Перевод МММ / 3_%%%% 0648bacc A Study of Nonequilibrium Diffusion Modeling-
.pdfFor individual use by an IEEE Electron Devices Society member purchasing this product.
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FURNACEANNEALING |
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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 39, NO 3, MARCH 1992
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Flg. I I . Collector and base currents as a function of base-emitter voltage. Vcb = 0 V , emitter area is 2.2 X 20 pm2, and emitterresistance RE = 7 0.The doping profiles used in these simulations have been reportedin Fig.
9.
tailed models for this simulation have been described in [44], [45]. Fig. 1 I shows the Gummel plots using the profiles reported in Fig. 9. As expected from the doping profiles, the new model offers a better way to reproduce the actual results.
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lprn) |
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(b)
Fig. 9 . Simulated arsenic andboron profiles in the case of 900°C furnace annealing and companson with experimental results (SIMS). (a) Using the. standardmodel. (bj Using thenonequilibrium model.
...-
Fig. I O . Forthe simulateddopingprofilefrom Fig.9(b), concentrations of the different species, atthe end of the simulation.
C. Two-DimensionalBehavior |
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Withthehelp |
of asteady-stateformulation, |
it was |
shown that two-dimensional profiles can be dramatically affected by the inclusion of point defects, for boron and phosphoruspredeposition [lo]. Thesamekind of result has been observed with the present model.However, there
is only a single report dealing with the effect |
of ion-im- |
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plantationdamageonlateraldiffusion,whichanalyzed |
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qualitativelythechanges |
in junctionprofilesfortwo |
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MOSFETstructures [37]. In order tostudyinaprecise mannerpossibletwo-dimensionaleffects,thefollowing simulationhasbeenperformedwiththepresentmodel:
boron wasimplantedatadoseandenergyof4 |
X I O l 3 |
at/cm2 and 20 keV, and annealed at 800°C for |
10 min. |
From the resultsof the previous section, this is oneof the cases where anomalous diffusion is the most remarkable. A 2 pm X 2 pm mesh was used and boron was implanted using amask at x = 1.6 pm. As theareaofinterestis located near the top surface, and as the point-defect distributions are mainly determined by the interactions with dopants, this mesh is sufficient. It was confirmedby com-
paringtheresultswiththoseobtained |
by usinga |
20 pm |
X 20 pm mesh. |
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Fig. 12 displaystheboroncontours |
at theend |
of the |
simulation. Tee maximum vertical displacement ison the order of 6T A, whereas the lateral displacement is only about 320 A . Hence, as in the case of predeposition, the
surfaceeffectslimitthesupersaturation |
of pointdefects |
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andthuslimittheamountofanomalousdiffusion |
in the |
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lateraldirection.Anotheroriginalpointcan |
be |
seen in |
For individual use by an IEEE Electron Devices Society member purchasing this product.
MODELlNtiDIFFUSIONNONEQUILIBRIUMBACCUSOF et 01.: STUDY |
659 |
-o‘81.Z |
I 4 |
1.6 |
1.8 |
20 |
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X Imicronsl |
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Fig. 12. Boron contours alier 10 nun of diffusion at 800°C
-2.0 |
0 5 |
I O |
15 |
2 0 |
0 |
X (mlcronsl
Fig. 13. Vacancy contours after 0.05 s of diffusion. The insert shows the distnbutlon of some species in a lateral cross section at y = -0.1 pm.
Good agreement is obtained as a function of temperature, time, and type of dopant. From the calculation, it is also deduced that a precise knowledge of the ramp-up conditions is needed if quantitative results are expected about thedisplacement.Theinfluenceofthechoice ofinitial defectdistributionshasbeenalsodiscussed.Itisshown
that for low-dose experiments, using the results fromMC calculationsslightlyoverestimatestheanomalousdiffusion. For high-dose arsenic implants, it seems sufficient, as a first approach,tousesimplythedopant-implanted profile for the defect distributions. Two-dimensional calculationssuggestthattheanomalousdisplacements due to ion-implantation damage differ significantly in the lateral and vertical directions.
