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First Principles Calculation for Point Defect Behavior, Oxygen Precipitation and Cu Gettering in Czochralski Silicon
Abstract:
Theoretical consideration for technologically important phenomena in defect engineering of Czochralski silicon was performed with first principles calculation. (i) Point defect behaviour during crystal growth, (ii) enhanced oxygen precipitation in p/p+ epitaxial wafers, and (iii) Cu gettering by impurities are main topics in this work. Following results are obtained. (i) Interstitial Si I is dominant in p type Si while vacancy V is dominant in n type Si during crystal growth when dopant concentration is higher than about 1x1019atoms/cm3. (ii) In initial stage of oxygen precipitation including a few interstitial oxygen (O) atoms, BOn complex is more stable than On complex. The diffusion barrier of O atom in p+ Si is reduced to about 2.2eV compared with the barrier of about 2.5eV in intrinsic Si. (iii) In substitutional B, Sb, As, P and C atoms, only B atom can be an effective gettering center for Cu.
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Pages:
365-372
Citation:
Online since:
December 2005
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Сopyright:
© 2005 Trans Tech Publications Ltd. All Rights Reserved
Citation:
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[2] For example, S. Pantelides, M. Ramamoorthy and F. Reboredo, in Defects in Silicon III, T. Abe, W. Bullis, S. Kobayashi, W. Lin and P. Wagner, Editors, The Electrochem. Soc., Pennington, NJ, PV99-1 (1999) p.3.
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DOI: 10.1149/1.1393266
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[22] R. Mulliken, J. Chem. Phys., 23 (1955).
[3] 82.
[3] 82.
[3] 82.
[2] 75.
[3] 30.
[3] 85.
[1] 64.
[2] 75.
[3] 85 H p int. n.
[3] 56.
[3] 56.
[3] 56.
[3] 11.
[3] 66.
[4] 21.
[2] 83.
[3] 93.
[5] 03 Bc p int. n.
[4] 89.
[4] 89.
[4] 89.
[4] 03.
[4] 58.
[5] 13.
[3] 26.
[4] 36.
[5] 46 D p int. n.
[3] 51.
[3] 51.
[3] 51.
[3] 22.
[3] 77.
[4] 32.
[3] 01.
[4] 11.
[5] 21 Table 3 Calculated binding energy Eb of V and V, V and X through the reaction of V + V →V2, and V + X → VX, respectively with charge state and Fermi level taken into consideration. Eb > 0 indicates the formation of stable complex. p type indicates that Fermi level is at the top of valence band, while n type indicates that Fermi level is at the bottom of conduction band. int. indicates intrinsic Si. Formed Complex Type Reaction Eb (eV) V2 V2 +2 V2 -2 V2 -2 p int. n V +2 + V +2 + e -2 → V2 +2 V 0 + V 0 + e -2 → V2 -2 V -2 + V -2 → V2 -2 + e -2.
[1] 14.
[2] 58.
[1] 50 PV PV 0 PV -2 int. n P +1 + V 0 + e -1 → PV 0 P +1 + V -2 + e -1 → PV -2.
72.
[1] 31 AsV AsV 0 AsV -2 int. n As +1 + V 0 + e -1 → AsV 0 As +1 + V -2 + e -1 → AsV -2.
79.
[1] 33 SbV SbV +1 Sb -2 int. n Sb +1 + V 0 → SbV +1 Sb +1 + V -2 + e -1 → Sb -2.
74.
[1] 43 BV BV +1 BV -1 p int. B 0 + V +2 + e -1 → BV +1 B -1 + V 0 → BV -1.
43.
35 CV CV -1 int. C 0 + V 0 + e -1 → CV -1.
98 SnV SnV 0 int. Sn 0 + V 0 → SnV 0 0. 89 OV OV +2 OV 0 OV -2 p int. n O 0 + V +2 → OV +2 O 0 + V 0 → OV 0 O 0 + V -2 → OV -2.
[1] 40.
[1] 29.
