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Si(001) interfaces
Materials Science in Semiconductor Processing 3 (2000) 85±89
Segregation of phosphorus to SiO2/Si(001) interfaces J. Da° browski a,*, H.-J. MuÈssig a, R. Baierle b, M.J. Caldas c, V. Zavodinsky d a
IHP GmbH, Im Technologiepark 25, D-15236 Frankfurt (Oder), Germany Departamento de Fisica, Universidade Federal de Santa Maria, 9711030, Santa Maria, RG, Brazil c Instituto de Fisica da Universidade de SaÄo Paulo, 05508-900, SaÄo Paulo, Brazil d Institute for Automation and Control Processes, 5 Radio Str., Vladivostok, 690041, Russia
b
Abstract Dopant atoms segregate to SiO2/Si(001) interfaces. This causes problems during manufacture of submicron microelectronic devices. On the basis of ab initio calculations, we identify the physical mechanism by which P atoms are trapped and deactivated at SiO2/Si(001). We argue that segregation can occur to defected as well as to defectfree interfaces. In the latter case, the interfacial stress stabilizes pairs of threefold-coordinated phosphorus atoms. Implications for Complementary Metal-Oxide-Semiconductor (CMOS) process design are discussed. 7 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction A typical feature of CMOS technology is that SiO2 is placed next to doped regions of silicon [1]. Segregation to SiO2/Si(001) interfaces causes signi®cant redistribution of dopant atoms [2]. As much as 50% of the implanted dopants can be lost during the pad oxide etch [3]. Changes in the dopant pro®le below gate oxides can aect threshold voltage by 50% [4]. The interface can collect at least 3 1014/cm2 dopant atoms, that is, nearly a monolayer (1 ML=7 1014/ cm2). The segregated atoms are deactivated. In the literature, these issues have been so far treated on a phenomenological level. Details of dopant-interface interactions are unknown. It is unclear what causes the segregation, what are the atomic and electronic structures of the segregated donors, and what are their
* Corresponding author. Tel.: +49-335-5625-316; fax: +49335-5625-651. E-mail address: jarek@ihp-o.de (J. Da° browski).
energies. A simple but physically correct description of the segregation mechanism would facilitate modeling of technological processes [2]. The purpose of this work is to provide fundamental insight into the physics of dopant segregation by ab initio studies of a typical donor, phosphorus. The existing models used to simulate the segregation [5±9] assume that the interface has a ®xed number (01 ML) of sites at which dopant atoms can be trapped. Such a high number of traps is surprising, at least for P and As donors, because chemical bonds between atoms of these species and oxygen are weaker than between Si and oxygen, that is, P and As are not expected to be ``chemisorbed'' at the interface by substituting interfacial silicon. Moreover, 1 ML of trapping sites appears to be inconsistent with the measured dependence of the dose loss on the implanted P dose (``traps only'', Fig. 1(a)). This inconsistency indicates that such models would fail when the dopant concentration changes strongly along the interface (as under oxide sidewalls in MOS transistors), even though they work over a limited concentration range.
1369-8001/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 9 - 8 0 0 1 ( 0 0 ) 0 0 0 1 4 - 7
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J. Da° browski et al. / Materials Science in Semiconductor Processing 3 (2000) 85±89
pairing dominates at high implanted doses (above approximately 1014/cm2); trapping at defects prevails at low doses (below approximately 1013/cm2). 3. At high implant doses (pairing regime), the segregation coecient S is expected to decrease exponentially with the interfacial stress, due to a decrease in the binding energy of the pairs. Dose losses after source/drain implantation should thus be minimal, if the surface passivation ®lm is stress-relaxed. 4. The pairing causes a nonlinear enhancement of segregation at dopant concentrations above a few times 1018 cmÿ2. Simulations of 2-D pro®les under the oxide must take this eect into account.
Fig. 1. Dopant pairing and dose loss. Thin lines: trapping only. Thick solid lines: pairing and trapping. Broken lines: contributions from pairing (thick) and trapping (thin). (a) Dependence of P dose loss Nd on P implant dose N, SIMS data [3]. If traps only are accounted for, the functional dependence is qualitatively incorrect. Pairing and traps together give an excellent ®t. It is assumed that the number of P atoms diused to the interface is proportional to the implant dose. (b) Dependence of P dose loss Nd on P concentration CP close to the interface, SIMS data [10,8]. The trap-dominated (low CP) and pairing-dominated (high Nd) regimes are clearly visible.
