IL NUOV0 CIMENT0 VoL. 7 D, N. 6 Giugno 1986

Electron Diffraction Study of Melt-Grown InSe Crystals.

C. DE BLAS~, D. M A ~ O , S. MO~GEL~ and A. ~ Izzo

Dipartimento di _Fisica dell' Universitd - Levee, Italia Gruppo ~Vazionale di Struttura della Materia, G.IV.S.M. del C.~.t~. - Leeee, Italia

(ricevuto i l 24 Ottobre 1985)

Summary. - - Electron diffraction has been performed on thin crystals of indium selenide, cleaved from ingots grown from stoichiometric and nonstoichiometric melt by the Bridgman.Stoekbarger method. The analysis of the selected area diffraction patterns has shown the presence of two phases, whose lattice parameters have been calculated. The stacking sequence of the polytypes has been observed through the moird patterns.

PACS. 61.14. - Electron determination of structures.

1 . - I n t r o d u c t i o n .

The InSe is a semiconductor crys ta l belonging to the t ype A~IIB w layer compounds, which are ve ry interest ing s t ructures because of their two-di-

mensional i ty and the ensuing anisot ropy of the physical properties. I t has

been compara t ive ly less invest igated t han other layered compounds, for in- s tance gall ium selenide or gall ium sulphide. E v e n if the first a t t e m p t to de- t e rmine the crys ta l s t ruc ture was done in 1954 (1.a), only in the last years

(1) K. SCHUBERT, E. DORR]~ and E. GUNZEL: Naturwissenseha]ten, 41, 448 (1954). (2) S. SUOAIKE: Mineralog., 3, No. 2, 63 (1957). (a) S.A. SEMILETOV: Kristallogra]iya, 3, 288 (1958).

795

796 C. DE BLASI, D. MANNO, S. MONG]~LLI and A. mZZO

this problem has been the object of several investigations (4-1~); however, it has not been completely resolved, since in the published papers there ~re some disagreements about the polytypes. Ind ium selenide crystallizes (~2) for stacking of slabs which are bound together by Van der Waals t ype forces. Each slab consists of four layers of close-packed-like atoms, the bond be- tween the layers of each slab being of covalent type.

Therefore, the atoms are s tacked in the sequence Se-In-In-Se along the e-axis and easy cleavage occurs among the slabs.

This fact allows several stacking sequences of the slabs and the mater ia l exhibits various polytypes , which are quoted in *he l i tera ture (9). In part icular , it seems tha t two structl~re modifications are more f requent ly reported, the former called y corresponding to a rhombohedra l s t ructnral modification, the lat ter , called fl or ~ according to thei r own space group, corresponding to a hexagonal lattice. In this paper , we repor t the results of the diffraction per-

formed by a trasmission electron microscope on thin samples, cleaved from various ingots, grown from the melt by the Bridgman-Stockbarger method.

The presence of two polytypes has been evidenced in every sample and thei r lat t ice parameters have been calculated.

2 . - E x p e r i m e n t a l .

Several ingots of InSe have been grown f rom stoichiometric and nonstoi- chiometric mel t by the Bridgman-Stockbarger method ; the exper imenta l ap- paratus and procedure have been described elsewhere (x3,~4).

In order to obtain high qual i ty samples, only the middle region of every ingot has been used, since this port ion is character ized b y a layered s t ruc ture

easily cleavable (ima). l~epeated cleavages have supplied ve ry thin single crystals with a typical

area of about 1 mm 2 and thickness less t h a n I ~zm. Of course, this me thod

(a) B. CELVSTK• and S. PoPovIc: J. Phys. Chem. Solids, 35, 287 (1974). (5) A. LIKFOR~AN, D. CAtCRE, J . ETIE:N:N:E a n d B. BACtIET: Aeta CrystaUogr. Sect. B, 31, 1252 (1975). (s) K.C. NAGeAL and S.Z. ALI: Indian J. Pure Appl. Phys., 13, 258 (1975). (7) A. CH~VY, A. K~MN and IV[. S. MAn'TIN: J. Cryst. Growth, 38, 118 (1977). (a) S. JANDr. and C. C~LO~E: Solid State Commun., 25, 5 (1978). (~) A. CHEVY: J. Cryst. Growth, 51, 157 (1981). (lO) S. I~ov~, T. YOSHID~ and T. MORI~A: Jpn. J. Appl. Phys., 21, 242 (1982). (11) T. IKARI, S. SHIGETOMI and K. HASm~OTO: Phys. Status Solidi :B, 111, 477 (1982). (1~) R.M.A. LI]~T~ (Editor) : Preparation and Crystal Growth o] Mate/rials with Layered Structures (Reidel, Dordrecht, 1976). (la) C. D:E B~,AS~, G. MlcoccL S. MONGELLI and A. TEPO~V, : J. Cryst. Growth, 57, 482 (1982). (14) C. D~ BLASI, G. MIcoccI, S. MONG~.LI, A. TEPO~ ~nd F. ZVAN~I: Mater. Chem. Phys., 9, 55 (1983).