[1] 12 Table 4 Calculated binding energy Eb of isolated n number of O atoms, and one B atom and isolated n number of O atoms through the reaction of nO → On and B + nO → BOn. Eb > 0 indicates the formation of stable complex. p type indicates that Fermi level is at the top of valence band. int. indicates intrinsic Si. Eb (eV) Formed Complex Type Reaction n=1 n=2 n=3 n=4 On On0 nO 0 → On0 0. 23 0. 54 0. 82 BOn BOn0 BOn-1 p int. B 0 + nO 0 → BOn0 B -1 + nO 0 → BOn-1.
32.
23.
58.
31.
84.
53.
[1] 22.
93 Table 2 Calculated binding energy Eb of V 0 and Vn-1 0, V 0 and X 0 through the reaction of V 0 + Vn-1 0 → Vn 0, and V 0 + X 0 → VX 0, respectively. Note that Eb > 0 indicates the formation of stable complex. Formed Complex Reaction Eb (eV) V2 0 V3 0 V4 0 V 0 + V 0 → V2 0 V2 0 + V 0 → V3 0 V3 0 + V 0 → V4 0.
[1] 68.
[1] 77.
[1] 87 PV 0 P 0 + V 0 → PV 0 1. 25 AsV 0 As 0 + V 0 → AsV 0.
[1] 30 SbV 0 Sb0 + V 0 → SbV 0.
[1] 48 BV 0 B 0 + V 0 → BV 0 0. 67 CV 0 C 0 + V 0 → CV 0 0. 68 SnV 0 Sn 0 + V 0 → SnV 0 0. 89 OV 0 O 0 + V 0 → OV 0 1. 29 Table 5 Calculated binding energy Eb of interstitial Cu atom and substitutional B, Sb, As, P or C atom. Eb > 0 indicates the formation of stable complex. Distance of Cu and impurity in stable complex is also shown. Impurity Site of Cu Eb ( eV ) Distance ( Å ) B T 1. 15 2. 07 Sb T -1. 28 2. 85 As T 0. 06 2. 61 P T -0. 14 2. 47 C T -0. 13 2. 29 Fig. 1 (a) T, H, Bc and S site, and (b) D site in the diamond structure. Fig. 2 Formation energy EF of vacancy V as Fig. 3 Formation energy EF of vacancy V as a a function of Fermi level. function of crystal temperature with changing dopant concentration Na (p type) and Nd (n type).
[3] 2.
[3] 3.
[3] 4.
[3] 5.
[3] 6.
[3] 7.
[3] 8.
[3] 9.
[4] 0 1100 1150 1200 1250 1300 1350 1400 Crystal temperature (oC) V formation energy EF (eV) Nd = 1x1020/cm3 Nd= 5x1019/cm3 Nd = 3x1019/cm3 Na < 1x1020 /cm3 Nd = 1x1019 /cm3.
DOI: 10.3403/30308865
[3] 2.
[3] 3.
[3] 4.
[3] 5.
[3] 6.
[3] 7.
[3] 8.
[3] 9.
[4] 0.
[3] 2.
[3] 3.
[3] 4.
[3] 5.
[3] 6.
[3] 7.
[3] 8.
[3] 9.
[4] 0 1100 1150 1200 1250 1300 1350 1400 Crystal temperature (oC) V formation energy EF (eV) Nd = 1x1020/cm3 Nd= 5x1019/cm3 Nd = 3x1019/cm3 Na < 1x1020 /cm3 Nd = 1x1019 /cm3 Table 6 Calculated binding energy Eb of V and n type dopants. Eb > 0 indicates the formation of stable complex. Dopant Eb ( eV ) Sb 1. 48 As 1. 30 P 1. 25 Table 7 Calculated Eb of interstitial Cu and SbV, AsV, PV. Cus indicates substitutional Cu atom. Distance of Cu and dopant in stable complex is also shown. Formed Complex Eb ( eV ) Distance of Cu and dopant ( Å ) SbCus 2. 85 2. 45 AsCus 3. 18 2. 33 PCus 3. 32 2. 27 Si Bc H S T (a) Bc H S T Si Bc H S T (a) Bc H S T b) D b) D b) D (b) D b) D b) D b) D (b) D.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00.