Finally,this kindofmodel seemsverypromisingfor investigationoftheproblemsarisingin ULSI technologies. For example,phenomenalike(pre)amorphization, solid-phase epitaxy, and solid solubilities exceeding equi- libriumvaluesduringlow-temperatureannealing,might beinvestigatedwhenusing an extendedversion of the workpresentedhere.Thissophisticatedmodelinglevel
can also help greatly in defining the range of validity of
eachdiffusionformulation,whenapplied |
toveryshort |
time annealing. |
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Fig. 12: as the initial gradient of the point defects is ex-
tremely large in the vicinity of the top surface, higher vallike to thank Dr.D. Collard and Dr. E. Dubois from ISEN
uesofdopantconcentrations |
arepredictedinthisarea. |
for their support and encouragement. |
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This is in fact the same type of phenomenon as |
reported |
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in [ 9 ] , [111 and referred to as “up-hilldiffusion.” In these |
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REFERENCES |
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references,thegradientofinterstitialswasduetosome |
[I] C. P . Ho, J. D. Plummer, S . E. Hansen, and R. W . Dutton, “VLSI |
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recombination term in a damage layer (amorphousicrys- |
||||||||||||||
|
process modeling-SUPREM |
Ill,” IEEE T r a m ElectronDevices, |
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talline interface). Here thiseffect is observed near the sur- |
|
vol. ED-30. pp. 1438-1453. |
1983. |
|
|
|
|
|
||||||
faceand |
mainly. occursforlow-temperatureconditions |
[ 2 ] R . B . Fair and G . A. Ruggles, “Thermal |
budget issues for deep sub- |
|||||||||||
(typicallyaround 8O0”C-85O0C).Thiscouldbeimpor- |
|
micron ULSI.” Solid-StateTechno/., pp. 107-113, May 1990. |
|
|||||||||||
[3] |
A . E. Michel. W . Rausch, P. A. Ronsheim, and R. H. Kastl, “Rapid |
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tantwhenconsideringthechannelprofileinadvanced |
|
|
annealing and the anomalous diffusion of ion implanted boron into |
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MOS technologies which use now this range of tempera- |
|
sllicon,” Appl. t‘hys. Letr.. vol. 50, no. 7. pp. 416-418, Feb. 16, |
||||||||||||
tures. Finally, Fig. |
13 shows the vacancy contours during |
|
1987. |
|
|
|
|
|
|
|
||||
[4] |
M. Norishima, Y.Niitsu, G. Sasaki, H. Iwai. and K. Maeguchi, “Bi- |
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the beginning of diffusion, after 0.05 s. The decrease of |
|
polartransistor |
design for |
low process-temperature |
0.5 pm |
Bi- |
||||||||
vacancynearthesurface |
is obvious,andthere |
isalsoa |
|
CMOS.” in IEDM Tech. D i g . , Dec. 1989, pp. 237-240. |
and |
|||||||||
significantlowering |
in theregionof high boron/intersti- |
[51 P. M.Fahey,P. |
B. Griffin, and J. D. Plummer,“Pointdefects |
|||||||||||
|
dopant ditfuslon |
In sllicon,” |
Rev.Mod. |
Phys.. vol 61, no. 2, |
pp. |
|||||||||
tial pair concentrations. This is partially due to direct re- |
|
289-384, Apr. 1989. |
|
|
|
|
|
|
||||||
combination with interstitials,andmainlydue |
to there- |
[6] |
D. Collard and K . Taniguchi. “IMPACT-A |
point-defect-based two- |
||||||||||
action (4). This effect has been already reported |
for one- |
|
dimensional process simulator: Modeling the lateral oxidation-en- |
|||||||||||
|
hanced diffusion of dopants in silicon,” |
IEEE Trans.ElectronDe- |
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dimensional calculations in[17] and is also carefully taken |
|
vices, vol. ED-33. no. 10, pp. 1454-1462, Oct. 1986. |
|
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into account here. |
|
|
|
[7] |
M. E. Law and R . W . Dutton, “Venficatlon |
of analytic point defects |
||||||||
|
|
|
|
|
|
models using SUPREM IV,” IEEE Truns. Computer-Aided Des., vol. |
||||||||
|
|
|
|
|
|
7, no. 2 , pp. 181-190. Feh. 1988. |
|
|
|
|
|
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|
|
V . CONCLUSIONS |
|
[8] |
D.Mathlot and J . C . Pfister,“Dopant |
diffusion in silicon: A con- |
||||||||
In addition to a precise physical insight into the diffu- |
|
sistent view involving non-equilibrium |
defects.” J. Appl. Phys., vol. |
|||||||||||
|
5 5 . no. I O , pp. 3518-3530. |
May 15, |
1984. |
|
|
|
||||||||
sion mechanisms, the detailed inclusion of point defects |
[9] |
M. Orlowski, “Unified model for impunty diffuslon in silicon,” Appl. |
||||||||||||
under nonequilibrium condition allows to explain the ef- |
|
Phys. Lett., vol. 53, no. 14, pp. 1323-1325, |
Oct. 3 , |
1988. |
|
|||||||||
[IO] |
E.Rorris, R. R. O’Brien, F. F. Morehead, R . F. Lever, J. P. Peng, |
|||||||||||||
fects of |
ion-implantationdamageondopantdiffusion. |
|
and G. R. Srinivasan, “A new approach to the simulation of the cou- |
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For individual use by an IEEE Electron Devices Society member purchasing this product.