ELECTRON DIFFRACTION ST~JDY OF M:ELT-GRO~VN InSe CRYSTALS ~

introduces latt ice defects such as dislocations, etc., but t hey are not relevant, since our observation aims at latt ice parameters .

The samples have been mounted in folding grids and, in order to avoid contaminations in the microscope column, huvc been dipped in high-puri ty e thyl alcohol for about ten hours, before using them.

Diffraction pat terns have been taken for m an y samples of each ingot and the observations have been performed on several points of the same sample, also by varying the angles of the double til t specimen holder. A Philips Elec- t ron Microscope E m 400 T has been used with ~n analyt ical objective and a condenser system, excited so as to light the sample by a parallel beam of elec- trons, at an accelerating voltage of 100 kV.

At 28000X, in the selected-area magnification mode, an aperture of 150 tLm of diameter has been set in the imaging plane of the objective~ in or- der to ensure tha t the selected-area diffraction pat terns (SA.DP) were carried out on a controlled area of the sample, with diameter of about 5 ~m.

We have paid part icular a t ten t ion to the calibration of the camera con-

stunt. I t is well known (1~) tha t in a diffraction camera of length L a dif- f racted beam forms a spot on the plate a t distance R from tha t of the t ransmit-

ted one, according to the equat ion

( t ) R d -~ ,~L ,

where d is the usual spacing of diffracting planes and ~ the wave-length of

the beam. I t is possible to show (1~) tha t the camera length depends strongly on the

excitat ion of the objective and diffraction lenses. To minimize this second effect, we have worked with a fixed excitation of

the diffraction lens. To do this, we have tu rned off the objective lens, have inserted an aper-

ture in the back focal plane of this lens and, in the diffraction mode, we have focused the edge of the aper ture with the diffraction lens.

This was f requent ly checked during the calibration and observations. Then we have calibrated the camera length inserting a gold single crys-

ta l in the gap of the objective with the [001] direction parallel to the incident beam, we have focused the image and recorded the diffraction pat tern . By measuring the value of /~ on the photographic plate, we have computed Z.

Finally, we have measured the objective current with an Elect rometer Kei th lcy 616.

(15) B.E. :P. BEESTON, R. W. HORN~ and R. MARKHAM : Electron Di]]raction and Optical Di/]raction Techniques (North-Holland, Amsterdam, 1973). (le) K.W. ANDREWS, D.J . DYSON and S. R. K~owN: Interpretation o] Electron Di]. fraction Patterns (Adam ttilger L.t.d., London, 1968).

7 ~ C. DE BLASI, D. ~IANN0, S. I~IONG~LLI a n ~ A. l~IZZ0

Varying the height of the gold in the gap and, consequently, the objective lens current to focus the image, we have obtained the variation of camera constant with objective lens current in the range of interest. These ranges were those used in calculating the d-spacings from the diffraction patterns of InSe crystals, recorded in the same way.

We have estimated that the error in determining the camera constant is about 1%, much greater than the error due to the measure of the distances on the photographic plate between the spots. This error is about at 0.1~o, since we have measured the distances with a microphotometer Hilger & Watts L501.

3. - R e s u l t s a n d d i s c u s s i o n .

To index each diffraction pattern, we have followed the approach described by ANDREWS e$ al. (pug. 33 of ref. (~e)) based on the analysis of the relation- ship between the squares of the reciprocal values of d-spacings, namely l id ~.

In doing this, we have been successful only when we have used the equation of the hexagonal system (~e):

1 4 H 2 q- H/i: q-/iC~ L~

where a and e are the hexagonal lattice constunts and (HK.L) the usual Miller- Bravais indices.

When Z --~ 0 between pairs of spots, the ratio of 1/d ~ values gives the ratio of the related (H 2 ~ K ~ ~- RK), which can get the values (~e) 1, 3, 4, 7, 9, 12, etc. Hence it is possible to index the diffraction pattern.

On the contrary, when two pairs of spots have the same value (H ~ q- K ~ q-HK) , the subtraction between the related l id 2 values gives ( L ~ - L22)/e s.

Since Z ~ - L~ is the difference between the squares of integers, one can evaluate Z and v, having many spots to index.