[5] 50.
[6] 00 V0 V V Fermi Energy (units of E_g) VB CB.
0 0. 2 0. 4 0. 6 0. 8 1. 0.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00.
[5] 50.
[6] 00.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00.
[5] 50 Formation Energy EF (eV).
[6] 00 V-2 Fermi Energy (units of ) VB.
0 0. 2 0. 4 0. 6 0. 8 1. 0 Fermi ) VB.
0 0. 2 0. 4 0. 6 0. 8 1. 0.
0 0. 2 0. 4 0. 6 0. 8 1. 0 -1 V+2 V+1.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00.
[5] 50.
[6] 00.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00.
[5] 50.
[6] 00 V0 V V Fermi Energy (units of E_g) VB CB.
0 0. 2 0. 4 0. 6 0. 8 1. 0 Fermi Energy (units of E_g) VB CB.
0 0. 2 0. 4 0. 6 0. 8 1. 0.
0 0. 2 0. 4 0. 6 0. 8 1. 0.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00.
[5] 50.
[6] 00.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00.
[5] 50 Formation Energy EF (eV) Formation Energy EF (eV).
[6] 00 V-2 V-2 Fermi Energy (units of ) VB.
0 0. 2 0. 4 0. 6 0. 8 1. 0 Fermi ) VB.
0 0. 2 0. 4 0. 6 0. 8 1. 0.
0 0. 2 0. 4 0. 6 0. 8 1. 0 Fermi Energy (units of ) VB.
0 0. 2 0. 4 0. 6 0. 8 1. 0.
0 0. 2 0. 4 0. 6 0. 8 1. 0 Fermi ) VB.
0 0. 2 0. 4 0. 6 0. 8 1. 0.
0 0. 2 0. 4 0. 6 0. 8 1. 0.
0 0. 2 0. 4 0. 6 0. 8 1. 0.
0 0. 2 0. 4 0. 6 0. 8 1. 0 -1 V+2 V+2 V+1 V+1 Fig. 4 Formation energy EF of interstitial Si I 0 Fig. 5 Formation energy EF of interstitial silicon I at D site and I +2 at T site as a function of as a function of crystal temperature with changing Fermi level. dopant concentration Na (p type) and Nd (n type). Fig. 6 Binding energy Eb of V and V, and P and V as a function of crystal temperature. Fig. 7 Stable structures of (a) one O atom, and On complexes including (b) two, (c) three, or (d) four O atoms (Si: white balls, O: black balls). Bond length is shown in order of Å. Fig. 8 Stable structures of (a) BO complex of one O atom and one B atom, and BOn complexes including (b) two, (c) three, or (d) four O atoms (Si: white balls, B: gray ball, O: black balls). Bond length is shown in order of Å. 1x1020/cm3 5x1019/cm3 3x1019/cm3.
[2] 0.
[2] 2.
[2] 4.
[2] 6.
[2] 8.
[3] 0.
[3] 2.
[3] 4.
[3] 6 1100 1150 1200 1250 1300 1350 1400 Crystal temperature (oC) I formation energy EF (eV) n type p type 1x1019 /cm3 1x1020/cm3 5x1019/cm3 3x1019/cm3.
DOI: 10.3403/30308865
[2] 0.
[2] 2.
[2] 4.
[2] 6.
[2] 8.
[3] 0.
[3] 2.
[3] 4.
[3] 6 1100 1150 1200 1250 1300 1350 1400 Crystal temperature (oC) I formation energy EF (eV).
[2] 0.
[2] 2.
[2] 4.
[2] 6.
[2] 8.
[3] 0.
[3] 2.
[3] 4.
[3] 6.
[2] 0.
[2] 2.
[2] 4.
[2] 6.
[2] 8.
[3] 0.
[3] 2.
[3] 4.
