**7. Metallic nano-cluster open new ways to enhancement of solar cell' efficiency**

Novel high ecfective solar devices are based not only on semiconductors (bulk or thin films), but also on nano-scaled clusterized structures. These structures are fabricated using various chemical technologies.

For example, Chen et al. describe synthesis of silver particles on copper substrates using ethanol-based solution (Chen et al., 2014). Previously we have reported success of wet chemical technology in manufacture of Ag/Co-nanocluster wires forming the contact grid for common silicon-based solar cells with enhanced efficiency [54].

Along with structural and morphological analysis the interpretation of experimental electrical measurements is also of great importance. Basing on our analysis of manufactured solar devices we should note that semi-classical theories widely used for interpreting properties of semiconductor-based devises are not always applicable for end-description of characteristics observed experimentally. In particular, role of semiconductor channel carrier concentration is analysed by [72]. Carrier escape mechanisms can also play a significant role in effective function of solar devices [66].

**Figure 9.** Current–voltage dependences for (1) a contact SGE (Stripe-Geometry Element) made of silver, (2) a contact SGE with copper clusters positioned in the silver pores, and (3) SGE with a copper layer positioned on the surface and with copper clusters positioned in the silver pores.

Current-voltage characteristics are of special importance and interest. Their analysis is helpful for estimation of efficiency limitations in solar cells [29]. Open-circuit voltage and the driving force of charge separation in solar cells based on different junctions are particular features defining efficiency of the device (Hara et al., 2013).

Below we report our experimental results and first attempts to model them.

The experimental setup was described in detail previously [54]. The measurements were performed for two specimens placed in a box with black walls and a solar simulator. The main part of the experimental equipmen was a tungsten contact-needle. Its role is explained below. The experimental results are presented in Figs. 9-10.

As we can see, the curve 1 is the current–voltage dependence for the initial silver contact SGEs (Stripe-Geometry Element) arranged at a wafer surface. Other curves in Fig. 9 are the current– voltage dependences for contacts obtained after copper deposition. All the curves support the metallic conduction of the contact SGEs. The distinction between them resides in the fact that, in the case of contacts with copper clusters, these curves do not pass through the origin for either the forward current or for the back one. The phenomenon of a current flowing through a metal in the absence of an applied electric field is not outlined in the literature. In our experiment, the luminous current of 450 μA flows along the contact with copper clusters disposed only in silver pores and that of 900 μA flows along the contact with copper clusters disposed in the pores and at the silver surface.

technology in manufacture of Ag/Co-nanocluster wires forming the contact grid for common

Along with structural and morphological analysis the interpretation of experimental electrical measurements is also of great importance. Basing on our analysis of manufactured solar devices we should note that semi-classical theories widely used for interpreting properties of semiconductor-based devises are not always applicable for end-description of characteristics observed experimentally. In particular, role of semiconductor channel carrier concentration is analysed by [72]. Carrier escape mechanisms can also play a significant role in effective

**Figure 9.** Current–voltage dependences for (1) a contact SGE (Stripe-Geometry Element) made of silver, (2) a contact SGE with copper clusters positioned in the silver pores, and (3) SGE with a copper layer positioned on the surface and

Current-voltage characteristics are of special importance and interest. Their analysis is helpful for estimation of efficiency limitations in solar cells [29]. Open-circuit voltage and the driving force of charge separation in solar cells based on different junctions are particular features

The experimental setup was described in detail previously [54]. The measurements were performed for two specimens placed in a box with black walls and a solar simulator. The main part of the experimental equipmen was a tungsten contact-needle. Its role is explained below.

As we can see, the curve 1 is the current–voltage dependence for the initial silver contact SGEs (Stripe-Geometry Element) arranged at a wafer surface. Other curves in Fig. 9 are the current– voltage dependences for contacts obtained after copper deposition. All the curves support the metallic conduction of the contact SGEs. The distinction between them resides in the fact that, in the case of contacts with copper clusters, these curves do not pass through the origin for

Below we report our experimental results and first attempts to model them.

silicon-based solar cells with enhanced efficiency [54].

function of solar devices [66].

140 Solar Cells - New Approaches and Reviews

with copper clusters positioned in the silver pores.

defining efficiency of the device (Hara et al., 2013).

The experimental results are presented in Figs. 9-10.

