ELECTRICAL MEASUREMENTS OF THE GRAIN BOUNDARY LEVELS IN SEMICONDUCTORS

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BOUNDARY LEVELS IN SEMICONDUCTORS

A. Broniatowski

To cite this version:

A. Broniatowski. ELECTRICAL MEASUREMENTS OF THE GRAIN BOUNDARY LEV- ELS IN SEMICONDUCTORS. Journal de Physique Colloques, 1982, 43 (C1), pp.C1-63-C1-73.

�10.1051/jphyscol:1982110�. �jpa-00221763�

JOURNAL DE PHYSIQUE

CoZZoque C l , supple'ment au n o 10, Tome 43, octobre 1982 page Cl-63

E L E C T R I C A L MEASUREMENTS OF T H E G R A I N BOUNDARY L E V E L S I N SEMICONDUCTORS

A. Broniatowski

C. N. R. S., Laboratoire PMTM, Universite' Paris-Nord, Avenue J. B. CZiment, 93430 Vi l letaneuse, France

RESUME

AprSs un rappel des principales caractdristiques du modsle de barriPre de potentiel associge aux joints de grains, on dgcrit les mdthodes utilisses pour mesurer la densit6 et les sections de capture des dtats d'interface, notamment la technique de spectroscopie capacitive (DLTS). Une revue de rgsultats rscents sur les 6tats associds aux joints de grains dans le silicium, le germanium et l'arscniure de gallium est ggalement prdsentge.

ABSTRACT

After recalling the basic features of the grain boundary barrier model, we discuss some of the methods used to measure the density and the capture cross-sections of the interface states, with an emphasis on the transient capacitance technique derived from Deep Level Transient Spectroscopy (DLTS). A review of recent results on the grain boundary states in silicon, germanium and GaAs is given.

1 . Introduction.- A significant part of the work done on polycrystalline semicon-

ductors is aimed at measuring the properties of the electronic levels localized at the grain boundaries. Some of the methods used will be surveyed, with an emphasis on the transient capacitance technique derived from Deep Level Transient Spectroscopy Ill.

Section 2 presents the well-known model of the electrostatic potential barrier associated with carrier trapping at the interface /2/. Besides the boundary charge, the dopant distribution is of major importance in determining the shape of the potential barrier, and means of detecting the amount of dopant segregation will be considered in section 3. Spectroscopic measurements of the boundary levels using the transient capacitance technique are discussed in section 4, and the optical methods are considered more briefly in section 5. A review of recently published data on the grain boundary states in silicon, germanium and GaAs bicrystals will be given last (section 6).

2. The grain boundary barrier model /2/.- Fig. la shows the bending of the energy bands near an electrically charged boundary in n-doped material. A similar picture holds for p-type semiconductors. As the boundary states are filled with electrons, a depletion layer forms on both sides of the boundary and a (negative) electrostatic potential barrier builds up. At equilibrium, the rates of electron capture and

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982110

e m i s s i o n a d j u s t s o t h a t t h e e l e c t r o n s i n t h e b o u n d a r y s t a t e s f o r m a F e r m i d i s t r i b u - t i o n . I f a v o l t a g e b i a s i s a p p l i e d a c r o s s t h e b o u n d a r y , t h e c a p t u r e r a t e w i l l b e i n c r e a s e d a n d t h e o c c u p a n c y o f t h e b o u n d a r y s t a t e s w i l l b e c h a n g e d . As a r e s u l t , t h e b a r r i e r h e i g h t r e m a i n s a p p r o x i m a t e l y f i x e d on t h e n e g a t i v e l y b i a s e d s i d e o f t h e b o u n d a r y , w h e r e a s most o f t h e v o l t a g e d r o p o c c u r s on t h e p o s i t i v e s i d e ( f i g . I b ) . The b a r r i e r e v e n t u a l l y b r e a k s u n d e r i n c r e a s i n g b i a s ; breakdown v o l t a g e s a s h i g h a s 100 V h a v e b e e n m e a s u r e d / 2 /

C.B.

V. 6.

levels

!

F i g u r e 1 : l a - G r a i n b o u n d a r y i n e q u i l i b r i u m , s h o w i n g t h e b a r r i e r h e i g h t Vo and t h e b a r r i e r w i d t h w ; I b - G r a i n b o u n d a r y u n d e r a p p l i e d b i a s V = V1 - V2.

