Exciton effects in band-edge electroluminescence of silicon barrier structures

A theoretical analysis of the band-edge electroluminescence efficiency in silicon diodes and p-i-n-structures has been made. We have shown that maximal possible efficiency can achieve 10 % both at room and liquid nitrogen temperatures. Maximal values of the efficiency are restricted by the interband...

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Datum:	2004
Hauptverfasser:	Sachenko, A.V., Gorban, A.P., Korbutyak, D.V., Kostylyov, V.P., Kryuchenko, Yu.V., Chernenko, V.V.
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Veröffentlicht:	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України 2004
Schriftenreihe:	Semiconductor Physics Quantum Electronics & Optoelectronics
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spelling	irk-123456789-1181042017-05-29T03:03:18Z Exciton effects in band-edge electroluminescence of silicon barrier structures Sachenko, A.V. Gorban, A.P. Korbutyak, D.V. Kostylyov, V.P. Kryuchenko, Yu.V. Chernenko, V.V. A theoretical analysis of the band-edge electroluminescence efficiency in silicon diodes and p-i-n-structures has been made. We have shown that maximal possible efficiency can achieve 10 % both at room and liquid nitrogen temperatures. Maximal values of the efficiency are restricted by the interband Auger recombination process. It is found that electroluminescence efficiency decreases rapidly with the decrease of characteristic Shockley- Reed-Hall nonradiative lifetime for minority carriers. It is shown that even at room temperatures the main contribution into the edge electroluminescence in silicon barrier structures is given by excitonic effects. Dark I-V characteristics of directly biased silicon diodes measured both at room and nitrogen temperatures are used to explain anomalous temperature dependencies of silicon diode electroluminescence. 2004 Article Exciton effects in band-edge electroluminescence of silicon barrier structures / A.V. Sachenko, A.P. Gorban, D.V. Korbutyak, V.P. Kostylyov, Yu.V. Kryuchenko, V.V. Chernenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 1-7. — Бібліогр.: 20 назв. — англ. 1560-8034 PACS: 71.35.-y, 72.20.jv, 78.20.-e, 78.60.-b, 78.60.Fi http://dspace.nbuv.gov.ua/handle/123456789/118104 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
description	A theoretical analysis of the band-edge electroluminescence efficiency in silicon diodes and p-i-n-structures has been made. We have shown that maximal possible efficiency can achieve 10 % both at room and liquid nitrogen temperatures. Maximal values of the efficiency are restricted by the interband Auger recombination process. It is found that electroluminescence efficiency decreases rapidly with the decrease of characteristic Shockley- Reed-Hall nonradiative lifetime for minority carriers. It is shown that even at room temperatures the main contribution into the edge electroluminescence in silicon barrier structures is given by excitonic effects. Dark I-V characteristics of directly biased silicon diodes measured both at room and nitrogen temperatures are used to explain anomalous temperature dependencies of silicon diode electroluminescence.
format	Article
author	Sachenko, A.V. Gorban, A.P. Korbutyak, D.V. Kostylyov, V.P. Kryuchenko, Yu.V. Chernenko, V.V.
spellingShingle	Sachenko, A.V. Gorban, A.P. Korbutyak, D.V. Kostylyov, V.P. Kryuchenko, Yu.V. Chernenko, V.V. Exciton effects in band-edge electroluminescence of silicon barrier structures Semiconductor Physics Quantum Electronics & Optoelectronics
author_facet	Sachenko, A.V. Gorban, A.P. Korbutyak, D.V. Kostylyov, V.P. Kryuchenko, Yu.V. Chernenko, V.V.
author_sort	Sachenko, A.V.
title	Exciton effects in band-edge electroluminescence of silicon barrier structures
title_short	Exciton effects in band-edge electroluminescence of silicon barrier structures
title_full	Exciton effects in band-edge electroluminescence of silicon barrier structures
title_fullStr	Exciton effects in band-edge electroluminescence of silicon barrier structures
title_full_unstemmed	Exciton effects in band-edge electroluminescence of silicon barrier structures
title_sort	exciton effects in band-edge electroluminescence of silicon barrier structures
publisher	Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
publishDate	2004
url	http://dspace.nbuv.gov.ua/handle/123456789/118104
citation_txt	Exciton effects in band-edge electroluminescence of silicon barrier structures / A.V. Sachenko, A.P. Gorban, D.V. Korbutyak, V.P. Kostylyov, Yu.V. Kryuchenko, V.V. Chernenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 1. — С. 1-7. — Бібліогр.: 20 назв. — англ.
