On the diffusion mechanisms and diffusivity of the III and group dopant in silicon material

ScanGate document

VNU JOURNAL N THE THE OF SCIENCE, Nat Sci., t-XVI, DIFFUSION IIl AND V n?4 - 2000 MECHANISMS GROUP AND DOPANT Vu Ba IN DIFFUSIVITY SILICON OF MATERIAL Dung Faculty of Physics Mining and Abstract Diffusion task University, Hanoi of impurity into silicon materials plays an important ductor device fabrication difficult Geology technology The determination So far the diffusion mechanisms in silicon of diffusion have been role in semic« mechanism discussing is ve There three dominated main mechanisms of the III and V group impurity element a S icon crystal such as interstitial mechanism, vacancy mechanism and interstitialcy mei anism In this report, the author estimated the diffusivities in three cases An expressi of boron diffusitivity in silicon based on interstitialey mechanism that the diffusion Diffusion mechanism and affected strongly on diffusion mechanism 1.1 Fick theory of diffusion The simple theory of the diffusion diffusitivity of atoms given by of impurity diffusion Fick was presented in 1958 It show in silicon in silicon crystal with basic contents cc sisting two laws of Fick I and Fick II as following: J 9Œ ot The Fick I and Fick Il laws describe only on basis of phenomenology The F theory also indicates that the diffusivity D is constant However, in fact, the diffusiy depends on many dependence Diffusion diffusion exchange mechanism, dumbbell mechanism (can be seen impurities factors What does the Fick theory of the diffusitivity on the mechanism 1.2 The different below mechanisms of dopants ring crowding in are dominated Fig.1) of diffusion? may happen interstitial mechanism, [1,2] about in silicon into silicon mechanism, conimunicate The as following mechanisin, mechanism: interstitialey vacancy mechanism and diffusion mechanism of the by interstitial, vacancy 12 and mechanis relaxion III Dir mechani and interstitialcy mechanisms V gro On the diffusion mechanisms and diffusivity of O©OO O © OC CO oo ooa@moo ỔØ 0 9.0000 G Ø O- OO Ring CC OO ƠOCG 0 o O©O Go Interstitaley D0) 0.0) OOO: OF oe 00 OC: -O Đo Or O© ©:O:O O O Fig.1: Diffusivity of dopants 2.1 general The OO OOO oo 0: 90 0:0): 0-0 OC 60 Crowdion mechanism On O © OO ° Oe gy © Go 0-0: oO c7 o5 0-9 mechanism Ø.Ố AWS ©tG.o =o: Or OOF B ©: © O08 COO) S Oro oooo0o970890 Relaxion mechanism atom Some ©.Ø.GG ao mechanism - Silicon 0 © O CG-O 0:'0-0: theory, A is the average distance between two jum @ is the average velocity of diffuse internal field enhanced factor [9] impurity atoms, pe |’ is the correlation factor h is Jt+4() 2.2 Diffusivity of the III and V group impurity element diffused i: silicon crystal If the impurities in silicon have been diffused in depth d,byn; jumping steps ba on the interstitial mechanism The average distance of each jumping is A, the time which the jump were happened is tI and the average velocity of diffused impu iy is: substitute into the Eq (4) we have: Dgce= ch f The Eq (7) is the diffusivity of the pure interstitial mechanism If the impurities in silicon have been diffused in depth d by ny jumping based the vacancy mechanism, the average distance of each jumping is A, the time in which jump were happened is tV and the average velocity of diffused impurity we have: The Eq (9) is the diffusivity If the impurity of the pure vacancy mechanism diffuse due to the interstitialey mechanism depth, the percentage of jumps due to the interstitial mechanism to the vacancy mechanism mechanism of impurity is fy atoms Therefore is n;fy the number in order is f; and that of1 of jumps due , the time in which to reac the jumps to the intersti realized is m,;/, Similarly, due to the vacancy mechanism the number of jumps of impurity atoms is 1, the time n =n, in which the jumps realized is ny fy7, The time in which the atoms w + ny jumps to pass diffusion distance d is: try = n'frT† + nƑVTv ( the diffusion The average mechanisms velocity 15 of diffusivity and in the interstitialcy mechanism he following fori: Tú will be This can be written ữ (11) ?