Here, we formulate, verify, and discuss a general segregation model based on ab initio calculations and AugerElectron Spectroscopy (AES) measurements, and on analysis of published SIMS data. We use segregation of P as a case study. Our primary results are as follows. 1. Mechanical strain promotes pairing and deactivation of dopants. 2. Contrary to the common view, high- and low-coverage segregations are qualitatively dierent. Dopant 1
Car-Parrinello
type
of
pseudopotential
calculations,
fhi96md code [11] with Local Density Approximation
(LDA) after Ceplerley and Alder [12] in the parameterization of Perdew and Zunger [13], and nonlocal pseudopotentials [14,21] in Kleinman±Bylander form [15]. Si(001)-type supercells with lateral dimensions 2 2 to 4 4, typically six to eight Si layers and a single oxide layer with various boundary conditions described in the text. Convergence: 40 Ry cuto for plane waves, tests between 16 Ry and 40 Ry; Brillouin zone sampled at the points equivalent to (1/4, 1/4) point of the fully symmetric 4 4 surface cell, test done at G and (1/4, 1/4) points from 4 4, 3 3, and 2 2 cells.
This paper begins with a brief description of the numerical approach and remarks on the accuracy of the calculations (Section 2). Section 3 introduces the atomic geometries considered in this work. Section 4 formulates the segregation mechanism. The concluding Section 5 comments on the practical implications of our ®ndings.
2. Approach, approximations, and accuracy The calculations were done by a standard ab initio supercell approach.1 The reliability of the results was veri®ed through comparison with optimized geometries, electronic structures, and energy dierences for test silicon-oxygen and silicon-oxygen-phosphorus structures computed with other ab initio codes (full-potential LMTO code [16] and LCAO-based ab initio pseudopotential code [17]) and with energy dierences obtained by a semi-empirical method applied to clusters of roughly the same size as the supercells. We estimate that the numerical accuracy for energy dierences between two atomic geometries associated with the same interface model is 00.1±0.2 eV per unit cell1. The accuracy of binding energies is 00.1±0.2 eV per bonded atom in the complex. The numerical error is dominated by k-point sampling, small distance between defects in the neighboring supercells, and the LDA band-gap problem. The latter aects energy dierences and binding energies when defects with deactivated donor atoms are compared to a substitutional donor. A band-gap correction was employed in such cases.
3. Microscopic models The atomic geometries addressed in this work include (a) several models of the interface, (b) phosphorus atoms placed in various con®gurations at or near the interface, and (c) P atoms bonded in bulk-like defect complexes with and without oxygen. The bulk
J. Da° browski et al. / Materials Science in Semiconductor Processing 3 (2000) 85±89
defects were considered in order to verify the possibility that phosphorus is bonded below the interface in complexes containing P and O atoms. Moreover, the comparison between energies of certain defects in the bulk and under the interface provided an internal consistency test of our segregation model. The details of these calculations will be given in a separate publication. Here, we focus on the hitherto unexpected eect of dopant pairing below the interface. The interfacial atomic structures (Fig. 2) were designed in such a way that as few atoms as possible represented the key features of the interface. These models were then systematically expanded towards increasingly realistic geometries. The fundamental geometry is built on the basis of a bulk Si(001) 1 1 8 cell with two oxygen atoms inserted into Si0Si bonds in one of the (001) planes (Fig. 2(a)). The resulting SiOSi sandwich is stretched along the (001) axis to accommodate the compressive stress created by the insertion of oxygen. This makes a crude model of an amorphous SiO2/Si(001) interface: each interfacial Si atom of the substrate has two O neighbors. There is no real SiO2 in this system, but since phosphorus atoms are expelled from SiO2 into silicon and since Si0O bonds are much stronger (stier) than Si0Si bonds, this numerically ecient model reasonably simulates an interface-like environment for exploratory studies of the interaction between phosphorus, oxygen, and silicon atoms. We found that at least two atomic con®gurations allow covering any SiO2/Si(001) interface with nearly a full monolayer of P (Fig. 3). These structures involve no pre-existing defects, neither in Si nor in SiO2/ Si(001). Each of them is built on the basis of two threefold-coordinated, electrically neutral P atoms (Fig. 3). One of these complexes (Fig. 3(a)) employs a
87
