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Effective Auger excitation of erbium luminescence by hot electrons in silicon
Physica B 273}274 (1999) 334}337
E!ective Auger excitation of erbium luminescence by hot electrons in silicon M.S. Bresler!,*, T. Gregorkiewicz", O.B. Gusev!, P.E. Pak!, I.N. Yassievich!,# !A.F. Iowe Physico-Technical Institute, Politekhnicheskaya 26, 194021 St. Petersburg, Russia "Van der Waals-Zeeman Institute, University of Amsterdam, NL-1018 XE Amsterdam, Netherlands #Department of Theoretical Physics, Lund University, S-223 62 Lund, Sweden
Abstract In an electroluminescent structure based on erbium-doped crystalline silicon we have found and studied a new mechanism of excitation of erbium ions involving Auger recombination of electrons from the upper subband of the conduction band with holes from the valence band. The new excitation mechanism is weak at low temperatures, but it is resonantly enhanced at 160 K, when the energy distance of the edge of the upper subband of the conduction band from the valence band edge coincides with the energy of the second excited state of the erbium ion due to temperature shrinking of the silicon energy gap. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Erbium-doped crystalline silicon; Auger excitation; Electroluminescence
The interest to electroluminescent structures based on erbium-doped crystalline silicon is connected with their possible use as light-emitting diodes compatible with silica-glass optical "bers. The most promising results up to now were obtained with p}n junction electroluminescent structures operating at reverse bias in which the n-region was doped by erbium (it is well known that erbium}oxygen complexes introduce donor states in silicon) [1}7]. In these works [1}4,6,7] hotelectron luminescence besides erbium luminescence was observed and the excitation process was attributed to impact excitation of erbium ions produced by hot electrons. In the present work we demonstrate that in a reversely biased p}n junction another e$cient excitation mechanism can occur which is a resonance Auger process. Electroluminescent structures with p`}n` junctions provided by N.A. Sobolev (Io!e Institute) were fabricated
* Corresponding author: Tel.: #7-812-247-9140; fax: #7812-247-1017. E-mail address: [email protected]!e.rssi.ru (M.S. Bresler)
by co-implantation of erbium and oxygen in a crystalline silicon substrate doped by phosphorus (n`-layer) and implantation of boron onto the substrate surface (p`layer) [7]. Our structures di!ered from those described in Refs. [1}6] in that they were fabricated from (1 1 1) rather than (1 0 0) substrates and erbium concentration in them was lower, not exceeding 2]1017 cm~3. The I}< characteristics had a conventional rectifying shape. Erbium luminescence was measured at reverse bias on the structure as a function of temperature in the temperature range 77}300 K. Parallel with the measurements of the luminescence intensity the voltage on the structure at constant current through it or the current at constant voltage were registered during the temperature runs. The electroluminescence (EL) spectra at ¹"77 and 300 K consisted of lines of erbium emission at 1.54 lm and a broad band of luminescence induced by hot electrons. In Fig. 1a temperature dependences of the intensity of erbium EL are given and the voltage on p`}n` junction of the electroluminescent structure for two values of current through the structure. In the temperature range 140}160 K, where the intensity of erbium EL at 1.54 lm sharply increases, a rise of the voltage on the p}n junction (in the constant current regime) simultaneously
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 4 7 0 - 6
M.S. Bresler et al. / Physica B 273}274 (1999) 334}337
Fig. 1. Experimental (a) and calculated (b) temperature dependences of erbium EL intensity (1,2) and voltage drop on p}n junction (3,4) in the constant current regime for two values of current through the structure: (1,3) 60 mA; (2,4) 240 mA.