660 |
IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 39, NO, 3, MARCH 1992 |
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pled pointdefectsandimpuritydiffusion,”IEEETrans.Compurer- |
|||||||||
|
AidedDes.,vol. |
9, no. 10, pp. 1113-1122, Oct. 1990. |
|
|||||||
1111 |
M. Orlowski,“Impurity |
and pointdefectredistribution in thepres- |
||||||||
|
enceofcrystaldefects,” in IEDM Tech. Dig . , Dec. 1990, pp. 729- |
|||||||||
[I21 |
731. |
|
|
|
|
|
|
|
|
|
F. F. Morehead and |
R. F. Lever, |
“A steady-state model for coupled |
||||||||
|
defect-impurity diffusion in silicon,”J. Appl. Phys., vol. 66, no. 1 I , |
|||||||||
|
pp. 5349-5352, |
Dec. 1, |
1989. |
|
|
|
|
|||
1131 |
S . M. Hu, P. Fahey, and R. W.Dutton, |
“On models of phosphorus |
||||||||
|
diffusion in silicon,” J . Appl. Phys., vol. 54, no. 12, pp. 6912-6922, |
|||||||||
|
Dec. 1983. |
|
|
|
|
|
|
|
|
|
[14] W.B. Richardson and B.J. Mulvaney,“Plateau and kinkin |
P pro- |
|||||||||
|
filesinto Si: A result of strongbimolecularrecombination?” |
Appl. |
||||||||
[I51 |
Phys. Lett., vol. 53, no. 20, pp. |
1917-1919, Nov. 14, 1988. |
|
|||||||
-, |
“Non-equilibriumbehavior |
of chargedpointdefectsduring |
||||||||
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phosphorusdiffusion in silicon,” |
J. Appl. Phys., vol. 65, no. 6, pp. |
||||||||
|
2243-2247, Mar. 15. 1989. |
|
|
|
|
|
||||
1161 |
B. J. Mulvaney and W. B. Richardson, “The effect of concentration- |
|||||||||
|
dependent defect recombination reactions on phosphorus diffusion in |
|||||||||
|
silicon,” J . Appl. Phys.,vol. |
67, no. 6, pp. |
3197-3199, Mar. 15, |
|||||||
|
1990. |
|
|
|
|
|
|
|
|
|
1171 |
T.L.Crandle,W.B. |
Richardson,and |
B. 1. Mulvaney, “A kinctic |
|||||||
|
model |
foranomalousdiffusionduringpost-implantannealing,” |
in |
|||||||
|
IEDM Tech. Dig., Dec. 1988, pp. 636-639. |
|
|
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1181 |
M. Heinrich, M. Budil, and H. W. Potzl, “Simulation of arsenic and |
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borondiffusionduringrapidthermalannealing |
in silicon,” in Proc. |
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|
ESSDERCPO ConJ, W . Ecclestonand |
P. 1. Rosser, Eds.(Not- |
||||||||
|
tingham,UK,Sept. |
1990). pp. 205-208. |
|
|
||||||
1191 G. Hobler, S. Halama, K. Wimmer, S . Selberherr, and H. W. Potzl, |
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|
“RTA-simulations |
with the 2D process simulator PROMIS,” |
in NU- |
|||||||
|
PADIII(Hawaii, |
June 3-4,1990). pp. 13-14. |
|
|
||||||
[20] C. S . Nichols, C. G . Vande |
Walle, and S . T. Pantelides, “Mecha- |
|||||||||
|
nisms of dopant impurity diffusionin silicon,” Phys. Rev. B, vol. 40, |
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|
no. 8. pp. 5484-5496, Sept. |
15. |
1989. |
|
|
|
||||
[21] |
N.E.B. |
Cowern, K.T.F.Janssen,G. |
F . A. van de Walle, and D. |
|||||||
|
1 . Gravesteijn,“Impuritydiffusion |
viaan intermediatespecies:The |
||||||||
|
B-Si system,” Phys. Rev. Lerr., vol, 65, no. 19, pp. 2434-2437, Nov. |
|||||||||
|
5 , 1990. |
|
|
|
|
|
|
|
|
|
[22] |
N. E. B.Cowern,“General |