In the general case, we have performed various trials ~nd, finally, we have calculated the values of a and v by eq. (2) with obvious algebraic manipu- lations.

In any case we have checked both the vector sum of each spot of the diffrac- tion pattern, and the angle between any pair of spots, given for the hexagonal system (~e) by the following formula:

(3) COS ~0 -~

-~ [(H~ + X~ -~ H~K~ + (3a~/4c~)L~)'(H~ + K~ + H2.K~ -~ (3a2/4c~)L~)] t"

The analysis of the diffraction patterns has shown the presence of two different phases:

ELECTRON DIFFRACTION STUDY OF MELT-GROWN InSe CRYSTALS 79~

Fig. 1. - Typical electron mierograph of selected.area diffraction: a) hexagonal phase, zone axis is [45.3]; b) rhombohedral phase referred to hexagonal axes, zone axis is [23.]']. In both cases we have not labelled all the spots, but only those necessary to assign the indices.

TABLE ]. -- Observed and calculated vah~es o] the angles between She reciprocal vectors o] ]ig. 1. a) Hexagonal l~hase, b) rhar~boh~ral phase re]~fre, d $o h e ~ o n a l axes.

Reciprocal vectors H=X~'/~ q~ob~ q~=l Hx K 1. L 1 (degrees) (degrees)

a) hexagonal phase 01.2 11.3 53.5 53.5 11.3 10.1 58.4 58.5 10.1 01.3 68.0 68.0 0]'.2 13.5 28.0 29.0 12.5 2].4 52.9 52.5 2]'.4 11.]- 65.8 66.6 I1.]- 12.5 61.3 60.9 10.1 21.0 22.9 22.3 21.0 12.3 25.3 25.3

b) rhombohedral phase

01.4 10.1 68.3 68.3 10.1 11.5 60.9 61.0 11.5 0]-.4 50.8 50.7 01.4 11.3 31.6 31.8 11.3 2]-.6 70.0 70.1 2]'.6 13.9 52.1 51.9 01.4 12.7 19.7 19.5 12.7 21.3 25.3 25. t 13.13 2-1.2 62.0 62.5

~00 C. D~. BLASI , D . MA~qN0, S. MONGELLI &Ild A. R I Z Z 0

1) One has lattice parameters a -~ (4.00:~0.04)/~ and c ~ (16.7:~0.2)/~. A typical diffraction pa t te rn is shown in fig. la ) : the assigned indices are also reported. The calculated value of the zone axis is [~5.3].

The measured values of the angles between the reciprocal vectors of fig. la) , together with the calculated ones, are listed in table In). A good agreement is evident. A]l the d-spacings observed in the hexagonal phase and the indices assigned to them are summarized in table I I ; for comparison are also re- ported those obtained by I N o ~ et al. (10), which have performed X-ray diffraction in heat- t reated InSe sample grown from the melt. The values of table I I are also in good agreement.

We can, therefore, conclude tha t this phase is equal to tha t reported in the l i terature as a hexagonal fl-structure (space group D~) (8.11) or a hexagonal ~-strueture (space group D~h ) (3,4,~-i~).

2) The other ph&se has lattice parameters a : (~.00=L0.04) ~ and e---- = (25.3=L0.3)/~. A typical diffraction pa t te rn of this phase is shown in fig. lb): the Miller-Bravais four indices are also shown; the calculated zone axis is [2~. 1]. Table. Ib) reports the measured values of the angles between the recip- rocal vectors shown in fig. lb) ; t hey are in very good agreement with the com- puted ones.

Fig. 2. - Selected-area diffraction pattern: the (10.1)~ spot belongs to the hexagonal polytype, while the (10.4)~ one to the rhombohedral phase.

ELECTRON DIFFRACTION STUDY OF M:ELT-GROWN InSe CRYST~S 801

T , ~ L n I I . - Comparison o] d-spacings o] the hexagonal phase, observed in the present work and calculated by means o/ eq. (2) using a = 4.00/~ and e = 16.7/~, and those quoted by INov~ et al. (~o).

