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Sulphur doped silicon light emitting diodes
Materials Science and Engineering B 124–125 (2005) 435–439
Sulphur doped silicon light emitting diodes S.F. Galata ∗ , M.A. Lourenc¸o, R.M. Gwilliam, K.P. Homewod Advanced Technology Institute, School of Electronics and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, UK
Abstract We report electroluminescence experiments from sulphur doped silicon light emitting diodes. Sulphur was implanted into boron doped silicon p–n junctions making use of dislocation engineering. The devices emit at 1.1 and 1.3 m due to the Si TO phonon assisted transition and the sulphur related impurity, respectively. We show the effect of injection conditions on the silicon and sulphur emission. It is observed that the sulphur integrated intensity is increasing sublinearly, whereas the silicon integrated intensity is increasing superlinearly with increasing injection. We present a model which describes this behaviour showing that there are two major routes via the silicon and sulphur that take place, which are competing with each other, along with a non-radiative route coming from the sulphur related level. Our model describes the trends in our experimental data well. © 2005 Elsevier B.V. All rights reserved. Keywords: Sulphur; Electroluminescence; Dislocation engineering; Light emitting diode
1. Introduction Silicon is the most fundamental material in the semiconductor technology, due to its excellent electronic properties, its low cost and its wide availability still in nature. Therefore, more than 90% of the fabricated semiconductor devices are based on silicon. Computer processor power and speed has grown exponentially because more and more transistors are integrated on a single chip. However, there is a fundamental limitation due to ‘the interconnects’ [1]. Metallic contacts are used to interconnect the increasing number of transistors on a single chip. However, the time delay associated with electron transport in the metallization does not decrease. Therefore, there will be a point where the computer chips will not keep getting faster. A solution to this problem could be the replacement of some of the metallic interconnects with optical ones on the chip [2]. A silicon based light emitter would be the optimum solution. Although, sulphur related luminescence from silicon has been reported since the 1980s [3–5] no room temperature luminescence has been achieved and no compatible devices that can be integrated with silicon technology exist. This study describes a silicon light emitting diode achieved by introducing dislocation loops into Si with additional sulphur impurities, under a range of implant and process conditions. The dislocation loop engineering first proposed by Ng et al. [6], introduces a local
∗
Corresponding author.
0921-5107/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2005.08.081
strain field, which modifies the band structure and provides spatial confinement of the charge carriers. This spatial confinement of carriers favours the radiative recombinations by preventing the non-radiative ones. The use of sulphur is to create emission at different wavelengths, apart from the one due to band edge emission in silicon. Fig. 1 depicts (a) a characteristic interstitial dislocation loop and (b) the hydrostatic pressure created along its sides. Well outside the edge of the dislocation loop the hydrostatic pressure is zero. Just inside the dislocation loop, because the distance between the very adjacent row of atoms and the extra one is getting smaller, the silicon lattice is under positive pressure. Just outside the dislocation loop atoms are pushed apart and the lattice is placed under negative pressure. The magnitude and the form of the pressure dependence can be calculated using elastic theory of dislocations [7], also showing that the pressure decays inversely with distance. The band gap of silicon is pressure dependent, and it decreases with increasing pressure and increases under negative pressure. In Fig. 1(c) is depicted a schematic diagram of the modification of the silicon band gap energy due to the presence of a dislocation loop. The exact distribution of modification of the band gap between the bands is not clear yet, but the sum Ec + Ev is calculated to be in the region of 0.33–0.75 eV [6]. Ec and Ev are the shift from the conduction and the valence band, respectively, from the energy gap Eg . The effect of the hydrostatic pressure around the dislocation loops is to locally modify the band gap of the silicon, causing it to decrease with increasing pressure and to increase
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Fig. 1. (a) Schematic diagram of a typical interstitial dislocation loop used in our LEDs. (b) Hydrostatic pressure along the dislocation loop. (c) Modification of the silicon band gap energy due to the presence of dislocation loops.
under negative pressure [8]. The dislocation loops all lie on the (1 1 1) planes and consequently a two dimensional array of such loops, closely enough spaced, presents a positive egg-box-like potential barrier towards the junction. Consequently, carriers being injected across the junction see only a positive potential and are prevented from entering the loops or further onward diffusion. The basic characteristics of a dislocation engineered Si:S LED are illustrated in Fig. 2. Compared with a conventional silicon ‘LED’ device (Fig. 2(a)), where the dominant recombination is non-radiative and takes place at the bulk defects and surface states, the introduction of dislocations (Fig. 2(b)) causes a modification of the band gap. The modification of the band gap due to the introduction of dislocations is shown schematically. The carriers are effectively confined in the region containing the sulphur centres placed between the right edge of the depletion region and the edge of the dislocations, as shown in Fig. 2(b). Consequently, by achieving carrier confinement and preventing diffusion to the bulk and surface, the rate of the radiative recombinations at these centres is enhanced in the sulphur doped region, which leads to light emission at the wavelength of 1.3 m.
