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ON THE GROWTH FROM THE AMORPHOUS PHASE IN SEMICONDUCTORS
J. Bourgoin, R. Asomoza
To cite this version:
J. Bourgoin, R. Asomoza. ON THE GROWTH FROM THE AMORPHOUS PHASE IN SEMICONDUCTORS. Journal de Physique Colloques, 1983, 44 (C5), pp.C5-175-C5-177.
�10.1051/jphyscol:1983527�. �jpa-00223112�
JOURNAL DE PHYSIQUE
Colloque C5, suppl6rnent au nOIO, Tome 44, octobre 1983 page C5-175
ON THE GROWTH FROM THE AMORPHOUS PHASE IN SEMICONDUCTORS
J . C . Bourgoin* and R. Asomoza
Centro de Investigaeion y de Estudios Avanzados deZ I.P.N., Departamento de Ingeneria Ezectrica, Apartado Postaz 14-740, 07000 Mexico D.F., Mexico
Resume
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On developpe un modPle de croissance d'une phase ordonnee base sur l a c l i f f u s i o n des lacunes thermiques produi t e s t 1 'i n t e r f a c e avec 1 'amorphe.I1 fournit pour Ge e t Si l a dependance exacte du taux de croissance pour l e s couches evaporees e t l e s couches implantees avec l a temperature, l ' e t a t de l ' o r i e n t a t i o n c r i s t a l l i n , l e dopage, l ' i o n i s a t i o n e t l a nature des ions implantes.
Abstract
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A model of growth based on the diffusion of thermally generated vacancies t o the i n t e r f a c e i s developed which provides the exact dependence of the growth r a t e with temperature, crystal l i n e o r i e n t a t i o n , doping, ionisation and nature of implanted ions i n evaporated as well as implanted layers, f o r both Ge and S i .I
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IntroductionThe aim of t h i s communication i s t o show t h a t t h e growth, being an i n t r i n s i c property of the material, i s related t o i t s fundamental c h a r a c t e r i s t i c s . Basically, we shall demonstrate t h a t t h e growth i s r e l a t e d t o self-diffusion and quenching phenomena i n c r y s t a l s which a r e d i r e c t l y connected t o the formation energy of the i n t r i n s i c defect present a t thermal equilibrium. This allows us t o j u s t i f y quantita- t i v e l y the variation of the growth r a t e with the temperature, the c r y s t a l l i n e orientation and various other parameters such as doping, ionization and l a s e r i r r a d i a t i o n . In turn, t h i s provides a proof t h a t the thermally induced defects i n semiconductors a r e vacancies and explains how self-diffusion and quenching data are related (1). Finally, we shall see how t h e difference of growth behaviour between evaporated and implanted layers necessarily implies ( 2 ) t h a t implanted layers a r e not amorphous b u t disordered ( i . e . contain vacancy c l u s t e r s ) .
I1
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The growth in semiconductorsDue t o i t s potential i n t e r e s t s , the growth of semiconductors from the s o l i d (amorphous) phase has been extensively studied ( f o r a compilation of the references see r e f . 2 ) . However, the way atomic rearrangement i s induced a t the c r y s t a l l i n e - amorphous i n t e r f a c e has n o t been determined and the activation energy Q associated w i t h the growth r a t e Vg has not been j u s t i f i e d . Moreover, the discrepancy between the growth behaviour (see Table 1 ) i n evaporated and implanted layers ( a variation of Q by a f a c t o r of .L 2 in both Ge and S i ) has not been explained,
In the next section, we describe a model which j u s t i f i e s quantitatively these activation energies and t h e i r difference i n evaporated and implanted layers, f o r both S i and Ge. Then, i n section IV, we b r i e f l y discuss how such model provides the exact dependence o f Vg with the c r y s t a l l i n e orientation and explains the variation of V with the nature and concentration of the doping (as well as with ionization and Yaser i r r a d i a t i o n ) , and with the nature of the implanted ions.
*Permanent a d d r e s s : Groupe d e Physique d e s s o l i d e s d e l f E . N . S . , U n i v e r S i t 6 P a r i s V I I , Tour 2 3 , 2 p l a c e J u s s i e u , 75251 P a r i s Cedex 05, F r a n c e
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983527
JOURNAL DE PHYSIQUE
Table I
A c t i v a t i o n energies Q ( e V ) associated w i t h t h e growth r a t e i n Ge and S i evaporated (QE) and implanted (QI) l a y e r s and comparison o f these energies w i t h a c t i v a t i o n energies associated w i t h s e l f - d i f f u - s i o n (QSD) and quenching (QQ). A c o m p i l a t i o n o f t h e references can
be found i n r e f . 2 f o r QE and QI and i n r e f . 3 f o r QSD and QQ.