occurs. This fact points to annihilation of electron}hole pairs in the process of excitation of erbium EL, i.e. a strong recombination mechanism is switched on (the resistance of the p}n junction increases). To check this assumption we have measured temperature dependences of the intensities of erbium EL, hot electron EL (j"1.35 lm) and current through the sample at constant bias at p-n junction (Fig. 2a). In the temperature range around 160 K an abrupt jump of erbium EL is observed which is accompanied by a signi"cant drop of the current through the p`}n` junction and of the intensity of hot electron EL. This result draws unambiguously to the conclusion that the process of erbium excitation occurs via Auger recombination of nonequilibrium carriers rather than impact excitation. Auger excitation of erbium ions involving the recombination of conduction electrons with free holes was considered by Yassievich and Kimerling [8]. (The energy band diagram demonstrating this process is shown in Fig. 3.) They have shown that in the case of recombination of electrons from the main D subband of the con1 duction band with free holes the Auger process is highly ine$cient, since the Bloch amplitudes of these bands are orthogonal. On the other hand, the probability of an Auger process with the participation of the electrons from the upper D@ subband is fairly high. It is important 2
335
Fig. 2. Experimental (a) and calculated (b) temperature dependences of erbium EL intensity (1) and current through the structure (2) in the constant bias regime; (3) hot-electron EL intensity.
Fig. 3. Energy band diagram with schematic representation of the Auger process of erbium ion excitation (1) and optical transitions responsible for hot electron EL (2).
also that the recombination energy of the D@ electrons 2 with the holes is close to an energy of the transition of an erbium ion from the ground 4I to the second excited 15@2 state 4I (1.26 eV). We assume that the energy of Auger 11@2 recombination of the D@ electrons and the valence band 2 holes at 77 K is slightly larger than that of the 4I }4I transition in the 4f shell of the Er3` ion, and 15@2 11@2 therefore such a transition can occur only with emission of phonons. The rise of the temperature to 160 K leads to a shrinking of the silicon energy gap by 10 meV approximately, and the Auger recombination with excitation of
336
M.S. Bresler et al. / Physica B 273}274 (1999) 334}337
Er3` ion from the ground 4I to the second excited 15@2 state 4I of 4f-shell becomes resonant. This results in 11@2 a sharp increase of the rate of the Auger excitation process, the e$ciency of which is very high (cf. Fig. 2a). Due to the symmetry properties of the Bloch amplitudes of the conduction and the valence bands [9] the electrons making tunnel transitions in the reversely biased p}n junction appear predominantly in the D@ subband of the 2 conduction band. The broad band observed in the EL spectrum is caused by allowed optical transitions of electrons heated by electric "eld in the D@ subband to the D subband. 2 1 The reduction of the intensity of hot electron EL simultaneously with the sharp rise of erbium EL in the same temperature range (cf. Fig. 2a) points directly to an Auger excitation of erbium ions with a participation of electrons from the D@ subband of the conduction 2 band. The probability of the Auger process under discussion is proportional to a product of concentration of nonequilibrium electrons n by concentration of equilibrium holes in the depletion layer of the p}n junction, which is controlled by a temperature tail of the Boltzmann distribution: p"p exp(!qU/k¹), where p is 0 0 the concentration of holes in the p` contact, U is a characteristic potential at the point of maximum electric "eld in the p}n junction (due to high concentration of holes in the p-region (5]1019 cm~3) and comparatively low concentration of electrons in the n-layer (2]1017 cm~3) this point is very close to the p-contact). The experimental results can be described with the set of balance equations for the concentration of nonequilibrium electrons generated in the `activea zone (p}n junction) and the concentration of excited erbium ions G"cnp exp(!qU/k¹)N #nv/¸, 0 5
(1)
cnp exp(!qU/k¹)(N !NH ) 0 E3 E3
C
"NH q~1#ap exp(!qU/k¹) E3 3 0