Fig. 2. (a) Schematic energy diagram of a conventional silicon LED showing the non-radiative recombination at the bulk defects and the surface states. (b) Energy diagram of our dislocation engineered Si:S after the incorporation of sulphur and boron atoms. The modification of the band gap due to the dislocation loops is also shown.
1013 , 1014 S cm−2 at 30 keV, into n-type (1 0 0) crystalline (CZ) Si of 2–7 cm resistivity. Rapid thermal annealing (RTA) at 1000 or 1100 ◦ C for 10 s was then done in order to activate the sulphur atoms. A subsequent ion implantation with boron took place at 1015 B cm−2 at 30 keV, in order to form the p–n junction and also to introduce the dislocation loops into the active region of the junction. After boron implantation a subsequent RTA at 950 ◦ C for 1 min also took place in order to activate the boron atoms and to form the dislocation loops layer. Two sets of samples consisting of four samples in each set were compared. In Fig. 3 is illustrated a schematic diagram of the sulphur doped silicon light emitting device. The Ohmic contacts were formed by evaporation of Al and AuSb at the boron doped side (p-type
2. Experimental The sulphur doped silicon light emitting diodes were fabricated by sulphur implantation at four different doses: 1011 , 1012 ,
Fig. 3. A Schematic diagram of the structure of the sulphur doped silicon light emitting diode (LED).
S.F. Galata et al. / Materials Science and Engineering B 124–125 (2005) 435–439
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region) and the n-type substrate, respectively. Contacts were sintered at 360 ◦ C for 2 min. In order to isolate the p–n junction the devices were mesa etched (25 H2 O:1 HF:25 HNO3 ). A window was left at the n-type side to allow the electroluminescence out of the devices. The area of the device was 8 × 10−3 cm2 . Electroluminescence (EL) experiments were performed on all eight samples at operating temperatures ranging from 80 to 300 K at 25 mA (current density of 2 A/cm2 ) under forward bias. In this paper, we concentrate on the EL under variable current injection conditions. Devices were subjected to currents ranging from 0 up to 200 mA at 80 K. They were mounted in a liquid nitrogen continuous-flow cryostat situated in front of a half-meter spectrometer. The electroluminescence from the devices was measured from the back window, and detected with a liquid nitrogen cooled Ge p–i–n diode. 3. Results and discussion Electroluminescence experiments on our sulphur doped silicon LEDs showed two strong emissions at 1.13 m due to Si TO phonon and at 1.33 m due to sulphur as observed previously [3] and [4]. This emission was attributed to bound exciton luminescence from sulphur related isoelectronic complexes in Si [3]. Both lines were still present at 300 K with the sulphur emission less strong than the silicon emission. In Fig. 4 are illustrated the current dependence of the silicon, sulphur and total integrated intensity trends for a sample implanted with S at 1011 S cm−2 at 30 keV, annealed at 1100 ◦ C for 10 s, further implanted with B at 1015 B cm−2 at 30 keV and then further annealed at 950 ◦ C for 1 min at 80 K. From Fig. 4 we see that the sulphur integrated intensity trend is sublinear, increasing faster at the low current regime then increasing very slowly with increase in the applied current. The silicon integrated intensity trend though is superlinear, increasing slower at low currents than the S integrated intensity then further increasing faster with increase in the applied current. This behaviour is shown more clearly in Fig. 4(b). This can be attributed to the saturation of the sulphur related levels responsible for the 1.33 m emission at high injection conditions [9]. The total integrated intensity which is the sum of the sulphur and silicon integrated intensity is increasing with increasing injection. The integrated intensity is closely linear at low injection currents and follows the Si trend at higher currents. A simple phenomenological model that is described can explain our results is analogous to a model used by Rosenweig et al. [10] for the recombination via a Zn–O complex in GaP. In our case the sulphur forms a radiative recombination centre. As illustrated in the band diagram of Fig. 5, an electron in the conduction band may recombine radiatively with a hole in the valence band, with the help of the TO phonon, with an associated lifetime τ Si . In addition, an electron trapped in the sulphur related centre may recombine with a hole in the valence band radiatively as a bound electron–hole pair with a lifetime of τ S , or it may return to the valence band non-radiatively having a lifetime of τ NR . The rate equation model which represents our EL results is illustrated in Fig. 6. The radiative recombination rate from Si, RSi , is equal to the generation rate, G, minus the
Fig. 4. (a) Current dependence (data points) of the silicon, sulphur and total EL integrated intensity at 80 K of the sample implanted at 1011 S cm−2 , annealed at 1100 ◦ C for 10 s and further implanted with 1015 B cm−2 at 30 keV. The lines in (a) are provided as a guide to the eye. (b) Same as (a), but expanded to lower currents. The lines are fits to the data, showing the radiative recombination rates as a function of generation rate, obtained from the phenomenological model described in the text normalized to the point where the sulphur and silicon intensities are equal.
