ArticlePDF Available

Abstract

In this work, the first experimentally discovered effect of flexophotovoltaics (FPV) in silicon p-n-structures under the influence of local mechanical stress on the frontal surface is theoretically substantiated.. The regularities of the manifestation of the FPV effect are determined depending on the magnitude of the local pressure force and the intensity of photoexcitation.. Statistical processing of the experimental data by the least squares method was carried out and a new empirical formula was obtained for the experimentally determined dependence of the short circuit photocurrent of a silicon structure on the local mechanical stress.
Turkish Journal of Computer and Mathematics Education Vol.12 No.7 (2021), 947-950
Research Article
947
On The Flexophotovoltaic Effect In Semiconductor P-N-Structures
R.Aliev1, F.Behrendt 2, J.Gulomov1, M.Abduvohidov1, S.Aliev3, B.Rashidov1
1Andijan State University, Andijan, Uzbekistan.
E-mail: alievuz@yahoo.com
2Berlin Technical University, Berlin, Germany.
3Andijan Machine-Building Institute, Andijan, Uzbekistan.
Article History: Received: 11 January 2021; Revised: 12 February 2021; Accepted: 27 March 2021; Published
online: 16 April 2021
Abstract: In this work, the first experimentally discovered effect of flexophotovoltaics (FPV) in silicon p-n-
structures under the influence of local mechanical stress on the frontal surface is theoretically substantiated.. The
regularities of the manifestation of the FPV effect are determined depending on the magnitude of the local
pressure force and the intensity of photoexcitation.. Statistical processing of the experimental data by the least
squares method was carried out and a new empirical formula was obtained for the experimentally determined
dependence of the short circuit photocurrent of a silicon structure on the local mechanical stress.
Keywords: Silicon, pn-junction, flexophotovoltaics, deformation, mechanical stress, crystal, band gap.
INTRODUCTION
The authors of [1] proposed a new way to increase the efficiency of photoelectric conversion (PC) due to
the local pressure of semiconductor crystals when they are illuminated with optical light of a certain wavelength.
The application of local pressure to a crystal leads to the appearance of a mechanical stress gradient in it and,
therefore, the flexophotovoltaic (PVV) effect is observed. Based on the crystallographic representation of
semiconductor materials, it can be assumed that the FPV effect can be observed in all types of semiconductors,
including silicon.. However, the physical nature of the FPV is practically not studied.. In order to recommend
the FPV effect to improve the efficiency of any electronic device, in particular, the FP, we must present the
process of charge transfer in the considered structure. On the other hand, according to the physics of well-known
semiconductor devices, we know that if a p-n-junction is formed in the volume of a semiconductor, then the
sensitivity to external influences of such a (diode) structure is much increased in comparison with a structure
without a p-n-junction (resistor) [2]. Therefore, it is of important physical and practical interest - a purposeful
study of local mechanical stress on the process of photoelectric conversion in silicon structures with p-n-
transition to which this work is devoted.
In an n-type semiconductor, when an electric field with an intensity E is applied, the main charge carriers
(ChC) - electrons with a charge q and a mobility µе get an ordered motion with a speed vе. For such an electric
current and other basic physical parameters, the following well-known expressions can be taken:
I = -qneve S; ve = µе E; E = - grad(φ), (1)
there φ is the height of the potential barrier of the pn junction and S FP area.
In the case of considering the electron flow in only one direction with a length l and an intensity E = -ΔU /
l, one can obtain an expression for the [3]:
I = -qneve S (ΔU/l) (2)
According to the theory of the phase transition with a p-n junction, the current is determined by the expression:
I = I0 [e(Ue/kT)-1] (3)
Taking into account expression (2) and the fact that the dark current I0 is determined by the sum of the diffusion
current of electrons and holes through the p-n junction, we obtain:
I = S qni2 [(Dp/LpNd)+(Dn/LnNa)] × [e(Ue/kT)-1] , (4)
there ni - concentration of electrons in its own semiconductor, Dp - hole diffusion coefficient, Lp - hole diffusion
length, Nd - concentration of donors in the emitter,
Dn - electron diffusion coefficient Ln - electron diffusion length, Na - concentration of acceptors in the base, U -
barrier height, k - Boltzmann coefficient, T - absolute temperature.
In a more generalized form, one can imagine that
I = (β/L) f(U) , (5)
where a certain form for the coefficient β can be chosen from expressions (2) or (4).