[3] 6 1100 1150 1200 1250 1300 1350 1400 Crystal temperature (oC) I formation energy EF (eV) n type p type 1x1019 /cm3 Na, Nd = 1x1020/cm3 5x1019/cm3 3x1019/cm3.
DOI: 10.3403/30308865
[2] 0.
[2] 2.
[2] 4.
[2] 6.
[2] 8.
[3] 0.
[3] 2.
[3] 4.
[3] 6 1100 1150 1200 1250 1300 1350 1400 Crystal temperature (oC) I formation energy EF (eV) n type p type 1x1019 /cm3 1x1020/cm3 5x1019/cm3 3x1019/cm3.
DOI: 10.3403/30308865
[2] 0.
[2] 2.
[2] 4.
[2] 6.
[2] 8.
[3] 0.
[3] 2.
[3] 4.
[3] 6 1100 1150 1200 1250 1300 1350 1400 Crystal temperature (oC) I formation energy EF (eV).
[2] 0.
[2] 2.
[2] 4.
[2] 6.
[2] 8.
[3] 0.
[3] 2.
[3] 4.
[3] 6.
[2] 0.
[2] 2.
[2] 4.
[2] 6.
[2] 8.
[3] 0.
[3] 2.
[3] 4.
[3] 6 1100 1150 1200 1250 1300 1350 1400 Crystal temperature (oC) I formation energy EF (eV) n type p type 1x1019 /cm3 Na, Nd =.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o (b) O2 complex 1. 58.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o (c) O3 complex.
[2] 31 152. 7o.
[1] 60 1. 59 1. 62.
[1] 61 129. 5o.
[1] 60.
[1] 65123. 9o (d) O4 complex.
[1] 59136. 2o.
[1] 59.
[1] 64.
[1] 62.
[1] 64 116. 9o.
[1] 62121. 2o 161. 2o.
[1] 57.
[1] 66.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o (b) O2 complex 1. 58.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o (b) O2.
[1] 58.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o (c) O3 complex.
[2] 31 152. 7o.
[1] 60 1. 59 1. 62.
[1] 61 129. 5o.
[1] 60.
[1] 65123. 9o (c) O3.
[2] 31 152. 7o.
[1] 60 1. 59 1. 62.
[1] 61 129. 5o.
[1] 60.
[1] 65123. 9o (d) O4 complex.
[1] 59136. 2o.
[1] 59.
[1] 64.
[1] 62.
[1] 64 116. 9o.
[1] 62121. 2o 161. 2o.
[1] 57.
[1] 66 (d) O4.
[1] 59136. 2o.
[1] 59.
[1] 64.
[1] 62.
[1] 64 116. 9o.
[1] 62121. 2o 161. 2o.
[1] 57.
[1] 66.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o (b) O2 complex 1. 58.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o (b) O2 complex 1. 58.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o (c) O3 complex.
[2] 31 152. 7o.
[1] 60 1. 59 1. 62.
[1] 61 129. 5o.
[1] 60.
[1] 65123. 9o (c) O3 complex.
[2] 31 152. 7o.
[1] 60 1. 59 1. 62.
[1] 61 129. 5o.
[1] 60.
[1] 65123. 9o (d) O4 complex.
[1] 59136. 2o.
[1] 59.
[1] 64.
[1] 62.
[1] 64 116. 9o.
[1] 62121. 2o 161. 2o.
[1] 57.
[1] 66 (d) O4 complex.
[1] 59136. 2o.
[1] 59.
[1] 64.
[1] 62.
[1] 64 116. 9o.
[1] 62121. 2o 161. 2o.
[1] 57.
[1] 66.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o (b) O2 complex 1. 58.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o.
[2] 28 (a) O atom 1. 60.
[1] 60.
[2] 22 2. 35 165. 2o (b) O2.
[1] 58.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o.
[2] 30 166. 1o.
[1] 581. 57 1. 61 2. 30 149. 5o (c) O3 complex.
[2] 31 152. 7o.
[1] 60 1. 59 1. 62.
[1] 61 129. 5o.
[1] 60.
[1] 65123. 9o (c) O3.
[2] 31 152. 7o.
