Study of charge distribution and atomic arrangement at interfaces using fast electron scattering

M I'M DOOM,

N K I - N o - - 4 2 . t

Study of

charge distribution and atomic arrangement at interfaces

using fast electron scattering

By B. Hugsted

Dissertation for the degree Doctor scientarium.

Department of Physics, University of Oslo, 1993.

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Study of

charge distribution and atomic arrangement at interfaces

using fast electron scattering

By B. Hugsted

Dissertation for the degree Doctor scientarium.

Department of Physics, University of Oslo, 1993.

C o n t e n t s

Preface Background

A survey of the papers Concluding remarks P a p e r 1

B. Hugsted, K. Gjønnes, J. Taftø, J. Gjønnes, and H. Matsuhata.

'Determination of electrostatic potentials and charge distribution in bulk and at inter- faces by electron microscopy techniques'

SPIE. Physical Concepts of Materials in Novel Optoelectronic Device Applications 1361. 751 (1990).

P a p e r 2

B. Hugsted, J. Taftø, T. G. Finstad and C. J. Palmstrom.

'The polarity of small MBE-grown {HljGaAs domains on (100)Sco.32Er0.68As.' Appl. Phys. Lett, (submitted).

P a p e r 3

B. Hugsted, R. Sivertsen, J. Gjønnes, G. Salomonsen, and J. Taftø.

'Electron Microscopy of Mean Inner Potential Change Across Interfaces in Electronic Materials.'

Micron and Microscopica Acta 22, 145 (1991).

P a p e r 4

J. Gjønnes and B. Hugsted.

'Scattering Integrals at Solid-Solid Interfaces' Physica'Scripta T 44, 155 (1992).

Paper 5

B. Hugsted, J. Gjønnes and J. Taftø.

'Potential Step Imaging of Interfaces in MBE-Grown Structures' Applied Surface Science 63, 277 (1992).

Paper 6 B Hugsted.

'A Robust Real Space method for the Calculation of Fast Electron Forward Scattering.' Ultramicroscopy (in press).

Appendix

Listing of programs used in Paper 6.

Preface

T h e present work has been done at the s t r u c t u r e physics group a t t h e D e p a r t m e n t of Physics, University of Oslo. T h e a u t h o r wishes to express t h a n k s to advisor J o h a n TaftO, to J o n Gjønnes, A r n e Olsen and Erik Sørbrøden.

F u r t h e r m o r e t h a n k s are d u e to Chris P a l m s t r o m (Bell C o m m u n i c a t i o n s Research Lab) a n d Terje Finstad for introducing us to t h e S c E r A s / G a A s system. As a c a n d i d a t e for m a k i n g a buried epitaxial metallic conducting layer this system h a s been widely s t u d i e d . O u r contribution to this work is r e p o r t e d in P a p e r 2 of this thesis. A special t h a n k to Terje F i n s t a d for inspiration.

We also had great benefit from cooperation with G u t t o r m Salomonsen a n d Ronald Sivertsen at Norwegian Telecom. T h e main motivation for this c o o p e r a t i o n was t h e c h a r a c t e r i z a t i o n of G a A s / A l A s high electron mobility transistor ( H E M T ) s t r u c t u r e s . T h e very nice G a A s / A l A s and G a A s / A l G a A s samples t h a t were used during large p a r t s of this work were grown at t h e Norwegian Telecoms M B E facility.

Financial support from Norwegian Council of Science and Technology a n d from Nor- wegian Telecom is greatfully acknowledged.

Background

T h e development of epitaxial growth techniques such as molecular b e a m e p i t a x y (MBE)[1]

a n d metalorganic chemical vapor deposition (MOCVD)[2] has enabled t h e growth of high quality h e t e r o s t r u c t u r e s which offer i m p o r t a n t opportunities b o t h for t h e develop- m e n t of novel devices a n d for the a d v a n c e m e n t of fundamental solid s t a t e science. Such s t r u c t u r e s as t h e semiconductor superlattice and the q u a n t u m well are now c o m m o n l y used in high speed s e m i c o n d u c t o r devices a n d optoelectronics. W i t h the decreasing dimensions t h e interfaces between t h e dissimilar materials become increasingly impor- t a n t . T h e most fundamental characteristic of such heterojunction s t r u c t u r e s is t h e difTerence in energy between t h e valence (conduction) band edges on t h e t w o sides of t h e interface. This energy difference of t h e band edges is usually referred t o as t h e b a n d offset. A n u m b e r of spectroscopic techniques are available for t h e c h a r a c t e r i z a t i o n of t h e band offsets, among t h e m : x-ray photoelectron spec tros copy [3], optical absorbtion[4J a n d luminescence[5], current-voltage 6] a n d capacitance-voltage m e a s u r e m e n t s ' ? ] , t h e charge-transfer method[8] and the internal photoemission ( I P E ) m e t h o d [ 9 ] .

In c o n t r a s t to t h e techniques mentioned above transmission electron microscopy ( T E M ) using a high energy of t h e incident electron beam is capable of probing t h e specimen with high spatial resolution. O n e promising m e t h o d for elucidating t h e electronic

s t r u c t u r e of materials at a local scale is electron energy loss s p e c t r o s c o p y ( E E L S ) [ 1 0 , 11].

In recent years much progress has been m a d e in this field, b u t a t present t h e b a n d s t r u c t u r e is not available for measurement by T E M , while t h e electrostatic p o t e n t i a l as d e t e r m i n e d by the positions of t h e nuclei and t h e electrons is. It is this p o t e n t i a l t h a t d e t e r m i n e s the energy levels and t h e electronic states, and therefore d e t e r m i n e s t h e energy of the valence a n d conduction b a n d edges. T h e Hamiltonian describing this s y s t e m is given by

T h e positions of t h e a t o m s are assumed to be known, by t h e set of vectors R . N is t h e t o t a l n u m b e r of electrons with positions rt-. W h e n this Hamiltonian is i n s e r t e d into t h e Schrodinger equation

ftil> = Ei> (2) t h e p r e s e n c e of t h e last t e r m in (1) (the electron-electron repulsion) m a k e s t h e solution

of (2) i n t r a c t a b l e . T h e problem m a y b e reformulated a n d / o r a p p r o x i m a t e d a n d t h e most successful technique at present is t h e functional density m e t h o d [ 1 2 , 13] t h a t is capable of handling e x t e n d e d system such as heterojunctions and interfaces. Still t h e problem is a formidable one. In t h e vicinity of the interface the d i s t r i b u t i o n of charge will differ from t h e distribution in the bulk of t h e material. While we m a y e x p e c t t h e core electrons of t h e atoms to be only negligible p e r t u r b e d from t h a t in t h e bulk, t h e distribution of t h e m o r e losely b o u n d electrons close to the interface m a y differ considerably from t h a t in bulk. A m e a s u r e m e n t of t h e charge d i s t r i b u t i o n in t h e interface region would therefore be of great interest both for device c h a r a c t e r i z a t i o n a n d for fundamental research such as t h e calculation of t h e electronic s t r u c t u r e . In a large perfect crystal t h e position of t h e nuclei and t h e distribution of t h e electrons can be determined with a high degree of accuracy by a combination of t h e related diffraction techniques x-ray, neutron and electron scattering. N e u t r o n s i n t e r a c t with t h e nuclei of the sample and do not provide information or t h e electron d i s t r i b u t i o n , x- rays are sensitive to electrons and may be used to investigate surface and interface layers when a glancing angle incident beam direction is selected. Still t h e sensitivity is low and a large s a m p l e is required. Electron scattering provides b o t h the high sensitivity and t h e high spatial resolution necessary for the s t u d y of a single interface. C o n t r i b u t i o n s to interface investigation by transmission electron microscopy have been m o s t l y in the form of high resolution electron microscopy ( H R E M ) ' l 4 , 15] a n d to a lesser e x t e n t in the form of t h e Fresnel diffraction method[16, 17], for both of these m e t h o d s t h e electron b e a m is directed along the interface. These m e t h o d s provide i m p o r t a n t information of t h e position of atoms along the interface, but little knowledge has been o b t a i n e d of t h e distribution of t h e conduction electrons (or holes). Tafto , J o n e s a n d Heald[18]

p r e s e n t e d a dark field m e t h o d t h a t could highlight an interface between m a t e r i a l s with

different mean inner potential, and also obtain the direction of the potential change across the interface. This thesis is a contribution to the development of this method into a quantitative tool.

