APPLICATION OF DISLOCATION-INDUCED ELECTRIC POTENTIALS IN Si AND Ge

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APPLICATION OF DISLOCATION-INDUCED ELECTRIC POTENTIALS IN Si AND Ge

S. Mil’Shtein

To cite this version:

S. Mil’Shtein. APPLICATION OF DISLOCATION-INDUCED ELECTRIC POTENTIALS IN Si AND Ge. Journal de Physique Colloques, 1979, 40 (C6), pp.C6-207-C6-211.

�10.1051/jphyscol:1979641�. �jpa-00219057�

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JOURNAL DE PHYSIQUE ColZoque C6, suppldrnent au n06, tome 40, j u i n 1979, page C6-207

APPLICATION OF DISLOCATION-INDUCED ELECTRIC POTENTIALS I N S i AND ~ e * S. M i l ' s h t e i n

Department o f Physics, Faculty o f Natural Sciences, Ben G w i o n University, Beer-Sheva, I s r a e l

Resume.- On examine l a b a r r i e r e e l e c t r i q u e (DEB) creee p a r une d i s l o c a t i o n dans l e s semiconducteurs du p o i n t de vue de l a recherche. En analysant l a dependance de l a temperature du DEB, on o b t i e n t des re-

s u l t a t s q u a l i t a t i f s nouveaux sur l e s niveaux d l @ n e r g i e dans l e s d i s l o c a t i o n s . On propose l a p o s s i b i l i -

t e de determiner l a d e n s i t e des d i s l o c a t i o n s a l ' a i d e de mesures e l e c t r i q u e s . Un modele de d i s l o c a t i o n i s o l e e e t des c i r c u i t s m o n o l i t i q u e s bases sur e l l e , sont d i s c u t e s .

Abstract .- U t i 1 iz a t i o n o f d i s l o c a t i o n e l e c t r i c b a r r i e r (DEB) i n semiconductors f o r fundamental r e - search purposes, as w e l l as DEB device a p p l i c a t i o n i s considered. Analyzing the DEB temperature dependence new q u a l i t a t i v e i n f o r m a t i o n on d i s l o c a t i o n energy s t a t e s i s obtained. Determination o f d i s - l o c a t i o n d e n s i t y by e l e c t r i c a l measurements i s proposed. Model o f s i n g l e d i s l o c a t i o n and m o n o l i t h i c c i r c u i t s based on i t a r e discussed.

1. I n t r o d u c t i o n . - From t h e very beginning t h e p r o - gress o f semiconductor e l e c t r o n i c s was connected w i t h s t u d i e s o f i m p u r i t i e s i n semiconductor c r y s t a l s . The same s i t u a t i o n now e x i s t s concerning i n v e s t i g a - t i o n s on d i s l o c a t i o n s . I n comparison w i t h i m p u r i t i e s t h e r o l e played by d i s l o c a t i o n s i n c r y s t a l s i s no l e s s s u b s t a n t i a l . The e l e c t r i c p o t e n t i a l due t o t h e p o i n t d e f e c t ( i m p u r i t y ) drops w i t h a distance r l i k e l / r , b u t DEB drops l i k e Ln r. Therefore, i n t h e case of d i s l o c a t i o n we w i l l have an extensive e l e c t r i c f i e l d .

The presence o f DEB i n semiconductors causes t h e d i s l o c a t i o n i n f l u e n c e on t h e i r c o n d u c t i v i t y /1-2/, e l e c t r o n mean p a t h /3-4/, c a r r i e r ' s l i f e t i m e /5-6/, o p t i c a l p r o p e r t i e s /7-8/, e t c . . ^,

The modern t r e n d i n m i c r o e l e c t r o n i c s towards higher d e n s i t y o f devices leads t o a s i t u a t i o n where the d i s l o c a t i o n s p l a y a s i g n i f i c a n t r o l e . Even f o r devices o f an a c t i v e area o f o n l y 100 (urn)', a crys- t a l m a t e r i a l of say l o 6 d i s l o c a t i o n s p e r cm2 puts an average o f one d i s l o c a t i o n on every j u n c t i o n surface.