radiative recombination rate from the conduction band to the S-related level, RSi–S , i.e. RSi = G − RSi−S ⇒ RSi = G − BN(N0 − N )
(1)
Fig. 5. Band diagram of recombination via the S level in Si. τ Si is the lifetime of an electron from the conduction band which has recombined radiatively with a hole of the valence band with a help of a phonon, τ S is the lifetime of an electron from the S level which has recombined radiatively with a hole of the valence band as a bound electron–hole pair and τ NR the lifetime of an electron from the S level which returns to the valence band non-radiatively. EC and EV are the energy of the conduction and the valence bands, respectively.
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(2) can be written using formulas (4)–(6) as follows: RS =
BN0 RSi τSi 1 + BRSi τSi τS + τS /τNR
(7)
In addition, the radiative recombination rate from Si, RSi , Eq. (1) can be also written using formulas (4) and (5) as follows: RSi = Fig. 6. Schematic representation of the rate equation model. G is the input generation rate, RSi , the radiative recombination rate from Si, RS the radiative recombination rate from S, RNR the non-radiative recombination rate from S and RSi–S the radiative recombination rate from the conduction band to the S-related level. N is the density of electrons in the conduction band and N the density of electrons trapped in the sulphur related level.
where N is the density of electrons in the conduction band, N the density of electrons trapped in the sulphur related level and No the total density of traps due to sulphur. B is a coefficient for conduction band-to-S level recombination. Therefore, in Eq. (1) the radiative recombination rate from the conduction band, RSi , is equal to the generation rate minus the radiative recombination rate from the conduction band to the S-related level, RSi–S , which is equal to the product of density of electrons in the conduction band by the total density of traps in the S-related level minus the density of electrons trapped in the S-related level by the coefficient factor B. The radiative recombination rate from S, RS , is given by the formula:
RS = RSi−S − RNR ⇒ RS = N(N0 − N ) − RNR
(2)
where RSi–S is the radiative recombination rate from the conduction band to the S-related level as described in Eq. (1) and RNR is the non-radiative recombination rate from S. The total radiative recombination rate which is the sum of the radiative recombination rates from Si and S is given by the following formula, using also formulas (1) and (2): Rtot = RSi + RS ⇒ Rtot = G − RNR
(3)
The density of electrons in the conduction band, N, and the density of electrons trapped in the sulphur related level, N , are given by the following formulas: N = RSi τSi
(4)
N = RS τS
(5)
where τ Si is the lifetime of an electron from the conduction band which has recombined radiatively with a hole of the valence band with a help of a phonon and τ S is the lifetime of an electron from the S level which has recombined radiatively with a hole of the valence band as a bound electron–hole pair. The non-radiative recombination rate from S, RNR , is given by: RNR =
N RS τS ⇒ RNR = τNR τNR
(6)
where the second formula in Eq. (6) has been derived from Eq. (5). Therefore, the radiative recombination rate from S, RS , Eq.
