3D Modelling of Temperature Dependent Power Distribution During Microwave Annealing of Doped c-si

Transcription

1 IOSR Jounal of Eletial and Eletonis Engineeing (IOSR-JEEE) e-issn: ,p-ISSN: , Volume 9, Issue 1 Ve. V (Feb. 2014), PP D Modelling of Tempeatue Dependent Powe Distibution Duing Miowave Annealing of Doped -Si S D Das Cente of Exellene fo Geen Enegy and Senso Systems, BESU, India Abstat: Reystallized silion sola ells using miowave annealing will equie adequate modelling of miowave powe distibution to pedit the unifomity of e-ystallization of silion, speially at high tempeatues. Sine, eystallization will have to be aied out of doped silion, doping dependene of suh poesses at high tempeatues is also vey impotant. This wok epots modelling esults fo tempeatue and doping dependene of miowave spatial powe distibution in -Si wafe duing miowave annealing. Tempeatue dependene was intodued though bandgap, effetive mass and lattie satteing tems in Dude model of fee-aie onentation. Dependene of doping was intodued though fee-aie dependent omplex dieleti funtion. Absoption of powe was then alulated fom the omplex pat of the dieleti onstant. The 3D Modelling was aied out using Exat Finite Diffeene Method. All esults pesented in this pape ae fo Industial, Sientifi and Medial (ISM) fequeny of 2.45 GHz. Keywods: sola ells, 3D, miowave, annealing, doping I. INTRODUCTION Sustainable tehnology is key to long tem advanement of enewable enegy seto. Miowave heating is one suh sustainable tehnology whih ould be adopted fo manufatuing of sola ells. Many suh shemes have been identified in the eent past and eystallized silion sola ell using miowave annealing is one suh tehnique [1]. The onept alls fo ion implantation of doped -Si wafe to fom p-n juntion. Miowave annealing should then be aied out fo eystallization and implantation damage emoval [2-3]. Suh high tempeatue annealing poess may also ativate the dopants depending upon tempeatue ahieved inside the sample and doping speies. To pedit the spatial unifomity of eystallization poess using miowave annealing, spatial distibution of absobed miowave powe by silion needs to be modelled auately. To model eystallized silion sola ells, undestanding of the poesses in implanted egion and doped -Si substate egion sepaately is neessay; sine based on spatial distibution of mateial popety suh as dieleti funtion seletive heating due to miowave absoption will take plae. Full system 3D modelling tehnique using Exat Finite Diffeene Tehnique (efdm) of doped -Si at 300K has been epoted elsewhee [4], whih desibes the impotane of avity dimensions on suh poedue. In this wok, fist tempeatue and doping dependene of mateial dieleti funtion will be intodued though Dude's model; followed by epoting of esults fom full system 3D modelling of spatial distibution of absobed miowave powe in doped -Si substate using efdm tehnique. Dependene of suh poess on tempeatue between 300K 800K at diffeent doping levels of -Si substate will be pesented. II. MODELLING TEMPERATURE DEPENDENCE OF DIELECTRIC FUNCTION IN DOPED SILICON In non-pola semiondutos suh as -Si the mehanism of absoption at ISM fequeny is pimaily fee-aie absoption whih depends upon doping levels and tempeatue of the mateial. Miowave powe absobed by non-magneti mateials is dietly popotional to elative imaginay pat of omplex dieleti funtion ε [5]. The omplex dieleti funtion ε fo -Si dependent on fee-aie absoption is given by Dude's model [6, 7]: ε= ε + i ε ε feeaie = ε oe + 4πi ω [ n e e 2 τ e m e (1 iωτ e ) + n h e 2 τ h m h (1 i ωτ h )] (1) Dude model alulates omplex dieleti funtion fom omplex ondutivity of the mateial and ondutivity of a mateial is elated to total fee aie onentation whih depends on doping onentation and tempeatue via Femi level. Total fee aie onentation is dependent on themally geneated and photogeneated aies. In this wok photo-geneation is negleted as at -Si bandgap this ould be negleted fo miowave annealing unde dak onditions. The Femi level depends dietly on doping onentation and tempeatue, and to impove auay of the modelling tempeatue dependene of effetive masses and 46 Page