A survey of the papers

Paper 1

A general review of transmission electron microscopy methods for the determination of electron distribution in materials is given in Paper 1. Theoretical aspects of the potential at interfaces and scattering of fast electrons by the potential step at an interface are discussed. It is shown that the mean inner potential strongly modifies the scattering in near forward direction. We also show how interfaces between materials with different mean inner potential are visualized by a dark field technique that utilizes an objective aperture placed close to the central beam.

P a p e r 2

While ScErAs grows epitaxial on (100)GaAs the opposite is not true. In the case of GaAs grown by MBE on (100)ScErAs several growth orientations are observed, among them two equivalent orientations of GaAs with a {111} plane parallel to the (100) plane of ScErAs. Paper 2 presents an electron channeling experiment showing the {111} oriented crystallites to have the [ i l l ] direction pointing outward from the original (100)ScErAs surface. This shows that although the ScErAs itself is non-polar, the bonding structure to the ongrown GaAs does determine the GaAs polarity (when there first is a { i l l } oriented domain). This information is used in an discussion of the interface structure, suggesting that the first atomic monolayer of GaAs is a Ga layer, and that the bonding between the ScErAs and GaAs is weak.

P a p e r 3

In Paper 3 we return to the topic of the investigation of the charge distribution at an interface. A kinematical expiession for contrast calculation is given. We also show images highlightening the interface between GaAs and AlAs. As the parts of the interface that are parallel to the beam are most visible, wavyness of the interface in the beam direction will show up as multiple bright lines in the image.

P a p e r 4

A theoretical study of electron scattering at interfaces, using scattering integral meth­

ods, is presented in Paper 4. Calculation of scattering from a single potential step shows an asymmetric intensity in resiprocal space. The intensity distribution is shown to have a maximum at a scattering angle equal to the angle of total reflection. We also conclude that the usual methods for calculation of fast electron scattering are not well suited for the calculation of scattering at an interface.

P a p e r 5

While t h e calculations presented in paper 4 predict a m a x i m u m in reciprocal s p a c e we realize t h a t t h e n o r m a l dark field procedure in most microscopes does not p r o v i d e t h e resolution (in reciprocal space) necessary to locate this m a x i m u m . P a p e r 5 i n t r o ­ duces a convergent beam technique t h a t improves t h e resolution in reciprocal s p a c e a n d at t h e s a m e t i m e enhances the intensity of t h e image. DaTk field images of t h e G a A s / A l A s interface, where t h e location of t h e dark-field a p e r t u r e is known to w i t h i n 0 . 2 n m- 1 in reciprocal space, are shown. In principle t h e calculations shown in P a p e r 4 in combination with images of t h e type shown in P a p e r 5 m a y be used t o e x t r a c t information of t h e p o t e n t i a l step at an interface.

P a p e r 6

While t h e principle of t h e scattering a t an heterojunction has been shown in P a p e r 4 a fully dynamical t r e a t m e n t is necessary in order to e x t r a c t q u a n t i t a t i v e information from image? of t h e t y p e shown in P a p e r 5. In these experiments t h e s a m p l e is non-periodic (employing a single interface), and not well suited for reciprocal space calculation techniques as t h e Bloch wave method[19, 20] or t h e m u l t i s l k e m e t h o d [ 2 1 , 22, 2 3 , 24, 25]. P a p e r 6 introduces t h e Crank-Nicolson finite difference m e t h o d [ 2 6 , 27, 28] as a real space m e t h o d for t h e calculation of electron scattering in transmission e l e c t r o n microscopy. T h i s m e t h o d may be applied t o b o t h periodic and non-periodic b o u n d a r y conditions, a n d also has t h e advantage of unconditional stability. T h e Crank-Nicolson m e t h o d is *reU suited for t h e interpretation of images of t h e t y p e shown in p a p e r 5.

Concluding remarks

T h e principle of fast electron scattering at a potential step has been elucidated. It has been shown t h a t electrons scattered in the n e a r forward direction bring signifi­

cant information of t h e potential step at an interface. E x p e r i m e n t s has been shown w h e r e t h e interface between AlAs and GaAs in a MBE-grown s a m p l e is visible as a bright or dark line in t h e image depending on t h e location of t h e d a r k field a p e r t u r e . T h e a s y m m e t r i c intensity distribution in reciprocal space has been shown using an improved phase g r a t i n g approximation. We put forward t h e a r g u m e n t t h a t neither t h e n o r m a l dark-field technique in t h e electron microscope nor the usual reciprocal s p a c e calculation techiques for image simulation are suited for this t y p e of e x p e r i m e n t s . T h i s a r g u m e n t a t i o n is followed by t h e proposal of an improved dark field t e c h n i q u e with high resolution in reciprocal space, and t h e development of a calculation t e c h n i q u e (performed in real space) t h a t is suitable for the calculation of electron scattering from n o n - p e n o d i c o b j e c t s .

References

i'lj A. V. Gho a n d J. R. A r t h u r , Prog. Solid S t a t e C h e m . 10, 157 (1975), :2! H. M. M a n a s e v i t , J . Electrochem. Soc. 1 1 8 , 647 (1971).

f3] R. W. G r a n t . J . R. Waldrop, and E. A. K r a u t , P h y s . Rev. Lett. 4 0 , 656 (1978)

\i\ R Dingle, W . W i e g m a n , and C. H. Henry, P h y s . R e v . Lett. 3 3 , 827 (1974).

[5] R. C. Miller, D. A. Kleinman, and A. C. Gossard, P h y s . Rev. B 2 9 , 7085 (1984).

(61 T . W . H i c k m o t t , P. M. Solomon, R. Fisher, a n d H. Morkoc, J . Appl. P h y s . 5 7 , 2844 (1985).

[71 H. Kroemer, W . Y. Chien, J. S. Harris, and D. Edwall, Appl. P h y s . L e t t . 3 6 , 295 (1980).

|8j W . I. W a n g . E. E. Mendez, and F . Stern, Appl. P h y s . Lett. 4 5 , 634 (1984).

(9) M. Heiblum, M. I. N a t h a n , a n d M. Eizenberg A p p l . P h y s . Lett. 4 7 , 503 (1985).

[10] P. E. B a t s o n in: Proceedings of t h e 47th a n n u a l M e e t i n g of t h e Electron Mi- croscopy Society of America, ed: G. W. Bailey. (San Francisco P r e s s , I n c . 1989).

I l l P. E. Batson P h y s . Rev. Lett. 5 7 , 2729 (1986).

121 A n d r e w Zangwill, Physics a t surfaces, ( C a m b r i d g e University Press 1988).

13j C. G. Van de Walle and R. M. M a r t i n , Phys. R e w . B 3 5 . 8154 (1987).

14; O. L. Krivanek, S. Isoda, and K. Kobayashi, Phil. M a g . 3 6 , 93i (1977).

15' J. M. Gibson, Ultramicroscopy 1 4 , 1 (1984).

;i6] L. A. Bursill, J . C. Barry, and P. R. W . Hudson, P h i l . M a g . A, 3 7 , 789 (1978).

17j W . M. Stobbs and F . M. Ross in: Evaluation of A d v a n c e d Semiconductor Materials by Electron Microscopy, Ed. D. Cherns, N a t o A S I Series. Series B , Physics; vol 203. ( P l e n u m P r e s s , New York, 1989).

IS] J. Taftø , R. H. J o n e s , a n d S. M. Heald, J. A p p . P h y s . 6 0 , 4316 (1986).

IP; M. A. B e t h e , A n n . Physik (Leipzig) 8 7 , 55 (1928).

20 A. Howie, in: M o d e r n Diffraction and Imaging Techniques in Material Science, E d s . S. AmeUnckx, G R e m a u t , and J . van L a n d u y t , ( N o r t h - H o l l a n d , A m s t e r d a m , 1970).