Of fundamental importance is the fact that, in the absence of an applied electric field, the electric current continues to flow along the same samples when a solar simulator was taken out of service. The luminous and dark currents flowing along the contact SGEs are presented in Fig. 10. As can be seen, under the zero bias, in the case of darkness, the generation of charge carriers is kept constant in the duration of the experiment. In the silver contact, the dark current is associated with charge carriers generated in the contact itself. The silver clusters positioned in pores and at the silver surface serve as a source of charge carriers for the dark current.

We should note that various nanoscaled solar devices are proposed for high-effective photon harvesting [40, 74, 76, 77]. Now let us describe our results and first attempts of their numerical simulation.

**Figure 10.** Time dependencies of dark and luminous currents in the absence of applied bias at contact SGEs (Stripe-Geometry Element) with copper clusters positioned in silver pores.

As we have shown previously [53], the first attempting for explanation is to consider a Si-based p-n-junction with Ag/Cu-contacts with different heights of barriers formed at the metalsemiconductor interfaces: ¢Beff=¢Bn+¢Bp ~ 0.05 eV (this value characterizes the effective barrier heights for electrons and holes, respectively) [53] and Refs. therein) and, on the other side, the barrier may be formed due to the difference of work functions of the contact metals: φB=φCuφAg=0.17 eV [53] and Refs. therein). Remembering how the solar cell operates (under illumi‐ nation the device harvests generated carriers and in darkness our active element produces practically no work, therefore, it should be no current!), we tried to calculate possible currents according to the semi-classical theory of semiconductor devices [53] and Refs. therein):

$$I\_{\alpha} \triangleq A\_{\ast} A\_{\ast} \stackrel{\sim}{T} \stackrel{\ast}{T} T\_{\ast \ast} \exp(\,^{e} \phi\_{\ast \ast} / k\_{\ast} ^{T}) \exp(\,^{e} V\_{\ast} / k\_{\ast} ^{T}) . \tag{26}$$

where ICu denotes the current producing by illumination of the sample where Cu-atoms are in Ag-pores and on the surface of the Ag-finger, Ael is an electrical area of the contact, A\*\* is the effective Richardson constant, Ttun is a coefficient of the barrier tunneling transparency, kB is the Boltzmann constant, Va is an applied voltage.

What can we obtain for a dark current, when only the deformation of clusters in the contact stripe due to difference between the lattice constants of silver and copper can change the work function and the barrier height, respectively?

**Figure 11.** (a)-current-voltage characteristics (numerical experiment!) of the Cu/Ag-cluster contacts of the Si-based so‐ lar cell: the calculation is performed according to the expressions (65)-(66): (a)-"forward" sections of the experimental dependencies, (b)-both sections of the experimental dependencies.

The expression is as follows:

$$I\_{\odot \circ} = A\_{\ast} \bar{A}\_{\ast} \bar{T}\_{\ast}^{\ast} T\_{\ast \ast}^{\ast} \exp(-\epsilon \oint\_{\mathbb{S}^{1}} \langle \bar{\mathbf{k}}\_{\ast}^{\ast} \rangle \exp(\epsilon \bar{\mathbf{v}}\_{\ast} \cdot \langle \bar{\mathbf{k}}\_{\ast}^{\ast} \rangle \cdot \tag{27}$$

where ICu1 denotes the current observed under illumination of the sample with cu-atom in Agpores of the Ag-finger only; we should note that values of the tunneling transparency coeffi‐ cient are in the range 10-7 – 10-5 (they are determined numerically basing on the experimental data). Fig. 11 show results of the numerical experiment.

As one can see, the numerical experiment performed in the region of very small applied bias (up to 40 mV) produces only a qualitative agreement with the measurements. First, there is no a "solar-cell feature" (calculated IVCs are beginning from zero unlike that of the illuminated solar cells), second, the values of experimental and calculated currents are also different. The semi-classical approximation (we introduced it by using the tunneling transparency coeffi‐ cient) does not take into account all features of the conductivity of nanoscaled cluster struc‐ tures. Before we discuss the further results we would like to say some words about currentvoltage dependencies of nanostructures. The overlap energy between different sites is related to the width of the energy bands. The second factor is disorder-induced broadening of the energy levels. If the ratio of these values is small, it is hard to match the width of the energy level on one site with that of a neighboring site to that the allowed energies do not overlap and there is no appreciable conductivity through the sample. On the other hand, if the ratio is large, the energy levels easily overlap and we have bands of allowed energy, so that there are extended wave functions and a large conductance through the sample [53] and Refs. therein).