local rearrangement of Si lattice bonds which we name ``{113} rebonding'' [18]. The geometry of {113}rebonded atoms is analogous to the atomic con®guration which is temporarily acquired near the barrier along the concerted-exchange path of Si self-diusion [19]. The other structure is simply a distorted nearestneighbor PP pair (Fig. 3(b)). These complexes are unstable in the bulk. But they are stabilized next to the interface, with the binding energy 00.5 eV/defect in intrinsic material and 01 eV/ defect in n-type material. The stabilization takes place because the oxide helps to accommodate the stress caused by the deformation of the bonds around the defects and because the removal of a substrate bond makes the network more ¯exible, assisting in the relaxation of the interfacial stress. 4. Segregation mechanism Our reasoning which leads to the mechanism of the dopant segregation is as follows. First, our ab initio calculations and AES measurements through native oxides show that phosphorus atoms avoid oxygen bonds. This indicates that a monolayer of traps is unlikely and is also consistent with the fact that phosphorus is expelled from SiO2 during thermal oxidation of silicon. However, it is clear that certain interfacial defects can trap and deactivate phosphorus. This happens when a P atom replaces an interfacial Si which has a dangling bond and is not bonded to oxygen. Such trapping resembles trapping and deactivation of P at free surfaces or at silicon vacancies in the bulk Si. Second, the calculations show that phosphorus atoms pair under SiO2/Si(001). The energy gain is Es 20.5 eV/ defect in intrinsic and 01.0 eV/defect in n-type ma-
Fig. 2. Classes of idealized models of the SiO2/Si(001) interface. The most important dierences between these classes are: (1) the boundary conditions perpendicular to the interface; (2) the arrangement of substrate Si atoms in the interfacial layer; and (3) the degree of relaxation in the oxide. (a) Oxide layer sandwiched between bulklike Si slabs. Models of this type simulate high stress in the oxide. (b) The opposite extreme: the oxide is substituted by a free silicon dihydride surface. The interface is very soft and there is virtually no lateral stress on the ``oxide'' side. (c) The oxide surface is terminated by H, the interface may be dimerized.
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terial. Third, we use a thermodynamical model to estimate the dependence of the segregated dose Nd on the concentration CP of active phosphorus under the interface. For this purpose, we assume that: 1. N0 deactivation sites exist under the interface. 2. Dopant atoms can be deactivated by pairing or trapping. 3. The corresponding reaction constants are thermally activated. 4. The active and inactive dopants under the interface are in quasi-equilibrium. ``Quasi-equilibrium'' means here that activation rates =deactivation rates. This leads to Nd
N0 C P2 C B exp ÿEs =kT 2 P
2
1
when segregation is dominated by pairing and to the usual Nd
N0 C P CP B exp ÿEs =kT
2
when trapping dominates. Es is here the segregation energy and B corresponds to the reaction constant. Analysis of the literature data in terms of this simple model veri®es the plausibility of the segregation mechanism proposed in this work. Indeed, our predictions compare favorably with the published data (Fig. 1). The Nd(CP) dependence is recovered for the whole dopant concentration range under the gate and sidewall oxides in MOS transistors. The segregation energy due to pairing is 00.6 eV/defect from Fig. 1 (800 and 9008C) and from the data in Ref. [20] (10008C, not shown), the segregation energy due to trapping is 01.3 eV. These values are close to our
ab initio estimates for pairing and trapping of phosphorus at broken bond sites, respectively. The density of ``deactivating sites'' of N0 for pairing corresponds to a monolayer, while N0 for trapping is 03 1013/ cm2, which is about 10 times more than the typical number of electrically active interfacial defects. This indicates that such defects as nonstoichiometric sites (Si0Si bridges) may act as dopant traps. Alternatively, some phosphorus atoms may be trapped by silicon vacancies which were created during implantation of dopants and afterwards migrated towards the interface. In order to account for 03 1013/cm2 trapping sites (5% of a monolayer, or 0.05 ML), one needs approximately 0.01 ML vacant sites (each vacancy can trap up to four P atoms). Assuming that these vacancies are localized between one to ®ve atomic layers below the interface, the volume concentration of the segregated vacancies must be around 5±1 1020 cmÿ3. Calculations verifying the stability of such a high vacancy concentration under SiO2/Si(001) are in progress. Our analysis indicates that any predictive simulation model which attempts to describe the segregation coef®cient for P concentrations around 1018 cmÿ3 must account for the dopant pairing. The coexistence of pairing and trapping causes a two-regime dependence of the segregation coecient on the implant dose (Fig. 1(b)). High- and low-coverage segregation are qualitatively dierent. At high implant doses, the segregation coecient S is expected to decrease exponentially with the interfacial stress, because the stress aects the segregation energy. At low doses, S is proportional to the interfacial defect density. The interface has much less than 1 ML of defect-related dopant traps, as expected of a high-quality boundary between two materials.
Fig. 3. Generic structures of phosphorus (black) trapped and deactivated under SiO2/Si(001). The phosphorus atoms of these P2 complexes are deactivated (electrically neutral). (a) The dashed Si atom and its P neighbor form a pair of {113}-rebonded lattice atoms. (b) Threefold-coordinated P atoms of a distorted nearest-neighbor P2 pair.