E i s t h e q u a s i - F e r m i l e v e l o f t h e b o u n d a r y s t a t e s / 4 , 5 / . F t

The c a p a c i t a n c e a n d . t h e c o n d u c t a n c e o f t h e b o u n d a r y and t h e v o l t a g e d e p e n d e n c e of t h e b o u n d a r y c h a r g e w i l l be c o n s i d e r e d i n t u r n .

2 . 1 . The grain-b_o~"_~ar_)!_capac~_tance.- The d e p l e t i o n r e g i o n i s a l m o s t d e v o i d o f f r e e c a r r i e r s , s o t h a t t h e s y s t e m i s e q u i v a l e n t t o a p l a n e c a p a c i t o r w i t h i t s p l a t e s a t b o t h e d g e s o f t h e d e p l e t i o n z o n e , i n p a r a l l e l w i t h a weak l e a k a g e c o n d u c t a n c e . I n t h e h i g h f r e q u e n c y l i m i t t h e s p e c i f i c c a p a c i t a n c e i s r e l a t e d t o t h e b a r r i e r w i d t h w by t h e e q u a t i o n :

w h e r e E i s t h e d i e l e c t r i c c o n s t a n t o f t h e medium ( S . I . u n i t s ) . (More c o m p l i c a t e d e f f e c t s w i l l o c c u r i f t h e p e r i o d of t h e m e a s u r i n g s i g n a l c o m p a r e s w i t h t h e t i m e f o r c h a r g e r e a d j u s t e m e n t on t h e b o u n d a r y l e v e l s ; s e e r e f . / 3 / ) . T y p i c a l v a l u e s f o r w a r e 100 A - ^{10 p ,} d e p e n d i n g i n p a r t i c u l a r on t h e d o p i n g l e v e l o f t h e s a m p l e . The b a r r i e r h e i g h t and t h e b o u n d a r y c h a r g e c a n be o b t a i n e d from c a p a c i t a n c e m e a s u r e m e n t s p r o v i d e d t h e d o p a n t d i s t r i b u t i o n i s known, s o t h a t P o i s s o n ' s e q u a t i o n c a n b e s o l v e d f o r t h e s h a p e of t h e p o t e n t i a l b a r r i e r . I f t h e s a m p l e i s u n i f o r m l y d o p e d , t h e n t h e s p e c i f i c b o u n d a r y c h a r g e i s g i v e n by :

c = - q Nd d C ( 2 )

w h e r e Nd i s t h e d o p i n g l e v e l and q i s t h e ( p o s i t i v e ) e l e m e n t a r y c h a r g e . The z e r o - b i a s c a p a c i t a n c e Co and t h e b a r r i e r h e i g h t Vo are r e l a t e d by t h e e q u a t i o n :

Vo = - ^{q Nd} € 1 8 Co 2

( 3 ) T y p i c a l v a l u e s f o r Vo a r e 0 . 1 - 1 V ( n o t e x c e e d i n g t h e b a n d g a p i n a n y c a s e ) and f o r C , 10" - l o 1 * e l e c t r o n s . c m - 2 .

2 . 2 . The grai~_bp_~~$~_ry~~p_"_d_u_c~t_a~_~_e.- G r a i n b o u n d a r i e s e x h i b i t non ohmic c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s , s i m i l a r i n many r e s p e c t s t o t h e c a s e o f two d i o d e s i n

series, one being polarized in the forward and the other in the reverse directions /2/. Carrier transport across the boundary involves two different theories, depen- ding on the relative values of the barrier width and the mean free path of the electrons 1.

i) if 7 << w, then the diffusion theory applies /2,4/. The current-voltage relationship is obtained by integrating the equation j = a E + q(dn/dx) between the current density j, the electric field E and the gradient of the electronic density n at the distance x from the boundary. u = nqp is the local conductivity and D = kTu/q is the diffusion coefficient, where p is the electron mobility. The following solu- tion is obtained :

where V1 and V2 cre thc barrier heights for electrons coming respectively from the left and from the right hand sides of the boundary (fig. lb) and F1 and F2 are the field strengths on either side of the boundary place. In particular, the zero-bias conductance is given by :

q v o

Go = (q/kT). qNd.v( IFo1/2). exp - l . , ~ (5)

where IFO 1 ⁼ (2qNd lvol/E)li2 is the magnitude of the electric field on the boundary plane.