As a r e s u l t o f growing, d i f f u s i o n , i m p l a n t a t i o n , e t c . . t h e process-generated d i s l o c a t i o n d e n s i t i e s a r e o f t e n even h i g h e r than the f i g u r e o f l o 3

quoted f o r "good" c r y s t a l . But even t h i s number o f d i s l o c a t i o n s has a bad a f f e c t on t h e m o n o l i t h i c c i r - c u i t w i t h t h e device-density o f about l o 9 elements p e r I m3.

A t the same time new devices based on d i s l o c a - t i o n s a r e created / 9 - l o / . Therefore, the DEB a p p l i - cation, i n our opinion, means i n the f i r s t p l a c e u t i l i z a t i o n of these p o t e n t i a l s i n attempts t o ob-

i t a l s o i m p l i e s device a p p l i c a t i o n o f DEB.

2. C r y s t a l s w i t h h i g h d i s l o c a t i o n density.- L e t us discuss f i r s t , under which c o n d i t i o n s the DEB e x i s t s i n semiconductor c r y s t a l s . The n-type S i i s taken l i k e an example. Considering t h e DEB due t o t h e d i s - l o c a t i o n c l u s t e r i n n-type s i l i c o n we used the elec- t r i c n e u t r a l i t y equation forsemiconductor which becomes e l e c t r i c a l l y inhomogeneous a f t e r p l a s t i c deformation .(S. M i l 's h t e i n , A. Senderihin, unpublished) .

Our model /11/ deals w i t h two p a r t s o f t h e c r y s t a l : t h e undeformed, n-type c o n d u c t i v i t y p a r t and p-type zone w i t h h i g h d i s l o c a t i o n d e n s i t y o f about 10' 0'101 . I n p r a c t i c e t h e problem i s r e - duced t o f i n d i n g the Fermi l e v e l s i n b o t h p a r t s .

The d i f f e r e n c e i n t h e p o s i t i o n o f the Fermi l e - v e l s r e s u l t s i n the bending o f t h e bands, i.e., i n t h e emergence o f an e l e c t r i c p o t e n t i a l b a r r i e r . Re- s o l v i n g the e l e c t r i c n e u t r a l i t y equation separately t h e n- and p-type p a r t s o f a c r y s t a l , we o b t a i n the h e i g h t o f DEB dependent on temperature on t'he f r e e c a r r i e r s c o n c e n t r a t i o n and p o s i t i o n o f s i n g l e d i s l o - c a t i o n acceptor o r on the d i s l o c a t i o n band. A d i s l o - c a t i o n acceptor l e v e l o f 0.39 eV i s assumed f o r S i .

F i g u r e 1 i l l u s t r a t e s t h e temperature dependence o f the DEB i n S i w i t h various i n i t i a l donor i m p u r i - t i e s c o n c e n t r a t i o n from 1011cm-3 t o 1016cm-3 i n p l a s t i c a l l y deformed n-type Si assuming s i n g l e d i s - l o c a t i o n l e v e l a t E = 0.39 eV, t h e r e c o u l d e x i s t a DEB, whose h e i g h t changes from 0.739 eV t o 0.176 eV w i t h the r i s e o f temperature from -200°C t o +200°C.

When the presence o f empty d i s l o c a t i o n band o f 0.39- 0.2 eV i s taken i n t o account, t h e p o t e n t i a l b a r r i e r t a i n new information about t h e d i s l o c a t i o n . Secondly, decreases form 0.95 eV t o about 0.2 eV i n t h e same

"

Supported by t h e U.S. A i r Force temperature range.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979641

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JOURNAL DE PHYSIQUE

F i g . 1 : DEB t e m p e r a t u r e dependence i n S i f o r t h e case o f ~ i n g l e ~ d i s l o c a t i o n l e v e l and c o n c e n t r a t i o n s 1 - 1 0 " ~ m - ~ , 2 - 1 0 ' ~ c m - ~ , 3-1013cm-3, 4 - 1 0 l ' ~ m - ~ , 5-1015cm- , 6 - 1 0 l 6 ~ m - ~ .