A
E #q~1 exp ! !# 0 k¹
BD
,
(2)
where G is the generation rate of nonequilibrium carriers in the p}n junction due to tunnel transitions, c is the coe$cient of Auger-excitation of erbium ions, a is the coe$cient of de-excitation of erbium ions due to their interaction with free holes, NH, N , and N are concenE3 5 tration of excited erbium ions, concentration of optically active erbium ions and total concentration of erbium ions, respectively, ¸ is the thickness of the p}n junction, and q is the radiative lifetime of an erbium ion in the 3 excited state. We have included also the back-transfer de-excitation mechanism which contributes a term q~1 exp(!E /k¹) to the probability of de-excitation of 0 !#
erbium ion. (This back-transfer process corresponds to a generation of an electron on previously empty donor and a hole in the valence band; the donor states are depopulated in the high electric "eld of the p}n junction.) The characteristic energy of the back-transfer process is E "E !E !E where E "1.17 eV !# ' &&{ $ ' is the silicon bandgap, E "0.8 eV the excitation &&{ energy of an erbium ion and E "0.15 eV the energy $ of the donor level connected with the erbium}oxygen complex. The concentration of free electrons in the region of erbium ions excitation (in the p}n junction) is controlled by two factors: Auger recombination of free electrons with holes and drift of electrons from the `activea zone under the action of high electric "eld with a limiting velocity v. In the regime of constant current through the structure j 0
C
D
cj cj ~1 0 #1 I "I.!9 0 EL EL va q va q "I.!9pq( j /q)[pq( j /q)#1]~1, EL 0 0
(3)
where I "NH/q , I.!9"N /q and we have introducEL 3 EL E3 3 ed the notations p"cp exp(!qU/k¹)/v and q~1+ 0 (ap exp(!qU/k¹)#q~1 exp(!E /k¹))
(4)
where E is a characteristic electric "eld. # A strong enhancement of p at the resonance threshold leads to a marked rise of the voltage on the structure. Since p enters the logarithm argument, the change in the voltage is much weaker than the variation of p. In the constant voltage regime according to the formula j"j /(pN ¸#1), 0 5
(5)
the current starts to decrease compared to the j value 0 even below the resonance threshold due to an increase of hole concentration in the recombination region and
M.S. Bresler et al. / Physica B 273}274 (1999) 334}337
su!ers an additional drop at the threshold. A further decrease of the current at higher temperatures is connected again with the rise of the hole concentration (c is again constant above the threshold). The intensity of electroluminescence in this regime is I +I.!9pq( j /q)[pq( j /q)#pN ¸#1]~1. (6) EL EL 0 0 5 We have calculated the intensity of erbium EL, voltage on the structure (in the constant current regime) and current through the structure (in the constant reverse bias regime) using formulas (3)}(6). The results of calculations are shown in Fig. 1b and Fig. 2b. It is clear that the calculated temperature dependences are in fair agreement with the experimental results. In conclusion, we have demonstrated that a new mechanism of excitation of erbium ions, i.e. an Auger recombination process with participation of D@ electrons and 2 valence band holes, acts in reversely biased EL structures based on erbium-doped crystalline silicon. This work was supported by the grants 98-02-18246 and 99-18079-a from the Russian Foundation of Basic Research, the grant 97-1036 of Russian Ministry of
337
Science and NATO Linkage grant HTECH. LG 972032. I.N.Y. thanks Swedish Natural Science Research Council for "nancial support (grant O-AH/KG 03996-322). References [1] S. Lombardo, S.U. Campisano, J. Appl. Phys. 77 (1995) 6504. [2] J. Stimmer et al., Appl. Phys. Lett. 68 (1996) 3290. [3] S. Co!a, G. Franzo, F. Priolo, Appl. Phys. Lett. 69 (1996) 2077. [4] G. Franzo, S. Co!a, F. Priolo, C. Spinella, J. Appl. Phys. 81 (1997) 2784. [5] M. Matsuoka, Sh. Tohno, Appl. Phys. Lett. 71 (1997) 96. [6] N.A. Sobolev, A.M. Emel'yanov, K.F. Shtel'makh, Appl. Phys. Lett. 71 (1997) 1930. [7] A.M. Emel'yanov, N.A. Sobolev, A.N. Yakimenko, Appl. Phys. Lett. 72 (1998) 1223. [8] I.N. Yassievich, L.C. Kimerling, Semicond. Sci. Technol. 8 (1993) 718. [9] G.L. Bir, G.E. Pikus, Symmetry and strain-induced e!ects in semiconductors, Israel Program Sci. Translations, Jerusalem, 1974.