Present work X- ray ro ta t ion da ta (10)

dob8 d~l HK" J~ dob8 dr HK" L (h) (4) (}~) (~)

3.46 3.46 10.0 3.39 3.39 01.1 3.20 3.20 01.2 2.94 2.94 01.3

2.66 2.67 01.4 2.42 2.42 01.5 2.15 2.17 01.6

1.99 1.99 ~ 11.0 t 11.1

1.94 1.94 11.2 1.88 1.88 12.3 1.80 1.80 11.4

0.20 1.73 1.73 [ 15.5

1.69 1.70 02.2

1.63 1.62 12.6 1.60 1.60 02.4

1.54 1.53 12.7 1.47 1.47 02.6 ] .44 ] .44 J2.8

1.33 1.33 20.8 21.0

1.31 1.31 [21.1

/ 32.2 1.29 1.29 ( 11.10

1.27 1.27 3i .3 1.25 1.25 35.4 1.22 1.22 23.5 1.20 ].20 02.10

1.15 1.16 03.0

1.13 1.13 30.3

1.07 1.07 03.6

8.376 8.375 00.2 4.200 4.188 00.4 3.483 3.487 01.0 3.422 3.414 01.1 3.226 3.219 01.2 2.963 2.957 01.3 2.796 2.792 00.6 2.685 2.679 01.4 2.421 2.416 01.5 2.183 2.179 01.6

02.0 1.740 1.743 [ 02.1

1.710 1.707 02.2 00.10

1.669 1.675 [ 02.3

1.642 1.642 01.9

1.549 1.546 02.5

1.481 1.479 02.6

1.411 1.409 02.7 1.395 ] .396 00.12

1.271 1.272 02.9

1.208 1.208 02.10 1.195 1.195 00.14 1.163 1.162 03.0 1.150 ].151 03.2

1.121 1.120 03.4 1.074 1.073 03.6 1.046 1.047 00.16 1.017 1.016 03.8 0.9300 0.9306 00.1

~ 0 2 C . D : E B L A S I , D . M A N N O , S . M O N G E L L I and A . R I Z Z 0

hO

t - i r

r

e~ v

g

r162

v

m*

a~

~ v

r ~ e.D

r r

t".. 00

@.1

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,---t ~ r

~ ' ~ ' ,-~ ~ ~ ~ 1 r c e ~ ' ~ . ~ t ~ l .~ r " . D r ' , . ,~D ~ ~ ~ r ~r~ ~ .,~ ,,,~ Le o k~ r r ~". ~",-

Ce~ ~ @.1 r r r ,."-~ ,-"~ ,-...t ,-..~ ,"~ ,,,.-.i ,.-,~ ,..~

~ ~ @.1 ~ ~ ' ~ r ' ~ ~ ~ , ,-',,t ~ u " - ~

E L ] ~ C T R O N D I F F R A C T I O N S T U D Y O F M ] ~ L T - G R O W N InSe CRYSTALS 8 0 ~

off r162 oO r a'q

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r162

5 3 - I I Nuovo Cimvnto D.

8 0 4 c . :DE BLASI, D. MANNO, S. MONG]~LLI and A. ~ i z z o

In t a b l e III a r e l i s t e d a l l t h e d - s p a c i n g s of t h i s p h a s e o b t a i n e d i n t h i s w o r k

a n d t h e r e l a t e d i n d i c e s , t o g e t h e r w i t h t h o s e o b s e r v e d b y I ~ o v E et al. (1o) ( o b t a i n e d b y X - r a y d i f f r a c t i o n on m e l t - g r o w n c r y s t a l s a n d p o w d e r s o f I n S e ) .

TABL~ IV. - Summary of the lattice parameters found by different methods.

La t t i c e S t ruc tu re Crysta l g rowth Reference pa rame te r s (4) de te rmina t ion

a) Hexagona l s t ruc tu re

a = 19.2 q- 0.1 Osci l la t ion S to ieh iomet r ic B r idgman (~) v = 4.00 4-0.02 d iag ram

a = 4.04 E lec t ron Th in fi lms (a) e = 16.93 dif f ract ion

a = 4.005 =k 0.005 Powder d iag ram Zone me l t ing (~) c ~ 16.640 =k 0.004 osci l la t ion

Weissenberg

Four -c i rc le Vapour phase (*) d i f f rac tometer chemica l t r anspor t

a = 4.00 v = 16.70

a = 4.026 q- 0.003 e = 1 6 . 7 5 q - O . O 1

a = 4 . 0 1 6 q- 0.001 r .= 16.69 q--0.01

a - - 4.00 :J: 0.04 e-----16.7 -t-0.2

Laue ro t a t ing c rys ta l Weissenberg

E lec t ron diffract ion

b) R h o m b o h e d r a l s t ruc tu re

a = 4.02 e = 25.05

a ~ 4.00 c ----- 25.32

a = 4.0046 =k 0.0005 c -~ 24.960 =k 0.004

a = 4.00 c -~ 24.85

a = 4.002 c ~ 24.946

a ~ 4.023 j : 0 .007 v ~ 24.81 ~:0.03 a ~ 4.023 4- 0.004 0 ~ 2 4 . 8 9 • a ~ 4.018 -]: 0.00] c ~ 25.01 q-0.01

a ~ 4.00 q-0.04 c ~ 25.3 q-0.3

Four -c i rc le d i f f rae tometer

P o w d e r d iagram Weissenberg

Weissenberg

Four -c i rc le d i f f rae tometer

Laue Weissenberg ro ta t ing-c rys ta l

E lec t ron diffract ion

Nons to ich iomet r i c modif ied Br idgman -/- hea t t r e a t m e n t

(~o)