I11
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Model o f growthExamination o f Tab1 e I shows t h a t , w i t h i n experimental accuracy, t h e a c t i v a t i o n energies QE associated w i t h V i n evaporated l a y e r s , f o r b o t h Ge and S i , i s equal t o the a c t i v a t i o n energy associafed w i t h s e l f - d i f f u s i o n . Therefore, s e l f - d i f f u s i o n i s t h e l i m i t i n g process o f the growth : growth occurs when vacancies c r e a t e d t h e r m a l l y m i g r a t e t o t h e i n t e r f a c e , thus a l l o w i n g t h e jump o f an atom from t h e amorphous t o
the c r y s t a l l i n e phase. The growth r a t e Vg i s then p r o p o r t i o n a l t o t h e p r o b a b i l i t y t o form a vacancy times t h e Boltzman f a c t o r associated w i t h t h e m i g r a t i o n :
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where 6 , V, E and EF are r e s p e c t i v e l y t h e i n t e r a t o m i c distance, t h e atomic v i b r a t i o n - a l frequency,?he m i g r a t i o n and f o r m a t i o n o f t h e vacancy ( 4 ) . Since EF + Em = QSD, we have : QE = QSD. Such model f i t s the v a r i a t i o n o f V versus temperature u s i n g
reasonable entropy f a c t o r s (2). g
What about t h e growth i n implanted l a y e r s ? An implanted l a y e r , o r i g i n a l l y c r y s t a l l i n e o r even amorphous, contains n e c e s s a r i l y vacancy c l u s t e r s formed f o l l o w i n g t h e cascade o f displacements produced by t h e implanted i o n s . I n t h a t case, vacancies o r i g i n a t e from these c l u s t e r s because, as shown i n r e f . 1, t h e f o r m a t i o n energy o f a vacancy o r i g l ' n a t i n g from a c l u s t e r surface i s s m a l l e r : 0.5 E
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Thus, t h e a c t i v a t i o n energy associated w i t h the growth o f implanted l a y e r i s Q1 = 6.5 QE s i n c e Em i s v e r y small compared t o EF (vacancies m i g r a t e w e l l below room temperature). T h i s s i t u a t i o n i s s i m i l a r t o t h e s ~ t u a t i o n encountered i n a quench : c o o l i n g induces t h e sursatura- t i o n o f vacancies and r e s u l t s i n vacancy c l u s t e r s ; indeed, as shown i n Table I : QI = QQ, t h e a c t i v a t i o n energy associated w i t h quenching.Thus, t h e model j u s t i f i e s q u a n t i t a t i v e l y Q and QE f o r b o t h Ge and Si; t h e d i f f e r e n c e between QI and QE i s a r e s u l t from t i e f a c t t h a t implanted l a y e r s c o n t a i n vacancy c l u s t e r s , i . e . i's, d ~ s o r d e r e d and n o t amorphous.
I Y
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ConsequencesThe model i s a b l e t o do more than t o p r o v i d e the exact values o f Q and QI i n b o t h Ge and S i
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As i t i s developed elsewhere, i t accounts f o r t h e depen$ence o f V w i t h t h e v a r i o u s parameters so f a r s t u d i e d ( a c o m p i l a t i o n o f the corresponding references i s i n r e f . 2), thus p r o v i d i n g several o t h e r p r o o f s o f i t s v a l i d i t y .IV.1
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orie3t_atio!-depex?denceAccording t o the model, V i s proportional t o t h e distance s between growth planes and inversely proportiona? t o the density of atoms in these planes. The calculation (2) provides the exact experimental variation of V with the c r y s t a l l i n e orientation. Only, f o r orientation close t o t h e (111) d i r e c t i o j , i s t h e calculated r a t e larger than the experimental one. This i s not surprising since, f o r such orien- t a t i o n , the i n t e r f a c e i s perturbed by the easy reconstruction between (111) dangling bonds.
Iv.2
- Oeee!de_nc_~ -on_-the_-!a_t_urs-of - the-Ime1a_!t_ei-io!!s
Because migrating vacancies can be trapped by impurities (such as 0 t o form A centers) or voids (formed by implanted r a r e gases), i t i s not surprising t h a t oxygen andotherimpurities, a s well a s r a r e gases, decrease the r a t e of growth.
IV.3
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Dopj!g-dependenceSelf-diffusion i s dependent on t h e nature and concentration of the dopant because the migration energy of the vacancy varies strongly with i t s charge s t a t e , function of the Fermi level position. The growth r a t e varies accordingly. This explains q u i t e readily the enhancement of Vg under ionization, such as the ones produced by electron o r l a s e r i r r a d i a t i o n ( i n t h i s l a s t case i t i s not possible t o predict quantitatively the variation of V g because the increase of temperature i s not well known).
V
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ConclusionIn conclusion, we have demonstrated t h a t the growth i n semiconductors i s induced by thermally generated vacancies. This simple model provides the exact values of t h e activation energies associated with the growth r a t e Vg i n both Ge and S i , f o r both evaporated and implanted layers and i s i n complete agreement with s e l f - diffusion and quenching data. I t explains the c r y s t a l l i n e orientation dependence of V i t s variation with doping, ionization and nature of the implanted ions. Finally, i?'shows t h a t implanted layers a r e not amorphous but contain vacancy c l u s t e r s .
References
1. BOURGOIN J.C., unpublished.
2. BOURGOIN J.C. and ASOMOZA R, t o be published in Phys. Rev. Letters.
3. LANNOO M. and BOURGOIN J.C., Point Defects i n Semiconductors, I
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Theoretical Aspects (Springer, Berlin, 1981) chaps. 6 and 7.4. I t i s shown i n r e f . 1 t h a t vacancies a r e the thermally generated defects because self-diffusion and quenching data cannot be reconciled i f the defects a r e i n t e r s t i t i a l s .