Acceptance of the concept makes it possible to assume that if the I - V characteristic of a semiconductor PC
obeys expression (5), then for any diode without bias the condition: U → 0 and f(U) → 0; for lighted ФП: U →
0 and f(U) → 1 .
Now consider the crystal lattice of semiconductor silicon. For the force of attraction between neighboring
atoms, one can choose the well-known expression [4]:
F = Akq2/r2 , (6)
On The Flexophotovoltaic Effect In Semiconductor P-N-Structures
948
4
3
1
2
h
ν
I = 4, 53400
mA
U = 0, 00000
there A proportionality coefficient depending on the type of interatomic bond, r interatomic distance.
If the supplied external force Fk causes a change in the interatomic distance and the conditions:
r ~ L, r = γ L, dr = γdL , (7)
there γ aspect ratio.
then it can be imagined that an external force causes a change in the initial force of interatomic attraction (F +
ΔF)due to a change in the interatomic distance (r+Δr):
F + ΔF = Akq2/(r+Δr)2 (8)
From this you can get:
ΔF = Akq2 [Δr(2r-Δr)/(r-Δr)2r2] (9)
Now we will try to estimate how a small change in the force of attraction F affects the change in the
interatomic distance r. Let's do some mathematical transformations:
ΔF/Δr = Akq2 [(2r-Δr)/(r-Δr)2r2]
dF/dr = limΔr→0 (ΔF/Δr) = - Akq2 (2/r3)
and we get: dF = - Akq2 (2/r3) dr (10)
Considering (7) we can get: dL = - 2L3/2Akq2) dF . (11)
Now, in order to determine the dependence of the current on the diffusion length of the ChC, we
differentiate (5): dI = - (βγ2L/2Akq2) f(U) dF , (12)
From here we find: L = (Akq2)1/2/γF f(U) , (13)
dI = [βγ/2(Akq2)1/2] f(U) dF/F1/2 , (14)
For current short circuit FP you can get the expression:
dIк.з. = [βγ/2(Akq2)1/2] dF/F1/2 , (15)
Integrating (15) and taking into account F=Fk+F0, we obtain:
Iк.з. = Iк.з.0 + [βγ/(Akq2)1/2]× [(Fk+F0)1/2 F01/2] , (16)
there F0 interatomic force of attraction without external force.
An experimental study was carried out using a special device (block 3, Fig. 1), which, by means of a
vertical needle with a sharp end of ≈50 µm, fixed at one end of an elastic thin rod, allowed local pressure on the
frontal surface (n-type) of silicon FP 1 s diffusion p-n-junction with a depth of 0.5 microns. The thickness of the
p-type silicon base was ≈170 μm.
The value of mechanical pressure in block 3 varied in the range from zero to 1 N with an increase in the
gravity of the load. The effect of mechanical pressure on the structure under study was assessed by measuring
the I - V characteristic of an illuminated photovoltaic system using a 4 FP system using a laboratory measuring
complex 2 with a digital display of the readings of the measured photoelectric parameters.
The obtained experimental results are shown in Fig. 2 in the form (curve 2) of the Isc. = f (Fk). As can be
seen from the graph (Fig. 2), with an increase in the magnitude of the external force exerting local pressure on
the silicon surface, the value of the photocurrent short circuit. The choice of the upper limit for the increase in
the external force is due to the fact that higher values exceed the critical value of the mechanical strength of the
silicon wafer and cause failure of the structure.
The additional experiments carried out indicated a significant role of the dislocation of the point of local
action relative to the frontal electrode strips.. Moreover, a stronger change in the values of the photocurrent sh.c.
is clearly manifested. at points closer to the contact than distant. It was also found that the increase in the values
of the photocurrent sh.c. at higher light levels becomes more significant than at low light (Fig. 3).
R.Aliev1, F.Behrendt 2, J.Gulomov1, M.Abduvohidov1, S.Aliev3, B.Rashidov1
949
Figure: 1. Block diagram of an experimental device for measuring the dependence of the photocurrent sh.c.