[1] 60 1. 59 1. 62.
[1] 61 129. 5o.
[1] 60.
[1] 65123. 9o (d) O4 complex.
[1] 59136. 2o.
[1] 59.
[1] 64.
[1] 62.
[1] 64 116. 9o.
[1] 62121. 2o 161. 2o.
[1] 57.
[1] 66 (d) O4.
[1] 59136. 2o.
[1] 59.
[1] 64.
[1] 62.
[1] 64 116. 9o.
[1] 62121. 2o 161. 2o.
[1] 57.
[1] 66 (d) O4 complex.
[1] 59136. 2o.
[1] 59.
[1] 64.
[1] 62.
[1] 64 116. 9o.
[1] 62121. 2o 161. 2o.
[1] 57.
[1] 66 (d) O4.
[1] 59136. 2o.
[1] 59.
[1] 64.
[1] 62.
[1] 64 116. 9o.
[1] 62121. 2o 161. 2o.
[1] 57.
[1] 66.
[1] 58.
[2] 04.
[1] 59.
[2] 04.
[2] 36 176. 1o (a) B and O atom (b) B－O2 complex.
[1] 38.
[2] 31 171. 9o.
[1] 591. 36 1. 61 2. 30 142. 9o (c) B－O3 complex.
[2] 31 156. 9o.
[1] 601. 39.
[1] 62.
[1] 60 124. 5o.
[1] 40.
[1] 64126. 6o (d) B－O4 complex.
[1] 61133. 4o.
[1] 62.
[1] 47.
[1] 65.
[1] 65 106. 1o.
[1] 42 121. 1o 153. 0o.
[1] 58.
[1] 64.
[1] 58.
[2] 04.
[1] 59.
[2] 04.
[2] 36 176. 1o (a) B and O atom.
[1] 58.
[2] 04.
[1] 59.
[2] 04.
[2] 36 176. 1o (a) BO (b) B－O2 complex.
[1] 38.
[2] 31 171. 9o.
[1] 591. 36 1. 61 2. 30 142. 9o (b) BO2.
[1] 38.
[2] 31 171. 9o.
[1] 591. 36 1. 61 2. 30 142. 9o (c) B－O3 complex.
[2] 31 156. 9o.
[1] 601. 39.
[1] 62.
[1] 60 124. 5o.
[1] 40.
[1] 64126. 6o (c) BO3.
[2] 31 156. 9o.
[1] 601. 39.
[1] 62.
[1] 60 124. 5o.
[1] 40.
[1] 64126. 6o (d) BO4.
[1] 61133. 4o.
[1] 62.
[1] 47.
[1] 65.
[1] 65 106. 1o.
[1] 42 121. 1o 153. 0o.
[1] 58.
[1] 64.
[1] 58.
[2] 04.
[1] 59.
[2] 04.
[2] 36 176. 1o (a) B and O atom.
[1] 58.
[2] 04.
[1] 59.
[2] 04.
[2] 36 176. 1o (a) B and O atom (b) B－O2 complex.
[1] 38.
[2] 31 171. 9o.
[1] 591. 36 1. 61 2. 30 142. 9o (b) B－O2 complex.
[1] 38.
[2] 31 171. 9o.
[1] 591. 36 1. 61 2. 30 142. 9o (c) B－O3 complex.
[2] 31 156. 9o.
[1] 601. 39.
[1] 62.
[1] 60 124. 5o.
[1] 40.
[1] 64126. 6o (c) B－O3 complex.
[2] 31 156. 9o.
[1] 601. 39.
[1] 62.
[1] 60 124. 5o.
[1] 40.
[1] 64126. 6o (d) B－O4 complex.
[1] 61133. 4o.
[1] 62.
[1] 47.
[1] 65.
[1] 65 106. 1o.
[1] 42 121. 1o 153. 0o.
[1] 58.
[1] 64.
[1] 58.
[2] 04.
[1] 59.
[2] 04.
[2] 36 176. 1o (a) B and O atom.
[1] 58.
[2] 04.
[1] 59.