J. Da° browski et al. / Materials Science in Semiconductor Processing 3 (2000) 85±89
5. Summary and conclusions We presented results of an ab initio study of dopant segregation to SiO2/Si(001) interfaces. A simple and physically plausible model of the segregation of P atoms was formulated. The general implications of our work are: 1. Dopants will segregate to the interface with any dielectric (not only SiO2) that introduces interfacial strain. 2. High dose losses are intrinsically nonlinear. 3. Since P0O bonds are unfavorable, dose loss might be reduced by an etch that does not remove surface P.
Acknowledgements We are grateful to S. Dunham, A. Fischer, P. Masri, and A. Ourmazd for helpful discussions, and R. Casali for doing test calculations with the LMTO code. This study was partially supported by the Deutsche Forschungsgemainschaft (DFG) project Nr. DA 308/5-1. The calculations were made possible by a grant of Cray T3E computer time by the von Neumann Institute for Computing (NIC) in JuÈlich, Germany. References [1] Sze SM. Physics of semiconductor devices. 2nd ed. Wiley, 1981. [2] Da° browski J, MuÈssig HJ, Duane M, Dunham ST, Goossens R, Vuong H-H. Basic science and challenges in process simulation. Adv Sol State Phys 1999;38:565 PostScript ®le available at http://www.ihp-o.de/chipps/ 97/Ddoc/dpg.html. [3] Grin PB, Crowder SW, Knight JM. Dose loss in phosphorus implants due to transient diusion and interface segregation. Appl Phys Lett 1995;67:482. [4] Vuong H-H, Raerty CS, Eshraghi SA, Lentz JL, Zeitzo PM, Pinto MR, Hillenius SJ. Eects of oxide interface traps and transient enhanced diusion on the process modeling of pMOS devices. IEEE Trans ED 1996;43:1144. [5] Orlowski M. New model for dopant redistribution at surfaces. Appl Phys Lett 1989;55:1762.
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[6] Sakamoto H, Kumashiro S. A new diusion algorithm during oxidation which can handle both P pile-up and B segregation at Si±SiO2 interface, SISPAD, 97, 81 1997. [7] Vuong H-H, Raerty CS, McMacken JR, Ning J, Chaudhry S. Modeling of the eect of P dose loss at the SiO2 interface on CMOS device characteristics, SISPAD, 97, 85 1997. [8] Vuong H-H, Raerty CS, Ning J, McMacken JR, McKinley J, Stevie DA. Modeling of the trapping and de-trapping of P at the Si to SiO2 interface, SISPAD, 98, 380 1998. [9] Kasnavi R, Grin PB, Plummer JD. Dynamics of arsenic dose loss at the SiO2 interface during TED, SISPAD, 98, 48 1998. [10] Lau F, Mader L, Mazure C, Werner Ch, Orlowski M. A model for phosphorus segregation at the Si/SiO2 interface. Appl Phys A 1989;49:671. [11] Bockstedte M, Kley A, Neugebauer J, Scheer M. DFT calculations for poly-atomic systems: electronic structure, static and elastic properties and ab initio molecular dynamics. Comp Phys Commun 1997;107:187. [12] Ceperley DM, Alder BJ. Ground state of the electron gas by a stochastic method. Phys Rev Lett 1980;45:567. [13] Perdew JP, Zunger A. Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev 1981;B23:5048. [14] Hamann DR. Generalized norm-conserving pseudopotentials. Phys Rev 1982;B40:2980. [15] Kleinman L, Bylander DM. Ecacious form for model pseudopotentials. Phys Rev Lett 1982;48:1425. [16] Bott E, Methfessel M, Krabs W, Schmidt PC. Nonsingular Hankel functions as a new basis for electronic structure calculations. J Mat Phys 1998;39 M. Methfessel, NFP manual, IHP Copyright, 1997. [17] Sanchez-Portal D, Ordejon P, Artacho E, Soler JM. Density-functional method for very large systems with LCAO basis-set. Int J Quantum Chem 1997;65:453. [18] Da° browski J, MuÈssig H-J, Wol G, Hinrich S. Surface reconstruction suggests a nucleation mechanism in bulk: Sb/Si(113) and {113} planar defects. Surf Sci 1998;411:54. [19] Pandey KC. Diusion without vacancies or interstitials: a new concerted exchange mechanism. Phys Rev Lett 1986;57:2287. [20] Sato Y, Watanabe M, Imai K. Characterization of phosphorus pile-up at the SiO2/Si interface. J Electrochem Soc 1993;140:2679. [21] Bachelet GB, Hamann DR, SchluÈter MA. Pseudopotentials that work: from H to Pu. Phys Rev 1982;B26:4199.