G 1 + BN0 τSi − BRS τS τSi
(8)
If we substitute the term of RS in Eq. (8) from its analytical form as shown in Eq. (7), Eq. (8) can be written as: τS R2Si (BτSi τS ) + RSi (1 + BN0 τSi ) 1 + − BGτSi τS τNR τS =0 (9) −G 1 + τNR The above formula is a quadratic equation in terms of RSi . Solving Eq. (9), we have found the solution: −AB + Γ + A2 B 2 + Γ 2 − 2Γ [B (A − 2)] RSi = G (10) 2Γ where A = 1 + BN0 τSi τS B = 1 + τNR
(11)
Γ = BGτSi τS
(13)
(12)
derive from Eq. (9). Substituting the solution RSi from Eqs. (10) to (7), we obtain: ( − AB + Γ + A2 B + Γ 2 − 2Γ [B (A− 2)])A− 2Γ G RS = (−AB + Γ + AB 2 + Γ 2 − 2Γ [B (A − 2)])Γ (14) where A, B and Γ come from Eqs. (11)–(13). The total radiative recombination rate which is the sum of the radiative recombination rates from Si and S is given by the sum of Eqs. (10) and (14): Rtot −AB + Γ +
A2 B 2 Γ 2 − 2Γ [B (A − 2)] G 2Γ (−AB + Γ + A2 B 2 + Γ 2 − 2Γ [B (A − 2)])A − 2Γ + G (−AB + Γ + A2 B 2 + Γ 2 − 2Γ [B (A − 2)])Γ (15)
=
In Eqs. (10), (14) and (15) the radiative recombination rates for Si, S and total (RSi , RS and Rtot , respectively) are equivalent to the integrated intensities that we have measured in our experimental results (Fig. 4(a)), and the generation rate G is proportional to the applied current. The values of the dimensionless parameters of our model used are listed in Table 1. Thus, using Eqs. (10)–(15) and the values from Table 1 we can plot the radiative recombination rates for Si, S and the total, RSi , RS , and Rtot ,
S.F. Galata et al. / Materials Science and Engineering B 124–125 (2005) 435–439 Table 1 List of the model parameters used for the fits shown in Fig. 4(b) Dimensionless fitting parameters
Values
A B Γ
8 2 0–5000
The parameters are defined in the text.
respectively, as a function of the generation rate G. In Fig. 4(b), we compare this with the experimental values abstracted from Fig. 4(a) as a function of applied current. We can see that our model accurately describes the experimental behaviour. In addition, as observed in Fig. 4(b), at low injection currents, the total integrated intensity trend is closely linear. This indicates that at low currents the emission results from competition between the sulphur and silicon centres only. 4. Conclusions In this paper, we have shown the effect of injection condition on silicon and sulphur emission. It is observed that the sulphurintegrated intensity is increasing sublinearly whereas the silicon integrated intensity is increasing superlinearly with the increase
439
of injection condition. We provided a model explaining the current dependence experiments which showed that there are two major radiative routes via the silicon and the sulphur that take place, which are competing at each other along with a nonradiative route coming from the sulphur-related level. Our model provides a good match to the behaviour of our experimental data. References [1] L. Pavesi, J. Phys. Condens. Matter 15 (2003) R1169. [2] M.A. Lourenc¸o, W.L. Ng, G. Shao, R.M. Gwilliam, K.P. Homewood, SPIE Proc. 4654 (2002) 138. [3] T.G. Brown, D.G. Hall, Appl. Phys. Lett. 49 (1986) 245. [4] T.G. Brown, P.L. Bradfield, D.G. Hall, Appl. Phys. Lett. 51 (1986) 1585. [5] P.L. Bradfield, T.G. Brown, D.G. Hall, Appl. Phys. Lett. 55 (1989) 100. [6] W.L. Ng, M.A. Lourenc¸o, R.M. Gwilliam, S. Ledain, G. Shao, K.P. Homewood, Nature 410 (2001) 192. [7] J.P. Hirth, J. Lothe, Theory of Dislocations, second ed., John Wiley & Sons, 1968. [8] M.A. Lourenc¸o, M.S. Siddiqui, G. Shao, R.M. Gwilliam, K.P. Homewood, in: L. Pavesi, et al. (Eds.), in: Towards the First Silicon Laser, Kluwer Academic Publishers, The Netherlands, 2003, p. 11. [9] M.A. Lourenc¸o, M. Milosavljevic, S. Galata, M.S. A. Siddiqui, G. Shao, R.M. Gwilliam, K.P. Homewood, Vacuum, in press. [10] W. Rosenweig, W.H. Hackett, J.S. Jayson, J. Appl. Phys. 40 (1969) 4477.