2 3D Modelling of Tempeatue Dependent Powe Distibution Duing Miowave Annealing of Doped bandgap have been inluded as well whih affets Femi level indietly. Tempeatue dependant effetive masses also dietly influene the dieleti funtion and they have been modelled using Geen et. al. model [8]: E g (T )) 2 m l m e (T ) m 0 = 6 2/3[( C E g (0) m 0] (1/3) m h (T) m 0 =( a+ bt+ T 2 + d T 3 + e T 4) 4 2/3 1+ ft + g T 2 + ht 3 + i T whee, m e and m h ae effetive mass of eleton and hole, espetively. Fo tempeatue dependene bandgap standad Vashni equation has been used [9]. (2) (3) Doping onentation Tempeatue Doping Speies Femi level Fee dak aie onentation Bandgap(T) Effetive mass (T) Total fee aie onentation Dude's Model Lattie satteing (T) Mobility Relaxation time onstant Fig.1. Intodution of doping and tempeatue dependene to Dude's model of dieleti funtion. The tempeatue and doping dependene of elaxation time onstants fo minoity and majoity aie ( τ e τ h ) ae obtained fom Reggiani et. al. tempeatue and doping dependent mobility model fo -Si [10] : and μ L μ 0 μ(n D, N A,T )= μ o + 1+( N D α 1 C 1) +( N A α 2 C 2) μ 1 1+( N D C s1 + N A 2 C s2) (4) whee, μ L gives the tempeatue dependant lattie satteing of fee-aie. Both elaxation time onstants and fee aie onentation depends on the doping speies like phosphoous (P), aseni (As) o boon (B). Fo moe auate esults bandgap naowing due to doping should be intodued. Change in bandgap due to high doping is of the ode of few mev and only seveely affets ionised impuity onentation at low tempeatues and at vey high doping levels. As this wok fouses on high tempeatues, effets of doping dependene on bandgap will be ignoed fo this publiation. III. RESULTS AND DISCUSSIONS Vaiation of omplex pat of elative dieleti funtion with doping onentation and tempeatue as desibed by (1) to (4) is shown in the Fig. 3. The dopant speies is phosphoous (P) and impotant modelling values ae tabulated in Table 1. Fom Fig. 3, it is evident that ε values ineases with dono onentation fist and then ate of inease slows down. The slowing down sets in at highe tempeatues fo highe values of doping onentation. This is due to the fat that at a given tempeatue and at high values of doping onentation, numbe of ionized dopants tend to satuate aoding to govening distibution of aie ove themal enegy and with the inease in tempeatue this satuation effet stats at highe values of doping 47 Page

3 3D Modelling of Tempeatue Dependent Powe Distibution Duing Miowave Annealing of Doped onentations. This fat is lealy efleted in ε in Dude model values as ε is dietly dependant on fee aie onentation K 400K 500K 600K 700K 800K N D (m 3 ) Fig. 2 Imaginay pat of elative dieleti funtion ε as a funtion of dono onentation (N D ) fo tempeatues T = 300K to 800K. (f = 2.45GHz). Paametes Table 1. Modelling values fo omplex dieleti onstant Values ε oe 11.9 μ L = μ max ( T T γ+ 300 )( 300 ) μ L = 1441( T 0.07 T )( 300 ) τ e = m e m o μ e q τ e = 9.1x x10 8 μ e q, μ e is given by (4) N a 1x10 14 m K 400K 500K 600K 700K 800K f (GHz) Fig. 3 Imaginay pat of elative dieleti funtion ε as a funtion of fequeny (f) with tempeatue as paamete fom 300K to 800K. In a household miowave oven, the fequeny of opeation is not limited to 2.45 GHz, but has a ange defined by ±50 MHz. Fig. 3 shows typial vaiation of ε values with fequeny at vaious tempeatue values between 48 Page

4 3D Modelling of Tempeatue Dependent Powe Distibution Duing Miowave Annealing of Doped 300K to 800K fo dono onentation (N D ) of 2x10 18 m -3. These esults indiate ε ompaed to tempeatue of -Si and fequeny of opeation. is moe sensitive to N D as Fig. 4. Full system miowave powe distibution (vetial oss setion otated 90 O lokwise) with -Si wafe plaed vetially at the middle left one. f = 2.45 GHz The full system modelling of absobed miowave powe was aied out by solving the Helmholtz equation using 3D efdm tehnique[3]. In this wok full system ompised of a -Si wafe plaed inside a metal avity without any mateial suppot. Dimensions of the oven avity was kept as ealie, while dimensions of -Si wafe was m 3. A dense mesh was used in the z-dietion to maintain easonable numbe of nodes fo solving Helmholtz equation inside the wafe, oesponding points pe unit wavelength was maintained at (15,15,1000) fo (x,y,z) dietions. This gave ise to matix with 1,998,792 numbe of elements. Miowave powe distibution esults fo full system ae shown in the Fig. 6. Fom this figue it is evident that most of the enegy is onentated inside the wafe. Fom elative peak absoption powe uves (Fig. 7(a) & 7(b)) of -Si, it an be infeed that absoption ineases by an ode of magnitude if doping density is ineased by an ode of magnitude, howeve inease in absoption powe is muh smalle when doping density is kept onstant and tempeatue of wafe is ineased. This is due to little hange in ε with tempeatue, as is evident fom Fig. 2. Fig. 5() povides elative peak powe spetum of the absobed powe inside the wafe at 800K and N D = 1x10 18 m -3, showing some fequenies ae well suppoted while othes ae not and peak of absoption is lose to f = 2.45 GHz. (a) (b) 49 Page

