Electrophysical Properties of a Solar Cell with Non-Traditional Contact Structures

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INTRODUCTION

The gradual reduction of hydrocarbon reserves and many energy collapses in recent years have led people to think about the need to urgently search for new sources of energy. Naturally, people’s attention was focused on renewable energy sources (RES). First of all, they are attracted by their inexhaustibility and unlimited amounts of energy. This is especially true for solar energy.

The possibilities of solar energy are truly impressive in their inexhaustibility, which, unfortunately, cannot be said about the applied possibilities of its development. The main problem is the low efficiency of solar panels and a number of operational problems in using solar electricity. Therefore, this problem attracts the attention of many researchers.

The competitive efficiency of a solar cell with non-traditional contact structures is substantiated in detail in the works [1–19] based on some experiments published and patented in the works:

• Tsoy on improving the converting properties and efficiency of a single solar cell with a decrease in its size; [20; 21]
• I. Klimov et al. about the positive role of lead chalcogenide nanocrystals on the surface of amorphous silicon. They showed that a fairly large contribution to photoconversion is made by the effect of multi-exciton generation [22; 23];
• Stancu V. et al. on the behavior of lead chalcogenide nanocrystals during growth on a silicon substrate by molecular beam epitaxy (MBE) [24], in which, in accordance with the phenomenon of self-organization [25; 26], the formation of “islands” of NCs PbX most likely occurs in places of crystallinity contacting objects, that is, on randomly located crystal grains.

INNOVATIVE SOLAR CELL

The main primary component of solar energy, which is responsible for its efficiency, is the solar cell (SC), or more precisely, its p-n-junction, where the conversion of solar radiation into electricity mainly occurs. The efficiency of the p-n-junction, in turn, depends on the choice of contacting materials.

The work examines the properties of a solar cell consisting of a special, absolutely non-traditional for solar energy, innovative combination of contacting components. The innovative combination is that structureless non-crystalline (SNC) macrosilicon and nano-sized crystalline lead chalcogenide (PbX – X can be S; Se; Te) are selected as components of the SC.

Any solid contains a certain number of various defects, that is, foreign bodies, such as structural defects, interstitial vacancy atoms, lattice imperfections, etc. In the energy band spectrum of a solid, they are determined by their discrete energy levels. In allowed zones these are delocalized energy states, and in forbidden zones these are localized defective energy states (LDES).

It is known that the contact field is usually formed by transitions of free carriers between contacting materials in the process of alignment of their Fermi levels.

The absolute unconventionality of the SC in this work is that one of the contacting materials, SNC silicon, does not contain free carriers, but, nevertheless, a fairly strong contact field is created. The reason for this is that in SNC silicon the carriers are in bound deep “band gap” states, that is, within the potential wells of defect formations. And the presence of special specific electrophysical properties of the second material, nanocrystalline PbX, ensures the unhindered flow of electrons from silicon into it.

In other words, it is when Si comes into contact with nanocrystalline lead chalcogenide (with its special specific electrophysical properties) that current carriers receive direct energy access to PbX, as a result of which a contact field and a space charge region (SCR) arise in silicon.

SPECIFICS OF THE ELECTRICAL PROPERTIES OF PbX AND Si

Let us first determine the individual unique optical and electrophysical properties of nanosized crystalline lead chalcogenides.

1. Nanocrystals of lead chalcogenides in the form of individual “islands” in accordance with the pRSCIiple of self-organization of matter [26–31] are formed on the surface of non-crystalline silicon by the method of molecular beam epitaxy (MBE) [25; 32].
2. In nano-sized PbX crystals, the energy bands of the allowed states of the electron are strongly deformed and appear in the form of narrow energy bands. They are so narrow that they resemble discrete levels of a single atom (Fig. 1). The dash-dot lines in the figure demonstrate how a wide conduction energy band turns into a narrow single “quasi level” C₁ (and the valence band into a “quasi level” V₁).
3. The density of quasi levels is inversely proportional to the geometric size of the nanocrystal.
4. Due to the approximate equality of the effective masses of current carriers in the “valence band” and in the “conduction band” (m_n ≈ m_p), the distance between “quasi-levels” in both bands is almost the same [33]. Their values are inversely proportional to the geometric size of the nanocrystal.
5. The peculiarity of nanosized crystals of lead chalcogenides is that the width of the “band gap” does not decrease, but grows with a decrease in their dimensions. For example, E_g^PbS at 300K is 0.4 eV, and in nano-sized PbS it increases by 1.3–2 times [33].
6. An important distinctive feature of lead chalcogenides is the extremely high value of static dielectric constant: at 77K: ε_PbS = 178÷184, ε_PbSе = 227, ε_PbТе = 1300 [34]. The relatively large values of their static permittivity follow from the ionic nature of the interactions of atoms in their crystal lattices [35].
7. The main attractive side of PbX nanocrystals is that two phenomena are especially strongly manifested simultaneously in them: MEG – multi-exciton generation of carriers [33] and the corresponding phenomenon of CM – carrier multiplication [36].
8. The birth of n secondary photons and secondary electrons in nanosized PbX upon absorption of one high-frequency photon demonstrates the possibility of higher quantum yield values (for example, in PbS nanocrystals the generation of four, and in PbSe even seven, electron-hole pairs were observed [37]).