We can see t h a t t h e DEB o f d i s l o c a t i o n c l u s t e r e x i s t s , i n a wide temperature range, i n c r y s t a l w i t h a v a r i e d c o n c e n t r a t i o n o f i m p u r i t i e s .

We made an a t t e m p t t o o b t a i n t h e q u a l i t a t i v e i n f o r m a t i o n about d i s l o c a t i o n energy s t a t e s f r o m t h e DEB temperature dependences. It f o l l o w s f r o m o u r c a l c u l a t i o n s , t h a t i n a case o f t h e empty d i s l o c a - t i o n band t h e h e i g h t o f DEB i s a b o u t 0.5-0.6 eV i n c r y s t a l s w i t h an i n i t i a l donor c o n c e n t r a t i o n o f 10' 3-10'5cm-3. T h i s i s a p p r o x i m a t e l y t w i c e t h e v a l u e measured b y us on i d e n t i c a l c r y s t a l s a t room tempe- r a t u r e 1111. A t l o w t e m p e r a t u r e t h e b a r r i e r almost reaches t h e magnitude o f t h e f o r b i d d e n bandwidth.

These exaggerated v a l u e s f o r t h e e l e c t r i c p o t e n t i a l s can be o b t a i n e d , i f i t i s c o n j e c t u r e d , t h a t i n s t e a d o f a empty d i s l o c a t i o n band i t ' s b o t t o m t a k e n i n t o account (Ea = 0 . 2 eV o r even more s h a l l o w l e v e l ) .

Our c a l c u l a t i o n s were i n agreement w i t h experiment /11-12/ i f d e e p - l y i n g s i n g l e l e v e l s o r more t h a n h a l f - f i l l e d d i s l o c a t i o n band had been t a k e n i n t o ac- c o u n t , i .e..0.35-0.39 eV a r e t h e 1 im i t s f o r Fermi l e v e l .

I n t h e case o f t h e empty d i s l o c a t i o n band a t t e m p e r a t u r e below -150°C t h e DEB becomes so h i g h t h a t Fermi l e v e l i n t h e nondeformed n - t y p e p a r t o f S i touched t h e b o t t o m o f c o n d u c t i o n band, and, i n t h e p - t y p e i t passes t h r o u g h t h e values o f t h e d i s - l o c a t i o n band. I n t h a t case t h e v o l t a g e - c u r r e n t c h a r a c t e r i s t i c s must resemble t h e c h a r a c t e r i s t i c s o f t u n n e l diodes. The t u n n e l i n g e f f e c t has, however,

n o t been observed by anyoney even though l o w tempe- r a t u r e measurements were made on b i c r y s t a l s /13/ and on h e a v i l y d i s l o c a t e d S i /12/, where t h e d e n s i t y o f d i s l o c a t i o n a c c e p t o r s up t o 1017cm-3 has been i n d i - c a t e d . T h i s f a c t enabled us t o assume, t h a t t h e deep- l y i n g d i s l o c a t i o n band, w i t h w i d t h o f about s e v e r a l hundredths o f an e l e c t r o n - v o l t , i s i n v o l v e d i n DEB emergence.

The method d e s c r i b e d above can a l s o be used on n - t y p e Ge and p-type m a t e r i a l s as w e l l . I n h o l e ma- t e r i a l s t h e p - ~ + t y p e b a r r i e r s can be computed.