Sulphur doped silicon light emitting diodes S.F. Galata ∗ , M.A. Lourenc¸o, R.M. Gwilliam, K.P. Homewod Advanced Technology Institute, School of Electronics and Physical Sciences, University of Surrey, Guildford, Surrey GU2 7XH, UK
Abstract We report electroluminescence experiments from sulphur doped silicon light emitting diodes. Sulphur was implanted into boron doped silicon p–n junctions making use of dislocation engineering. The devices emit at 1.1 and 1.3 m due to the Si TO phonon assisted transition and the sulphur related impurity, respectively. We show the effect of injection conditions on the silicon and sulphur emission. It is observed that the sulphur integrated intensity is increasing sublinearly, whereas the silicon integrated intensity is increasing superlinearly with increasing injection. We present a model which describes this behaviour showing that there are two major routes via the silicon and sulphur that take place, which are competing with each other, along with a non-radiative route coming from the sulphur related level. Our model describes the trends in our experimental data well. © 2005 Elsevier B.V. All rights reserved. Keywords: Sulphur; Electroluminescence; Dislocation engineering; Light emitting diode
1. Introduction Silicon is the most fundamental material in the semiconductor technology, due to its excellent electronic properties, its low cost and its wide availability still in nature. Therefore, more than 90% of the fabricated semiconductor devices are based on silicon. Computer processor power and speed has grown exponentially because more and more transistors are integrated on a single chip. However, there is a fundamental limitation due to ‘the interconnects’ [1]. Metallic contacts are used to interconnect the increasing number of transistors on a single chip. However, the time delay associated with electron transport in the metallization does not decrease. Therefore, there will be a point where the computer chips will not keep getting faster. A solution to this problem could be the replacement of some of the metallic interconnects with optical ones on the chip [2]. A silicon based light emitter would be the optimum solution. Although, sulphur related luminescence from silicon has been reported since the 1980s [3–5] no room temperature luminescence has been achieved and no compatible devices that can be integrated with silicon technology exist. This study describes a silicon light emitting diode achieved by introducing dislocation loops into Si with additional sulphur impurities, under a range of implant and process conditions. The dislocation loop engineering first proposed by Ng et al. [6], introduces a local
∗
Corresponding author.
0921-5107/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2005.08.081
strain field, which modifies the band structure and provides spatial confinement of the charge carriers. This spatial confinement of carriers favours the radiative recombinations by preventing the non-radiative ones. The use of sulphur is to create emission at different wavelengths, apart from the one due to band edge emission in silicon. Fig. 1 depicts (a) a characteristic interstitial dislocation loop and (b) the hydrostatic pressure created along its sides. Well outside the edge of the dislocation loop the hydrostatic pressure is zero. Just inside the dislocation loop, because the distance between the very adjacent row of atoms and the extra one is getting smaller, the silicon lattice is under positive pressure. Just outside the dislocation loop atoms are pushed apart and the lattice is placed under negative pressure. The magnitude and the form of the pressure dependence can be calculated using elastic theory of dislocations [7], also showing that the pressure decays inversely with distance. The band gap of silicon is pressure dependent, and it decreases with increasing pressure and increases under negative pressure. In Fig. 1(c) is depicted a schematic diagram of the modification of the silicon band gap energy due to the presence of a dislocation loop. The exact distribution of modification of the band gap between the bands is not clear yet, but the sum Ec + Ev is calculated to be in the region of 0.33–0.75 eV [6]. Ec and Ev are the shift from the conduction and the valence band, respectively, from the energy gap Eg . The effect of the hydrostatic pressure around the dislocation loops is to locally modify the band gap of the silicon, causing it to decrease with increasing pressure and to increase
436
S.F. Galata et al. / Materials Science and Engineering B 124–125 (2005) 435–439
Fig. 1. (a) Schematic diagram of a typical interstitial dislocation loop used in our LEDs. (b) Hydrostatic pressure along the dislocation loop. (c) Modification of the silicon band gap energy due to the presence of dislocation loops.
under negative pressure [8]. The dislocation loops all lie on the (1 1 1) planes and consequently a two dimensional array of such loops, closely enough spaced, presents a positive egg-box-like potential barrier towards the junction. Consequently, carriers being injected across the junction see only a positive potential and are prevented from entering the loops or further onward diffusion. The basic characteristics of a dislocation engineered Si:S LED are illustrated in Fig. 2. Compared with a conventional silicon ‘LED’ device (Fig. 2(a)), where the dominant recombination is non-radiative and takes place at the bulk defects and surface states, the introduction of dislocations (Fig. 2(b)) causes a modification of the band gap. The modification of the band gap due to the introduction of dislocations is shown schematically. The carriers are effectively confined in the region containing the sulphur centres placed between the right edge of the depletion region and the edge of the dislocations, as shown in Fig. 2(b). Consequently, by achieving carrier confinement and preventing diffusion to the bulk and surface, the rate of the radiative recombinations at these centres is enhanced in the sulphur doped region, which leads to light emission at the wavelength of 1.3 m.