2 i ; J. M. Cowley and A. F. Moodie, Acta Cryst. 1 0 , 609 (1957).

(22i j . M. Cowley and A. F . Moodie, Proc. Roy. Soc. ( L o n d o n ) 7 1 , 533 (1958).

[23] J. M. Cowley a n d A. F . Moodie, Acta Cryst. 12, 353 (1959).

i24j J. M. Cowley and A. F . Moodie, A c t a Cryst. 12, 360 (1959).

,'25.' P G o o d m a n a n d A. F . Moodie, A c t a Cryst. A 3 0 , 280 (1974).

-[26; J. C r a n k a n d P. Nicolson Proc. C a m b . Phil. Soc. 4 3 , 50 (1947).

[271 G. D. S m i t h . N u m e r i c a l Solution of P a r t i a l Differential E q u a t i o n s : F i n i t e Differ­

ence M e t h o d s (Claredon Press, Oxford, 1978).

:2dj W. H. Press, B . P. Fiannery, S. A. Teukolsky, W . T . Vetterling, N u m e r i c a l Recipes in C, T h e Art of Scientific C o m p u t i n g (Cambridge university press, 1988).

Paper 1

PROCEEDINGS REPRINT

^ S r i E - T h c lnttfrn.UMn.il S'Citftv fur Optic.il En..:nuvnn-_:

Reprinted from

Physical Concepts of Materials for Novel Optoelectronic Device Applications I:

Materials Growth and Characterization

28 October-2 November 1990 Aachen, Federal Republic of Germany

Volume 1361

"--'-:-::. x' :. r. : electrostatic potentials and charge distributions in bulk and at interfaces by electron microsocpy techniques.

3. Hugsted. K.Gjønnes, J. Taftø and J. Gjønnes

:-:--.:—•.:'. •: Physics. University of Oslo, PO box 1054 Blindern, 0316 Oslo 3 Norway H. Matsuhata

Eiectro techn i cal laboratory Umezono 1-1-4 Tsukuba 302 Ibaraki Japan ABSTRACT

••'. -h -'r.ergy electron diffraction is sensitive to details in charge and potential i: f r ii.utio.n, since scattering occurs by the net charge - or electrostatic :. •' f-r.t ial. Several techniques have been developped for characterization the atomic .>:.j electronic structure at or near interfaces: convergent beam profiles, critical v- 1 • =;_'» effee t in electron diffraction, reflection/refraction at interfaces.

/>:-: p: i *rat ions are shown to bulk semiconductors, single interfaces and multilayers.

1. INTRODUCTION

The reduced dtr.ensions of features in integrated circuitry and the increasing ct..n\piexi ty of novel electronic and optoelectronicmaterials have made electron microscopy an invaluable characterization tool in microelectronics, notably of

interlaces. Applications such as low-magnification imaging of configurations at sub-micron level, identification of process-induced defects, or high resolution studies of interface perfection may be regarded as standard. Spectroscopic and diffraction techniques devoted to analysis of composition, local strain and even to local energy levels are now developped, for a review see e.g. Cherns . In the present paper we shall discuss techniques for studying the distribution of charge or electro-static potential. The techniques presented are based on a salient factof high energy electron diffraction: the incident electron is scattered by the electro-static potential derived from nuclei and electrons, as expressed by the well-known Mott formula for the atomic scattering amplitude: f = (Z-f )/s , where s - sinø/X Electron scattering, especially at small s-values, is thus very sensitive to details in electron distributions, e.g. ionicity and bonding, and may be used to determine the Coulomb component of the effective potential appearing in the energy band description of valence electrons.

2. THEORY: THE ELECTROSTATIC POTENTIAL AND THE CONCEPT OF A WAVE VECTOR "GAP IN HIGH ENERGY ELECTRON DIFFRACTION

Elastic scattering of high energy electrons by crystals is governed by the Coulomb potential written as

U(r) = Z <Z e/|r-r |> = £ U expUnirg] (1)

:r. terns of the particles j. plus an imaginary component which is associated with absorption and may be formulated in terms of Fourier components of fluctuations:

iW(r) = iSW exp[2Tiirg]

z ^g

see e g. Reimer .

The Fourier components U are commonly expressed in terras of the x-ray atomic

'35' a-.sca- Concepts ot Materials tor Novel Optoelectronic De^cé ADD<iCat>ons i :350,

c-t-.ering factors f , i.e. by the scattering amplitudes fe l!s) =(2/a )lZ-fX)/s2

where- ri=sin0>'.\ and a the first Bohr radius. Note that the scattering amplitude at f5=<"> is obtained as the limit

(2/a MZ-FX)/s = (l/3a )Z <r²> (3)

H H j j

for neutrm atoms. For ions an additional ionization term is obtained in the expression:

U = (2/a ){2trfs + £A R cosa } + surface term, (3a)

o H j i i i i

where d is the ionicity and a the angle between R and the direction of the scatter ing vector s -» 0. The sensitivity of U to details in the electron distribution is apparent.

Sue to the strong interaction with the periodic potential, electron diffraction must nearly always be treated as dynamical, i.e. beyond the first Born or kinematical approximation. Depending on the experimental conditions different methods of computation may be applied, see e.g. Reimer . In high resolution imaging the sc-cailed multislice approach is commonly used. In the diffraction experiments to be discussed here, with the incident beam off major axes and relatively few strongly scattered beams, a Bloch wave formulation akin to the standard band theory for valence electons may provide a better description. In the eigenvalue equation of the form

AC = 2kyC (4) fsr Eioch states C, the matrix A contains the Fourier potentials U = A. as off-

gh gh diagonal elements. The diagonal elements A = 2ks are derived from the excitation errors s , i.e. the deviations from Bragg condition - or distance from the Brillouin zone boundary. The eigenvalue y is here an increment to the z-component of the inc ident electron wave vector, i.e. k = k + y. where k i s a wave vector in

Z 02 O vacuum; 2ky may be taken to represent the corresponding additional kinetic energy.

T'ner. the magnitudes 2k(y -y ) which appear at the Brillouin zone boundaries as separations between eigenvalue branches may be seen as analogous to energy gaps in the band theory of solids - and play a somewhat similar role in governing the behaviour of solutions. In particular it is often found that the intensity profile cf a Bragg reflection, i.e. across the Brillouin zone can be approximated by a IwD-beaT. like expression,

Sin 2[ t / ( U =f f)

752 SP-Eiol '36' P t o m t e r t u ' l ' ^ u - '• .* Oaoeleclrtmc DfxetpplicMionslitSSO.

: u : v j r e i.-

•:i-at:on. iiscussv.l

:ped i:::ra:r.g t.-s -neir

be .-.•:difi'jJ

?d by Taf to and Gjonr.es ng: e a c h B l o c h w a v e j

this ?=:-.

i: see *n

•;":! = •-; l\'r; j> = U + 2 kJy

••LL: :T:.-•:;;:J;ES FCR LSW ORDER FOURIER POTENTIALS

.'. : '. :.::.-.£ i ::•:; a p p r o x i m a t e

.-j :.". " i s : . Hvveral such v ~ •„.: r.r. i r.p ' : :i i: f e ren t g a p -ir-?nt. A I s: n-".* g a p results

••v leaped s u b = i d i a r y f r i n g e :: -'an b e fitted to

i'. „ulat ions b a s e d on the exact C-ilL.dt Ions at e a c h

For small g a p s n o fringes i.-. i n t e g r a t e d intens i ty c a n

• r o m t h e p r o f i l e R e c e n t i ;.JU order r e f l e c t i o n in

'it ai', Z u c , S p e n c e a n d n in e x a m p l e s of both, e.g.

-.1 h d e p e n d u p o n i o n i z a t i o n

•\".0. w h i c h is s e n s i t i v e to ::"•/. Cotr.bined w i t h o t h e r

=?y m a y b e used to s y n t e s i z e Fig.l C B E D p a t t e r n from ,lnS near [V.

ir.sity . o r i e n t a t i o n . N o t e vanishir.f? c i n t r i s ' 4 2 2 Kossel line.