L e t us d i s c u s s one more example o f DEB a p p l i c a - t i o n s f o r purposes o f fundamental r e s e a r c h . The p-n j u n c t i o n s , formed by t h e d i s l o c a t i o n c l u s t e r has c a p a c i t y p e r cm2 ( C ) which we measured b y s p e c i a l b r i d g e (model 4270A H e w l e t t Packard) a t room tempe- r a t u r e . The DEB h e i g h t Q o f about 0.3 eV was measu- r e d b y methods developed i n o u r r e c e n t work /11/.

F i g u r e 2 p r e s e n t s c2 versus r e v e r s e b i a s v o l - t a g e V. I n case o f q@ >> kT we can use t h e model o f a b r u p t p-n i n a c t i o n . T h e r e f o r e , c a p a c i t a n c e measurements /14/ f u r n i s h a s i m p l e way o f d e t e r m i n i n g t h e d e n s i t y o f a c c e p t o r s i n a deformed p a r t o f t h e c r y s - t a l , i . e . , t h e d i s l o c a t i o n d e n s i t y :

Using e q u a t i o n ( 1 ) f o r S i w i t h Na - 1 0 " ' ~ m - ~ , we f i n d t h e d e n s i t y o f d i s l o c a t i o n a c c e p t o r s o f about

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S . Mil' shtein C6-209

Z X ~ O ' ~ and t h a t i s equivalent t o t h e d i s l o c a t i o n d e n s i t y N d i s z 1.3x109 Control measurements by t h e a i d o f t h e e l e c t r o n microscope revealed N d i s of about 8.6x108 cm2,which agrees well with our calcu- l a t i o n .

Fig. 2 : C2 dependence on r e v e r s e b i a s voltage.

The semiconductor devices bases on d i s l o c a t i o n s /9-lo/ have s u b s t a n t i a l l y improved t h e i r characte- r i s t i c s and a r e especial l y advantageous a s regards t h e i r temperature s t a b i l i t y . They recover a f t e r both e l e c t r i c a l and thermal breakdowns. Their production technology i s very simple because n e i t h e r d i f f u s i o n of dopants nor e l e c t r i c a l processing a r e necessary.

This technology can be used f o r producing diodes, a s well a s f o r d i f f e r e n t types of semiconductors devices ( p h o t o c e l l s , f i e l d e f f e c t t r a n s i s t o r s , e t c . ) . I t must be pointed o u t , however, t h a t t h e question of t h e i r a p p l i c a t i o n i s s t i l l open because t h e i r n o i s e parameters ( e s p e c i a l l y l / f noise) have s t i l l not been i n v e s t i g a t e d .

I t i s proposed t o produce the above semicon- d u c t o r devices on d i s l o c a t i o n s introduced i n t o t h e c r y s t a l by p l a s t i c deformation. Laser i r r a d i a t i o n could be used t o introduce d i s l o c a t i o n s . Thus, paper /15/ i n d i c a t e s t h a t p-n j u n c t i o n s of a small a r e a were obtained by t h e l a s e r i r r a d i a t i o n of a s i l i c o n p l a t e . True, such i r r a d i a t i o n /15/ burned i m p u r i t i e s i n t o t h e c r y s t a l and t h e r e c t i f i c a t i o n obtained

cannot be ascribed t o t h e d i s l o c a t i o n alone. I t can however be expected t h a t l a s e r i r r a d i a t i o n , leading t o melting and r e c r y s t a l l i z a t i o n of a small volume of t h e c r y s t a l and c r e a t i n g d i s l o c a t i o n s , w i l l be a cheap and a c c u r a t e method of manufacturing devices bases on d i s l o c a t i o n s .

3. C r y s t a l s containing s i n g l e d i s l o c a t i o n s . - The s i n g l e d i s l o c a t i o n e l e c t r i c a l b a r r i e r (SDEB) i n Si and Ge can be obtained solving the Poisson's equa- t i o n i n c y l i n d r i c coordinates :

where + ^-i s a p o t e n t i a l of SDEB, under combined boundary conditions :

where X - i s t h e d e n s i t y of charge a t t h e d i s l o c a t i o n core.