Fig. 2. (a) Schematic energy diagram of a conventional silicon LED showing the non-radiative recombination at the bulk defects and the surface states. (b) Energy diagram of our dislocation engineered Si:S after the incorporation of sulphur and boron atoms. The modification of the band gap due to the dislocation loops is also shown.
1013 , 1014 S cm−2 at 30 keV, into n-type (1 0 0) crystalline (CZ) Si of 2–7 cm resistivity. Rapid thermal annealing (RTA) at 1000 or 1100 ◦ C for 10 s was then done in order to activate the sulphur atoms. A subsequent ion implantation with boron took place at 1015 B cm−2 at 30 keV, in order to form the p–n junction and also to introduce the dislocation loops into the active region of the junction. After boron implantation a subsequent RTA at 950 ◦ C for 1 min also took place in order to activate the boron atoms and to form the dislocation loops layer. Two sets of samples consisting of four samples in each set were compared. In Fig. 3 is illustrated a schematic diagram of the sulphur doped silicon light emitting device. The Ohmic contacts were formed by evaporation of Al and AuSb at the boron doped side (p-type
2. Experimental The sulphur doped silicon light emitting diodes were fabricated by sulphur implantation at four different doses: 1011 , 1012 ,
Fig. 3. A Schematic diagram of the structure of the sulphur doped silicon light emitting diode (LED).
S.F. Galata et al. / Materials Science and Engineering B 124–125 (2005) 435–439
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region) and the n-type substrate, respectively. Contacts were sintered at 360 ◦ C for 2 min. In order to isolate the p–n junction the devices were mesa etched (25 H2 O:1 HF:25 HNO3 ). A window was left at the n-type side to allow the electroluminescence out of the devices. The area of the device was 8 × 10−3 cm2 . Electroluminescence (EL) experiments were performed on all eight samples at operating temperatures ranging from 80 to 300 K at 25 mA (current density of 2 A/cm2 ) under forward bias. In this paper, we concentrate on the EL under variable current injection conditions. Devices were subjected to currents ranging from 0 up to 200 mA at 80 K. They were mounted in a liquid nitrogen continuous-flow cryostat situated in front of a half-meter spectrometer. The electroluminescence from the devices was measured from the back window, and detected with a liquid nitrogen cooled Ge p–i–n diode. 3. Results and discussion Electroluminescence experiments on our sulphur doped silicon LEDs showed two strong emissions at 1.13 m due to Si TO phonon and at 1.33 m due to sulphur as observed previously [3] and [4]. This emission was attributed to bound exciton luminescence from sulphur related isoelectronic complexes in Si [3]. Both lines were still present at 300 K with the sulphur emission less strong than the silicon emission. In Fig. 4 are illustrated the current dependence of the silicon, sulphur and total integrated intensity trends for a sample implanted with S at 1011 S cm−2 at 30 keV, annealed at 1100 ◦ C for 10 s, further implanted with B at 1015 B cm−2 at 30 keV and then further annealed at 950 ◦ C for 1 min at 80 K. From Fig. 4 we see that the sulphur integrated intensity trend is sublinear, increasing faster at the low current regime then increasing very slowly with increase in the applied current. The silicon integrated intensity trend though is superlinear, increasing slower at low currents than the S integrated intensity then further increasing faster with increase in the applied current. This behaviour is shown more clearly in Fig. 4(b). This can be attributed to the saturation of the sulphur related levels responsible for the 1.33 m emission at high injection conditions [9]. The total integrated intensity which is the sum of the sulphur and silicon integrated intensity is increasing with increasing injection. The integrated intensity is closely linear at low injection currents and follows the Si trend at higher currents. A simple phenomenological model that is described can explain our results is analogous to a model used by Rosenweig et al. [10] for the recombination via a Zn–O complex in GaP. In our case the sulphur forms a radiative recombination centre. As illustrated in the band diagram of Fig. 5, an electron in the conduction band may recombine radiatively with a hole in the valence band, with the help of the TO phonon, with an associated lifetime τ Si . In addition, an electron trapped in the sulphur related centre may recombine with a hole in the valence band radiatively as a bound electron–hole pair with a lifetime of τ S , or it may return to the valence band non-radiatively having a lifetime of τ NR . The rate equation model which represents our EL results is illustrated in Fig. 6. The radiative recombination rate from Si, RSi , is equal to the generation rate, G, minus the
Fig. 4. (a) Current dependence (data points) of the silicon, sulphur and total EL integrated intensity at 80 K of the sample implanted at 1011 S cm−2 , annealed at 1100 ◦ C for 10 s and further implanted with 1015 B cm−2 at 30 keV. The lines in (a) are provided as a guide to the eye. (b) Same as (a), but expanded to lower currents. The lines are fits to the data, showing the radiative recombination rates as a function of generation rate, obtained from the phenomenological model described in the text normalized to the point where the sulphur and silicon intensities are equal.