J.1'.:, is s e n s i t i v e also to c o m p o s i t i o n as s h o w n in th« F:,'. 2 . . which :?*j an?,Ie «convergent b e a m ) p a t t e r n taken at in ir.ter: : ~e : "he c h a n g e in p r o f i l e at the interface is c l e a r l y H—.T.. In ~ln;,>'.

20C the F o u r i e r p o t e n t i a l 'J..

•\ T.iy be •_>: t -.-rec zy the spec ial cases w h e r e 'J"

't-r.eracy*. i ' = >; reveai&d a s v a n i s h i n g of the - u»« a n d z.iir? * : c n -. cr.d i t i en. O r i g i n a l l y this '

;;c;ona crier :•-•: Iv. t it-r/i n o t e d ir. high v o l t a g e e i t .i ;:.: Fuk-jn^r-.' I •.:-.- it w a s shewn by jjennes and

r.2*. cucr. degeneracies may appear in nore ger.o

?'i -jltctron microscopy at the so-called

^nfisurations found for the sphalerite Zn5 a;

•a 1 cases and the -cn-syste~.at ic ::r i showr. in Figure Table 1 Fourier pote

Ga Al As. in Å- 3

ials

C O 0. 1 0.2 0.3

U zoo .00143 .GO IS4 .0C226 .0026S

.00153 .C0234 .C0251 . C'0298

Table 2. ^22 critical voltage, as : P. 3a.

for some diamond and sphalerite type materials, in kV.

7.C patterns o€ 200 and

:.s ill a CaAs. G* Al As 2nS GaAs

-y=-'-j :y Mar:hinsen et ai the degeneracies are derived for cer.trosym ::"s. Hut -it '.he symmetry orientations 3a-f the - the degeneracy still

'.A'I f.eam voltages. These can be

•:' with high accuracy and compared .-••'•-. . -1--. ..."- -ilTuiation based on equat ion (4). / '".,'* *

-in approximate treatment based on •' . . * ; . . ' ;' * * / iT.B Indicated in the Figure will be \ '• '' '~ \ • • \

jpprcximation. Formulae like •-..- '*••. . •"' "' -.

;etri:al obtains

.:20 •V . _•122

u

2 2 D 17)

r : j the case 3a (cf also Fig 1) en derived for a number of cases.

'. vcl tages for this conf iguration materials are given in Table Z.

:Surements such relations between r.^tentials can be obtained with

•.u:acy and used to determine .(•£³:r bond c h a r g e s⁵

Fig. 3 a-h Observed beam L jnf igurat icr.s for critical voltages in sphalerite ZnS CTION AND REFRACTION AT INTERFACES. MEAN INNER POTENTIALS.

n inner potential nanifests itself in electron diffraction as a refract:

.md can in principle be measured in several ways, by refraction at wedge i":petry experiments e'c. The planar interfaces in microelec! ronics offer t l.:v )f dete: t i.-.e • :.<? .iifference in electrostatic potential between *.

:es at the twc s:Jo? : t.-.e ir.terface. in an experiment designed by Taf*.

r-.d J-jr.esV Fif4. ':.•.- :•-::"; •.-""/reflection in the interface region gives :

*. -. i : iint streak in the diffraction pattern, at one side of the central spot, :..'...-.'Lr.g tcward the higher electrostatic potential llower U ). With a dark field aperi-Tr1 around the streak, i.e. slightly off the central spot, the specimen area ..int; . L -it ing *o the streak is seen as a bright area at one side of the interface.

rhis .nn be used to display interface structures and to determine the sign of '.'. •• -" ' B) A further possibility was t

phcwn ":v Taftø and Gjønnes who utilized '3 -

'he err active mean inner potetnial, which A ' ^a .ar. ::•?• varied by exciting a strong Bragg

reflection in one of the two crystals. By -

*:i;ir.g the specimen in such a way that

•f{l :AI = U(3). the difference U(A) - U<31 can Determined as 2Mm>, referring to equation (6) above.

We have studied this refraction effect in multiple layer of Si/V/Si.prepared by vapour deposition and in the MBE grown heterostructure GaAs/ScErAs/GaAs¹¹. Patterns are shown in Figure 5 and 6. In the dark field patterns from the s:1 i con-vanadium specimen, taken from either side of the central spot, the two sides of the vanadium layers are clearly seen. the periodicity of SO A is reflected in the fine structure along the st reak. The si 1 icon and vandium layers are amorphous, the diffraction spot comes from the silicon substrate.

The GaAs/ScErAs/GaAs structure is shown also as a high resolution micrograph.

Figure 6d, with characteristic faults in the top GaAs. The dark field pictures from the refraction streaks show the bright line at the ScErA.=-side as expected. A weaker bright line is here seen also on the other side, indicat'ng perhaps a more

Fig 5. V/Si/V/Si multilayers a] diffraction pattern, b) and d) dark field, c) bright field images.

=ft"E = \

Fig.4. Refraction at an interface

Sp'£ '• --• ' 3 i: P'-.s-ca' Concepts of Materials tor Ntuel Optoelectronrc De^ce A?pl nations i ' °?C * ^ 5

GaAs/ScErAs/GaAs. Diffraction pattern (a), central spot (b and c), lattice image (d).

dark field images from two

complicated potential variation across the interfaces than in the structures studied previously. Referring to the equation (3a), we may note that ionization in either of ;he two structures may change the potential appreciably - its manifestation will depend upon the direction of the interface. There will be also be a contribution t rcji the atom layers at the interface, as sketched in Figure (8a). Note also the var iat ions in contrast along the interface and that variation in diffraction ccr.dit ion at ei ther side may influence the effective inner potential according to eq^at ion (6).

Calculations of the refraction effects can be nerformed by a modified version of the so-cal led thin phase object approximation12: instead of integrating along the direction of the incident beam, we tilt the integration path through the object so as tc bisect the angle between the incident and diffracted beam direction.in the phase object integral

#(x) exp[i/Udz/2k]

p.t reducing the parameter a = tsinø where t is thickness.

:•*?. in as a main contribution to the scattered amplitude

k=2rz/\ and s=2ksin6

J"*aexp[ iUt/2ka] exp[isx]dx = 2a sin(Ut/2k + sa)

- which is seen to have a maximum at sa = -Ut/2k, corresponding to total reflection angle The calculations may be extended to include divergence of the incident beam and aperture size and Fresnel diffraction effects in calculation of contrast.

5. DISCUSSION

Electron diffraction offer many possibilites for determination of structure details cr. a iir.e scale, including the charge distribution or the Coulomb potential in snail

:p?izr.s as well as at interfaces. Dynamical scattering complicates the ir.:*rpretat ion. but can also be exploited to achieve high sensitivity in special -<;r.f l«'irat ions. The parameters thus obtained will usually depend upon a combination

•*: ui:.i.T.eters, e.g a relation between Fourier potentials, cf equation (7) and may be s'-i.:fj for determination of magnitudes such as composition or ionicity in an

• •r.er-ise known structure - or for comparison between related structures.

The refraction/reflection effects originating from differences in mean inner potential can be used to image interfaces an offers the possibilites to study charge distributions. The variations seen along the interface may be related to diffraction effects included in equation (6) or to variations in the surface term. A rr.ore detailed description of the potential difference at the interface may be required also in order to account for the observations of the GaAs/ScErAs/GaAs interface.

Our thanks are due to C.J. Palmstrøm, Bellcore for the GaAs/ScErAs/GaAs specimen.

REFERENCES

1. D. Cherns, ed: Evaluation of Advanced Semiconductor Materials by Electron Microscopy, NATO ASI Series B. vol 203, Plenum: New York, 1989.

2. L. Reimer, Transmission Electron Microscopy, 2.ed Springer:Berlin 1989.

3. J. Tafta and J. Gjønnes, Acta Cryst A44, pp. 833-837, 1988.

4. K. Gjønnes, J.M. Zuo, J. Gjønnes and J.C.H. Spence, Acta Cryst. A44, pp. 810-820 (19SS)

5. J.M. Zuo, J.C.H. Spence and M. O'Keeffe, Phys. Rev. Lett. 61, pp. 353-356. 1988.

6. D.watanabe, R. Uyeda and A. Fukuhara, Acta Cryst. A25, pp 138-140, 1968.

7. _'. Gjønnes and R. Haier, Acta Cryst. A27, pp 313-316, 1971.