series	Semiconductor Physics Quantum Electronics & Optoelectronics
work_keys_str_mv	AT sachenkoav excitoneffectsinbandedgeelectroluminescenceofsiliconbarrierstructures AT gorbanap excitoneffectsinbandedgeelectroluminescenceofsiliconbarrierstructures AT korbutyakdv excitoneffectsinbandedgeelectroluminescenceofsiliconbarrierstructures AT kostylyovvp excitoneffectsinbandedgeelectroluminescenceofsiliconbarrierstructures AT kryuchenkoyuv excitoneffectsinbandedgeelectroluminescenceofsiliconbarrierstructures AT chernenkovv excitoneffectsinbandedgeelectroluminescenceofsiliconbarrierstructures
first_indexed	2025-07-08T13:22:19Z
last_indexed	2025-07-08T13:22:19Z
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fulltext	1© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 1. P. 1-7. PACS: 71.35.-y, 72.20.jv, 78.20.-e, 78.60.-b, 78.60.Fi Exciton effects in band-edge electroluminescence of silicon barrier structures A.V. Sachenko, A.P. Gorban, D.V. Korbutyak, V.P. Kostylyov, Yu.V. Kryuchenko, V.V. Chernenko V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine, 45, prospekt Nauky, 03028 Kiev, Ukraine E-mail: sach@isp.kiev.ua, phone: +380 (44) 2655734 Abstract. A theoretical analysis of the band-edge electroluminescence efficiency in silicon diodes and p-i-n-structures has been made. We have shown that maximal possible efficiency can achieve 10 % both at room and liquid nitrogen temperatures. Maximal values of the efficiency are restricted by the interband Auger recombination process. It is found that electroluminescence efficiency decreases rapidly with the decrease of characteristic Shockley- Reed-Hall nonradiative lifetime for minority carriers. It is shown that even at room tempera- tures the main contribution into the edge electroluminescence in silicon barrier structures is given by excitonic effects. Dark I�V characteristics of directly biased silicon diodes measured both at room and nitrogen temperatures are used to explain anomalous temperature depend- encies of silicon diode electroluminescence. Keywords: excitons, electroluminescence, internal quantum efficiency, silicon barrier struc- tures. Paper received 04.11.03; accepted for publication 30.03.04. 1. Introduction In recent years, a substantial interest has grown to the investigations of electroluminescence (EL) in silicon bar- rier structures at room temperatures (see, for example, [1�3]). This interest is associated, in particular, with pos- sibilities to develop large-scale silicon-based integration circuits with optical coupling elements. Both structures used for photoconversion [1] and semiconductor diodes [2,3] were studied intensively. In [1,2] for the external quantum efficiency of the edge radiation the value of about 1% was obtained, and in [3] the edge radiation of silicon alloyed diodes was shown to be determined by annihila- tion of free excitons. Still earlier, the spectral and tem- perature dependencies of edge electroluminescence were studied in silicon p-i-n-structures, and the exciton effects in absorption and radiation were shown to play a sub- stantial role even at room temperatures in these struc- tures too (see, for example, [4]). In [5�10] the influence of excitons on effective life- time of electron-hole pairs, edge photoluminescence, I� V characteristics, and efficiency of photoconversion in silicon and silicon barrier structures at room tempera- tures was analyzed. In particular, it was shown that in many cases the effective lifetime of electron-hole pairs is determined by nonradiative exciton Auger recombina- tion with the participation of deep centers, and the inter- nal quantum efficiency of edge photoluminescence can reach the values of about 10 %. The analysis of exciton effects in cited works was based on the account of two subsystems of quasiparticles in a semiconductor: electron- hole and exciton ones, which are in a quasiequilibrium due to an approximate balance between the number of electron-hole pairs binding into excitons and the number of excitons decomposing into electron-hole pairs per unit time. Using the approach of [5�10], the extreme values of EL quantum efficiencies have been obtained in the present work as functions of structure parameters. We have analysed also temperature dependencies of the in- tensity and quantum efficiency of the edge EL in silicon barrier structures. An attempt has been made to separate probabilities of exciton and band-to-band radiative re- combination. Two types of barrier structures have been considered: diode structures and p-i-n-structures, the lat- ter being shown to be promising for optoelectronics ap- plications. 