ii) if 7 > w, then the thermnelectronic emission theory applies /4,5/. Only the electrons with a kinetic energy larger than the barrier height are able to cross through the grain boundary and the net current is the difference in the electron flows crossing the barrier from the right to the left and from the left to the right respectively. The current-voltage relationship is given by :

and the zero-bias conductance is :

Go = (q/kT). q ~ ~ .exp ;qvo ~ ~

where Gth is the mean thermal velocity of the electrons.

2.3. The voltage dependence of-t-h-e--b_o_u_~d_ary char=. - The dependence of the boun- dary charge on the applied voltage has been discussed under steady state conditions, implying that equilibrium was achieved among the electrons in the various boundary levels /4,5/. Then, a common quasi-Fermi level EFt can be defined for all boundary

- -

traps, so that the occupancy of a boundary state (Et) is given by :

ft = [L ^{+ exp(Et - qVl - EFt)/k~]}

-'.

EFt

-

I-V c u r v e s / 5 / . F i g . 2 shows t h e r e s u l t o b t a i n e d f o r a g r a i n boundary i n a s i l i c o n b i c r y s t a l : t h e i n t e r f a c e s t a t e s form a continuum w i t h a d e n s i t y of a b o u t 5 x 10 12 e v - l . cm-2.

3 . Dopant segreg&i_o>-_effects.- Although few r e s u l t s a r e a v a i l a b l e y e t , c a p a c i t a n c e measurements s h o u l d p r o v i d e a s e n s i t i v e method of d e t e c t i n g d o p a n t s e g r e g a t i o n e f f e c t s a t g r a i n b o u n d a r i e s . I t i s w e l l known t h a t t h e d o p a n t p r o f i l e o f a S c h o t t k y j u n c t i o n c a n be o b t a i n e d from a p l o t of l / c L v s . V / 6 / . The s i t u a t i o n i s somewhat more c o m p l i c a t e d i n t h e c a s e of a g r a i n boundary, a s t h e c a p a c i t a n c e v a r i a t i o n g e n e r a l l y i n v o l v e s a change i n t h e boundary c h a r g e a s w e l l a s d i f f e r e n c e s i n t h e d o p i n g l e v e l a t b o t h e d g e s o f t h e d e p l e t i o n l a y e r ( f i g . 3 a ) .

F i g u r e 2 : D e n s i t y of s t a t e s f o r a g r a i n boundary i n s i l i c o n , computed from t h e c u r r e n t - v o l t a g e c h a r a c t e r i s t i c s ( a f t e r

151).

P I I

8x10''

P-* 0 distance

6 w ~ 6W2 from the

2 -

7 -

6

- 5

-

E

YE -

.

$ 2

boundary

0 .

.

T

.

- 6.0. 0 3 O s V

-

-

3 -

F i g u r e 3 : 3a - The s c r e e n i n g c h a r g e d e n s i t y i n a h e t e r o g e n o u s l y doped b i c r y s t a l , showing t h e s h i f t s of t h e d e p l e t i o n e d g e s u n d e r a n a p p l i e d b i a s ;

X d (c m-3)

10"

1oi3

1012 10"

3b - The v a r i a t i o n of

4

2 d 2

( d ( l / C )/dV)V,O a t v a r i o u s t e m p e r a t u r e s , f o r a low a n g l e (3.5 d e g r e e s ) t i l t boundary i n a n n-type germanium b i c r y s t a l . Boundary p l a n e (111) ;

. doping level

. - ^(bulk)

. _.

. . ..

t i l t a x i s TO]. Doping l e v e l ( b u l k ) : 2 x 10 1 3 cm-3

However, a s i m p l e r e l a t i o n h o l d s f o r t h e s l o p e of t h e C-V c u r v e s a t t h e o r i g i n , owing t o t h e f a c t t h a t t h e boundary c h a r g e r e m a i n s s t a t i o n a r y w i t h r e s p e c t t o s m a l l v a r i a t i o n s i n t h e a p p l i e d v o l t a g e a b o u t V=O. Then, a s t r a i g h t f o r w a r d e x t e n s i o n of t h e S c h o t t k y d i o d e c a s e y i e l d s :

where Ndl and Nd2 s t a n d f o r t h e d o p i n g l e v e l a t b o t h e d g e s o f t h e d e p l e t i o n zone.