silicon р-n -structure on the value of local mechanical stress on the frontal surface
Figure: 2. Dependence of the photocurrent sh.c. silicon р-n -structure on the value of local mechanical stress on
the frontal surface: 1 - experiment, 2 - calculations
Figure: 3. Dependence of the photocurrent sh.c. silicon p-n-structure on the relative increase in
illumination at different values of local mechanical stress on the frontal surface
According to Fig. 3, it can be noted that the dependence of the photocurrent sh.c. silicon p-n-structure from
the relative increase in illumination at different values of the local mechanical stress on the frontal surface there
is a significant increase in the increase in the photocurrent sh.c. with an increase in the force of mechanical
pressure in the illumination range from zero to 0.8 times solar radiation. With an increase in the pressure force
on the local point from zero to 1 N, a gradual increase in the photocurrent is observed due to the
flexophotovoltaic effect. Moreover, the increase in the photocurrent sh.c. more significantly in the pressure
force range of 0-0.5 N, with more than 0.5 N the gain weakens. On the investigated samples, the upper limit of
gravity was no more than 1 N. Exceeding this limit was accompanied by a breakdown of the structure, which is
associated with the excess of the mechanical strength of the plate of the studied thickness.
Based on the insignificance of the F0 values (in the order of 10-9 N), it can be assumed that Fk » F0..
Therefore, taking into account βγ/(Akq2)1/2 = α, expression (16) can be simplified:
Iк.з. = Iк.з.0 + α Fk1/2 , (17)
where photocurrent sh.c.. in the absence of mechanical stress is expressed as:
Iк.з.0 = Sqni2[Dp/(LpNd) + Dn/(LnNa)] .
The obtained simplified formula (17) is of practical interest for analyzing the experimental dependences of
the photocurrent sh.c. semiconductor FP on the magnitude of the applied external force.
For experimental graphic Ish.c. = f (Fk) dependence (Fig. 1) corresponded to expression (17). Statistical
processing of the experimental data by the least squares method made it possible to determine the values of the
proportionality coefficient of expression (17): α = 0,8114.
On The Flexophotovoltaic Effect In Semiconductor P-N-Structures
950
We believe that the results presented in [5] on an increase in the lifetime, therefore, the diffusion length of
charge carriers in silicon wafers after mechanical treatment of ultrasonic frequency, can confirm the hypothesis
of the theoretical mechanism of the studied flexophotovoltaic effect.
CONCLUSION
We consider it expedient to finalize and introduce into production a method for increasing the conversion
efficiency of silicon PCs by p-n-junction. This requires the development of new designs of FPs, allowing them
to locally deform their frontal surface.. It seems that as the base thickness of silicon PCs decreases over the next
several years, a higher photoelectric sensitivity to local deformation can be observed..
It can also be noted that the presented results can serve as a basis for the creation of mechanical pressure
sensors or photodetectors sensitive to mechanical influences based on fairly widespread crystalline silicon..
In conclusion, we note that a theoretical substantiation of the flexophotovoltaic effect discovered by the
authors for the first time in silicon p-n-structures has been carried out.. The regularities of the manifestation of
the flexophotovoltaic effect depending on the local mechanical stress are established, a new empirical formula is
obtained for the experimentally determined dependence of the short-circuit photocurrent of a silicon structure on
the local mechanical stress.
The predominant correlation between the theoretically proposed regularity and experimental data has been
established..
The research results also serve to develop new types of flexophotovoltaic photodetectors..
The study was carried out within the framework of the innovative project AMF-2/7, financed by the World
Bank.
References
1. M.-M. Yang et al. // Science, 2018. Mark Garlick. Физики выдавили из солнечных батарей
дополнительную энергию. // University of Warwick. // http://www.nanonewsnet.ru/news/
2018/fiziki-vydavili-iz-solnechnykh-batarei-dopolnitelnuyu-
energiyu?utm_campaign=subscribe_techno&utm_medium=email&utm_source=subscribe
(Опубликовано 20 апреля, 2018).
2. С.Зи, Физика полупроводниковых приборов. Книга 1 - М.: Мир, 1984. - 456 c.
3. Jeffery L. Gray “The physics of the solar cell”, Purdue university, West Lafayette, Indiana, USA.
4. Kim, Jiseok, "Band Structure Calculations of Strained Semiconductors Using Empirical
Pseudopotential Theory" (2011). Open Access Dissertations. 342.
5. Р.Алиев, Б.Урманов, М.Муйдинова, Ж.Каххаров Стимулирование времени жизни носителей
заряда за счет флексо-электрического эффекта на поверхности кремния. // Материалы IV
Международной конференции по «Оптическим и фотоэлектрическим явлениям в
полупроводниковых микро - и наноструктурах» ФерПИ, 26-27 мая 2018, Фергана. С. 277-279.