2 SQO, 7(1), 2004 A.V. Sachenko et al.: Exciton effects in band-edge electroluminescence of silicon ... 2. Band-edge electroluminescence in silicon diodes Let us consider a case when the thicknesses of n- and p- regions exceed diffusion lengths of electrons and holes in these regions. This enables excluding the influence of surface recombination. A linearity over excitation level is also assumed (a case of low-injection conditions is con- sidered in this section), that means that inequalities nn >> pn exp(qU/kT) and pp>>np exp(qU/kT) are reali- zed, where nn and pp are the concentrations of majority charge carriers in n- and p-regions, respectively, pn and np are the concentrations of minority charge carriers in these regions, q is the electron charge (modulo), k is the Boltzman constant, Ò is the temperature and U is the applied voltage. The expression for the efficiency of the current-re- lated EL for a long-based diode within the framework of the approach of [5�10] can be written in the following form: r J JJ JJ + − = 0η , (1) where J = q(Dppn /Lp + Dnnp/Ln) exp(qU / kT) is the sur- face density of the diffusion current in a long-based di- ode, Jr is the recombination current surface density in the space charge regions (SCR), Lp and Ln, Dp and Dn are diffusion lengths and coefficients of minority charge car- riers, respectively, in n- and p-regions. Taking into ac- count the linearity over the excitation level the following expressions for Lp and Ln can be obtained in accordance with [5, 6]: 1 2)( 11 − ∗         ++        ++= npnn x i rp pp nCCn n ADL ττ , (2) 1 2)( 11 − ∗         ++        ++= ppnp x i rn nn pCCp n ADL ττ , (3) where τrp and τrn are the Shockley-Reed-Hall lifetimes in n- and p-regions, respectively, Ai is the radiative recom- bination constant characterising the recombination from continuum electron-hole states correlated by Coulomb interaction [4], n* = (NcNv /Nx) exp(�Ex/kT), where Nc, Nv and Nx are the effective densities of states for elec- trons, holes and excitons, Ex is the exciton binding en- ergy, 1)/1/1( −+= n x r xx τττ , where r xτ is the radiative and n xτ is nonradiative lifetime of excitons, the last being as- sociated with the exciton Auger recombination with deep level participation [11], Cn and Cp are the parameters of interband electron and hole Auger recombination, respec- tively. Current density J0 is that obtained from the ex- pression for J when terms with r xn τ∗/1 and Ai are omitted in Eqs (2) and (3). If Jr is small compared to J, and, besides, those terms in square brackets in Eqs (2) and (3) which correspond to the radiative recombination processes are small compared to the terms corresponding to the nonradiative recombi- nation, then expression for current density of the band- edge EL takes up the following form: ( )       −             ++= ∗ 1exp 1 2 00 2 kT qU n ALLn q J r x inpie τ , (4) where Lp0 and Ln0 are obtained from the expressions for Lp and Ln if in the latter the terms in square brackets associated with the radiative recombination are omitted. The expression for the internal quantum efficiency of band-edge EL in correspondence with the work [3] takes up the following form         + + + ⋅= ∗ r x i nnnppp np pn n A LnDLpD LL pn τ η 1 // . (5) 3. Band-edge electroluminescence in silicon p-i-n-structures Let us further obtain an analytical expression for the internal quantum efficiency of the band-edge EL for a silicon p-i-n-structure assuming that the i-region is weakly doped, and high-injection conditions are reali- sed, so that the criterion nn << pn exp(qU / kT) or pp << np exp(qU/ kT) is met. Besides, we will consider that the i-region thickness is smaller than the hole or elec- tron diffusion length. By neglecting the recombination of electron-hole pairs at the surfaces of p+- and n+-re- gions and the recombination current in SCR compared to the diffusion one, the internal quantum efficiency of the EL in accordance with [8] can be written in the following form:     ++++    −    + = = ∗ ∗ kT qU nCC n A kT qU n n A ipn x i ri r x i 2 )( 1 2 1 1 expexp ττ τ η , (6) where τr is the Shokley-Reed-Hall time at high-injection conditions, and ni is the charge carrier concentration in intrinsic silicon. The current density of EL in this case is equal to              += ∗ kT qU n n AqdJ ir x ie exp 1 2 τ . (7) Noteworthy is that in the case under consideration the excess concentration of electron-hole pairs ∆p is de- termined by the relation )2/(exp kTqUnp i=∆ . (8) A.V. Sachenko et al.: Exciton effects in band-edge electroluminescence of silicon ... 