 

Fig. 1

 

These eight features of PbX nanocrystals, combined with structureless non-crystalline silicon, provide significant improvements in the converting properties of the solar cell.

Let us now consider the role of SNC silicon in a solar cell. A disordered structure is characterized by a lack of order in the immediate environment of the atom. They always have local regions that differ from neighboring regions in their ordered structure and have some interface with them. Contact potential electric fields can arise at these boundaries.

In SNC silicon, the concentration of localized defective energy states is high (about 10²¹–10²⁴ m^–3) [38]. They partially (or completely) uniformly cover the entire band gap, possessing both donor (located, as a rule, above the Fermi level) and acceptor properties (below the Fermi level).

The wave functions of carriers of defect states are spatially located (Fig. 2) near the corresponding defect at points r_i. They are characterized by Е_i(r_i) – binding energies (relative to the bottom of the conduction band) and continuous energy density g(E). An approximate diagram of the position of g(E) in the band gap of Si and a number of localized defect energy states on it in the form of discrete points a_i [38] are shown in Fig. 2 (where i runs through the values 1, 2, 3, ...).

 

Fig. 2. For a localized defective energy state a_{n + 1}, the arrow shows the value of E(r) – its binding energy

 

Silicon electrons flow during contact only when the levels а₁, а₂, а₃, … , a_n coincide with the narrow multi-exciton single “quasi-level” C₁ of nanocrystalline PbX.

 

Fig. 3

 

Levels а_i(Е_i, r_i) and а_{i + 1} (Е_{i + 1}, r_{i + 1}) are located at distances r = (r_{i + 1} – r_i), the value of which characterizes the average radius of a localized electron on uniformly distributed defect states of the band gap (Fig. 3).

MECHANISM OF CONTACT FIELD FORMATION

The formation of a contact field in the SC between the silicon SNC and PbX begins at the moment when their Fermi energies differ, that is, F_Si > F_PbХ by the amount ∆µ = F_Si – F_PbX, so that electrons move from silicon to PbX. The diagram of the sequential process of forming a contact field is shown in Fig. 4, а, b. Moreover, Fig. 4, а depicts the process of the beginning of contact formation, and Fig. 4, b – the completion of contact formation, when F_Si = F_PbХ. This relates to the image of only the upper part of the density curve of donor defect states in silicon (above the Fermi level).

 

Fig. 4. State before contact formation (a). The <Si:PbX> has been formed (b).For simplicity, from Fig. 2 only the upper part (above F_Si) of the g(E) curve is considered

 

At the beginning of formation, if the energy level of the electron on the defect (for example, at the a₁ level in Si) and the energy of the first multi-exciton “level” C₁ in PbX are equal, a fluctuation transition of an electron from Si to PbX is possible between them. The transition of the first electron causes:

• transformation of the LDES into a positively charged defect state (conditionally into a “hole”), thereby fixing the beginning of the formation of a space charge region;
• the appearance of a certain fraction of the contact potential, proportional to the magnitude of the energy difference between the two levels (a₁ – a₂);
• deformation of the Si energy spectrum with the ap-pearance of some band bending;
• jump-like shift in energy of the density of defect states g(E).

Despite the assumed uniform and continuous arrangement of electrons in energy along the density of states line g(E), the next transition cycle of the second electron will occur only when the energy of level a₂ in Si coincides with the electrically capacious level C₁ in PbX (a₂ coincides with C₁ due to a jump in the contact field and corresponding zone bending). In this case, the formation of a second “hole”, an additional contact field (a₂ – a₃) occurs, and the subsequent coincidence of the a₃ level with the multi-exciton “level” C₁ in PbX. This creates the possibility of a third electron transitioning to form a third “hole.”

Such a sequential process of electron flow from silicon to PbX (Fig. 4, b) will stop only with the transition of n electrons, when the quasi-Fermi levels of both contacting materials become equal and n “holes” are formed in Si along the length R (Fig. 5). This picture reflects the final establishment of a single Fermi level as a result of step-by-step jumplike transitions of n electrons from the levels а₁, а₂, а₃, … , an to the C₁ level in PbX and the emergence of a space charge region (SCR) of length R. The SCR consists of n charged defect centers of the donor type, uniformly located at distances r from each other, which is clearly demonstrated in Fig. 3.

 

Fig. 5

 

And in PbX, naturally, the same number of electrons are concentrated. In this case, the final value of the contact potential difference <Si:PbХ> – nano-heterojunction is formed:

${\phi }_0=\frac{∆\mu }{e}=\frac{F_{Si}-F_{PbX}}{e}.$ (1)

CALCULATION OF CONTACT FIELD PARAMETERS OF NANOHETEROJUNCTION <Si:PbХ>

Quantitative parameters of the <Si:PbX> nanoheterojunction such as φ(x) – potential and E(x) – electric field strength E(x) along the thickness of Si, as well as R – field extent, are determined from the solution of the Poisson equation [38]:

$\frac{d^2\phi }{d{x}^2}=-\frac{\rho }{{\epsilon }_{Si}{\epsilon }_0}=-\zeta \frac{\rho }{e},$ (2)

where ε_Si – is the dielectric constant;

ρ = eN/(b²L) – is the charge density (holes) in silicon (more precisely in the SCR);

ε₀ – is the dielectric constant;

ζ = e/ε_Siε₀;

n – is the number of electrons, transferred to PbX during the alignment of Fermi levels.