Eq. ( 8 ) shows t h a t t h e asymmetry o f t h e G-V c u r v e s a b o u t t h e C-axis can b e r e l a t e d q u a n t i t a t i v e l y t o d i f f e r e n c e s i n t h e d o p i n g l e v e l on e i t h e r s i d e o f t h e boundary.

R e l a t e d e x p r e s s i o n s h a v e b e e n u s e d t o c h e c k t h e l a c k of any s i g n i f i c a n t d o p a n t s e g r e g a t i o n a t v a r i o u s g r a i n b o u n d a r i e s / 2 , 7 / . We s h a l l c o n s i d e r a c a s e where a s t r o n g s e g r e g a t i o n e f f e c t i s o b s e r v e d (A. B r o n i a t o w s k i , u n p u b l i s h e d ) . The sample is a n n-doped ( 2 x 10 l 3 ~ m - ~ ) germanium b i c r y s t a l w i t h a low a n g l e (3.5 d e g r e e s ) t i l t boundary. F i g . 3b shows t h e v a r i a t i o n of 4 ^{= (1/Nd2 - l/Ndl)-l VS.} t h e t o t a l w i d t h of t h e s c r e e n i n g l a y e r , o b t a i n e d from t h e s l o p e o f 1/C 2 a t V = 0, measured a t v a r i o u s t e m p e r a t u r e s . T h e r e i s ample e v i d e n c e from t h e v a l u e o f w ( a b o u t 100 mi- c r o n s ) t h a t t h e d o p i n g l e v e l n e a r t h e boundary i s much l o w e r t h a n t h e l e v e l i n t h e b u l k . The v a l u e o f Xd ( a b o u t 5 x 10" ~ m - ~ ) may b e t a k e n a s a n o r d e r o f magnitude f o r t h e d o p i n g l e v e l w i t h i n t h e d e p l e t i o n l a y e r . T h i s v a l u e i s a l s o c o n s i s t e n t w i t h t h e r e s u l t s of c o n d u c t a n c e measurements ( e q . ( 5 ) ) g i v i n g v a l u e s o f a few t e n t h s of a v o l t f o r t h e b a r r i e r h e i g h t u n d e r z e r o - a p p l i e d b i a s . A p o s s i b l e e x p l a n a t i o n m i g h t be t h a t t h e donor atoms a r e p a r t l y compensated by a c c e p t o r i m p u r i t i e s , a l s o s e g r e g a t e d d u r i n g t h e g r o w t h o f t h e c r y s t a l .

4. Transient__capacitanc~_m_e_asurements /13,14,20/

4.1. I n t r o d u c t i o n . - I n a t y p i c a l t r a n s i e n t c a p a c i t a n c e e x p e r i m e n t , f i l l i n g p u l s e s a r e a p p l i e d a c r o s s t h e boundary and t h e r e l e a s e of t r a p p e d c a r r i e r s i s d e t e c t e d by r e c o r d i n g t h e c o n c o m i t a n t change i n t h e boundary c a p a c i t a n c e . An a n a l y s i s o f t h e e m i s s i o n t r a n s i e n t s u s i n g t h e Deep L e v e l T r a n s i e n t S p e c t r o s c o p y (DLTS) t e c h n i q u e 1 1 1 y i e l d s t h e e n e r g y l e v e l , t h e c a p t u r e c r o s s - s e c t i o n and t h e d e n s i t y of t h e v a r i o u s boundary t r a p s 113,141.

The b a s i c r e l a t i o n s f o r e m i s s i o n a n d c a p t u r e w i l l b e d e r i v e d f i r s t . The p r i n c i p l e of DLTS w i l l b e r e c a l l e d n e x t , w i t h a d i s c u s s i o n o f t h e c h o i c e o f e x p e r i m e n t a l parame- t e r s f o r e n e r g y l e v e l and c a p t u r e c r o s s - s e c t i o n measurements. A r e v i e w o f r e c e n t l y p u b l i s h e d r e s u l t s w i l l b e g i v e n i n s e c t i o n 6 .