3SQO, 7(1), 2004 4. Temperature dependencies of exciton electroluminescence in silicon barrier structures Let us first analyse the temperature dependencies of quan- tum efficiency and intensity of the exciton EL for long- based diodes. Taking into account that the radiative exciton recombination lifetime changes with temperature as ~Ò3/2, it follows from the expressions (1)�(5) that in the cases, when in the nonradiative recombination domi- nates (a) recombination of Shockley-Reed-Hall, (b) exciton Auger recombination, or (c) interband Auger re- combination, the following relationships are valid for the internal quantum efficiencies ηx and current densities Jex of the exciton EL: )/exp()(~ 2/3 kTETT xrx τη − , )(~ 2/3 TT rx τη − , (9) ])(/[)/exp(~ 22/3 jjxx nTCkTET −η , )/exp()()(~ 3 kTETTTDJ xrex −τ , )2/exp()()(~ 3 kTETTTDJ xrex −τ , (10) )/exp(])(/[)(~ 23 kTEnTCTTDJ xjjex − , where nj = nn for the n-regions and nj = pp for p-regions. As numerical estimates show, the exciton EL current density of silicon diodes in all the limiting cases men- tioned increases with temperature decrease. In the case (a) the exciton EL internal quantum efficiency increases with temperature drop as well. However, more topical are the cases (b), when the nonradiative recombination is determined by the exciton Auger recombination, and (c), when the interband Auger recombination dominates. In the case (b) everything depends on how the Shockley- Reed-Hall lifetime τr(T) changes with temperature, while in the case (c) on whether the exciton radiative recombina- tion or the interband Auger recombination grows faster with temperature drop. For deep recombination centers in silicon τr first decreases to a certain value with tempera- ture decrease from the room temperature, and then ceases to change. In this region of practical independence of τr from the temperature the exciton EL internal quantum ef- ficiency must grow with the temperature decrease as T�3/2. Just the same behaviour of EL quantum efficiency has to be observed also in p-i-n-structures when the case (b) is realised. Under the condition ni(T)exp(qU/2kT) = ∆n = = const, the exciton EL current density for p-i-n-structures is equal to r x ex n n qdJ τ∗ ∆= 2)( (11) and depends on temperature only due to temperature de- pendencies of n* and r xτ . In this case, Jex grows with the temperature decrease stronger than T�3/2. The results of the above theoretical analysis contra- dict to the experimental data on anomalous temperature dependence of the EL intensity in alloyed silicon diodes presented in [3]. To elucidate the reason for this discrep- ancy, we have measured dark I�V curves on a number of standard alloyed silicon diodes at room temperature and at liquid nitrogen temperature. The results on dark I�V measurements for one of such diodes are shown in Fig. 1. The I�V non-ideality factor for these diodes in the region of rather large currents amounted to about 1.5 at room temperature and 2.24 at liquid nitrogen temperature. This means that under condition of constant total current the contribution of the diffusion current component at Ò = 80 K is substantially smaller than at room temperature. At the same time, the exciton EL is associated only with the dark diffusion current component because all other mecha- nisms of current flow are strongly field-dependent, and in the region of strong fields ≥105 V/cm excitons are prac- tically absent in silicon. Therefore, it is clear that to de- termine correctly the temperature dependence of EL in- tensity in the case of alloyed silicon diodes, one needs to measure not the total dark current, but only its diffusion component. The modern silicon diffusion diodes have 0.2 0.4 0.6 0.8 1.0 1.2 10�6 10�4 10�2 100 102 21 Fig. 1. Dark I�V characteristics of an alloyed silicon diode. Curves: 1 � T = 300 K, 2 � T = 77 K. 4 SQO, 7(1), 2004 A.V. Sachenko et al.: Exciton effects in band-edge electroluminescence of silicon ... nonideality factor close to unity (see e.g. [1]) and the above discussed problems are absent at all. 5. Separation of electron-hole