Segregation of phosphorus to SiO2/Si(001) interfaces J. Da° browski a,*, H.-J. MuÈssig a, R. Baierle b, M.J. Caldas c, V. Zavodinsky d a
IHP GmbH, Im Technologiepark 25, D-15236 Frankfurt (Oder), Germany Departamento de Fisica, Universidade Federal de Santa Maria, 9711030, Santa Maria, RG, Brazil c Instituto de Fisica da Universidade de SaÄo Paulo, 05508-900, SaÄo Paulo, Brazil d Institute for Automation and Control Processes, 5 Radio Str., Vladivostok, 690041, Russia
b
Abstract Dopant atoms segregate to SiO2/Si(001) interfaces. This causes problems during manufacture of submicron microelectronic devices. On the basis of ab initio calculations, we identify the physical mechanism by which P atoms are trapped and deactivated at SiO2/Si(001). We argue that segregation can occur to defected as well as to defectfree interfaces. In the latter case, the interfacial stress stabilizes pairs of threefold-coordinated phosphorus atoms. Implications for Complementary Metal-Oxide-Semiconductor (CMOS) process design are discussed. 7 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction A typical feature of CMOS technology is that SiO2 is placed next to doped regions of silicon [1]. Segregation to SiO2/Si(001) interfaces causes signi®cant redistribution of dopant atoms [2]. As much as 50% of the implanted dopants can be lost during the pad oxide etch [3]. Changes in the dopant pro®le below gate oxides can aect threshold voltage by 50% [4]. The interface can collect at least 3 1014/cm2 dopant atoms, that is, nearly a monolayer (1 ML=7 1014/ cm2). The segregated atoms are deactivated. In the literature, these issues have been so far treated on a phenomenological level. Details of dopant-interface interactions are unknown. It is unclear what causes the segregation, what are the atomic and electronic structures of the segregated donors, and what are their
* Corresponding author. Tel.: +49-335-5625-316; fax: +49335-5625-651. E-mail address: jarek@ihp-o.de (J. Da° browski).
energies. A simple but physically correct description of the segregation mechanism would facilitate modeling of technological processes [2]. The purpose of this work is to provide fundamental insight into the physics of dopant segregation by ab initio studies of a typical donor, phosphorus. The existing models used to simulate the segregation [5±9] assume that the interface has a ®xed number (01 ML) of sites at which dopant atoms can be trapped. Such a high number of traps is surprising, at least for P and As donors, because chemical bonds between atoms of these species and oxygen are weaker than between Si and oxygen, that is, P and As are not expected to be ``chemisorbed'' at the interface by substituting interfacial silicon. Moreover, 1 ML of trapping sites appears to be inconsistent with the measured dependence of the dose loss on the implanted P dose (``traps only'', Fig. 1(a)). This inconsistency indicates that such models would fail when the dopant concentration changes strongly along the interface (as under oxide sidewalls in MOS transistors), even though they work over a limited concentration range.
1369-8001/00/$ - see front matter 7 2000 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 9 - 8 0 0 1 ( 0 0 ) 0 0 0 1 4 - 7
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J. Da° browski et al. / Materials Science in Semiconductor Processing 3 (2000) 85±89
pairing dominates at high implanted doses (above approximately 1014/cm2); trapping at defects prevails at low doses (below approximately 1013/cm2). 3. At high implant doses (pairing regime), the segregation coecient S is expected to decrease exponentially with the interfacial stress, due to a decrease in the binding energy of the pairs. Dose losses after source/drain implantation should thus be minimal, if the surface passivation ®lm is stress-relaxed. 4. The pairing causes a nonlinear enhancement of segregation at dopant concentrations above a few times 1018 cmÿ2. Simulations of 2-D pro®les under the oxide must take this eect into account.
Fig. 1. Dopant pairing and dose loss. Thin lines: trapping only. Thick solid lines: pairing and trapping. Broken lines: contributions from pairing (thick) and trapping (thin). (a) Dependence of P dose loss Nd on P implant dose N, SIMS data [3]. If traps only are accounted for, the functional dependence is qualitatively incorrect. Pairing and traps together give an excellent ®t. It is assumed that the number of P atoms diused to the interface is proportional to the implant dose. (b) Dependence of P dose loss Nd on P concentration CP close to the interface, SIMS data [10,8]. The trap-dominated (low CP) and pairing-dominated (high Nd) regimes are clearly visible.