radiative recombination rate from the conduction band to the S-related level, RSi–S , i.e. RSi = G − RSi−S ⇒ RSi = G − BN(N0 − N )
(1)
Fig. 5. Band diagram of recombination via the S level in Si. τ Si is the lifetime of an electron from the conduction band which has recombined radiatively with a hole of the valence band with a help of a phonon, τ S is the lifetime of an electron from the S level which has recombined radiatively with a hole of the valence band as a bound electron–hole pair and τ NR the lifetime of an electron from the S level which returns to the valence band non-radiatively. EC and EV are the energy of the conduction and the valence bands, respectively.
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(2) can be written using formulas (4)–(6) as follows: RS =
BN0 RSi τSi 1 + BRSi τSi τS + τS /τNR
(7)
In addition, the radiative recombination rate from Si, RSi , Eq. (1) can be also written using formulas (4) and (5) as follows: RSi = Fig. 6. Schematic representation of the rate equation model. G is the input generation rate, RSi , the radiative recombination rate from Si, RS the radiative recombination rate from S, RNR the non-radiative recombination rate from S and RSi–S the radiative recombination rate from the conduction band to the S-related level. N is the density of electrons in the conduction band and N the density of electrons trapped in the sulphur related level.
where N is the density of electrons in the conduction band, N the density of electrons trapped in the sulphur related level and No the total density of traps due to sulphur. B is a coefficient for conduction band-to-S level recombination. Therefore, in Eq. (1) the radiative recombination rate from the conduction band, RSi , is equal to the generation rate minus the radiative recombination rate from the conduction band to the S-related level, RSi–S , which is equal to the product of density of electrons in the conduction band by the total density of traps in the S-related level minus the density of electrons trapped in the S-related level by the coefficient factor B. The radiative recombination rate from S, RS , is given by the formula:
RS = RSi−S − RNR ⇒ RS = N(N0 − N ) − RNR
(2)
where RSi–S is the radiative recombination rate from the conduction band to the S-related level as described in Eq. (1) and RNR is the non-radiative recombination rate from S. The total radiative recombination rate which is the sum of the radiative recombination rates from Si and S is given by the following formula, using also formulas (1) and (2): Rtot = RSi + RS ⇒ Rtot = G − RNR
(3)
The density of electrons in the conduction band, N, and the density of electrons trapped in the sulphur related level, N , are given by the following formulas: N = RSi τSi
(4)
N = RS τS
(5)
where τ Si is the lifetime of an electron from the conduction band which has recombined radiatively with a hole of the valence band with a help of a phonon and τ S is the lifetime of an electron from the S level which has recombined radiatively with a hole of the valence band as a bound electron–hole pair. The non-radiative recombination rate from S, RNR , is given by: RNR =
N RS τS ⇒ RNR = τNR τNR
(6)
where the second formula in Eq. (6) has been derived from Eq. (5). Therefore, the radiative recombination rate from S, RS , Eq.
