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Physico−mathematical model of the voltage−current characteristics of light-emitting diodes with quantum wells based on the Sah−Noyce−Shockley recombination mechanism

Fedor I. Manyakhin1, Dmitry O. Varlamov1, Vladimir P. Krylov2, Lyudmila O. Morketsova3, Arkady A. Skvortsov1, and Vladimir K. Nikolaev1

+ Author Affiliations

 Corresponding author: Arkady A. Skvortsov, skvortsovaa2009@hotmail.com

DOI: 10.1088/1674-4926/23120044

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Abstract: Herein, a physical and mathematical model of the voltage−current characteristics of a p−n heterostructure with quantum wells (QWs) is prepared using the Sah−Noyce−Shockley (SNS) recombination mechanism to show the SNS recombination rate of the correction function of the distribution of QWs in the space charge region of diode configuration. A comparison of the model voltage−current characteristics (VCCs) with the experimental ones reveals their adequacy. The technological parameters of the structure of the VCC model are determined experimentally using a nondestructive capacitive approach for determining the impurity distribution profile in the active region of the diode structure with a profile depth resolution of up to 10 Å. The correction function in the expression of the recombination rate shows the possibility of determining the derivative of the VCCs of structures with QWs with a nonideality factor of up to 4.

Key words: light-emitting diodes with quantum wells, voltage−current relation, nonideality factor, recombination mechanism, Sah−Noyce−Shockley model