5 3D Modelling of Tempeatue Dependent Powe Distibution Duing Miowave Annealing of Doped () Fig 5. Relative peak powe absobed with in -Si wafe (a) as funtion of tempeatue ( f = 2.45 GHz); (b) as funtion of doping density at 300K ( f = 2.45 GHz) and () as a funtion of fequeny. The esults fo full system spatial distibution of miowave powe absoption in -Si wafe is shown in Fig. 6. Fom these figues it is evident that even at high tempeatue and high doping density the spatial distibution is not affeted by these paametes and dominant paametes ae dimensions of sample and miowave avity. As suggested by Fig 5(), peak absoption haateistis may be obtained at patiula fequeny fo given dimension of sample and miowave avity. (1) (a) (b) (2) (a) (b) (3) (a) (b) Fig 6. Miowave powe distibution; (a) hoizontal oss setion and (b) vetial oss setion (magnified and otated 90 O lokwise) fo f = 2.45 GHz, T = 800K at (1) N D = 1 x m -3, (2) N D = 1 x m -3 and (3) N D = 1 x m -3. IV. CONCLUSION In onlusion, 3D modelling esults fo spatial distibution of miowave powe in phosphoous doped -Si wafe has been pesented. Tempeatue and doping dependene in miowave annealing of -Si wafe was intodued though Dude's model of omplex dieleti onstant. Results fom modelling show that tempeatue has weak influene on omplex pat of dieleti funtion while doping do have signifiant influene on dieleti funtion but spatial distibution is not dominated by the two paametes. Thus unifomity issues of spatial distibution of absobed miowave powe at f = 2.45 GHz is not dominated by doping levels and tempeatue of -Si wafe. Futhe wok on unifomity issues will equie auate modelling of ion-implanted egion of the eystallized silion sola ells. Aknowledgements This wok was aied out as Reseah Assoiate at CEGESS, BESU unde the DST Pojet entitled 'Sola Photovoltai Hub at BESU''. Autho would like to thank institute, univesity and funding ageny fo thei full suppot and enouagement. 50 Page

6 3D Modelling of Tempeatue Dependent Powe Distibution Duing Miowave Annealing of Doped REFERENCES [1] S. D. Das, Pospets of Miowave Heating in Silion Sola Cell Fabiation A Review, IOSR-JEEE, 6(3), 2013, [2] R. N. P. Vemui, M. J. Gade, N. D. Theodoe, and T. L. Alfod, Dopant Ativation in Aseni -Implanted Si by Susepto- Assisted Low-Tempetue Miowave Anneal, IEEE Eleton Devie Lettes 32, 2011, [3] J. N. Lee, Y. W. Choi, B. J. Lee and B. T. Ahn, Miowave-indued low-tempeatue ystallization of amophous silion thin films, Jounal of Applied Physis, 82(6), 1997, [4] S. D. Das, Full wafe 3D modelling of powe distibution duing miowave annealing of doped -Si, IOSR-JEEE, 9 (1-IV), 2014, [5] T Basak, Role of lateal and adial iadiations on effiient miowave poessing of food ylindes, Chemial Engineeing Siene, 62, 2007, [6] D. C. Dibben, Numeial and Expeimental Modelling of Miowave appliatos (Univesity of Cambidge, 1995). [7] T. Sameshima, H. Hayasaka and T. Haba, Analysis of Miowave Absoption Caused by Fee Caies in Silion, Japanese Jounal of Applied Physis, 48, 2009, [8] M. A. Geen, Intinsi onentation, effetive densities of states and effetive mass in silion, Jounal of Applied Physis, 67(6), 1990, pp [9] Y. P. Vashini, Tempeatue dependene of Enegy gap in semionduto, Physia, 34, 1967, pp 149. [10] S. Reggiani, M. Valdinoi, L. Colalongo, M. Rudan, G. Baaani, A. D. Stike, F. Illien, N. Felbe, W. Fihtne, and L. Zullino, Eleton and Hole Mobility in Silion at Lage Opeating Tempeatues Pat I: Bulk Mobility, 49(3), 2002, pp Page