S. H.. Matsuhata an J. Gjønnes, EUREM 88, York. Inst. Phys. Conf. Ser. No. 93: Vol 2 pp. 19-20, 1988.

9. K. Marthinsen, H. Matsuhata, R. Høier and J. Gjønnes, Aust. J. Physics, 41, pp. 229-459, 1988.

10. J. Tafta, R.H. Jones and S.M. Heald, J. Appi. Phys. 60, pp.4316-4318, 1986.

11. C.J. Palmstrem, S. Mounier, T.G. Finstad and P.F. Micelli, Appl. Phys. Lett. 56, 382-3S4.

12. J.M. Cowley, Diffraction Physics, 2.ed. North-Holland, Amsterdam, 1981.

13. W.M. Stobbs and F.M. Ross in D. Cherns, ed: Evaluation of Advanced Semi ror.ductor Materials by Electron Microscopy, NATO ASI Series B. vol 203, Plenum: New York, 1989.

$Pl£ .'ex * Jf ' s"*s "J' Concepts of Matenals for Novel Optoelectronic De* ce Apphcatmns

Paper 2

i

The polarity of small MBE-grown {111}GaAs domains on (100)Sco.32Ero.68As.

B. Hugsled. J. Tafto. T. G. Finstad and C. J. Palmstrom

Department of Physics. University of Oslo. Blindern. Oslo. Norway Bellcore. 331 Newman Springs Rd.. Red Bank. NJ 07701. USA

ABSTRACT

MBE-growth of GaAs on (100)ScxErt-xAs can result in domains of various orientations.

Most of the GaAs domains are of the epitaxial 1100)- or the twin related (221) - orientation. A 11111 orientation is also common. We have studied the orientational relationships of these domains hy transmission electron microscopy. The polarity of small 11111 GaAs domains on (100)ScErAs have been determined by electron channeling. We unserve that [he polarity is such that the GaAs [11J J direction las opposed to the 1111J one) points outward from the original ScxEri.xAs( 100) surface. We use this observation in discussing possible models of the interface between ScErAs and GaAs.

1

Research efforts for obtaining materials with either new or improved electronic and

• 'plica! properties have been intensified and led to crystal growth of many different types of ..-..uenuls alone and onto one another. ••- One such combination explored for it's properties is ScErAs/GaAs junctions. -»* tn the present study we have applied transmission electron microscopy and electron channeling on {1111 oriented domains in a GaAs layer that is grown at a very low deposition rate on top of (100)Sco.i2Er0.68^s a I

400 C. ( The nation " M i l l oriented" means that a 11111 plane is parallel to the original

• 11X1) ScErAs surface. ) This last compound is grown lattice matched to GaAs by MBE. as

!.as been previously reported.4 ScErAs has the XaCl crystal structure and ionic bonding dominates in contrast to GaAs where covalent bonding dominates in the polar zinc-blende cr\ stal structure. For (100) substrates the ScErAs grown on GaAs has good crystalline quality. ⁴ The growth of GaAs on (lOO)ScErAsis three dimensional after one monolayer of growth. ? The resulting GaAs is heavily faulted and consists of domains of mainly three orientations. The most abundant orientations are the epitaxially oriented (lOO)GaAs and ihe twin related 1221) one. In chis case about 20 % of the interface area is covered by domains of the {111} orientation, as shown in the plan view electron diffraction pattern and dark field image of fig 1. These main features has also been reported on before.* We notice that in die plane of the interface the (111 |GaAs is registered such that one <0l 1>

direction is parallel to one of ihe two equivalent <011> directions in the ScErAs surface.

One can see that the domains are elongated along the registered <0l 1> direction. The length of the domains range from 25 nm to 175 nm with an average around 100 nm. From cross sectional microscopy we also observe that the {111} domains propagate all through the thickness of the GaAs lavert 50 nm). In order to fully describe the the crystallographic relations the question as to whether the 1111 ] or the [ I I I ] direction of the polar GaAs points outward from the original (lOOjScErAS surface must be addressed.

Several transmission electron microscope techniques are now available to determine the polarity of small crystals: Comergent Beam Electron Diffraction (CBED) based on

2

three or more beam interactions."-8 High Resolution Electron Microscopy! HREM) 9 and finally electron channeling using a small electron probe and collecting characteristic X-rays

• : ; or the corresponding electron energy losstEELiJ}.'- The optimum method depends

on the specific application. Although the CBED method depends upon multiple scattering.

the underlying effect for polarity determinations is in general observable for thin specimens. However strain and bending of the specimen washed out the details in the CBED disks in the present case with {111 JGaAs domains on ScErAs. The strain may arise as a consequence of TEM sample preparation or during growth. While HREM may be used for thin specimens and small areas, the small difference in scattering power of Ga and As makes it difficult to apply to GaAs. Electron channeling generally works best when the specimen thickness is comparable to or less than the extinction distance of the reflections involved.

Using electron channeling we have determined the polarity of the {111} oriented domains by recording the X-ray emission while placing either the 111 or the I I I reflection in Bragg condition. Figure 2 shows the X-ray intensity from a small domain of 11111 GaAs in a specimen prepared in cross section. Here each domain cover a sufficiently large area while the specimen is sufficiently thin that the electron beam only travels in one single domain. The X-ray intensity ratio of Ga to As changes significantly depending upon whether the 111 or the 111 reflection is at the Bragg position. This we use to identify the polarity of GaAs as shown by Tafto. | 0 We conclude that the GaAs (1111 direction is pointing out from the ScErAs interface. We have made the same jde ni i fi cation on seven separate 1111} domains. No domains with the GaAs [111]

direction pointing outward was observed. We thus conclude that the polarity observed is the preferred one for this system {when there first is a 111 If domain. J The sequence of planes is thus as sketched in Fig. 3a.

One should ask why is there one specific polarity preferred. We can consider two main factors dictating this during crystal growth. One is the affinity of Ga versus that ol"

As atoms to the ScErAs. This could determine which of Ga or As will be in the first

3

jtomic 11111 la\er. Another factor which could influence the polarity, especially if interface bonding was not important. is the surface energy of the growing GaAs when this w grown under an excess As flux as here. The observation of a 1111} orientation on a : 1 noj substrate itself suggest that what yield this orientation is weak atomic bonding between the GaAs and ScErAs. The two different crystals are not lattice matched for these orientations and the interface atoms are not in registry with a periodicity comparable to the unit cells of the enseals. However bonding to the substrate is not without influence as the [111! domains have specific rotations. The [ 110] direction of GaAs is parallel to a

*•() 1 ] > direction in ScErAs. This latter orientational relation can be viewed in light of the surface reconstructions observed for up to one monolayer GaAs coverage, which had 3\ 1/1x3 reconstructed areas with repetitions running along <0l I> surface directions.5-6 Further it is observed that the initial islands that grow are needle shaped along <011>

directions. It was speculated that there are "anchor" points along the <011> directions.5 So even if the GaAs has few strong bonds to the ScErAs substrate in a fully developed domain, it's nucleation could consist of a row of atoms along the <011> direction. There are several possible ways one could think that the (111 j orientation evolved from chains.

One of these is a "collapse" of the {221} orientation , by a {111} plane rotaung around a

<() 11> axis (in the interface plane) to become flush with the substrate. The island formation of course also suggest that the bonding between the GaAs and ScErAS is not strong compared with the GaAs surface energy.