[1]
Shockley W. The theory of p-n junctions in semiconductors and p-n junction transistors. Bell Syst Tech J, 1949, 28, 435 doi: 10.1002/j.1538-7305.1949.tb03645.x
[2]
Sah C T, Noyce R N, Shockley W. Carrier generation and recombination in P-N junctions and P-N junction characteristics. Proc IRE, 1957, 45, 1228 doi: 10.1109/JRPROC.1957.278528
[3]
Moeini I, Ahmadpour M, Mosavi A, et al. Modeling the time-dependent characteristics of perovskite solar cells. Sol Energy, 2018, 170, 969 doi: 10.1016/j.solener.2018.05.082
[4]
Sabity M R, Ali G M. Staggered heterojunction Pentacene/ZnO based organic−inorganic flexible photodetector. Results Opt, 2023, 11, 100403 doi: 10.1016/j.rio.2023.100403
[5]
Houshmand M, Zandi M H, Gorji N E. Degradation and device physics modeling of SWCNT/CdTe thin film photovoltaics. Superlattices Microstruct, 2015, 88, 365 doi: 10.1016/j.spmi.2015.09.023
[6]
Moeini I, Ahmadpour M, Gorji N E. Modeling the instability behavior of thin film devices: Fermi Level pinning. Superlattices Microstruct, 2018, 117, 399 doi: 10.1016/j.spmi.2018.03.045
[7]
Díaz S R. A generalized theoretical approach for solar cells fill factors by using Shockley diode model and Lambert W-function: A review comparing theory and experimental data. Phys B Condens Matter, 2022, 624, 413427 doi: 10.1016/j.physb.2021.413427
[8]
Sze S M, Ng K K. Physics of semiconductor devices. New Jersey: John Wiley & Sons, 2007, 1, 1
[9]
Torchynska T V, Polupan G P, Kooshnirenko V I, et al. Mechanism of injection-enhanced defect transformation in LPE GaAs structures. Phys B Condens Matter, 1999, 273/274, 1037 doi: 10.1016/S0921-4526(99)00633-X
[10]
Manuel H, Iván L, Carlos A, et al. Improved GaInP/GaAs/GaInAs inverted metamorphic triple-junction solar cells by reduction of Zn diffusion in the top subcell. Sol Energy Mater Sol Cells, 2022, 248, 112000 doi: 10.1016/j.solmat.2022.112000
[11]
Manyakhin F I, Vattana A B, Mokretsova L O. Application of the sah-noyce-shockley recombination mechanism to the model of the voltagecurrent relationship of led structures with quantum wells. Light Eng, 2020, 31
[12]
Grushko N S, Vostretsova L N, Ambrosevich A S, et al. Effect of temperature on luminance-current characteristics of the InGaN light-emitting diode’s structure. Semiconductors, 2009, 43, 1356 doi: 10.1134/S1063782609100182
[13]
Masui H. Diode ideality factor in modern light-emitting diodes. Semicond Sci Technol, 2011, 26, 075011 doi: 10.1088/0268-1242/26/7/075011
[14]
Masui H, Nakamura S, DenBaars S P. Technique to evaluate the diode ideality factor of light-emitting diodes. Appl Phys Lett, 2010, 96, 073509 doi: 10.1063/1.3318285
[15]
Pengchan W, Phetchakul T, Poyai A. The local generation and recombination lifetime based on forward diode characteristics diagnostics. J Cryst Growth, 2013, 362, 300 doi: 10.1016/j.jcrysgro.2011.11.087
[16]
de Vrijer T, van Nijen D, Parasramka H, et al. The fundamental operation mechanisms of nc-SiOX>0 :H based tunnel recombination junctions revealed. Sol Energy Mater Sol Cells, 2022, 236, 111501. doi: 10.1016/j.solmat.2021.111501
[17]
Bulyarskii S V, Vorob’ev M O, Grushko N S, et al. Deep-level recombination spectroscopy in GaP light-emitting diodes. Semiconductors, 1999, 33, 668 doi: 10.1134/1.1187753
[18]
Özdemir O, Sel K. Study of minority carrier injection phenomenon on Schottky and plasma deposited p−n junction diodes. Mater Sci Semicond Process, 2009, 12, 175 doi: 10.1016/j.mssp.2009.10.001
[19]
Manyakhin F I, Mokretsova L O. The regularity of the decrease in the quantum yield of quantum-wells LEDs at the long-term current flow from the ABC model position. Light Eng, 2021, 62
[20]
Yu P Y, Cardona M. Fundamentals of semiconductors: Physics and materials properties. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010, 1, 1
[21]
Adachi S. Handbook on physical properties of semiconductors. New York: Springer, 2004
[22]
Shockley W, Read W T. Statistics of the recombinations of holes and electrons. Phys Rev, 1952, 87, 835 doi: 10.1103/PhysRev.87.835
[23]
Kudryashov V E, Mamakin S S, Turkin A N, et al. Luminescence spectra and efficiency of GaN-based quantum-well heterostructure light emitting diodes: Current and voltage dependence. Semiconductors, 2001, 35, 827 doi: 10.1134/1.1385720
[24]
Manyakhin F I. Mechanism and behavior of the light flux decrease in light-emitting diodes based on AlGaN/InGaN/GaN structures with quantum wells upon prolonged direct-current flow of various densities. Semiconductors, 2018, 52, 359 doi: 10.1134/S1063782618030168
[25]
Manyakhin F I, Mokretsova L O. Modeling the energy structure of a GaN p−i−n junction. Russ Microelectron, 2018, 47, 619 doi: 10.1134/S1063739718080073
Fig. 1.  (Colour online) Voltage−current characteristics of light-emitting diodes with different energies of emitted quanta and power consumption (different current densities). Gray circles represent the currents where the voltage−current characteristics (VCCs) start to deviate from the exponential dependence of current on voltage.

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Fig. 2.  Distribution of impurity concentration in the region showing changes in the space charge of the GNL-3014PGC light-emitting diode. The gray circle indicates the position of the SCR edge in the absence of bias voltage.

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Fig. 3.  Volt−ampere characteristics of the GNL-3014PGC light-emitting diode. White dots refer to the VCC coordinates for a structure with one quantum well (QW), gray dots refer to the coordinates of the model VCC with three QWs, and black dots refer to the coordinates with five QWs. The calculation parameters are taken from Table 1.