4.2. The captur_e_and t h e e m i s _ J . ~ - r a t e s f o r t h e b o u n d a r y - s t a t e s 141.- C o n s i d e r a n e l e c t r o n t r a p w i t h t h e e n e r g y l e v e l Et and t h e c a p t u r e c r o s s - s e c t i o n U . L e t f r e p r e s e n t t h e occupancy o f t h e t r a p a t t h e t i m e t , e t h e e m i s s i o n and c t h e c a p t u r e r a t e . I t f o l l o w s t h a t : n

A t e q u i l i b r i u m , t h e c a p t u r e r a t e i s g i v e n by 2navth where n i s t h e d e n s i t y of c o n d u c t i o n e l e c t r o n s a t t h e i n t e r f a c e and = ( k T / 2 1 m 1 * ) ~ / ~ i s t h e mean t h e r m a l

t h

v e l o c i t y i n t h e d i r e c t i o n normal t o t h e b o u n d a r y , m* b e i n g t h e e f f e c t i v e mass o f t h e e l e c t r o n s . The e m i s s i o n r a t e i s r e a d i l y o b t a i n e d from t h e c o n d i t i o n t h a t t h e e l e c t r o n s form a Fermi d i s t r i b u t i o n and u s i n g eq. (9) w i t h d f l d t = 0 :

where N is the effective number of states and E the energy of an electron at the bottom of the conduction band. Suppose a voltage pulse is applied across the boundary. Henceforth the capture rate will be increased compared with equilibrium.

Its value according to the thermoelectronic emission theory /4/ is now given by :

where the doping level is assumed to be uniform over the sample for the sake of simplicity. As V1 and V clearly depend on the trap occupancy, eq. (9) is not linear

2

in f and no simple solution can be obtained. Qualitatively, f, 1 ^Vl 1 ^and 1 V2 1 ^are

increasing functions of the pulse duration. As a result cn decreases until a steady state is reached and df/dt = 0. If the pulse height is large enough to make Iv21

substantially larger than IV I, then the capture rate is simply proportional to the 1

current density across the sample (eq. (6)) :

This equation will be used for capture cross-section measurements (section 4.5).

Once the bias is returned to zero, carriers trapped in excess will be gradually released from the boundary states. The relaxation transient also obeys eq. (9) with the appropriate expression for c . DLTS measurements require that emission should strongly predominate over capture throughout the transient. This will be achieved provided the filling pulse is strong enough to vary the barrier height by a large amount compared with kT/q. If this condition is not fulfilled, then both capture and emission will be involved in the relaxation transient. As a result, the DLTS peaks (see next paragraph) may be shifted in the temperature scale, by an amount depending on the pulse width and height. Such shifts have been observed in various cases (/7,8/.and A. Broniatowski, unpublished) and it is believed they can be explained by the effect just mentioned. This effect could also make unreliable the capture cross- section measurements based on the dependence of the transient amplitude on the pulse duration 1141. A more sujtable procedure will b e djsrussed below.

4.3. DLTS ana_ly_s;z of the --c-apacitance tr_af3.s_i_e_"_t~ /I/.- In this technique, periodic filling pulses are applied across the sample, mounted in a variable temperature cryostat. The emission transients are processed by a dual-gate integrator and the resulting signal C(t,) - C(t2) (fig. 4a and b) is recorded as a

applied bias

n:, ⁿ

0 ; time showing the formation of the DLTS signal

amplitude i ^{C(tl) - C(t2).}

of the emission ,

b

O 9 12 time

function of the sample temperature. Consider the contribution to this signal, from a single trap level. As the temperature increases, the emission rate varies in accor- dance with eq. (10) and it can be shown that C(t.) - C(t?) goes through a maximum when e takes the value (t„ - t.)/ Log(t„/t ) /l/, fixed by the gate settings of the integrator. The DLTS signal combines the contributions from the various boundary levels. Fig. 5a shows a typical spectrum for a low angle tilt boundary in a ger- manium blc.rysta] (A. Broniatowski, unpublished). The sample is the same as fig. 3b.