Here, we formulate, verify, and discuss a general segregation model based on ab initio calculations and AugerElectron Spectroscopy (AES) measurements, and on analysis of published SIMS data. We use segregation of P as a case study. Our primary results are as follows. 1. Mechanical strain promotes pairing and deactivation of dopants. 2. Contrary to the common view, high- and low-coverage segregations are qualitatively dierent. Dopant 1
Car-Parrinello
type
of
pseudopotential
calculations,
fhi96md code [11] with Local Density Approximation
(LDA) after Ceplerley and Alder [12] in the parameterization of Perdew and Zunger [13], and nonlocal pseudopotentials [14,21] in Kleinman±Bylander form [15]. Si(001)-type supercells with lateral dimensions 2 2 to 4 4, typically six to eight Si layers and a single oxide layer with various boundary conditions described in the text. Convergence: 40 Ry cuto for plane waves, tests between 16 Ry and 40 Ry; Brillouin zone sampled at the points equivalent to (1/4, 1/4) point of the fully symmetric 4 4 surface cell, test done at G and (1/4, 1/4) points from 4 4, 3 3, and 2 2 cells.
This paper begins with a brief description of the numerical approach and remarks on the accuracy of the calculations (Section 2). Section 3 introduces the atomic geometries considered in this work. Section 4 formulates the segregation mechanism. The concluding Section 5 comments on the practical implications of our ®ndings.
2. Approach, approximations, and accuracy The calculations were done by a standard ab initio supercell approach.1 The reliability of the results was veri®ed through comparison with optimized geometries, electronic structures, and energy dierences for test silicon-oxygen and silicon-oxygen-phosphorus structures computed with other ab initio codes (full-potential LMTO code [16] and LCAO-based ab initio pseudopotential code [17]) and with energy dierences obtained by a semi-empirical method applied to clusters of roughly the same size as the supercells. We estimate that the numerical accuracy for energy dierences between two atomic geometries associated with the same interface model is 00.1±0.2 eV per unit cell1. The accuracy of binding energies is 00.1±0.2 eV per bonded atom in the complex. The numerical error is dominated by k-point sampling, small distance between defects in the neighboring supercells, and the LDA band-gap problem. The latter aects energy dierences and binding energies when defects with deactivated donor atoms are compared to a substitutional donor. A band-gap correction was employed in such cases.
3. Microscopic models The atomic geometries addressed in this work include (a) several models of the interface, (b) phosphorus atoms placed in various con®gurations at or near the interface, and (c) P atoms bonded in bulk-like defect complexes with and without oxygen. The bulk
J. Da° browski et al. / Materials Science in Semiconductor Processing 3 (2000) 85±89
defects were considered in order to verify the possibility that phosphorus is bonded below the interface in complexes containing P and O atoms. Moreover, the comparison between energies of certain defects in the bulk and under the interface provided an internal consistency test of our segregation model. The details of these calculations will be given in a separate publication. Here, we focus on the hitherto unexpected eect of dopant pairing below the interface. The interfacial atomic structures (Fig. 2) were designed in such a way that as few atoms as possible represented the key features of the interface. These models were then systematically expanded towards increasingly realistic geometries. The fundamental geometry is built on the basis of a bulk Si(001) 1 1 8 cell with two oxygen atoms inserted into Si0Si bonds in one of the (001) planes (Fig. 2(a)). The resulting SiOSi sandwich is stretched along the (001) axis to accommodate the compressive stress created by the insertion of oxygen. This makes a crude model of an amorphous SiO2/Si(001) interface: each interfacial Si atom of the substrate has two O neighbors. There is no real SiO2 in this system, but since phosphorus atoms are expelled from SiO2 into silicon and since Si0O bonds are much stronger (stier) than Si0Si bonds, this numerically ecient model reasonably simulates an interface-like environment for exploratory studies of the interaction between phosphorus, oxygen, and silicon atoms. We found that at least two atomic con®gurations allow covering any SiO2/Si(001) interface with nearly a full monolayer of P (Fig. 3). These structures involve no pre-existing defects, neither in Si nor in SiO2/ Si(001). Each of them is built on the basis of two threefold-coordinated, electrically neutral P atoms (Fig. 3). One of these complexes (Fig. 3(a)) employs a
87
local rearrangement of Si lattice bonds which we name ``{113} rebonding'' [18]. The geometry of {113}rebonded atoms is analogous to the atomic con®guration which is temporarily acquired near the barrier along the concerted-exchange path of Si self-diusion [19]. The other structure is simply a distorted nearestneighbor PP pair (Fig. 3(b)). These complexes are unstable in the bulk. But they are stabilized next to the interface, with the binding energy 00.5 eV/defect in intrinsic material and 01 eV/ defect in n-type material. The stabilization takes place because the oxide helps to accommodate the stress caused by the deformation of the bonds around the defects and because the removal of a substrate bond makes the network more ¯exible, assisting in the relaxation of the interfacial stress. 4. Segregation mechanism Our reasoning which leads to the mechanism of the dopant segregation is as follows. First, our ab initio calculations and AES measurements through native oxides show that phosphorus atoms avoid oxygen bonds. This indicates that a monolayer of traps is unlikely and is also consistent with the fact that phosphorus is expelled from SiO2 during thermal oxidation of silicon. However, it is clear that certain interfacial defects can trap and deactivate phosphorus. This happens when a P atom replaces an interfacial Si which has a dangling bond and is not bonded to oxygen. Such trapping resembles trapping and deactivation of P at free surfaces or at silicon vacancies in the bulk Si. Second, the calculations show that phosphorus atoms pair under SiO2/Si(001). The energy gain is Es 20.5 eV/ defect in intrinsic and 01.0 eV/defect in n-type ma-
Fig. 2. Classes of idealized models of the SiO2/Si(001) interface. The most important dierences between these classes are: (1) the boundary conditions perpendicular to the interface; (2) the arrangement of substrate Si atoms in the interfacial layer; and (3) the degree of relaxation in the oxide. (a) Oxide layer sandwiched between bulklike Si slabs. Models of this type simulate high stress in the oxide. (b) The opposite extreme: the oxide is substituted by a free silicon dihydride surface. The interface is very soft and there is virtually no lateral stress on the ``oxide'' side. (c) The oxide surface is terminated by H, the interface may be dimerized.