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Fig. 4.  (Colour online) Voltage−current characteristics of the quantum wells (a), VA is total VCC; numbers indicate the VCCs corresponding to location of quantum wells on the diagram of dependence of SCR edge and its middle (b), quantum wells are marked with black lines; (c) dependence of the VCC derivative in semilogarithmic coordinates of QW 3.

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Fig. 5.  (Colour online) Model dependences (on a semilogarithmic scale n) of VCC derivative on forward bias voltage, obtained using the parameters listed in Table 1 for a structure with (1) three QWs and (2) five QWs. The dots indicate the values of derivative of experimental VCC of the GNL-3014PGC LED structure.

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Fig. 6.  (Colour online) Scheme of the formation of a built-in electric field of free charge carriers in a high-bandgap p−n homostructure: 1) diagram of the electric field in the SCR at low current densities up to 1 A/cm2; 2) electric field diagram at high current densities J > 1 A/cm2: negative values indicate built-in field of free charge carriers creating voltage Ui.

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Fig. 7.  (Colour online) Schematic of the formation of the built-in electric field of free charge carriers of QWs in a high-bandgap heterostructure: 1) diagram of the electric field in the SCR at low current densities up to 1 A/cm2; 2) electric field diagram at high current densities J > 1 A/cm2: negative values indicate built-in field of free charge carriers creating voltage Ui.

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Table 1.   Initial parameters of the VCC model of the GNL-3014PGC light-emitting diode with one, two, and five quantum wells.