A number of peaks are observed, each of which corresponds to carrier emission from a definite boundary state with the emission rate given above. Majority and minority carrier traps are readily distinguished from the sign of the DLTS signal : negative peaks relate to majority carrier traps since filling these levels results in decrea- sing the boundary capacitance, whereas positive peaks should be associated with minority carrier traps. Both negative and positive peaks are observed in fig. 5a, suggesting the barrier model should be modified in the present case, to include a hole contribution in the current across the boundary /2,15/. (Special mention should be made of DLTS measurements on high resistivity material, as the sign of the capacitance transients will be reversed if the quality factor of the sample (given by CRw, where C is the boundary capacitance, R is the sample series resistance and w is the pulsation of the drive signal of the capacitance-meter) is larger than

unity (A. Broniatowski, A. Blosse, P.C. Srivastava and J.C. Bourgoin, unpublished) ; however, this difficulty did not arise with the spectrum presented in fig. 5a).

Figure 5 : 5a - DLTS spectrum of a low angle tilt boundary in a germanium bicrystal (same sample as fig. 3b). The symbols refer to the trap levels identified in fig. 5b. Pulse height : 4 V ; pulse width : 4 ms, emission rate : 300 s ; 5b - Activation energies for the electron and hole traps (same sample as fig. 3b). E = (boundary) electron trap ; the energies are referred to the bottom of the conduction band. H = (boundary) hole trap ; the energies are referred to the top of the valence band ; B = (bulk) electron traps (ref. /14/). From the energies of the (E) and (H) states, the (equilibrium) occupation limit of the boundary levels is located at 0.28 - 0.34 eV above the top of the valence band.

4.4. Energy level of the traps.- The dependence of e upon temperature can be measured for any particular trap, by recording the position of the corresponding peak in the DLTS spectrum for various gate settings. The activation energy for carrier emission is then obtained from an Arrhenius plot of Log(T /en) 2 VS. 1/T, where the factor T~ accounts for the temperature dependences of Nc and vth (eq.

- ~

(10)). This energy is a characteristic parameter for each boundary state ; it may differ however from the energy level of that state referred to the conduction or the valence band, if the capture cross-section is thermally activated. Fig. 5b shows the activation energies obtained for the same boundary as fig. 5a.

4.5. Capture cro_s_s_=~e_ction and trap d-e-n_s-ity measurements.- A rough estimate of the capture cross-section can be obtained by computing the pre-exponential factor in eq. (lo), once the activation energy has been measured. For an obvious reason this computation fails to indicate whether the capture cross-section is thermally activated. We propose a more accurate procedure, based on transient current and capture rate measurements (eq. (12)). While transient current measurements raise no difficulty in principle, capture rate measurements involve a determination of the trap occupancy and its dependence on the pulse width and amplitude (eq. (9)). As explained in section 4 . 2 . , long duration pulses should be used to avoid a shift in the position of the DLTS peaks. Thus, we are essentially concerned with the steady state occupancy of the traps. Assume this condition to be fulfilled ; then df/dt = 0 and c = enf/(l-f). The emission rate is known from the gate settings and f still has to be measured. For this purpose we consider the dependence of the amplitude of the emission transient on the pulse height (fig. 6a). As the latter increases, the transient amplitude saturates, corresponding to all the traps being filled, i.e. f =

1. If the variations in the boundary capacitance remain small compared with the zero-bias value, then a first order approximation can be used, giving f as the ratio 1/10 (fig. 6a). If large signals are involved (corresponding to a large trap den-

Cm (C-Co) sity), then f =

C(Cm-Co) where Co is the relaxed capacitance, Cm - C is the upper bound of the transient amplitude and C - C is the transient amplitude for which f is being computed. The latter expression follows from the fact that the capacitance varies as the reciprocal of the boundary charge (eq. (2)). The trap density is also obtained from C and Cm using eq. (2) : Nt = &Nd ~I/c, - ^l/Co I.

I

I I 0 I

1

0 V pulse height a

Figure 6 : 6a - The amplitude of the emission transient as a function of the pulse height, for steady state (long pulse) conditions. Co = relaxed capaci- tance, Cm - ^{Co =} upper bound of the transient amplitude ; 6b - dependence of the transient amplitude ( 0 ) and the current density ( @ ) on the pulse height, for the majority carrier trap El (fig. 5b).

