) [10] and the powder sintering metallurgy method ( ) [11]. The observed potential barrier temperature change can be described within the frame of the modified Seto model [12], according to which the barrier height depends upon IGB boundary charge i Q as shown in following Eq. (5): One may conclude from Eq. (5) that increasing charge i Q on localized traps in IGB leads to the rise of potential barrier. With the rising temperature number of trapped charge carriers increases faster than their emission, and when temperature decreases this process reverses, i.e. the emission prevails the trapping process. Such process confirms the existence of a feedback link between current ss J and change of barrier height δϕ . More important fact is that in addition to the current ss J such feedback link includes current th J as well which forms due to thermoionic emission over the barrier. The current th J is very sensitive to any variation in the barrier height, that is to the ratio of the trapping and emission processes and thus to the temperature change. Consequently the total current, being a sum of two mentioned currents as Eq. (6) shows: significantly depends on the ratio of the trapping and emission of charge carriers on surface of IGB. When number of trapped charge carriers is higher that the emitted ones, charge will move on the trapping levels along the border between two neighboring grains as the conductivity of the traps and the barrier height increases. Let us define this direction of current ss J as having negative sign. If the emission prevails the trapping, then charge moves in opposite direction, and one may define the direction of the current ss J as having positive sign. It has been shown experimentally [13][14][15] that in former case th J decreases which results in decreasing conductivity, and in later case the current th J increases along with conductivity. As temperature increases, charge carriers within IGB region become excited and eventually liberated from thef traps, and those obtained reasonably high kinetic energy start contributing into total electrical conductivity [13][14][15]. On the other hand, charge carriers with low kinetic energy are absorbed by surface region of IGB in the adjacent grain located on the path of moving charges thus they become removed from the flow. Similar mechanism is valid for IGB of n-type poly-Si ( Fig.1(b)).

Model of p-n Transition In the IGB Region
It was defined in [12][13][14][15] that IGB have various complicated structures. Analysis of the chemical composition of some parts of the grain surface, i.e. the IGB region, showed the presence of the following complexes: Mg, S, Cl, Ca, and Fe. The atomic structure of IGB in crystals with covalent bonds has failures like decayed bonds that form additional energy levels in the forbidden zone [3,16,17]. Besides, the precipitates SiO x orSi y O x are formed with oxygen atoms both in the near-surface region of the grains and in IGB [18]. While interaction of oxygen atoms with vacancies the different vacancy centers (А, Е, Н etc.) are formed. It is also known that the impurities of Pd, Na, Be, Cd, Au, Co, Pb, O, S, Mn form the deep acceptor levels within the range of 0.35-0.5 eV from the edge of the valent zone E v ; Ag, Mn, Au, Cd, Zn, Ni, O form the acceptor levels located 0.35-0.5 eV lower than the edge of the conductivity zone E c ; Cr, Se, Mn, Pb, Fe form the donor levels located 0.35-0.5 eV lower than E c ; and C, Pd, Ag, Au, Mo, Ge, K, Fe, W form the levels located 0.35-0.5 eV higher than E v [18]. Such vacancy centers are very sensitive to any outer influences. For example, in [20] the level changes were defined in the presence of impurities with the raise in temperature, within the temperature range 50-70°С the trap level is Е ≈ 0,15 eV The Features of Impurity Thermal-Photovoltaic and thermal-Voltaic Effect of Polycrystalline Structures and Е ≈ 0,17 eV; 100-170°СЕ ≈ 0,36 eV; 325-350°СЕ ≈ 0,3 eV. On the basis of these data with the help of the zone diagram of the charged IGB in PS of the p-and n-type in Fig  1a, b, a model of the zone diagram of the p-n transition in the IGB region can be presented as follows (Fig. 4) In Fig. 4 besides the Fermi level Е р there are levels Е i in the p and n region. These levels for the p and n region are the recombination centers forming the barrier height in IGB and connected with impurity segregation [13][14][15][16][17][18][19][20], as shown in Fig. 1a and b. Under the action of voltage or lightning the electron-hole pairs are formed which have sufficiently high kinetic energy and participate in electroconductivity. Some part of CC with insufficient kinetic energy can be absorbed by the recombination center, as stated above. Then the formed currents can be presented as follows As seen from formula (5), the changes in capture and emission of CC in IGB under outer actions lead to changing the characteristic of the p-n transition in the IGB region.

Mechanism of Formation of Impurity Thermal-Voltaic and Impurity Thermal-Photovoltaic Effects in IGB
As seen in Figs. 1 and 4 and formula (8), the characteristics of the p-n transition are defined by capture and emission of CC in the inter-grain layer. Under usual conditions, operation of the p-n transition in the IGB region is connected with formation and separation of the electron-hole pairs (eh) with participation of impurities while lightning or voltage. We impose the following conditions for the p-n transition to operate. In this case, the total current of the p-n transition is defined by the sum of photocurrent and dark current. This is observed when there are no impurities in the inter-grain layer.
3. When the CC emission prevails over the CC capture then these currents are positive (+). In this case, the total current is defined by formula (8). This takes place for the mean concentration of impurity in the inter-grain layer.
It is known that while voltage the acceptor and donor states in the level E gt are formed in the region of the p-n transition. The CC capture in the region of the p-n transition leads to increase in the acceptor and donor states in the p-n transition. With the raise in temperature the tunneling of CC occurs. It should be noted that besides the CC tunneling in the region of the p-n transition the CC emission from the recombination centers (the levels E i in the p and n regions) occurs and thermal generation of electron-hole pairs takes place in these regions. As shown in Fig. 4, all the thermally generated carriers move to the boundaries of the p-n transition, i.e. to E gt , and increase tunneling.
It is evident that this mechanism can be for the first and second cases. But in the first case because of great quantity of impurities in the inter-grain layer there is metallic conductivity, i.e. there are no p-n transitions. In the second case no thermal generation is observed because of the absence of impurities in the IGB region.
Thus, the ITV and ITPV effects manifest themselves in the third case only, i.e. for the mean concentration of impurities in the inter-grain layer and with the raise in temperature.