The electric field of the contact is formed by holes, linearly, uniformly and uniformly located LDES in Si. In fact, the binding energies of defect n electrons are different relative to each other. However, this difference is small (of the order of еφ₀/n) and, since it is at the level of the temperature spread kT, we neglect it.

Integration of the Poisson equation (2) taking into account the boundary conditions:

$\phi \left(0\right)={\phi }_0, \frac{d\phi }{dx}=-E_0$ at х =0;

$\phi \left(R\right)=0, \frac{d\phi }{dx}=0$ at х =R,

we have:

$\phi \left(x\right)=-\frac{\rho }{2{\epsilon }_{Si}{\epsilon }_0}{(R-x)}^2 ;$ (3)

$E\left(x\right)=-\frac{d\phi }{dx}=\frac{\rho }{{\epsilon }_{Si}{\epsilon }_0}(x-R) ;$ (4)

$\phi \left(0\right)={\phi }_0=\frac{\zeta N^3}{2L} ;$ (3ʹ)

$E\left(0\right)=E_0={\left(\frac{4\zeta n_0 }{L}\right)}^{1/3} {\phi }_0^{2/3} ,$ (4ʹ)

where Е = –grad φ;

E₀ and φ₀ – are the maximum values of potential strength;

n₀ = b^–3 = r^–3 – is the concentration of defects (LDES);

r – is the distance between the holes.

Using the boundary potential (3ʹ), based on Fig. 3, the field extent in silicon is found:

$R=rN={\left(\frac{2{\epsilon }_{Si}{\epsilon }_{0}L{\phi }_0}{e{n}_0}\right)}^{1/3}={\left(\frac{2L{\phi }_0}{\zeta n_0}\right)}^{1/3} ,$ (5)

as well as the number of electrons transferred from Si to PbX:

$n=\frac{R}{r}={\left(\frac{2L{\phi }_0}{\zeta }\right)}^{1/3} .$ (6)

It is known that a large field strength and its extent in Si indicate the high efficiency of the <Si:PbX> nanoheterojunction. And from the obtained relations (4ʹ), (5) and (6) it is clear that the values of E₀ and R in the <Si:PbX> nanoheterojunction ambiguously depend on the n₀ – concentration and L – thickness of Si. So for different φ₀:

• E₀ values increases as n₀^1/3, but decreases as L^–1/3;
• R values hyperbolically decreases as n₀^–1/3 and increases as L^1/3.

For each potential value φ₀ there is a concentration no and thickness L at which a sufficiently high field value and its extent can be achieved. Figures 6 in the built-in inserts show these most optimal values of concentration n₀ and thickness L.

 

Fig. 6

 

CONCLUSION

A detailed justification is given for the competitive effi-ciency of a solar cell with non-traditional contact structures.

An unconventional mechanism for the formation of a contact field through the use of localized defect states in the band gap of structureless non-crystalline silicon is considered.

The innovative choice of solar cell contact materials (nano-sized crystalline lead chalcogenide and structureless non-crystalline cheap silicon) determines its efficiency.

A significant improvement in the converting properties of a solar cell is achieved by considering in detail the specific electrophysical properties of PbX and Si. Due to the difference in Fermi levels of contacting materials, a natural process of current carriers flowing from localized defective energy states of the bandgap occurs with the formation of a contact field.

The parameters of the <Si:PbX> nano-heterojunction were calculated by solving the Poisson equation. Calculated dependencies and graphs are presented that confirm the expected effective parameters of the <Si:PbX> nano-heterojunction.

About the authors

Mardon A. Askarov

Karakalpak State University named after Berdakh of the Ministry of Higher and Secondary Specialized Education of the Republic of Uzbekistan

Author for correspondence.
Email: asqarovm@list.ru
ORCID iD: 0000-0003-4627-3170

PhD student at the Department of Semiconductors Physics

Uzbekistan, Nukus, Republic of Karakalpakstan

Erkin Z. Imamov

Tashkent University of Information Technologies named after Muhammad al-Khwarizmi (TUIT) of the Ministry for Development of Information Technologies and Communications of the Republic of Uzbekistan

Email: erkinimamov@mail.ru
ORCID iD: 0009-0007-4952-1842

Doct. Sci. (Phys. and Math.), Professor, Department of Physics

Uzbekistan, Tashkent

Ramizulla A. Muminov

Physical-Technical Institute of the SPA “Physics-Sun” of the Academy of Science of Uzbekistan

Email: detector@uzsci.net
ORCID iD: 0000-0001-7243-595X

Academician, Doct. Sci. (Phys. and Math.), Professor

Uzbekistan, Tashkent

References

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