Co = 3,3.10-~ F I ; ~I c ~ ~ - ^{CoI= 2.1.} ~ / n * . - 2 -1.5

- 1 -.5

- ^U '

- - 0

-

T=180 K

o w ; 1 b i

b pulse height ( V )

The data in fig. 6b relate to the majority carrier trap E, (fig. 5b). A capture

-14 9 -2

cross-section of 9 x 10 cm2 (at 180 K) and a trap density Lf about 10 cm have been measured using the method just described.

5. Photocond~sjjyjty and pho_~c_ap_~_m_e_a_sy-rementss.- Photocapacity and photoconduc- tivity measurements have been performed on grain boundaries in p-type silicon, using both sub-gap and over-gap illumination. In the first case, valence electrons are excited into vacant boundary states while the generation rate of electron-hole pairs is maintained at a low level in the bulk of the sample. The change in the boundary charge is measured as a function of the photon energy, under steady state illumi- nation /lo/. These data have been used to derive the grain boundary density of states in a silicon bicrystal (fig. 7) : the boundary states are found to form a continuum with a density increasing towards the edge of the conduction band.

If over-gap illumination is used, electron-hole pairs will be generated across the sample and the boundary charge will be varied owing to minority carrier recombina- tion at the interface. An analysis of the change in the boundary conductance yields the recombination velocity 116,171. The values obtained with silicon bicrystals 1111

are on the order of 100 to 1 000 cm.s-l and compare with previous data on low angle 1181 and twin 1191 boundaries in germanium. However, these results are not readily interpreted in terms of the density and the capture cross-section of the boundary states, as all the states are involved at once in the recombination process.

- 1 13

Figure 6 : Density of states for a grain boundary in a silicon bicrystal, computed from photocapacity and photoconductivity

v, measurements (after 1101).

13 0 . L E F O 0.6 C.8 1.0 E g

ENERGY I eV 1

6. Recent daf_a-_en_ grain boun-d-a-r-ies using - e J e _ ~ f ~ c a _ l - - $ e _ a _ s _ u r e m e n t s . - Transient capacitance measurements have been performed on grain boundaries in GaAs 17,131, silicon /8,12,20/ and germanium 19,141. The main conclusions are as follows : a) The DLTS data are generally consistent with the model of the boundary states as a discrete set of levels, as far as energy level and capture cross-section measure- ments are concerned 113,141. On the other hand, steady state (photocapacitance and current-voltage) measurements rather suggest a continuum of levels 15,101. The reasons for these conflicting results are still unclear.

b ) The DLTS spectra generally reveal a small number (usually one or two) of majority

carrier traps, responsible for the larger capacitance transients observed. Closer inspection reveals a number of additional levels, some of which are minority carrier traps (A. Broniatowski, unpublished).

C) Bulk traps are also detected in the boundary spectra 113,141. A simple explana- tion for this observation is that the traps within the screening layer are also filled by voltage pulses applied across the boundary, and therefore contribute to the emission transients.

d) The capture cross-sections of the boundary states are rather large in comparison with the values typical for bulk traps, being frequently in the range of 10 -14 to

-12 2 10 cm .

e) Less definite results are given for the individual trap densities, which seem to be in the range of lo9 to 1011 In one case /9,14/, the trap density measurement has been coupled with an electron microscopy study of the boundary dislocation structure. Assuming one dangling bond every lattice distance along the dislocations, the total number of available dangling bonds _{- -} (- l0I3 c m 2 ) was found to be much larger than the trap density (-lo9 cm -2 ) . This might suggest that a small fraction only of the boundary states are detected in DLTS experiments. Alternati- vely, it might be that the bonds are recorlstructed, so that there is o~uch less than one dangling bond per lattice distance along the dislocations.

f) Difficulties have been encountered in obtaining reproducible spectra on single samples (A. Broniatowski, unpublished). This difficulty has been resolved by perfor- ming an adequate annealing treatment before starting a set of measurements. This is taken as an evidence for the existence of slow states, the filling of which affects the overall properties of the sample.

Considering the limited amount of spectroscopic data available at the moment, it seems difficult to discuss in more detail the important issues regarding grain boundaries, such as the influence of impurity segregation on the electrical proper- ties or the relation between the density of states and the crystallographic struc- ture of the boundaries.

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