E!ective Auger excitation of erbium luminescence by hot electrons in silicon M.S. Bresler!,*, T. Gregorkiewicz", O.B. Gusev!, P.E. Pak!, I.N. Yassievich!,# !A.F. Iowe Physico-Technical Institute, Politekhnicheskaya 26, 194021 St. Petersburg, Russia "Van der Waals-Zeeman Institute, University of Amsterdam, NL-1018 XE Amsterdam, Netherlands #Department of Theoretical Physics, Lund University, S-223 62 Lund, Sweden
Abstract In an electroluminescent structure based on erbium-doped crystalline silicon we have found and studied a new mechanism of excitation of erbium ions involving Auger recombination of electrons from the upper subband of the conduction band with holes from the valence band. The new excitation mechanism is weak at low temperatures, but it is resonantly enhanced at 160 K, when the energy distance of the edge of the upper subband of the conduction band from the valence band edge coincides with the energy of the second excited state of the erbium ion due to temperature shrinking of the silicon energy gap. ( 1999 Elsevier Science B.V. All rights reserved. Keywords: Erbium-doped crystalline silicon; Auger excitation; Electroluminescence
The interest to electroluminescent structures based on erbium-doped crystalline silicon is connected with their possible use as light-emitting diodes compatible with silica-glass optical "bers. The most promising results up to now were obtained with p}n junction electroluminescent structures operating at reverse bias in which the n-region was doped by erbium (it is well known that erbium}oxygen complexes introduce donor states in silicon) [1}7]. In these works [1}4,6,7] hotelectron luminescence besides erbium luminescence was observed and the excitation process was attributed to impact excitation of erbium ions produced by hot electrons. In the present work we demonstrate that in a reversely biased p}n junction another e$cient excitation mechanism can occur which is a resonance Auger process. Electroluminescent structures with p`}n` junctions provided by N.A. Sobolev (Io!e Institute) were fabricated
* Corresponding author: Tel.: #7-812-247-9140; fax: #7812-247-1017. E-mail address: [email protected]!e.rssi.ru (M.S. Bresler)
by co-implantation of erbium and oxygen in a crystalline silicon substrate doped by phosphorus (n`-layer) and implantation of boron onto the substrate surface (p`layer) [7]. Our structures di!ered from those described in Refs. [1}6] in that they were fabricated from (1 1 1) rather than (1 0 0) substrates and erbium concentration in them was lower, not exceeding 2]1017 cm~3. The I}< characteristics had a conventional rectifying shape. Erbium luminescence was measured at reverse bias on the structure as a function of temperature in the temperature range 77}300 K. Parallel with the measurements of the luminescence intensity the voltage on the structure at constant current through it or the current at constant voltage were registered during the temperature runs. The electroluminescence (EL) spectra at ¹"77 and 300 K consisted of lines of erbium emission at 1.54 lm and a broad band of luminescence induced by hot electrons. In Fig. 1a temperature dependences of the intensity of erbium EL are given and the voltage on p`}n` junction of the electroluminescent structure for two values of current through the structure. In the temperature range 140}160 K, where the intensity of erbium EL at 1.54 lm sharply increases, a rise of the voltage on the p}n junction (in the constant current regime) simultaneously
0921-4526/99/$ - see front matter ( 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 0 4 7 0 - 6
M.S. Bresler et al. / Physica B 273}274 (1999) 334}337
Fig. 1. Experimental (a) and calculated (b) temperature dependences of erbium EL intensity (1,2) and voltage drop on p}n junction (3,4) in the constant current regime for two values of current through the structure: (1,3) 60 mA; (2,4) 240 mA.