When the stacking sequence of GaAs is the one observed, one can further argue that the first layer on ScErAs is likely to be a Ga layer. The argument we apply is that there is generally a limited range of inter-atomic distances that can yield minimization of the total energy. If one limits the possible interface structures to abrupt changes from a GaAs lattice to a ScErAs lattice, we consider two cases shown in Figs. 3b and 3c, both satisfying the observed polarity. In Fig. 3b the first atomic layer consists of As. The first atomic layer would have to be at least 0.15 nm above the interface to avoid inter-atomic distances shorter than 0.25 nm. The distance from this As- to the next Ga-plane is fixed by the GaAs lattice constant and is 0.24 nm. The resulting density of atoms would then be quite

4

iow in the interface regioni only a single atomic layer of As) and the energy would be expected to be higher than the alternative shown in Fig. 3c. where Ga constitutes the first atomic layer and a distance to the next As layer of 0.08 nm 1 resulting an interface bilayer of Gu and A.s.t The inter-atomic distances are those of GaAs. Since surface

reconstructions occur easily for GaAs. the difference in surface energy between reconstructed I ITT) and '111) surface is probably not very large. At the interface between GaAs and (100 >ScErAs. GaAs reconstruction is not easy and minimization of dangling bonds at the interface is probably the lowest energy configuration. Thus it may be argued that the configuration in Fig. 3c is more likely since the GaAs terminates towards the interface with Ga single bonds rather than the situation in Fig. 3b where the GaAs would terminate with three unsaturated As bonds at the interface. Since we know the (IDOiScErAs surface is quite inert (as surfaces of NaCl are), we consider the situation in Fig. 3b to be unlikely.

The 1111 }GaAs surface energy is quite low. This can be a factor in determining the polarity of GaAs domains during growth also. In the present case these are grown under an excess As flux and most of the time the surface will be As terminated. If die lattice were bulk terminated, then the ( i l l ) plane would have one unsaturated As bond per As atom whereas the (111) orientation would have three and thus a higher energy. The energy »vill of course change somewhat when die surface reconstruct and/or form a separate As over- layer . If one compares two simple situations: i) configurations based upon three unsaturated As bonds at the interface plus As-As bonds in an over-layer at the surface and iii Ga-As bonds plus an As reconstructed over-layer, one would always expect situation i) to have the highest energy. We can thus argue that the <I II>-rype GaAs polarity is probable also for situations where the magnitude of the Ga affinity versus the As affinity towards the substrate is not of major significance. A possible candidate substrate to test this can be an amorphous SiCh substrate. In line with what is said above about the volume density of atoms we would expect the first atomic layer to consist of Ga given the B-rype polarity. One should also note that this is similar to the situation if (vacuum

5

cleaved] GuAs ol" this polarity was put rigidly on lop of ScErAs.

In condition ive have seen that domains of J i l l JGaAs sometimes forms on 1100 iScErAs during MBE growth. These are all of the same [III) orientation, which can be understood by assuming the early nucleation process, determining the rotation and the actual stacking sequence of Gaand As atoms, is largely determined by minimizing the GuAs surface energy and the ScErAs/GaAs interface energy.

6

REFERENCES

R. Hull ar. 1 R. T. Tung. in Electronic Structure and Properties of Semiconductors.

W. Sehroteried.i. VCH Verlagsgesellshaft mbH. VVeinheim (1991)

: T. Sands. C. J. Palmstrom. J. P. Harbison. V. G. Keramidas. N. Tabatabaie. T. L.

Cheeks. R. Ramesh and Y. Silberberg. Materials Science Reports, 5, 99 (1990): C.J.

Palmstom and T. Sands, in " Contacts to Semiconductors', L. J. Brillson led.).

Noyes. Park Rige, NJ ) in press.

; C. J. Palmstrom. T.L. Cheeks. H. L. Gilchrest. J.G. Zhu. C. B. Carter and R. E.

Nahory. Mat. Res. Soc. Extended Abstracts. EA-21. 63. (1990): C. J. Palmstrom.

T.L. Cheeks. H. L. Gilchrest. J.G. Zhu. C. B. Carter. B. j . Wilkens and R. Martin.

J. Vac. Sei. Technol. A, 10. 1946 (1992)

4 C. J. Palmstrom. S. Mounier. T. G. Finstad and P. F. Miceli, Appl. Phys. Lett.. 56.

382(1990)

* T. G. Finstad, C. J. Palmstrom. S. Mounier, V. Keramidas, J. Zhu and B. Carter.

Mat. Res.Soc. Symp. Proe. 202, 579 (1991)

<• J. G. Zhu. C.B. Carter and C. J. Palmstrom , Mat. Res. Soc. Symp. Proc. 198. 177 (1990): J. G. Zhu. B. Carter , C. J. Palmstrom and S. Mounier. Appl. Phys. Lett..

56. 1323 (1990)

7 P Goodim •- and G. Lempfuhl. Acta. Cryst., A24. 339 (1968)

* J. Tafto and J. C. H. Spence, J. Appl. Cryst.. 15. 60 (1982)

" R. W. Glaisher, J. C. Barry and D. J. Smith, in Evaluation of Advanced Semiconductor Materials by Electron Microscopy, D. Chems (ed.). Plenum Press

Inc.. New York (1989)

i" J. Tafto. Phys. Rev. Lett., 51, 654 (1983)

11 J. Tafto and J. Gjonnes. Ultramicroscopy. 26, 97 (1988) i: J. Tafto. Acta. Cryst.. A43. 208 H987i

7

FIGURE CAPTIONS

FIG. 1. "Plan vie»" TEM pictures of a GaAs layer on ScErAs. a) Diffraction pattern b) Indexing of diffraction pattern, c) Dark field image using the the reflection indexed as 02 2( 11 Da.

FIG. 2 X-ray emission intensity from GaAs when the electron beam is channeled through a cross section of the sample, a) The 111 reflection is in the Bragg position b) the I I I reflection is in the Bragg position.

FIG. 3 Schematic models of 1111 }GaAs domains grown on a ScErAs substrate showing: a) the sequence of Ga and As planes for the [111] direction of GaAs.

and possible interface structures with undistorted GaAs bonding structure indicated for to") As layer first and c} Ga layer first on the substrate during GaAs overgrowth of domains showing { 111} orientation.

8

C22. 1 CO)

4 0 , , . -

3 2i 1 i - i b

0 2 0 „

0 2 2

, - ,

000

°2

il00l

22 Q i i - iS

FIGURE 1

I l l As - 25'

•la) „ •>*nii<i.>iiAi

5 0 -

o

<-' 2 5 -

As

" ' • - * • ' • " ' • ' iitl A m ÉI

.^ 500 1000 1500

< E

' Channel number

FIGURE 2

- " ^ " N ^ S ^ N - A As

FIGURE 3

Paper 3

ELECTRON MICROSCOPY OF MEAN INNER POTENTIAL CHANGE ACROSS INTERFACES IN ELECTRONIC MATERIALS.

B. Hugsted", R. Sivertsen*, J. Gjønnes', G. Salomonsen', and J. Tafta*

'Inst, of Physics, University of Oslo, P.O.B. 1048, Blindern, N-0316 Oslo 3, Norway 'Norwegian Telecom., P.O.B. 83, 2007 Kjeller, Norway

INTRODUCTION

The ever decreasing dimensions of electronic components into 2-dimensional behaviour and even "quantum wires" makes the interface regions {although of thickness comparable to interatomic distances) into a substantial part of the active volume of the component. We discuss e method for the study of buried interfaces that is sensitive to change in electrostatic potential and has the possibility to be developed into an quantitative tool.

THEORY

The charge distribution in solids are such as to lower the potential energy of fast electrons entering from vacuum. The charge distribution is linked to the electrostatic potential by Poissons equation o=-eV"<p (Bursill et. al. 1978). The space average of the potential is refered to as mean inner potential, Uc- When aligning the incident beam parallel (or close to) an internal interface between to materials with different mean inner potential the electrons traversing the interface are deflected Fig. 1. This results in a streak out from the sentral spot in the diffraction pattern. Placing a dark field aperture around the streak makes the interface region apper as a bright line in the image (Turner and Cowley 1981, Taftø et. al. 1986). By using the thin phase object approximation < Cowley 1975) and introducing an aperture function in reciprocal space the wave function in the image plane may be given as

* ( x ) = y:{ Q , ( x ) ^ f q ( x ) t|»'{x)]} (1)

where ^ is the wavefunction, 9 denotes Fourier transform, Qa is the aperture function, q = exp(i/Udz/2k) the transmission function of the phase*object and # ' the incident wavefield. To get an impression of the dependence of the beam tilt, one may use a similar approch where a thickness t is assumed and the integation path through the object are made to bisect the angle between the incident and diffracted beam direction. Introducing the parameters a = tsinø, k = l / i and s=2ksinø we obtain the scattering amplitude •miAti/sk

_J'exp(JUtx/2kaJ exp[isx]dx = 2a ---— -"- (2) The integration is done for a single step potential and AU is the potential difference

across the step. This expression is seen to have a maximum at sa = -dUt/2k corresponding to total reflection.