\*\* 2

the Boltzmann constant, Va is an applied voltage.

142 Solar Cells - New Approaches and Reviews

function and the barrier height, respectively?

dependencies, (b)-both sections of the experimental dependencies.

\*\* 2 1 1

data). Fig. 11 show results of the numerical experiment.

The expression is as follows:

exp( / )exp( / ), *Cu el tun Beff <sup>B</sup> a B e Te T I AATT* f

where ICu denotes the current producing by illumination of the sample where Cu-atoms are in Ag-pores and on the surface of the Ag-finger, Ael is an electrical area of the contact, A\*\* is the effective Richardson constant, Ttun is a coefficient of the barrier tunneling transparency, kB is

What can we obtain for a dark current, when only the deformation of clusters in the contact stripe due to difference between the lattice constants of silver and copper can change the work

**Figure 11.** (a)-current-voltage characteristics (numerical experiment!) of the Cu/Ag-cluster contacts of the Si-based so‐ lar cell: the calculation is performed according to the expressions (65)-(66): (a)-"forward" sections of the experimental

where ICu1 denotes the current observed under illumination of the sample with cu-atom in Agpores of the Ag-finger only; we should note that values of the tunneling transparency coeffi‐ cient are in the range 10-7 – 10-5 (they are determined numerically basing on the experimental

As one can see, the numerical experiment performed in the region of very small applied bias (up to 40 mV) produces only a qualitative agreement with the measurements. First, there is no a "solar-cell feature" (calculated IVCs are beginning from zero unlike that of the illuminated solar cells), second, the values of experimental and calculated currents are also different. The semi-classical approximation (we introduced it by using the tunneling transparency coeffi‐

*k Vk* <sup>=</sup> - (27)

exp( / )exp( / ), *Cu el tun B f <sup>B</sup> a B e Te T I AATT* f

*k Vk* <sup>=</sup> - (26)

The current flowing along a silver contact with copper clusters is induced by charge carriers generated in the semiconductor section of the wafer when the solar cell is illuminated. The density of carriers generated within the *p*–*n* junction is two orders of magnitude higher than that which occurred in the copper clusters, because the luminous current is two orders of magnitude larger than the dark one (Fig. 10).

Depositing copper onto silver does not result in the formation of the silver–copper solid solution. The contact between the crystal structures assures the electrical potential difference. The difference is inadequate to generate the charge carriers. However, the contact between the silver–copper crystal structures may result in the compressive deformation of a metallic SGE and in a decrease in the electron work function for copper clusters.

It is our opinion that, in darkness, charge carriers generated by copper clusters within a contact SGE (Stripe-Geometry Element), which is the component part of the solar cell, are governed by the deformation of the SGE [25]. It is known [63] that the deformation of metal cluster structures may also result in high temperature superconductivity. On the other hand, the experimental measurements are made with special needles which are mechanically contacting with the investigated structure. We have to account additional "external" mechanical defor‐ mation which, in turn, may cause appearance of additional external electric field without any voltage source. Going back to Chapter 5 of our book [54], see the scenarios about positive and negative pressures!) we should note that this "needle"-caused deformation brings the system "metallic Cu/Ag-cluster contact-Si-semiconductor surface" to the state with different local pressures, for example, negative pressure under the needle on the front side of the structure (-F1el) and positive pressure under clusters on the semiconductor surface (+F2el). Thus, we have no zero resultant force (F1el-F2el) acting between the electrons localized in the clusters. We suppose that these local pressures are of different values, and the resultant stress is σ=(F1-F2)/ Acluster, where Acluster is a cross-sectional area of the Cu/Ag-cluster. The second possibility to observe the dark current is the effect of nanovoids introduced as the first level of the structural organization of the crystal (see text above) serving as drains and sources for charge carriers. More detailed: the nanovoids play one of principal roles in the processes of pre-dissosiation of atoms building basic semiconductors for photovoltaics: Si, ZnSe, ZnTe, and other wide-gap materials. Experimental current-voltage characteristics of the structures can only be approxi‐ mately described by different theoretical models, while the charge carriers moving from the left contact to the right one (direct current) and in opposite direction (reverse current) are experiencing not only the barrier effects but they dissipate and exchange their energy in and with nanovoids.