Nd (1019 cm−3) Na (1017 cm−3) Nai (1016 cm−3) μ1 (10−6 cm) μ2 (10−6 cm) μ3 (10−6 cm) μ4 (10−6 cm) μ5 (10−6 cm) H (10−7 cm)
2 2 4 4.14 − − − − 4.0
2 2 4 2.1 4.5 6.9 − − 4.0
2 2 3 1.14 2.64 4.14 5.64 7.14 4.0
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[1]
Shockley W. The theory of p-n junctions in semiconductors and p-n junction transistors. Bell Syst Tech J, 1949, 28, 435 doi: 10.1002/j.1538-7305.1949.tb03645.x
[2]
Sah C T, Noyce R N, Shockley W. Carrier generation and recombination in P-N junctions and P-N junction characteristics. Proc IRE, 1957, 45, 1228 doi: 10.1109/JRPROC.1957.278528
[3]
Moeini I, Ahmadpour M, Mosavi A, et al. Modeling the time-dependent characteristics of perovskite solar cells. Sol Energy, 2018, 170, 969 doi: 10.1016/j.solener.2018.05.082
[4]
Sabity M R, Ali G M. Staggered heterojunction Pentacene/ZnO based organic−inorganic flexible photodetector. Results Opt, 2023, 11, 100403 doi: 10.1016/j.rio.2023.100403
[5]
Houshmand M, Zandi M H, Gorji N E. Degradation and device physics modeling of SWCNT/CdTe thin film photovoltaics. Superlattices Microstruct, 2015, 88, 365 doi: 10.1016/j.spmi.2015.09.023
[6]
Moeini I, Ahmadpour M, Gorji N E. Modeling the instability behavior of thin film devices: Fermi Level pinning. Superlattices Microstruct, 2018, 117, 399 doi: 10.1016/j.spmi.2018.03.045
[7]
Díaz S R. A generalized theoretical approach for solar cells fill factors by using Shockley diode model and Lambert W-function: A review comparing theory and experimental data. Phys B Condens Matter, 2022, 624, 413427 doi: 10.1016/j.physb.2021.413427
[8]
Sze S M, Ng K K. Physics of semiconductor devices. New Jersey: John Wiley & Sons, 2007, 1, 1
[9]
Torchynska T V, Polupan G P, Kooshnirenko V I, et al. Mechanism of injection-enhanced defect transformation in LPE GaAs structures. Phys B Condens Matter, 1999, 273/274, 1037 doi: 10.1016/S0921-4526(99)00633-X
[10]
Manuel H, Iván L, Carlos A, et al. Improved GaInP/GaAs/GaInAs inverted metamorphic triple-junction solar cells by reduction of Zn diffusion in the top subcell. Sol Energy Mater Sol Cells, 2022, 248, 112000 doi: 10.1016/j.solmat.2022.112000
[11]
Manyakhin F I, Vattana A B, Mokretsova L O. Application of the sah-noyce-shockley recombination mechanism to the model of the voltagecurrent relationship of led structures with quantum wells. Light Eng, 2020, 31
[12]
Grushko N S, Vostretsova L N, Ambrosevich A S, et al. Effect of temperature on luminance-current characteristics of the InGaN light-emitting diode’s structure. Semiconductors, 2009, 43, 1356 doi: 10.1134/S1063782609100182
[13]
Masui H. Diode ideality factor in modern light-emitting diodes. Semicond Sci Technol, 2011, 26, 075011 doi: 10.1088/0268-1242/26/7/075011
[14]
Masui H, Nakamura S, DenBaars S P. Technique to evaluate the diode ideality factor of light-emitting diodes. Appl Phys Lett, 2010, 96, 073509 doi: 10.1063/1.3318285
[15]
Pengchan W, Phetchakul T, Poyai A. The local generation and recombination lifetime based on forward diode characteristics diagnostics. J Cryst Growth, 2013, 362, 300 doi: 10.1016/j.jcrysgro.2011.11.087
[16]
de Vrijer T, van Nijen D, Parasramka H, et al. The fundamental operation mechanisms of nc-SiOX>0 :H based tunnel recombination junctions revealed. Sol Energy Mater Sol Cells, 2022, 236, 111501. doi: 10.1016/j.solmat.2021.111501
[17]
Bulyarskii S V, Vorob’ev M O, Grushko N S, et al. Deep-level recombination spectroscopy in GaP light-emitting diodes. Semiconductors, 1999, 33, 668 doi: 10.1134/1.1187753
[18]
Özdemir O, Sel K. Study of minority carrier injection phenomenon on Schottky and plasma deposited p−n junction diodes. Mater Sci Semicond Process, 2009, 12, 175 doi: 10.1016/j.mssp.2009.10.001
[19]
Manyakhin F I, Mokretsova L O. The regularity of the decrease in the quantum yield of quantum-wells LEDs at the long-term current flow from the ABC model position. Light Eng, 2021, 62
[20]
Yu P Y, Cardona M. Fundamentals of semiconductors: Physics and materials properties. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010, 1, 1
[21]
Adachi S. Handbook on physical properties of semiconductors. New York: Springer, 2004
[22]
Shockley W, Read W T. Statistics of the recombinations of holes and electrons. Phys Rev, 1952, 87, 835 doi: 10.1103/PhysRev.87.835
[23]
Kudryashov V E, Mamakin S S, Turkin A N, et al. Luminescence spectra and efficiency of GaN-based quantum-well heterostructure light emitting diodes: Current and voltage dependence. Semiconductors, 2001, 35, 827 doi: 10.1134/1.1385720
[24]
Manyakhin F I. Mechanism and behavior of the light flux decrease in light-emitting diodes based on AlGaN/InGaN/GaN structures with quantum wells upon prolonged direct-current flow of various densities. Semiconductors, 2018, 52, 359 doi: 10.1134/S1063782618030168
[25]
Manyakhin F I, Mokretsova L O. Modeling the energy structure of a GaN p−i−n junction. Russ Microelectron, 2018, 47, 619 doi: 10.1134/S1063739718080073

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    Received: 26 December 2023 Revised: 01 May 2024 Online: Accepted Manuscript: 23 May 2024Uncorrected proof: 28 May 2024Published: 15 August 2024