occurs. This fact points to annihilation of electron}hole pairs in the process of excitation of erbium EL, i.e. a strong recombination mechanism is switched on (the resistance of the p}n junction increases). To check this assumption we have measured temperature dependences of the intensities of erbium EL, hot electron EL (j"1.35 lm) and current through the sample at constant bias at p-n junction (Fig. 2a). In the temperature range around 160 K an abrupt jump of erbium EL is observed which is accompanied by a signi"cant drop of the current through the p`}n` junction and of the intensity of hot electron EL. This result draws unambiguously to the conclusion that the process of erbium excitation occurs via Auger recombination of nonequilibrium carriers rather than impact excitation. Auger excitation of erbium ions involving the recombination of conduction electrons with free holes was considered by Yassievich and Kimerling [8]. (The energy band diagram demonstrating this process is shown in Fig. 3.) They have shown that in the case of recombination of electrons from the main D subband of the con1 duction band with free holes the Auger process is highly ine$cient, since the Bloch amplitudes of these bands are orthogonal. On the other hand, the probability of an Auger process with the participation of the electrons from the upper D@ subband is fairly high. It is important 2
335
Fig. 2. Experimental (a) and calculated (b) temperature dependences of erbium EL intensity (1) and current through the structure (2) in the constant bias regime; (3) hot-electron EL intensity.
Fig. 3. Energy band diagram with schematic representation of the Auger process of erbium ion excitation (1) and optical transitions responsible for hot electron EL (2).
also that the recombination energy of the D@ electrons 2 with the holes is close to an energy of the transition of an erbium ion from the ground 4I to the second excited 15@2 state 4I (1.26 eV). We assume that the energy of Auger 11@2 recombination of the D@ electrons and the valence band 2 holes at 77 K is slightly larger than that of the 4I }4I transition in the 4f shell of the Er3` ion, and 15@2 11@2 therefore such a transition can occur only with emission of phonons. The rise of the temperature to 160 K leads to a shrinking of the silicon energy gap by 10 meV approximately, and the Auger recombination with excitation of
336
M.S. Bresler et al. / Physica B 273}274 (1999) 334}337
Er3` ion from the ground 4I to the second excited 15@2 state 4I of 4f-shell becomes resonant. This results in 11@2 a sharp increase of the rate of the Auger excitation process, the e$ciency of which is very high (cf. Fig. 2a). Due to the symmetry properties of the Bloch amplitudes of the conduction and the valence bands [9] the electrons making tunnel transitions in the reversely biased p}n junction appear predominantly in the D@ subband of the 2 conduction band. The broad band observed in the EL spectrum is caused by allowed optical transitions of electrons heated by electric "eld in the D@ subband to the D subband. 2 1 The reduction of the intensity of hot electron EL simultaneously with the sharp rise of erbium EL in the same temperature range (cf. Fig. 2a) points directly to an Auger excitation of erbium ions with a participation of electrons from the D@ subband of the conduction 2 band. The probability of the Auger process under discussion is proportional to a product of concentration of nonequilibrium electrons n by concentration of equilibrium holes in the depletion layer of the p}n junction, which is controlled by a temperature tail of the Boltzmann distribution: p"p exp(!qU/k¹), where p is 0 0 the concentration of holes in the p` contact, U is a characteristic potential at the point of maximum electric "eld in the p}n junction (due to high concentration of holes in the p-region (5]1019 cm~3) and comparatively low concentration of electrons in the n-layer (2]1017 cm~3) this point is very close to the p-contact). The experimental results can be described with the set of balance equations for the concentration of nonequilibrium electrons generated in the `activea zone (p}n junction) and the concentration of excited erbium ions G"cnp exp(!qU/k¹)N #nv/¸, 0 5
(1)
cnp exp(!qU/k¹)(N !NH ) 0 E3 E3
C
"NH q~1#ap exp(!qU/k¹) E3 3 0