EXPERIMENTAL

The technique is applied to the characterization of MBE grown layers of (100)GaAs/ALAs/GaA, Fig. 2. The displacement of the objective aperture along [-100]

enhances the inner GaAsMiAs interface, while the outer AlAs/GaAs interface appears as a dark line. This indicates that the mean inner potential for electrons are lower in GaAs than in AlAs. While the inner interface is planar the outer AlAs/GaAs interface has a wavy apperace. Unevenness along the interface is visible both in bright field and with the objective aperture displaced along [ 100], Fig. 3. The displaced aperture view- gives a better 3-dimensional impression of the interface by enhancing the parts that are parallel or close to parallel to the incident beam.

References

Bursill, L. A., Barn., J. C., and Hudson, P. R. w. , 1978 Phil. Mag. A, 6: 789-812 Cowley, J. M., 1975, Diffraction Physics (Amsterdam North Holland) 61.

Tafto, J. , Jones, R. H., and Heald, S. M., 1986, J. Appl. Phys. 60: 4316-1318 Turner, P. S.. and Cowley. J. M., 1981, L'ltramlcroscopy, 6: 125-138

i'r:;:cij)lc of imaging potential change. Fa^i -li-ctpona passes t h r o u g h a sample v.-iih H : nek led i n t e r f a c e region between materiala

\ ai.d b. Material A has the lower mean :::ier electrostatic potential f o r e l e c t r o n s .

•'% dark field a p e r t u r e displaced as indicated ,'...u!d enhance the interface regions that i f f parallel Cor near p a r a l l e l ! to the beam i w k h i g them appear as b r i g h t lines in the

d i f f r a c t i o p a t t e r n

r i g . 2

" H a r k f i e l d " {Objective a p e r t u r e displaced iil"]ig i -100]) images of outer a) and inner

\. : i n t e r f a c e s o f M B E g r o w n k'O >C.aAs A l A s ' G a A s . The outer interface .-.pperars as a dark l i n e , while i\w inner ^ : : , l e r f a . v is b r i g h t . I n d i c a t i n g deflection of i-iiTtrons towards GaAs- Thickness of the AlAo layer is SOOnm.

Hr:pht field a ; and "Dark fit-Id" (The hK-ttivp apt-riure displaced along 1100]) 1 -'imag.-s of the c u t e r interface of cross ,-'."11.11.1: aamplr- of (lOC'iGaAs AlAs GaAs VAM g r . v . n i.iyers. Thi- interface has a v. .1 v \ a p pora n et- i n bot h images. T he

!•: :'•••;• pi'l v. a w * al..:ig the mt erfare in b a r e :•!• i- U K (-nharif tment -if the parts of t h e i.'.-:'f,.,< u.ir.ilU-l : *Ju- beam.

GaAs

Paper 5

S c a t t e r i n g integrals a t solid—solid interfaces

J. Gjønnes and B. Hugsted

Department of Physics. University of Oslo, P. O. Box lOJS Blindern, Q'316 Oslo. Noruay

Solid/solid interfaces can be imaged in the transmission electron microscope by means of refraction/reflection arising from the difference in mean electro- static potential bttwceu the two adjoining solids. Standard approximations used in high ciicrgt election diffraction and microscopy are not directly appli- cable to treatment of tliis effect. Two modified procedures axe discussed: an adaption of tde mte^r.iJ expression for the scattering amplitude and a mod- ified thin phoic object approximation. Calculations of diffraction patterns and in-focus contract from an abrupt interface are shown as examples.

1 Introduction

Interfaces are important elements in a variety of technological and natu- rally occuring mir restructures - and prime objects for modern microscopic techniques, notably in transmission electron microscopy. Considerable ef- fort has been put into high resolution imaging [1,2]. e.g. of heterointerfaces in microelectronics: through careful choice of imaging conditions combined with extensive calculat ion of contrast, structural details at an atomic scale can be revealed.

Another imaging technique was demonstrated by Taft*, Heald and Jones [3]: The difference in the electrostatic potential across an interface will produce reflection ami refraction of an incident beam to one side of the interface With a small aperture, displaced off the primary beam, a dark-field image of quite high contrast and definition, as in Fig 1. can be oblaii.ed. A qtialuamv ttitepretalton of this contrast m»y appear simple:

an incident beam parallel to the interface is deflected towards one side. A maximum may be expected at or near the total reflection angle as given by the potential difference if the interface is sharp. Adaption of the standard approaches of electron infraction and microscopy calculation for the trans- mission case is much less straight-for ward. With the notations explained in Fig 2a. and a sharp potential step: U(x) = if sgn(x), Fig. 2b, we obtain

Si-Jtn-Ting integrals at sdid--A\.l mu-i'faa-.- :iu'j

Figure 1' Displaced aperture image* of CijAs/AlAs interface with the objective aperture displaced a.-, indicated, (a} the interface appears bright. | b | the interface appears dark

line ktriematira] expression

where t h e diffracted wave v prior u. wni ten (*. fc« + (J) In (1) t h e r e is no

Figure .' (a) notation* for uvr in .m.iliticil expressions, ko • incident beam wave lector k - >ca(ieml he.uti t>ate vector. 3 and C - x ^a" d i components of the -.callerinj; * « i o r i h | Hie potential step used in the calculations lei ra> path hi kc -.catuic.l into k and the path of integration crossing llie inletfactr

indication of reflection «-iFf-cl or m d r ^ d of an a s y m m e t r i c intensity T h e

J. Gjønnes and B. Hugsted thin phase ubjffi approximation [4]

Jts) = J exp[-isx]eXp[it^}dx (1.2)

with f i r ) = U ftt/ntJ) will yield a similar result.

Mure .iet.uh-il <-alriilanons can be pursued in a Bloch wave or mullishce formulation [A], !>> mean* of a periodic continuation and considerable com- puting effort Tins again auggests that the standard high-energy electron diffraction approaches are in fact not well suited for treatement of this re- flection/refraction -'ff<-ct. Let us therefore look for formulations which lead more directly 10 the .salient features of the present experiments of scatter- ing from a thin foil - and which also may include Bragg scattering from crystal planes. One audi formulation is the standard integral equations for the scattered amplitude [5]

r|ku — k ) = f exp[-ikr]U(r)*(r)dr

/ l ku - k) = / exp[-ikr]f/(r)*(p)rfr (1.3) where approximations beyond the plane incident wave can be introduced

for the amplitude d> Another possibility is a phase integral similar to the thin plia.se object approximation [4], but with the integral taken along a ray direction bi.vclmg the angle between k and ko - as in Fig. 2c. We have tried both expressions on the situation in Fig. 2b, i.e. the potential step. The beam direction i- here l it ken at or near the z-axis. with the interface parallel to the yz-plan.-. Icnce no y-dependence needs to be explicitly included in the expression;*

2 Theory and calculations

In the expression (.'!) let us use plane wave expressions inside the object, but with the wave vector modified by the mean inner potential: <PA — exp[ik^|.<l>j) = '•xpfikfll On introducing kAiB = (*o +C*.fl) w* obtain by standard integration

where eg ^ = C + 7? * £ ( - i3+ £/„): With VB = ^ md UA = £ . maximum intensity is found at the total reflection angle. The modified phase grating expression gives the contributions to the wavefunction at the exit surface associated with a specific scattering direction, k, corresponding

•Scattering integrals at .solul-^oliil mtfrfacea tr> ihe scattering variable s. see Fig. 2c

x < ^ : 0> = « x p ( i kor ) e x p ( ^ p )

^ <J- < | : * = e x p ( i k0r ) MP( ^ £ ) (2.2)

=f >x: * = exp(ftor)exp(fgS)

where a = ^ The scattering amplitude in the direction represented by s is obtained as a Fourier integral of these, viz:

/ ( s ) =

„ Æ 2 ^

:*i£±il

U is ( l l + f )

a* 4t T 4* '

— again with maximum near the totai reflection angle, i.e. s\s\ = —£'.