and exciton radiative recombination contributions Although attempts to separate contributions of band-to- band and exciton radiative recombinations in silicon were made already earlier, the problem is still far from its fi- nal solution. While considering it in the present work, we will suggest that two subsystems coexist in silicon, namely subsystem of free electron-hole pairs correlated by cou- lomb interaction and subsystem of bound electron-hole states, i.e. excitons. The quasi-equilibrium between them is described by the thermodynamic relations. Such an approach is true for the region of not too low tempera- tures when the criterion xx kTEn τγ10 /1)/exp( >>− is met, where γ1 is the probability of electron-hole pair binding into excitons. In this case the total probability of the radiative quadratic recombination can be written as r xi nA τ∗+ /1 , where A³ is the probability of the radiative band-to-band recombination, and r xn τ∗/1 is the probabil- ity of the radiative exciton recombination. At room tem- perature their total value amounts to approximately 2.5 10�15 cm3/s [5]. Temperature dependencies of this value obtained in different approximations are given in [4]. Separation of band-to-band and exciton contributions is associated with the following difficulties. Firstly, the value of r xn τ∗/1 may substantially depend on the equilib- rium or excess concentration of electrons or/and holes due to screening of Coulomb interaction between elec- trons and holes by mobile charge carriers. Secondly, in this case it is necessary to know the exact value of the intrinsic charge carrier concentration ni in silicon ac- counting for the temperature dependencies of the den- sity-of-state effective masses in the conduction and va- lence bands [12,13]. Due to effect of screening of Coulomb interaction be- tween electron and hole, the probability of the exciton radiative recombination strongly decreases while ap- proaching the exciton Mott transition (especially at low temperatures) down to zero at critical and higher con- centrations of free carriers. This can occur both at low injection levels due to increase of p- and n-regions dop- ing and at high injection levels due to increase of the applied voltage. In this work, the analysis and separa- tion of probabilities of band-to-band and exciton radiative recombinations have been carried out by accounting for the above peculiarities. In a general case, we used the following expres- sion for n* [6]: ( ) , )300/(103.8 2 1 300 567.0exp /)(10208.1 22/1 17 2/3 0 15                           ⋅ ∆+ −    × ×⋅⋅= ∗∗ T nn T mTmTn n x (12) where 0 * /)( mTmx is the ratio of the normalized density- of-state effective mass for an exciton in silicon to the mass of a free electron taking into account temperature de- pendencies of density-of-state effective masses for elec- tron and hole [12,13]. Numerical values of the concen- trations in this and subsequent formulae have to be sub- stituted in cm�3 units. As mentioned above, the total probability of edge band-to-band and exciton recombinations r xi nA τ∗+ /1 obtained in [5] from the dependence of electron-hole pair effective lifetimes in silicon on the excitation level amounts to 2.5⋅10�15 cm3/s at room temperature. This value coin- cides with both theoretical value obtained in [13], where the principle of detailed equilibrium between absorption and radiation was employed (the van Roosbroeck- Shockley approach), and experimental value obtained in [14] from spectral dependence of light absorption coeffi- cient in silicon near the intrinsic absorption edge. Using the data of [15], we have calculated in a simi- lar way the value r xi nA τ∗+ /1 =7.22⋅10�14 cm3/s at Ò = 90 K. In turn, this value practically coincides with the microscopic theory result obtained in [4]. As the tem- perature dependence of the radiative electron-hole recom- bination parameter Ai is rather weak (~T�1/2, see for in- stance [16]), and at T = 300 K the Ai value cannot be higher than 2.5⋅10�15 cm3/s, it is clear that the total radiative recombination probability at Ò = 90 K is in fact determined by the second term r xn τ∗/1 , which corre- sponds to the radiative exciton recombination. Using Eq. (12) and choosing 310−=r xτ s at Ò = 300 Ê, suggest- ing, as earlier, that the exciton radiative lifetime r xτ (T) changes with temperature as Ò3/2, we obtain for the dop- ing level 7⋅1015 cm�3 at which the absorption