A
E #q~1 exp ! !# 0 k¹
BD
,
(2)
where G is the generation rate of nonequilibrium carriers in the p}n junction due to tunnel transitions, c is the coe$cient of Auger-excitation of erbium ions, a is the coe$cient of de-excitation of erbium ions due to their interaction with free holes, NH, N , and N are concenE3 5 tration of excited erbium ions, concentration of optically active erbium ions and total concentration of erbium ions, respectively, ¸ is the thickness of the p}n junction, and q is the radiative lifetime of an erbium ion in the 3 excited state. We have included also the back-transfer de-excitation mechanism which contributes a term q~1 exp(!E /k¹) to the probability of de-excitation of 0 !#
erbium ion. (This back-transfer process corresponds to a generation of an electron on previously empty donor and a hole in the valence band; the donor states are depopulated in the high electric "eld of the p}n junction.) The characteristic energy of the back-transfer process is E "E !E !E where E "1.17 eV !# ' &&{ $ ' is the silicon bandgap, E "0.8 eV the excitation &&{ energy of an erbium ion and E "0.15 eV the energy $ of the donor level connected with the erbium}oxygen complex. The concentration of free electrons in the region of erbium ions excitation (in the p}n junction) is controlled by two factors: Auger recombination of free electrons with holes and drift of electrons from the `activea zone under the action of high electric "eld with a limiting velocity v. In the regime of constant current through the structure j 0
C
D
cj cj ~1 0 #1 I "I.!9 0 EL EL va q va q "I.!9pq( j /q)[pq( j /q)#1]~1, EL 0 0
(3)
where I "NH/q , I.!9"N /q and we have introducEL 3 EL E3 3 ed the notations p"cp exp(!qU/k¹)/v and q~1+ 0 (ap exp(!qU/k¹)#q~1 exp(!E /k¹))
(4)
where E is a characteristic electric "eld. # A strong enhancement of p at the resonance threshold leads to a marked rise of the voltage on the structure. Since p enters the logarithm argument, the change in the voltage is much weaker than the variation of p. In the constant voltage regime according to the formula j"j /(pN ¸#1), 0 5
(5)
the current starts to decrease compared to the j value 0 even below the resonance threshold due to an increase of hole concentration in the recombination region and
M.S. Bresler et al. / Physica B 273}274 (1999) 334}337
su!ers an additional drop at the threshold. A further decrease of the current at higher temperatures is connected again with the rise of the hole concentration (c is again constant above the threshold). The intensity of electroluminescence in this regime is I +I.!9pq( j /q)[pq( j /q)#pN ¸#1]~1. (6) EL EL 0 0 5 We have calculated the intensity of erbium EL, voltage on the structure (in the constant current regime) and current through the structure (in the constant reverse bias regime) using formulas (3)}(6). The results of calculations are shown in Fig. 1b and Fig. 2b. It is clear that the calculated temperature dependences are in fair agreement with the experimental results. In conclusion, we have demonstrated that a new mechanism of excitation of erbium ions, i.e. an Auger recombination process with participation of D@ electrons and 2 valence band holes, acts in reversely biased EL structures based on erbium-doped crystalline silicon. This work was supported by the grants 98-02-18246 and 99-18079-a from the Russian Foundation of Basic Research, the grant 97-1036 of Russian Ministry of
337
Science and NATO Linkage grant HTECH. LG 972032. I.N.Y. thanks Swedish Natural Science Research Council for "nancial support (grant O-AH/KG 03996-322). References [1] S. Lombardo, S.U. Campisano, J. Appl. Phys. 77 (1995) 6504. [2] J. Stimmer et al., Appl. Phys. Lett. 68 (1996) 3290. [3] S. Co!a, G. Franzo, F. Priolo, Appl. Phys. Lett. 69 (1996) 2077. [4] G. Franzo, S. Co!a, F. Priolo, C. Spinella, J. Appl. Phys. 81 (1997) 2784. [5] M. Matsuoka, Sh. Tohno, Appl. Phys. Lett. 71 (1997) 96. [6] N.A. Sobolev, A.M. Emel'yanov, K.F. Shtel'makh, Appl. Phys. Lett. 71 (1997) 1930. [7] A.M. Emel'yanov, N.A. Sobolev, A.N. Yakimenko, Appl. Phys. Lett. 72 (1998) 1223. [8] I.N. Yassievich, L.C. Kimerling, Semicond. Sci. Technol. 8 (1993) 718. [9] G.L. Bir, G.E. Pikus, Symmetry and strain-induced e!ects in semiconductors, Israel Program Sci. Translations, Jerusalem, 1974.