[2] 04.
[2] 36 176. 1o (a) BO (b) B－O2 complex.
[1] 38.
[2] 31 171. 9o.
[1] 591. 36 1. 61 2. 30 142. 9o (b) BO2.
[1] 38.
[2] 31 171. 9o.
[1] 591. 36 1. 61 2. 30 142. 9o (c) B－O3 complex.
[2] 31 156. 9o.
[1] 601. 39.
[1] 62.
[1] 60 124. 5o.
[1] 40.
[1] 64126. 6o (c) BO3.
[2] 31 156. 9o.
[1] 601. 39.
[1] 62.
[1] 60 124. 5o.
[1] 40.
[1] 64126. 6o (d) BO4.
[1] 61133. 4o.
[1] 62.
[1] 47.
[1] 65.
[1] 65 106. 1o.
[1] 42 121. 1o 153. 0o.
[1] 58.
[1] 64 (c) B－O3 complex.
[2] 31 156. 9o.
[1] 601. 39.
[1] 62.
[1] 60 124. 5o.
[1] 40.
[1] 64126. 6o (c) BO3.
[2] 31 156. 9o.
[1] 601. 39.
[1] 62.
[1] 60 124. 5o.
[1] 40.
[1] 64126. 6o (d) BO4.
[1] 61133. 4o.
[1] 62.
[1] 47.
[1] 65.
[1] 65 106. 1o.
[1] 42 121. 1o 153. 0o.
[1] 58.
[1] 64.
[1] 00.
[1] 50.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00 I+2 (T site) I0 (D site) VB CB.
0 0. 2 0. 4 0. 6 0. 8 1. 0 Fermi Energy (units of ) Formation Energy EF (eV).
[1] 00.
[1] 50.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00 I+2 (T site) I0 (D site) VB.
0 0. 2 0. 4 0. 6 0. 8 1. 0 Fermi Energy (units of E_g).
[1] 00.
[1] 50.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00 I+2 (T site) I0 (D site) VB CB.
0 0. 2 0. 4 0. 6 0. 8 1. 0 Fermi Energy (units of ) Formation Energy EF (eV).
[1] 00.
[1] 50.
[2] 00.
[2] 50.
[3] 00.
[3] 50.
[4] 00.
[4] 50.
[5] 00 I+2 (T site) I0 (D site) VB.
0 0. 2 0. 4 0. 6 0. 8 1. 0 Fermi Energy (units of E_g) 0.
5 1.
[1] 5 2.
[2] 5 3 1000 1030 1060 1090 1120 1150 Crystal temperature (oC) Binding energy Eb (eV) V-2 + V-2 → V2 -2 P+1 + V-2 → PV-2 P concentration (/cm3) 5 x 1020 1 x 1020 5 x 1019 0.
5 1.
[1] 5 2.
[2] 5 3 1000 1030 1060 1090 1120 1150 Crystal temperature (oC) Binding energy Eb (eV) V-2 + V-2 → V2 -2 P+1 + V-2 → PV-2 P concentration (/cm3) 5 x 1020 1 x 1020 5 x 1019 Fig. 9 Formation energy as a function of Fermi level for O 0 and O +2 in Si. The energy for the Bc site in the neutral state was taken as the reference energy. The top of the valence band was set to zero in horizontal axis. Fig. 10 Band structures and the local densities of states for neutral O atom at (a) Bc site and (b) S site. Density of states is calculated using.
1eV Gaussian broadening of the band structure. Energy is measured from the Fermi level, which is denoted by horizontal broken lines. (a) (b) (c) Fig. 11 Stable configurations and valence electron density of (a) interstitial Cu and substitutional B complex, (b) interstitial Cu and substitutional Sb complex, and (c) substitutional Cu and substitutional Sb complex in Si (110) plane. The maximum contour of the density is set to 0. 8 electron /Å.
[3] Cu Si Sb Cu Si Cu Si B.
[110] .
[1] Cu Si Sb Cu Si Cu Si B.
[110] .
[1] .
[110] .
[1] .
[110] .