coefficient was measured the value r xn τ∗/1 = 7.0⋅10�14 cm3/s at Ò = 90 K, which is in good agreement with the above results. At 300 K the exciton radiative recombination probability r xn τ∗/1 calculated with the parameters indi- cated above amounts to 6.1⋅10�16 cm3/s. This means that the value 1.9⋅10�15 cm3/s remaining after subtraction of 6.1⋅10�16 cm3/s from 2.5×10�15 cm3/s really is the sum of Ai and corresponding contribution into the radiative re- combination of conduction and valence bands states cor- related by Coulomb interaction [4]. Since theoretically calculated value of Ai in silicon using formulae of [16] and temperature dependencies of the density-of-state ef- fective masses for electrons and holes [12,13] is about 8⋅10�16 cm3/s at T = 300 K, it is clear that according to our estimates the part of radiative recombination prob- ability in silicon which is determined by exciton transi- tions and transitions in a subsystem of correlated elec- tron-hole band states at room temperature does not ex- ceed 1.7⋅10�15 cm3/s. 6. Numerical calculations of the internal quantum efficiency of electroluminescence in silicon barrier structures As was shown in [17], in the region of intermediate charge carrier concentrations, from 1015 to 1018 cm�3, the coeffi- A.V. Sachenko et al.: Exciton effects in band-edge electroluminescence of silicon ... 5SQO, 7(1), 2004 cient Cn of interband Auger recombination in silicon with electron participation strongly depends on electron-elec- tron and electron-hole Coulomb interaction and substan- tially exceeds the values typical for the case of high car- rier concentrations when the Coulomb interaction is strongly screened. In [5] empirical approximations were obtained for the Cn values determined from the experi- mental data of [17] and calculated theoretically. These approximations look like         ∆+ ⋅ +⋅= − − nn C n n 12 31 103.1 103.2 cm6 s�1 (13) and         ∆+ ⋅+⋅= − − 2/1 22 31 )( 105.2 108.2 nn C n n cm6 s�1, (14) respectively. As our analysis has shown, just the interband Auger recombination confines the EL internal quantum efficiency of silicon barrier structures in the case of extremely large Shockley-Reed-Hall recombination times, τr ≥ 10�3 s. Calculations have shown that for τr = 4⋅10�2 s the maxi- mal EL internal quantum efficiency in silicon at room temperatures amounts to about 10 %. To calculate η at 70 Ê we need to know the temperature dependence of τr. In many cases the Shockley-Reed-Hall recombination time first decreases with the temperature decrease and then ceases to depend on temperature [18,19]. It was shown, in particular, in [20], that with temperature de- crease from room to liquid nitrogen this parameter de- creases in silicon of n-type by a factor of 5. For nume- rical calculations we used the empirical dependence 2/31)10300/)(300()( −+= TT rr ττ , which gives approxi- mately the same decrease of τr. The calculations made with account for above-mentioned effects show that at Ò = 70 K the extreme values of EL internal quantum effi- ciency both in silicon diodes and p-i-n-structures is some- what greater than 10%. In Fig. 2, which illustrates our results for silicon di- odes with different doping levels of ð-type region, the dependencies of η on the doping level of n-type region are built for the temperatures 300 and 70 K. It is seen from the figures that maximal EL quantum efficiency is approximately the same at both temperatures. In both cases it is limited by the interband Auger recombination. This recombination provides some decrease of η with the growth of doping level of the diode n-region. In Fig. 3, the dependencies of η on the applied volt- age are built for p-i-n-structures with a short base at 300 and 70 K. Like in the case of diodes, the extreme values of η are limited by the interband Auger recombination. At the same time, at small enough Shockley-Reed-Hall lifetimes, τr ≤ 10�4 s, a limiting case (c), when nonradiative exciton recombination dominates, is realized. That is why the EL internal quantum efficiency remains constant within a certain range of applied voltages. It should be noted that the extreme η values at Ò = 70 K are somewhat lower than those at Ò = 300 K although the situation seemed to be opposite. This occurs 10 14 10 15 10 16 10 17 10 �3 10 �2 10 �1 10 0 10 1 300 K �3 n n , cm h , % 4 3 2 1 10 14 10 15 10 16 10 17 10�2 10�1 100 101 h , % �3 n n , cm 70 K 4 3 