model forintrinsicdopantdiffusion in |
||||||||
|
silicon under nonequilibrium point-defect conditions,”J. Appl. Phys., |
|||||||||
|
vol. 64, no. 9 , pp, 4484-4490, Nov. 1 , |
1988. |
|
|
||||||
[23]W. liingling. P. Pichler, S . Selberherr, E. Guerrero, and H. W. Potzl. “Simulation of critical IC fabrication pmcess using advanced physical and numerical methods.” IEEE Trans. Electron Devices. vol. ED-
32, no. 2, pp. 156-167, |
Feh. |
1985. |
|
|
|
|
[24] B.Baccus.E.Dubois. |
D. Collard. and D. Morel.“Efficienttwo- |
|
||||
dimensionalmultilayerprocesssimulation |
of |
advancedbipolarde- |
||||
vices,”Solid-StateElectron.,vol. 32. no. l l,pp. 1013-1023, Nov. |
||||||
1989. |
D.Collard, E. Dubois,andD.Morel,“IMPACT4-A |
|
||||
B.Baccus. |
|
|||||
general two-dimenslonal multilayer process simulator,” in Proc. SIS- |
||||||
DEP 111 Con$, G . BaccaraniandM.Rudan,Eds.(Bologna,Italy, |
|
|||||
Sept. 1988). pp. 255-266. |
|
|
|
|
||
N.Shigyo, |
S . Nakamura, T.Wada, and S . Yasuda, Mar. 1990, un- |
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published. |
|
|
|
|
|
|
G. B. Bonner and 1 . D. Plummer,“Gettering |
of goldinsilicod: |
A |
||||
tool fur understanding the propertiesof sllicon interstitials,” J . Appl. |
||||||
Phys., vol. 61, no. 12, pp. 5286-5298, |
June15, 1987. |
|
||||
W . A. Orr Arienzo,R.Glang, |
R. F. Lever, R. K . Lewis,and F. F. |
|||||
Morehead,“Borondiffusioninsiliconathighconcentrations,” |
J . |
|||||
Appl. Phys., vol. 63, no. I , pp. 116-120, Jan. I , 1988. M.Hirata,M.Hirata,and H. Saito.“Theinteractions of pointdefectswithimpurities in silicon,” J . Phys. Soc. Jupan,vol. 27, pp.
405-414,1969.
D.A. Antonladis and I. Moskowitz, “Diffusion of substitutional im-
purities in silicon at short oxidation times: An insight into point defect kinetics,” J.Appl. Phys., vol. 53, no. IO, pp. 6788-6796, Oct. 1982.
[31] B.Lojek,“CAD of processesforsdiconhighspeeddevices,” in Pror. 1990 VLSI ProcesslDevice Modeling Workshop (Kawasaki, Ja- pan,Aug. l990), pp. 118-121.
[32]U. Gosele, F. Morehead, w . Frank, andA. Seeger,“Diffusionof gold in silicon: A new model,” Appl. Phys. L e u , vol. 38, no. 3, pp.
157-159, Feh.1, 1981.
[33]F. Lau, “Modeling of polysilicon diffusion sources,” in fEDM Tech.
Dig., Dec. 1990, pp. 737-740.
1341 P. Fahey, R. W. Dutton,and |
S . M. Hu, “Supersaturation of self- |
interstitials and undersaturation |
of vacancies during phosphorus dif- |
interstitials and undersaturation of vacancies during phosphorus diffusion in silicon,”Appl.Phys. Lerr., vol. 44, no. 8, pp. 717-779,
Apr. 15, 1984.
1351 B. J . Mulvaney, W. B. Richardson,and T. L. Crandle,“PEPPER-
A process simulator for VLSI,” lEEE Trans. Compurer-Aided Des.. vol. 8, no. 4, pp. 336-349, Apr. 1989.
1361 T. K. Okada, S . Kambayashi, S. Onga, 1. Mizushima, K.Yamabe, and J . Matsunaga,“Non-equilibriumdiffusionprocessmodeling
based on three-dimensional simulator and a regulated point-defect injectionexperiment,” in IEDM Tech. D i g . , Dec. 1990, pp. 733-736.
[37]M. E.Law and 1. R.Pfiester,“Low-temperatureannealingofar- senieiphosphorus junctions,” IEEE Trans. Electron Devices, vol. 38, no. 2, pp. 278-284, Feb. 1991.