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J. Da° browski et al. / Materials Science in Semiconductor Processing 3 (2000) 85±89
terial. Third, we use a thermodynamical model to estimate the dependence of the segregated dose Nd on the concentration CP of active phosphorus under the interface. For this purpose, we assume that: 1. N0 deactivation sites exist under the interface. 2. Dopant atoms can be deactivated by pairing or trapping. 3. The corresponding reaction constants are thermally activated. 4. The active and inactive dopants under the interface are in quasi-equilibrium. ``Quasi-equilibrium'' means here that activation rates =deactivation rates. This leads to Nd
N0 C P2 C B exp ÿEs =kT 2 P
2
1
when segregation is dominated by pairing and to the usual Nd
N0 C P CP B exp ÿEs =kT
2
when trapping dominates. Es is here the segregation energy and B corresponds to the reaction constant. Analysis of the literature data in terms of this simple model veri®es the plausibility of the segregation mechanism proposed in this work. Indeed, our predictions compare favorably with the published data (Fig. 1). The Nd(CP) dependence is recovered for the whole dopant concentration range under the gate and sidewall oxides in MOS transistors. The segregation energy due to pairing is 00.6 eV/defect from Fig. 1 (800 and 9008C) and from the data in Ref. [20] (10008C, not shown), the segregation energy due to trapping is 01.3 eV. These values are close to our
ab initio estimates for pairing and trapping of phosphorus at broken bond sites, respectively. The density of ``deactivating sites'' of N0 for pairing corresponds to a monolayer, while N0 for trapping is 03 1013/ cm2, which is about 10 times more than the typical number of electrically active interfacial defects. This indicates that such defects as nonstoichiometric sites (Si0Si bridges) may act as dopant traps. Alternatively, some phosphorus atoms may be trapped by silicon vacancies which were created during implantation of dopants and afterwards migrated towards the interface. In order to account for 03 1013/cm2 trapping sites (5% of a monolayer, or 0.05 ML), one needs approximately 0.01 ML vacant sites (each vacancy can trap up to four P atoms). Assuming that these vacancies are localized between one to ®ve atomic layers below the interface, the volume concentration of the segregated vacancies must be around 5±1 1020 cmÿ3. Calculations verifying the stability of such a high vacancy concentration under SiO2/Si(001) are in progress. Our analysis indicates that any predictive simulation model which attempts to describe the segregation coef®cient for P concentrations around 1018 cmÿ3 must account for the dopant pairing. The coexistence of pairing and trapping causes a two-regime dependence of the segregation coecient on the implant dose (Fig. 1(b)). High- and low-coverage segregation are qualitatively dierent. At high implant doses, the segregation coecient S is expected to decrease exponentially with the interfacial stress, because the stress aects the segregation energy. At low doses, S is proportional to the interfacial defect density. The interface has much less than 1 ML of defect-related dopant traps, as expected of a high-quality boundary between two materials.
Fig. 3. Generic structures of phosphorus (black) trapped and deactivated under SiO2/Si(001). The phosphorus atoms of these P2 complexes are deactivated (electrically neutral). (a) The dashed Si atom and its P neighbor form a pair of {113}-rebonded lattice atoms. (b) Threefold-coordinated P atoms of a distorted nearest-neighbor P2 pair.