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      Article Navigation >  Journal of Semiconductors  > 2024  >  45(8): 082102
      Fedor I. Manyakhin, Dmitry O. Varlamov, Vladimir P. Krylov, Lyudmila O. Morketsova, Arkady A. Skvortsov, Vladimir K. Nikolaev. Physico−mathematical model of the voltage−current characteristics of light-emitting diodes with quantum wells based on the Sah−Noyce−Shockley recombination mechanism[J]. Journal of Semiconductors, 2024, 45(8): 082102. doi: 10.1088/1674-4926/23120044 ****F I Manyakhin, D O Varlamov, V P Krylov, L O Morketsova, A A Skvortsov, and V K Nikolaev, Physico−mathematical model of the voltage−current characteristics of light-emitting diodes with quantum wells based on the Sah−Noyce−Shockley recombination mechanism[J]. J. Semicond., 2024, 45(8), 082102 doi: 10.1088/1674-4926/23120044
      Citation:
      Fedor I. Manyakhin, Dmitry O. Varlamov, Vladimir P. Krylov, Lyudmila O. Morketsova, Arkady A. Skvortsov, Vladimir K. Nikolaev. Physico−mathematical model of the voltage−current characteristics of light-emitting diodes with quantum wells based on the Sah−Noyce−Shockley recombination mechanism[J]. Journal of Semiconductors, 2024, 45(8): 082102. doi: 10.1088/1674-4926/23120044 ****
      F I Manyakhin, D O Varlamov, V P Krylov, L O Morketsova, A A Skvortsov, and V K Nikolaev, Physico−mathematical model of the voltage−current characteristics of light-emitting diodes with quantum wells based on the Sah−Noyce−Shockley recombination mechanism[J]. J. Semicond., 2024, 45(8), 082102 doi: 10.1088/1674-4926/23120044
      shu

      Physico−mathematical model of the voltage−current characteristics of light-emitting diodes with quantum wells based on the Sah−Noyce−Shockley recombination mechanism

      DOI: 10.1088/1674-4926/23120044
      • 1.

        Dinamics, Strength of Machines and Resisance of Materials, Moscow Polytechnic University, Russia

      • 2.

        Biomedical and Electronic Means and Technologies, Vladimir State University, Russia

      • 3.

        Computer-Aided Design and Engineering, National University of Science and Technology "MISiS", Russia

      More Information
      • Fedor I. Manyakhin, PhD, DSci in Physics and Mathematics. Professor, Leading Researcher of the Scientific and Technical Center "Optoelectronics" of Moscow Polytechnic University, Moscow, Russia. Author and co-author more than 160 publications. Research interests: semiconductor electronics, physics of semiconductor devices
      • Dmitry O. Varlamov, Senior Lecturer of the Department of Electrical Equipment and Industrial Electronics of Moscow Polytechnic University, Moscow, Russia. Author and co-author of more than 40 publications. Research interests: microcontroller systems, LEDs
      • Vladimir P. Krylov, PhD, DSci in Engineering. Professor of the Department of Biomedical and Electronic Means and Technologies, Head of the Scientific and Educational Center "CALS in Electronics" of Vladimir State University, Vladimir, Russia. His scientific interests are related to the physics of semiconductors and semiconductor devices, as well as to the issues of reliability of semiconductor electronic component base
      • Lyudmila O. Morketsova, Associate Professor at the Department of Computer-Aided Design and Engineering, National Research National University of Science and Technology "MISiS", Moscow, Russia. Research interests: three-dimensional modeling in lighting design
      • Arkady A. Skvortsov, PhD, DSci in Physics and Mathematics, Professor, Head of the Department of Mechanics of Materials, Moscow Polytechnic University, Moscow, Russia. Author and co-author of more than 150 articles and monographs on the study of semiconductor materials and problems of degradation of micro- and nanoelectronic systems
      • Vladimir K. Nikolaev, Head of the Optoelectronics Science and Technology Center at Moscow Polytechnic University, Moscow, Russia. Author and co-author of more than 40 publications. Area of scientific interests: optoelectronics and instrumentation
      • Corresponding author: skvortsovaa2009@hotmail.com
      • Received Date: 2023-12-26
      • Revised Date: 2024-05-01
        • Available Online: 2024-05-23

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