=—=——— lu — mfim +HƒVTV Substitute parameters into the Eq (4), we have the diffusivity due to interstitialey hanism: d DIYSs =e.h.ƒ.ÀA.—————— eel We suppose that (12) nfity +nfyty = 1,f = and using equations (7), (9) and (12) yield them pự - _—PkDÝ 08) = DY + fvD5 | | The Eq we (13) is the diffusivity of the pure interstitialey mechanism onclusion The diffusion mechanism of impurities in semiconductor materials affects their sivity very much In the interstitialcy mechanism, the diffusivity depends on percentage of the numof the jumps of atoms, due to the interstitial mechanism (f7) and vacancy mechanism The velocity of the diffusion depends strongly on the mechanism of the diffusion REFERENCES ] Deo Khac An, PhD dissertation 1994, Hanoi ] Ve Ba Dung and Dao Khac An, Proceedings of the Third International on Materials Science (IWOMS'99) Nov.2-4, (1999), p.529 | R.B.Fair, C.W.Pearce, Jack Washburn ceedings, ISSN 0272-9172 | DShaw Materials Research Society Symposia Pro- vol.36, Pittsburgh, Pennsylvania, USA,1985 Atomic diffusion in semiconductor 1973, chapter | RASwalin Workshop Plenum Press, London and New York, Atomic diffusion in semicortductor, Plenum Press, London and New York, 1973, chapter | S.M-Hu Phys Rew 180, 3(1969), p.733 | G D Watkins, J R Troxell and Chatterjee © Ctapter (1978), p.16 8) B Tuck Atomic Diffusion in semiconductor ee [9] R Shrivastava, A H Marshak Unst Phys Cof (IOP, Bristol, 1988) $.S Electronic 23 (1980), p.23 Ser., No.46 16 Vu {10} Andrey Milchev, Jordan Brakov and Victor D.Pereyra p.4356 Phys B.58 (1998), p.16167 A.F.W.Willoughby, Impurity doping process in silicon L Rew., E58 4(11 {11] E.Zocthout, H.J.W.Zandvliel, George Rosenfeld and Bene Poelsema {12] Ba Phys North Holland , Publis Company, (1981) (13] S.M.Hu Diffusion in Silicon and Germanium, atomic diffusion in semicondu Plenum Press, London and New York, (1973), p.217 TẠP CHi KHOA HỌC ĐHQGHN, KHTN, t.XVI, nÖ4 - 2000 VỀ CƠ CHẾ KHUẾCH TÁN VÀ HỆ SỐ KHUẾCH TÁN TAP CHAT NHON III VÀ V TRONG VAT LIBU SILIC Vũ Bá Dũng Khoa Ly, Dai hoc Mo - Dia chat, Ha Noi Khuếch tắn tạp chất vào vật liệu bán dẫn khâu quan trọng công, chế tạo linh kiện bán dẫn Xác định chế khuếch tán việc khó tới chế khuếch tán silic vấn đề cịn có nhiều tranh luận Tuy nhiêt tạp chất thuộc nhóm III V khuếch tán silic theo ba chế chủ yếu co điền kẽ, chế nút khuyết chế hỗn hợp Trong báo tác giả ước hệ số khuếch tán ba trường hợp Biểu thức hệ số khuếch tán thị chế hỗn hợp đưa Các kết qủa ước tính ché kh tần ảnh hưởng nhiều đến hệ số khuếch tán tạp chất silic / ... main -Impurity atom mechanisms 72 - Vacancy of diffusion in silicon in silicon expression of the diffusivity based on jump theory Jump steps based on jump theory carried out the diffusion of. .. | | The Eq we (13) is the diffusivity of the pure interstitialey mechanism onclusion The diffusion mechanism of impurities in semiconductor materials affects their sivity very much In the interstitialcy... mechanism, the diffusivity depends on percentage of the numof the jumps of atoms, due to the interstitial mechanism (f7) and vacancy mechanism The velocity of the diffusion depends strongly on the mechanism