G 1 + BN0 τSi − BRS τS τSi
(8)
If we substitute the term of RS in Eq. (8) from its analytical form as shown in Eq. (7), Eq. (8) can be written as: τS R2Si (BτSi τS ) + RSi (1 + BN0 τSi ) 1 + − BGτSi τS τNR τS =0 (9) −G 1 + τNR The above formula is a quadratic equation in terms of RSi . Solving Eq. (9), we have found the solution: −AB + Γ + A2 B 2 + Γ 2 − 2Γ [B (A − 2)] RSi = G (10) 2Γ where A = 1 + BN0 τSi τS B = 1 + τNR
(11)
Γ = BGτSi τS
(13)
(12)
derive from Eq. (9). Substituting the solution RSi from Eqs. (10) to (7), we obtain: ( − AB + Γ + A2 B + Γ 2 − 2Γ [B (A− 2)])A− 2Γ G RS = (−AB + Γ + AB 2 + Γ 2 − 2Γ [B (A − 2)])Γ (14) where A, B and Γ come from Eqs. (11)–(13). The total radiative recombination rate which is the sum of the radiative recombination rates from Si and S is given by the sum of Eqs. (10) and (14): Rtot −AB + Γ +
A2 B 2 Γ 2 − 2Γ [B (A − 2)] G 2Γ (−AB + Γ + A2 B 2 + Γ 2 − 2Γ [B (A − 2)])A − 2Γ + G (−AB + Γ + A2 B 2 + Γ 2 − 2Γ [B (A − 2)])Γ (15)
=
In Eqs. (10), (14) and (15) the radiative recombination rates for Si, S and total (RSi , RS and Rtot , respectively) are equivalent to the integrated intensities that we have measured in our experimental results (Fig. 4(a)), and the generation rate G is proportional to the applied current. The values of the dimensionless parameters of our model used are listed in Table 1. Thus, using Eqs. (10)–(15) and the values from Table 1 we can plot the radiative recombination rates for Si, S and the total, RSi , RS , and Rtot ,
S.F. Galata et al. / Materials Science and Engineering B 124–125 (2005) 435–439 Table 1 List of the model parameters used for the fits shown in Fig. 4(b) Dimensionless fitting parameters
Values
A B Γ
8 2 0–5000
The parameters are defined in the text.
respectively, as a function of the generation rate G. In Fig. 4(b), we compare this with the experimental values abstracted from Fig. 4(a) as a function of applied current. We can see that our model accurately describes the experimental behaviour. In addition, as observed in Fig. 4(b), at low injection currents, the total integrated intensity trend is closely linear. This indicates that at low currents the emission results from competition between the sulphur and silicon centres only. 4. Conclusions In this paper, we have shown the effect of injection condition on silicon and sulphur emission. It is observed that the sulphurintegrated intensity is increasing sublinearly whereas the silicon integrated intensity is increasing superlinearly with the increase
439
of injection condition. We provided a model explaining the current dependence experiments which showed that there are two major radiative routes via the silicon and the sulphur that take place, which are competing at each other along with a nonradiative route coming from the sulphur-related level. Our model provides a good match to the behaviour of our experimental data. References [1] L. Pavesi, J. Phys. Condens. Matter 15 (2003) R1169. [2] M.A. Lourenc¸o, W.L. Ng, G. Shao, R.M. Gwilliam, K.P. Homewood, SPIE Proc. 4654 (2002) 138. [3] T.G. Brown, D.G. Hall, Appl. Phys. Lett. 49 (1986) 245. [4] T.G. Brown, P.L. Bradfield, D.G. Hall, Appl. Phys. Lett. 51 (1986) 1585. [5] P.L. Bradfield, T.G. Brown, D.G. Hall, Appl. Phys. Lett. 55 (1989) 100. [6] W.L. Ng, M.A. Lourenc¸o, R.M. Gwilliam, S. Ledain, G. Shao, K.P. Homewood, Nature 410 (2001) 192. [7] J.P. Hirth, J. Lothe, Theory of Dislocations, second ed., John Wiley & Sons, 1968. [8] M.A. Lourenc¸o, M.S. Siddiqui, G. Shao, R.M. Gwilliam, K.P. Homewood, in: L. Pavesi, et al. (Eds.), in: Towards the First Silicon Laser, Kluwer Academic Publishers, The Netherlands, 2003, p. 11. [9] M.A. Lourenc¸o, M. Milosavljevic, S. Galata, M.S. A. Siddiqui, G. Shao, R.M. Gwilliam, K.P. Homewood, Vacuum, in press. [10] W. Rosenweig, W.H. Hackett, J.S. Jayson, J. Appl. Phys. 40 (1969) 4477.