2 1 Fig. 2. The dependencies of the EL internal quantum efficiency of silicon diodes on the doping level of n-type region at Ò=300 K and Ò = 70 K. Characteristic Shockley-Reed-Hall nonradiative lifetime τrp and τrn at T = 300 K: 1 � 4⋅10�2 and 7⋅10�3; 2 � 10�2 and 7⋅10�3; 3 � 10�3 and 10�3; 4 � 10�4 and 10�4 s. The concentrations of majority charge carriers in p-region equal to 3⋅1016 (T = 300 K) and 2⋅1015 cm�3 (T = 70 K). a b 6 SQO, 7(1), 2004 A.V. Sachenko et al.: Exciton effects in band-edge electroluminescence of silicon ... due to strong influence of Coulomb interaction on the interband Auger recombination probability in silicon. As a result, at not too high charge carrier concentrations the Auger recombination probability grows stronger with temperature decrease than the radiative exciton recom- bination probability. In the range of rather low temperatures, when the Shockley-Reed-Hall lifetime ceases to change with tem- perature, we still may hope for a substantial increase in the EL internal quantum efficiency in silicon barrier struc- tures compared to the case of room temperatures, espe- cially, at comparatively low τr values. 7. Conclusions Thus, the theoretical analysis carried out in the present work has shown that even at room temperature the exciton effects in the radiative recombination give the main con- tribution into the band-edge EL of silicon barrier struc- tures. With temperature decrease the contribution of radiative exciton recombination into the total band-edge electroluminescence grows sharply and becomes domi- nant, i.e. determines latter practically completely. The obtained results indicate that under the extre- me quantum efficiency the silicon diodes are close to the ð-i-n-structures. However, to achieve maximum efficiency in silicon diodes, their thickness should be not smaller than 1 cm, i.e. be equal to or exceed the sum of the diffu- sion lengths in ð- and n-regions with maximal achieved Shockley-Reed-Hall lifetimes, while in the case of ð-i-n- structures the extreme values of EL quantum efficiency does not depend on the base thickness. For this reason, the electroluminescent silicon ð-i-n-structures, to our mind, are promising for optoelectronics applications. References 1. M.A. Green, J. Zhao, A. Wang, P. J. Reece, M. Gal. Effi- cient silicon light-emitting diodes // Nature, 412, pp. 805-808 (2001). 2. W.L. Ng, M.A. Lourenco, R.M. Gwilliam, S. Lewdain, G. Shao, K.P. Homewood. An efficient room-temperature silicon-based light-emitting duiode // Nature, 410, pp. 192- 194 (2001). 3. Ì.S. Bresler, Î.B. Gusev, B.P. Zakharchenya, I.N. Yassievich. Electroluminescence efficiency of silicon diodes // in Mate- rials of Symposium "Nanophotonics" (Nizhnii Novgorod, Rus- sia, 2003), vol. 1, pp. 59-62 (in Russian). 4. M. Ruff, M. Fick, R. Lindner, U. Rossler, R. Helbig. The spectral distribution of the intrinsic radiative recombination in silicon // J. Appl. Phys., 74(1), pp. 267-274 (1993). 5. A.V. Sachenko, A.P. Gorban, V.P. Kostylyov. Exciton-en- hanced recombination in silicon at high concentrations of charge carriers // Semiconductor Physics, Quantum Electron- ics & Optoelectronics, 3(1), pp. 5-10 (2000). 6. A.V. Sachenko, Yu V. Kryuchenko, Exciton effects in band- edge luminescence of semiconductors at room temperatures // Semiconductor Physics, Quantum Electronics & Optoelect- ronics, 3(2), pp. 150-156 (2000). 7. A.P. Gorban, A.V. Sachenko, V.P. Kostylyov, N.A. Prima. Effect of excitons on photoconversion efficiency in the p+-n- n+ and n+-p-p+ � structures based on single-crystalline silicon // Semiconductor Physics, Quantum Electronics & Optoelectronic, 3(3), pp. 322-329 (2000). 0.5 0.6 0.7 0.8 5 4 300 K 3 2 1 U, V h , % 10 10 �3 �4 10 �2 10 �1 10 0 10 1 a U, V 1.00 1.05 1.10 1.15 5 70 K 4 3 2 1 h , % 10 10 �3 �4 10 �2 10 �1 10 0 10 1 b Fig. 3. The dependencies of the EL internal quantum efficiency of silicon p-i-n-structures on applied voltage at Ò = 300 K and Ò = 70 K. Characteristic Shockley-Reed-Hall nonradiative lifetime τr at Ò = 300 K: 1 � 4⋅10�2, 2 � 10�2, 3 � 10�3, 4 � 10�4, 5 � 10�5 s. A.V. Sachenko et al.: Exciton effects in band-edge electroluminescence of silicon ... 7SQO, 7(1), 2004 8. A.V. Sachenko, A.P. Gorban, V.P. Kostylyov. 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Exciton effects in band-edge electroluminescence of silicon barrier structures

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