6. R.Aliev, J.Gulomov, M. Abduvohidov, S.Aliev, Z.Ziyoitdinov, N. Yuldasheva “Stimulation of
Photoactive Absorption of Sunlight in Thin Layers of Silicon Structures by Metal Nanoparticles”
Solar Engineering Materials Science, USA 2020, Vol. 56, No. 5, pp. 364370
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
This study is devoted to analysis by the method of modeling photoelectric processes of charge transfer in thin silicon structures with a p–n junction containing nanoparticles of various metals, their sizes, and volume distribution.The absorption and current–voltage (I–V) characteristics of thin-film silicon solar cells, which contain the metal nanoparticles localized on the surface dielectric antireflecting coating, in the emitter and base with high and low doping degree, and on the interfaces of these layers, are defined. As a basic method for research, the Sentaurus TCAD is chosen, which includes the Structure Device Editor, Sentaurus Device, Sentaurus Visual, and Sentaurus Workbench packages with wide capabilities for modelling silicon solar cells with a flat p–n junction. The absorption and I–V characteristics of photoelectric converters, containing metal nanoparticles in various thin layers of the structure, are determined by analyzing the computational results and discussing the physical nature of observable processes. The recommendations are offered for creating thin-film silicon plasmonic p–n junction solar cells with optimized sizes of metal nanoparticles, their distribution, and, hence, with improved efficiency of photoelectric conversion of energy. The expediency of creation of ultraviolet radiation detectors on the basis of thin-film silicon structures with metal nanoparticles is shown. The absorption and I–V characteristics of photoelectric converters, containing metal nanoparticles in thin layers of the dielectric coating, emitter, and base with high and low doping degrees and also on interfaces of these layers are compared. The most effective absorption of the solar spectrum in the region of the emitter up to the metallurgical border of the p–n junction and the best efficiency of photoelectric energy conversion of silicon solar cells are revealed. The optimum sizes of metals nanoparticles, regularities of their distribution, and depths of occurrence of the p–n junction for thin layers of crystalline silicon are defined. The recommendations for creation of third-generation thin-film silicon plasmonic solar cells and high-sensitivity photovoltaic detectors of ultra-violet radiation are developed.
Article
Electronic band structure of various crystal orientations of relaxed and strained bulk, 1D and 2D confined semiconductors are investigated using nonlocal empirical pseudopotential method with spin-orbit interaction. For the bulk semiconductors, local and nonlocal pseudopotential parameters are obtained by fitting transport-relevant quantities, such as band gap, effective masses and deformation potentials, to available experimental data. A cubic-spline interpolation is used to extend local form factors to arbitrary q and the resulting transferable local pseudopotential V(q) with correct work function is used to investigate the 1D and 2D confined systems with supercell method. Quantum confinement, uniaxial and biaxial strain and crystal orientation effects of the band structure are investigated. Regarding the transport relavant quantities, we have found that the largest ballistic electron conductance occurs for compressively-strained large-diameter [001] wires while the smallest transport electron effective mass is found for larger-diameter [110] wires under tensile stress.
Chapter
IntroductionFundamental Properties of SemiconductorsPN -Junction Diode ElectrostaticsSolar Cell FundamentalsAdditional TopicsSummaryReferences
Mark Garlick. Физики выдавили из солнечных батарей дополнительную энергию
  • M.-M Yang
M.-M. Yang et al. // Science, 2018. Mark Garlick. Физики выдавили из солнечных батарей дополнительную энергию. // University of Warwick. // http://www.nanonewsnet.ru/news/ 2018/fiziki-vydavili-iz-solnechnykh-batarei-dopolnitelnuyuenergiyu?utm_campaign=subscribe_techno&utm_medium=email&utm_source=subscribe (Опубликовано 20 апреля, 2018).
Каххаров Стимулирование времени жизни носителей заряда за счет флексо-электрического эффекта на поверхности кремния. // Материалы IV Международной конференции по «Оптическим и фотоэлектрическим явлениям в полупроводниковых микро -и наноструктурах» ФерПИ
  • Р Алиев
  • Б Урманов
  • М Муйдинова
Р.Алиев, Б.Урманов, М.Муйдинова, Ж.Каххаров Стимулирование времени жизни носителей заряда за счет флексо-электрического эффекта на поверхности кремния. // Материалы IV Международной конференции по «Оптическим и фотоэлектрическим явлениям в полупроводниковых микро -и наноструктурах» ФерПИ, 26-27 мая 2018, Фергана. С. 277-279.