J. Da° browski et al. / Materials Science in Semiconductor Processing 3 (2000) 85±89
5. Summary and conclusions We presented results of an ab initio study of dopant segregation to SiO2/Si(001) interfaces. A simple and physically plausible model of the segregation of P atoms was formulated. The general implications of our work are: 1. Dopants will segregate to the interface with any dielectric (not only SiO2) that introduces interfacial strain. 2. High dose losses are intrinsically nonlinear. 3. Since P0O bonds are unfavorable, dose loss might be reduced by an etch that does not remove surface P.
Acknowledgements We are grateful to S. Dunham, A. Fischer, P. Masri, and A. Ourmazd for helpful discussions, and R. Casali for doing test calculations with the LMTO code. This study was partially supported by the Deutsche Forschungsgemainschaft (DFG) project Nr. DA 308/5-1. The calculations were made possible by a grant of Cray T3E computer time by the von Neumann Institute for Computing (NIC) in JuÈlich, Germany. References [1] Sze SM. Physics of semiconductor devices. 2nd ed. Wiley, 1981. [2] Da° browski J, MuÈssig HJ, Duane M, Dunham ST, Goossens R, Vuong H-H. Basic science and challenges in process simulation. Adv Sol State Phys 1999;38:565 PostScript ®le available at http://www.ihp-o.de/chipps/ 97/Ddoc/dpg.html. [3] Grin PB, Crowder SW, Knight JM. Dose loss in phosphorus implants due to transient diusion and interface segregation. Appl Phys Lett 1995;67:482. [4] Vuong H-H, Raerty CS, Eshraghi SA, Lentz JL, Zeitzo PM, Pinto MR, Hillenius SJ. Eects of oxide interface traps and transient enhanced diusion on the process modeling of pMOS devices. IEEE Trans ED 1996;43:1144. [5] Orlowski M. New model for dopant redistribution at surfaces. Appl Phys Lett 1989;55:1762.
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[6] Sakamoto H, Kumashiro S. A new diusion algorithm during oxidation which can handle both P pile-up and B segregation at Si±SiO2 interface, SISPAD, 97, 81 1997. [7] Vuong H-H, Raerty CS, McMacken JR, Ning J, Chaudhry S. Modeling of the eect of P dose loss at the SiO2 interface on CMOS device characteristics, SISPAD, 97, 85 1997. [8] Vuong H-H, Raerty CS, Ning J, McMacken JR, McKinley J, Stevie DA. Modeling of the trapping and de-trapping of P at the Si to SiO2 interface, SISPAD, 98, 380 1998. [9] Kasnavi R, Grin PB, Plummer JD. Dynamics of arsenic dose loss at the SiO2 interface during TED, SISPAD, 98, 48 1998. [10] Lau F, Mader L, Mazure C, Werner Ch, Orlowski M. A model for phosphorus segregation at the Si/SiO2 interface. Appl Phys A 1989;49:671. [11] Bockstedte M, Kley A, Neugebauer J, Scheer M. DFT calculations for poly-atomic systems: electronic structure, static and elastic properties and ab initio molecular dynamics. Comp Phys Commun 1997;107:187. [12] Ceperley DM, Alder BJ. Ground state of the electron gas by a stochastic method. Phys Rev Lett 1980;45:567. [13] Perdew JP, Zunger A. Self-interaction correction to density-functional approximations for many-electron systems. Phys Rev 1981;B23:5048. [14] Hamann DR. Generalized norm-conserving pseudopotentials. Phys Rev 1982;B40:2980. [15] Kleinman L, Bylander DM. Ecacious form for model pseudopotentials. Phys Rev Lett 1982;48:1425. [16] Bott E, Methfessel M, Krabs W, Schmidt PC. Nonsingular Hankel functions as a new basis for electronic structure calculations. J Mat Phys 1998;39 M. Methfessel, NFP manual, IHP Copyright, 1997. [17] Sanchez-Portal D, Ordejon P, Artacho E, Soler JM. Density-functional method for very large systems with LCAO basis-set. Int J Quantum Chem 1997;65:453. [18] Da° browski J, MuÈssig H-J, Wol G, Hinrich S. Surface reconstruction suggests a nucleation mechanism in bulk: Sb/Si(113) and {113} planar defects. Surf Sci 1998;411:54. [19] Pandey KC. Diusion without vacancies or interstitials: a new concerted exchange mechanism. Phys Rev Lett 1986;57:2287. [20] Sato Y, Watanabe M, Imai K. Characterization of phosphorus pile-up at the SiO2/Si interface. J Electrochem Soc 1993;140:2679. [21] Bachelet GB, Hamann DR, SchluÈter MA. Pseudopotentials that work: from H to Pu. Phys Rev 1982;B26:4199.