Calculations of intensities for different thicknesses are shown as Fig. 3. As the thickness is increased, a maximum appears around the total reflection angle. In order to calculate image contrast a Fourier transform of the

J\

Sctctennq v«ctoi

Figure 3: Intensity of scattered beams from & IV potential step u a function of scattering vector s for lOOimi. 25Dnm, 500nm and lOOOnm sample thicknesses.

scattering amplitude must be multiplied with appropriate proagators for the optical system: aperture, defocus and lens parameters, see [4], and the variation in path length difference with s. The contrast profile Fig. 4,

J. Gjonnes a n d B . Hug, ted

wlm.li is c;ilci:l.iii--l (uv (;aiiB»ian focus with an ;n f i m t e a p e r t u r e c o r r e s p o n d s to t!ie nirrtfut ik'[i.-u> at d i e exit surface a n d t h u s t o s t r o n g channelling

••Ife-us in :..|-i-t-troivjiu- signals from t h e interface.

z j ,

25Cnm

- : c o 10 Distance from interface inm)

Figure 1 Im.iui- niUiiMty at exit surface of sample with thickness JSOnui liiifii-iu is normalized to 1 far away from the interface.

T h e expri".MGiiN above can he e x t e n d e d t o include B r a g g reflections a t one nr h o i h Milr> of t h e interface Of p a r t i c u l a r interest is t h e case with B r a g g reflection at urn¹ side T h i s can readily b e introduced in e q u a t i o n (.'!} above. ri'Mi!lni£ in exactly '.he s a m e form, b u t with two c o n t r i b u t i o n s corresponding t o two a p p r a r e n i p o t e n t i a l s t e p s UA - Ug + 2 j t r ' *^s T h e two Bloeh waves m D «ill ^ e diirerent p o t e n t i a l s

< v i n *1 > , < *2i y i *2>

(2.4)

= l\, + 2kr> - Z I C, |2 Usg

• which can aUu l-f i n t r o d u c e d in t h e ^ N a t i o n s ( 5 ) . W i t h Bloch waves on either Mcle. t r . m o t i o n a m p l i t u d e s between t h e m should b e worked o u t at the interface In tin— forward s c a t t e r i n g a p p r o x i m a t i o n , which is c o m m o n in all transmission H I T tron microscopy work, improved solutions can be o b t a i n e d by introducing t h e a m p l i t u d e in real s p a c e a t different levels a n d perform t h e mh'Kt.itiuii (3) a second time.

3 Conclusions

T h e iiMial coiiipni.itiuiul schemes for transmission electron microscopy i e the Bloch w*vr ,ind multislice m e t h o d s a r e n o t well suited for t r e a t i n g the details of rHh-t I M I a n d refraction at interfaces parallel t o t h e incident b e a m It is shown . J i m r t h a t simple integral formulations, b a s e d e i t h e r on

Sratifnns; integraU.it sulM-r^lid Miu-rl'.uy? 373 tlif integral equation for the scattered amplitude or a modified thin phase

grating expression are convenient approximations and bring out the salient features: Diffraction srreaks and dark field contrast arising from differences in electrostatic potential across the interface. The calculations can be ex­

tended to include Bragg scattering; channelling effects associated with the interface is also treated. It should lie emphasized that the potential U appearing in the expressions is the average electrostatic potential derived from the charge distribution in the two adjoining structures- with the pos­

sible addition of polarization effects at the interface. Further experimental work on the effect is in progress.

Acknowledgements

Our thanks are due to Norwegiai. Telecom for financial support and for the MBE-growth of the GaAs/AlA» sample.

References

[1] Smith, D- J. and Barry, J. ('.. in High-Resolution Transmission Elec­

tron Microscopy and Associated Techniques, eds. Peter Buseck. John Cowley and Leroy Eyring. Oxfoi.l University Press, New York, (1988).

['-'] Glaisher. R. VV.. Barry. J (."• .mil Smith. D. J., in Evaluation of Ad­

vanced Semiconductor MalermU l>y Electron Microscopy, editor D.

Cherns, NATO ASI Serie* H. Plenum Press. New York, (1989).

[3] Tafto, J.. Jones. R II and lh .ild. S. M.. J. Appl. Phys. 60, 4316 (1986).

[4] Cowley, J. M.. Diffraction PIIVMIX 2ed. North-Holland, Amsterdam.

(1981).

[5] Morse, P. M. and Feshhach. II . Methods of theoretical physics, McGraw-Hill. New York. (ll>r»;j>.

Paper 4

applied surface science

Potential step imaging of interfaces in MBE-grown structures

B. Huiisted. J. Gjonnes and J. Tat'to

:>,,-.:—n,.,: ,.• f*r^Tw^ ! >.;-.Ti;n ..t t hi,,, flfimiern. ».*/r> Ori,. V.imm R ^ r - c l : lunt 1 ^ : . j.vepied tor publication 31 Jul> I W

Tfci MJtienni: >>r UM cleaning is ttrnneh influenced h> ihe charpe distribution JI iniertuces IN in a J o'mennnnjl election ni.ri>...T- ihe ukiiinn di-.tr ihulmn Jt Jn miertace can be siudied in direct and reciprocal --pace We prceni J new TLWI ' >-. ri-i.tjiii.1 J modification ul i he convergent beam elcciron diffraction icchnniuc. ihm improves ihe resolution in momentum »p\jce Hie i.-.timyue :- .ippiied to G.iAs AlAs MBE-emun Uvers.

1, Introduction

Supcrlai i ice and thin lavers are important in semiconductor science and technology. As the volume or the components decreases, the inter­

lace Npecit'ic properties become increasingly im­

portant tor device characteristics and perfor­

mance. Of particular interest are ihe band offsets .ti interfaces between epitaxial crystals that deter­

mine the characteristics of such devices as the quantum well and heterojunction transistor. To -.urne extent these interfaces are characterized bv the difference in mean electrostatic potential be­

tween the two finite, and connected crystals. The electrons of a material obey the Pauli principle, whereas the fast electrons of 10U-500 keV used in a transmission electron microscope are gov­

erned h> the spatial variation of the electrostatic potential given bv the distribution of charge in i he material. Still minor redistribution of the silence electrons strongly influences (he scatter­

ing amplitude. iMs). for small momentum trans- ter. \. Thus electron scattering of fast electrons m.n provide valuable information about the elec­

tronic properties of interfaces. Several electron microscopic techniques have been used to studv huned interfaces: the Fresnel contrast method [1.2!. where the image contrast ar the interface is observed tor different focal conditions. a..d the parallel beam diffraction method [3.4). In this

paper we present a new diffraction technique to study the intensity in the diffraction pattern, with improved resolution in reciprocal space. This technique is applied to GaAs,/AlAs interlaces.

2. Theory

The observable property of the specimen un­

der examination by transmission electron mi­

croscopy and diffraction (when excluding mag­

netic materials) is the electrostatic (Coulomb) potential I ' M . connected lo the charge distribu­

tion by:

/ _ Z,e \ • mr')

Wr) - f X -; r : = / - d r . I l l

\ >^,r~ ^r ' / -r- r

where j numbers all the particles in the s\stem and a time average is implied, nir) is the charge distribution. For a finite system, of volume il. the mean value of the potennal is defined bv:

1 / / i t ' ' )

' ' " = nf ' r - d r ' d r . C I U ^}u^}tt i r - r

We are interested in the change in mean inner potential across an interface connecting two ma­

terials. It is a long-standing discussion whether this difference in mean inner potential can be deduced from quantities from the bulk materials alone, or depends on the detailed description of