[38]R.B . Fair, J. J. Wortman,and 1. Liu, “Modeling rapid thermaldif-
fusionofarsenicandboron |
in silicon,” |
J . Elecrrochem. SOC.,vol. |
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131, no. 10, pp. 2387-2394, Oct. 1984. |
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M. Norishima, H. Iwai, Y. Niitbu, and K. Maeguchi, “Impurity dif- |
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fusion behavior of hipolar transistor under low-temperature furnace |
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annealing End high-temperature RTA and their optimization |
for 0.5- |
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pm Bi-CMOS process,’’ IEEE Trans. Electron Devices, vol. |
39, no. |
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I , pp. 33-40, Jan. 1992. |
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G. Hobler and S.Selberherr. “Two-dimensional modeling of |
ion im- |
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plantation induccd point defects,“IEEE Trans. Computer-AidedDes., |
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vol. 7, no. 2, pp. |
174-180, Feb. 1988. |
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|
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D.Fink, 1. P. Biersack, H. D.Cartanjen, |
F. Jahnel, K. Muller,H. |
||||||||
Ryssel, and A. Osei, “Studies |
on the lattice position of boron in sil- |
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icon,” RadiationEfects,vol. |
77, pp. 11-33, |
1983. |
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N. E.B.Cowern, |
K. T. F. Janssen,and |
H. F. F. Jos, |
”Transient |
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diffusion of ion-implanted B i n Si: Dose, time,andmatrixdepen- |
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dence of atomic and electrical profiles.” J. Appl. Phys., vol. 68, no. |
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12, pp. 6191-6198, Dec. IS, 1990. |
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N. Shigyo, K . Sato,K.Kato,andT.Wada,“TRIMEDES:Atrian- |
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gular mesh device simulator linked with topographylprocess simula- |
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tion,”Trans.Insr.Electron.Insr.Electron. |
Inform.Commun. |
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vol. E71, no. IO, |
pp. 992-999, Oct. 1988. |
S . Yasuda,“Minority |
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N. Shigyo, H. Tanimoto, M. Norishima.and |
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camer mobility model for device simulation,” Solid-Srure Electron., |
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vol. 33, no. 6, pp. 727-731, |
June 1990. |
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N. Shigyo, N. Konishi, H. Satake.andY.Niitsu, |
“A new bandgap |
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narrowing model based on corrected intrinsic camer concentration,” |
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presented at the |
1991 VLSIProcessiDeviceModelingWorkshop, |
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Oiso,Japan, May 1991. |
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Bruno Baeeus wasbornin |
Lille. France, |
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tober 6 , 1962. He receivedtheingenieurdegree |
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from the lnstitut Superieur d’Electroniquedu Nord |
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(ISEN), Lille,in |
I985 and theDoctorat en Elec- |
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troniquedegree |
from the,UniversityofLille |
in |
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1990. His thesis dcalt with two-dimensional mul- |
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tilayer process simulation. |
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From May 1990 to May 199 I , |
he was a Visiting |
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Scientist attheToshiba |
ULSI Research |
Center, |
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Kawasaki, Japan, on leave from ISEN.He worked |
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on processmodelingofRTAanditsapplication |
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IO bipolar technologies. His research interests center |
on process modeling |
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and shallow junction formation. |
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Tetsunori Wada (A’88)was bornin |
Kamakura, |
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1951. HereceivedtheB.S.degree |
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appliedphysicsfromtheUniversity |
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Tokyo, |
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Tokyo,Japan, in |
1975. |
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He then joined the Toshiba Corporation where |
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he wasengaged |
indevelopingmicrolithography |
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technology from 1975 to 1981. He is currently en- |
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gaged in the numerical modeling |
of semiconduc- |
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tor devices at the ULSI Research Center. |
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Mr. Wada isamember |
of theJapanApplied |
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Physics Society. |
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For individual use by an IEEE Electron Devices Society member purchasing this product.
BACCUS et 01.: STUDY MODELINGOF NONEQUILIBRIUMDIFFUSION
Naoyuki Shigyo (M’89-SM’90) wab born in Nagasaki,Japan, on March10,1955.Hereceived
the B . S . degree in electronicsengineeringfrom ChibaUniversity,Chiba,Japan.in1977 and the M.S. degree in information science and the Ph.D. degree from Tohoku University, Sendai, Japan, In 1980 and 1988, respectively. His dissertation was on three-dimensional simulation of VLSI devices.
In 1980,hejoinedtheToshibaResearch |
and |
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DevelopmentCenter,ToshibaCorporation, |
Ka- |
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wasaki,Japan.Hehas |
been engazed in thenu- |
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66 I
Kazumi Inou was born in Yamaguchi Prefecture.
Japan,in 1963. He receivedtheB.S.degree |
in |
appliedphysicsfromtheScienceUniversity |
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Tokyo in 1986 and the M.E. degree from the To- kyo Institute of Technology m 1988.
In 1988, he joined the Toshiba ULSI Research Center,ToshibaCorporation,Kawasaki,Japan, where he has been engaged in advancedBIPOLAR technology.