[1] Cu Si Sb.
[110] .
[1] .
[110] .
[1] Cu Si Sb Cu Si Sb Cu Si Sb.
[110] .
[1] Cu Si Sb Cu Si Sb.
[110] .
[1] .
[110] .
[1] -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZ G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZG Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure (a) Bsite (b) Ssite Energy (eV) G F Q Z G 0. 0 0. 5 1. 0 1. 5 G F Q Z G 0. 0 0. 5 1. 0 1. 5 Density of States (electrons/eV) Density of States (electrons/eV) 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZ G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZG Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure (a) Bsite (b) Ssite Energy (eV) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZ G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZG Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure (a) Bsite (b) Ssite Energy (eV) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZ G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZG Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure (a) Bsite (b) Ssite Energy (eV) G F Q Z G 0. 0 0. 5 1. 0 1. 5 G F Q Z G 0. 0 0. 5 1. 0 1. 5 Density of States (electrons/eV) Density of States (electrons/eV) G F Q Z G 0. 0 0. 5 1. 0 1. 5 G F Q Z G 0. 0 0. 5 1. 0 1. 5 Density of States (electrons/eV) Density of States (electrons/eV) 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 (a) Bc site (b) S site -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZ G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZG Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure (a) Bsite (b) Ssite Energy (eV) G F Q Z G 0. 0 0. 5 1. 0 1. 5 G F Q Z G 0. 0 0. 5 1. 0 1. 5 Density of States (electrons/eV) Density of States (electrons/eV) 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZ G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZG Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure (a) Bsite (b) Ssite Energy (eV) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZ G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZG Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure (a) Bsite (b) Ssite Energy (eV) -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZ G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 GFQZG Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure -7 -6 -5 -4 -3 -2 -1 0 1 2 3 G Energy (eV) CASTEP Band Structure (a) Bsite (b) Ssite Energy (eV) G F Q Z G 0. 0 0. 5 1. 0 1. 5 G F Q Z G 0. 0 0. 5 1. 0 1. 5 Density of States (electrons/eV) Density of States (electrons/eV) G F Q Z G 0. 0 0. 5 1. 0 1. 5 G F Q Z G 0. 0 0. 5 1. 0 1. 5 Density of States (electrons/eV) Density of States (electrons/eV) 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 3 2 1 0 -1 -2 -3 -4 -5 -6 -7 (a) Bc site (b) S site -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 Formation energy (eV) VB CB Fermi energy (units of B (O0) T (O0) H (O0) S (O0) B (O ) S (O ) H (O ), T (O ) -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 Formation energy (eV) VB CB Fermi energy (units of B (O0) T (O0) H (O0) S (O0) B (O ) S (O +2 ) H (O ), T (O ) +2 +2 +2 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 Formation energy (eV) VB CB Fermi energy (units of B (O0) T (O0) H (O0) S (O0) B (O ) S (O ) H (O ), T (O ) -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 Formation energy (eV) VB CB Fermi energy (units of E_g) B (O0) T (O0) H (O0) S (O0) B (O ) S (O +2 ) H (O ), T (O ) +2 +2 +2 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 Formation energy (eV) VB CB Fermi energy (units of B (O0) T (O0) H (O0) S (O0) B (O ) S (O ) H (O ), T (O ) -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 Formation energy (eV) VB CB Fermi energy (units of B (O0) T (O0) H (O0) S (O0) B (O ) S (O +2 ) H (O ), T (O ) +2 +2 +2 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 Formation energy (eV) VB CB Fermi energy (units of B (O0) T (O0) H (O0) S (O0) B (O ) S (O ) H (O ), T (O ) -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 -1. 0.
[1] 0.
[2] 0.
[3] 0.
[4] 0.
[5] 0.
[6] 0 0 0. 2 0. 4 0. 6 0. 8 1 Formation energy (eV) VB CB Fermi energy (units of E_g) B (O0) T (O0) H (O0) S (O0) B (O ) S (O +2 ) H (O ), T (O ) +2 +2 +2.