A model has been proposed by us (S. M i l ' s h t e i n , A. Senderi h i n , unpublished) i n which the d i s l o c a t i o n charge i s not concentrated a t t h e l i n e , but i s spread throughout t h e c y l i n d e r of t h e radius ro of about t h r e e l a t t i c e c o n s t a n t s . Such an approach allows us t o o p e r a t e with a f i n i t e value of t h e e l e c - t r o s t a t i c p o t e n t i a l . In approximation q$ >> kT and q+ << kT two a n a l y t i c a l s o l u t i o n s can be obtained.

J o i n i n g t h e s e two r e p r e s e n t a t i o n s q u i t e a c c u r a t e l y , we have a form of SDEB i n t h e considered a r e a .

Figure 3 shows t h e 60' - SDEB i n Si with va- r i o u s donor concentration. A s i t can be seen from f i g u r e 1, with changing of donor concentration from 1 0 ' l c m - ~ t o 1018cm-3 t h e SDEB drops from 0.22 eV t o 0.03 eV a t room temperature. The d i s t a n c e a t which t h e p o t e n t i a l a c t u a l l y t u r n s i n t o n i l i s i n t o shown 1 im i t s : from 7 ~ 1 0 - ~ cm t o cm.

Figure 4 p r e s e n t s 60' - SDEB temperature dependence i n Si with Nd = 10' 3cm-3 with decrease i n temperature from +30°C t o -220°C t h e SDEB i n c r e a s e s from 0.17 eV t o 0.42 eV. All t h e curves t u r n t o n i l a t t h e d i s t a n c e 5 ~ 1 0 - ~ m.

We can s e e from f i g u r e s 3 a n d 4 t h a t i n n-type S i w i t h various concentrations of i m p u r i t i e s e x i s t anexten- s i v e S.DEB in wide temperature range. The same computa- t i o n can be done f o r n-type Ge and p-type m a t e r i a l s a s well. From t h e presented curves ( F i g s . 3and 4)we o b t a i - ned an a d d i t i o n a l information about t h e s t r u c t u r e of

SDEB. Our c a l c u l a t i o n shows t h a t t h e e l e c t r i c poten- t i a l drops l o g a r i t h m i c a l l y on t h e d i s t a n c e r = ^0.65

L D (LD - Debye screening length) and then decreases

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C6-2 10

e x p o n e n t i a l l y .

JOURNAL DE PHYSIQUE

F i g . 3 : SDEB dependence on t h e donor c o n c e n t r a t i o n F i g . 4 : SDEB temperature dependence i n S i , i n S i : 1 - 1 0 " ~ m - ~ , 2 - 1 0 ' Z ~ m - 3 , 3 - 1 0 ' 3 ~ m - 3 , 4-10''' 1 -+30°C, 2 - -20°C, 3 - -70°C, 4 - -12OoC, 5 -

~ m - ~ , 5 - 1 0 1 5 ~ m - 3 , 6-1016cm-3, 7 - 1 0 ' ~ c m - ~ , 8 - 1 0 ' ~ c m - ~ . -170°C, 6 - -220°C.

U I C R O P R O B E

S i n-type

Cwlhent Lines DALocaXion L ~ n e

Dd.tocat;ion Cote

0 6 ^ha& ro

A

U I C R O P R O B E

F i g . 5 : Model o f charged s i n g l e d i s l o c a t i o n

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S. Mil'shtein

On t h e b a s i s o f o u r c a l c u l a t i o n s and measurements which were p r e v i o u s l y c a r r i e d o u t by means o f m i c r o probes an e q u i v a l e n t diagram o f a charged d i s l oca- t i o n has been drawn ( c f . F i g . 5). Our c a l c u l a t i o n shows t h a t a p - r e g i o n n e a r t h e d i s l o c a t i o n l i n e does n o t e x i s t , and i t i s j u s t a s t r o n g l y i n t r i n s i c a r e a a l m o s t up t o room temperatures and i m p u r i t y concen- t r a t i o n f r o m 1 0 l ' ~ m - ~ t o 1 0 " ~ m - ~ . I t has been p r o - ved by o u r experiments t h a t , when c u r r e n t i s passed a l o n g t h e d i s l o c a t i o n , r e c t i f y i n g processes a r e developed o n l y a t t h e edges o f t h e c y l i n d r i c a l i - n s t r u c t u r e . The v a l u e s o f t h e r u n n i n g c u r r e n t s d i d n o t change when t h e d i s l o c a t i o n l e n g t h was changed by s e v e r a l o r d e r s o f magnitude. The v i o l e n t sprea- d i n g o f t h e c u r r e n t i s p r o b a b l y due t o t h e h i g h r e s i s t a n c e o f t h e p - r e g i o n . On t h e diagram t h i s r e - s i s t a n c e i s denoted by Ri. When c o l t a g e i s a p p l i e d t o t h e d i s l o c a t i o n ends, t h e c u r r e n t r u n s t h r o u g h t h e e q u i v a l e n t r e s i s t a n c e Rn ( t h e r e s i s t a n c e o f area-n) and t h e diodes Dl and D2 connected o p p o s i t e t o each o t h e r . The n o t i o n about d i s l o c a t i o n as about a l i n e w i t h a d i s t r i b u t e d r e s i s t a n c e and capa- c i t a n c e ( d e l a y l i n e s ) seems t h e r e f o r e t o be n o t q u i t e c o r r e c t . C a r r i e r s i n j e c t e d by l i g h t o r b y an e l e c t r i c a l f i e l d w i l l n o t pass t h r o u g h t h e d i s l o c a - t i o n d e l a y l i n e b u t t h r o u g h t h e d i o d e s l o o p because t h e r e s i s t a n c e Ri i s h i g h and comprises, t o o u r assessment, 10'" 10' 'ohm.

The e l e c t r i c a l e q u i v a l e n t scheme o f s i n g l e d i s l o c a t i o n ( b y p o i n t l i n e s ) can be u s e f u l l y u t i l i - zed i n m o n o l i t h i c c i r c u i t s , some o f them g i v e n l i k e examples on f i g u r e 6 : a ) f u l l - w a v e r e c t i f i e r , b) double d i o d e c l i p p e r , c ) g a t e "AND", d ) g a t e "OR".

It i s beyond t h e scope o f t h i s work any d i s c u s s i o n on e l e c t r o n i c e f f e c t s due t o f r e q u e n c y and l e v e l o f s i g n a l s and on t h e many v a r i o u s t y p e s o f c i r c u i t s as we1 1 .

I t must be p o i n t e d o u t t h a t t h e i n t r o d u c t i o n o f s i n g l e d i s l o c a t i o n s v i a mechanical d e f o r m a t i o n ( s c r a t c h i n g and bending) o f t h e c r y s t a l s , does n o t seem t o be t h e b e s t t e c h n o l o g y f o r mass-produc- t i o n o f e l e c t r o n i c d e v i c e s . W h i l e i t appears t h a t e p i t a x i a l growth i s e v e n t u a l l y g o i n g t o be t h e p r o p e r method t o o b t a i n m i s f i t d i s l o c a t i o n s i n a c o n t r o l l a b l e manner. There i s n o s a t i s f a c t o r y techno- l o g y a v a i l a b l e a t t h e moment.

F i g . 6 : P o s s i b l e a p p l i c a t i o n ( s e v e r a l examples) o f t h e s i n g l e d i s l o c a t i o n i n m i c r o e l e c t r o n i c s : a ) F u l l - wave r e c t i f i e r , b) double-diode c l i p p e r , c ) g a t e

"AND", d) g a t e "OR".

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