Sto ieh iomet r ie and non- present s to ich iomet r ie Br idgman work

(1)

Reac t ion (5) f rom e lements

Cooling of me l t (6)

B r i d g m a n f rom a ('q nons to ieh iomet r ie

Vapour phase (9) chemica l t r anspor t

Nons to ieh iomet r ie modif ied Br idgman q- hea t t r e a t m e n t

S to ieh iomet r ie and non- s to ich iomet r ic Br idgman

(1o)

present work

ELECTRON DIFFRACTION STUDY OF MELT-GROWN I n S e CRYSTALS ~ 5

The comparison of these values confirms our results. Hence we c~n state tha t

this phase is the poli type quoted by v~rious ~uthors ~s rhombohedral ?-struc-

ture (~,~,5-m0) (space group C~), usually referred to hexagonal axes. The l~t-

tice parameters obtained in this work are repor ted in table IV, together with those quoted in the l i terature. Our results are in very good agreement within the experimental errors, with those previously found, apar t from the data of a single author (2), who report~ completely different values.

Fig. 3. - Experimental evidence of moir~ fringes on the image obtained with the spots (10.1) H and (10.4)~ of fig. 2.

A diffraction pa t te rn is shown in fig. 2, where the two different polytypes are evident. The spot (10.1) belongs to the hexagonal phase, while the (10.4) one to rhombohedral phase. By measuring the d-spacing, one obtains dl

3.05A and d~ : 3 . 394 with an angle between them a ~ 0.0025 rad. I f we suppose tha t the two polytypes are stacked upon one another along the e-axis, on the image obtained with the previous beams we must observe the moirfi

806 C. D E BLASI , D. MANlffO, 8. MONGELLI and A. ~IZZO

fringes with spacing given by (~)

D -~ d~dz[(dx-- d,) ~ - - dxd, a~]-~ -~ 29.6 A .

Such an image is shown in fig. 3 where the spacing is D = 29.8 A.

These results agree very well with the predicted ones, thus confirming

the s tacking sequence of the two polytypes , as reported elsewhere ('~).

The authors are ve ry indebted to Prof. A. A~M~(~Lr.ATO of the Labora to ry

LAMEL of the CBII~ of Bologna for his suggestions, to Profs. G. F. MISSl~OL~,

G. Pozz~ and to Dr. G. MATTEUC~I Of the Physics Depa r tmen t of the Univecsity

of Bologna for valuable discussions. The authors would like to express their

grzt i tude to Mr. G. D'EL~A for his technical support.

(xv) p. Htaserr, A. HowI]~, R.B. NiermLso~, D.W. P a s ~ and M.J. WrrzLAN: Electro~ Microscopy o / T h i ~ Crystals (Robert E. Krieger Publ., Co. Malabar, Fla., 1977). (is) C. D~ BI.AsI, D. MaNNo and S. MO~G~LL~: Phys. S ta~s Solidi A , 90, K5 (1985).

�9 R I A S S U N T O

stata effottuata la diff-razione elettroniea su eristalli di seleniuro di indio, clivati da lingotti cresciuti col metodo di Bridgma~-Stoekbarger partendo dagli elementi puri, presi sia in rapporto stechiometrieo ehe in rapporti diversi. L'analisi delle figure di dif- frazione ottenute in area selezionata ha permesso d'individuare la presenza di due politipi, i cui parame~ri reticolaxi sono stati caleolatL L'impilamento dei due politipi b state osservato mediante le frange moird.

l/Ice.,ae~onanne ~H~pagntm 3~eK'TpOnOn Ha ~r InSe, mapanlnnaeMb~X H3 pacn~ana.

Pe3IoMe (*). - - PIccne:Iyerc~ ~n~par, Ila~ aaeKTpoaon na TOnrHX rpaeranaax InSe, BI, rpa- u~eanbix n3 cTexnoMeTpn~ec~coro ri necTexnoMeTprrqecroro paciInaaoB, e ~oMombm MeTo~a Bpn~rMaaa-CTOK6aprepa. AHa,rlH3 nn~}paIOIHOHHI, IX I~apTHH 06napymnBaer na- 3]Hqge ~IByX dpa3, HHa KOTOpI, IX BI~ItnIcJDItOTCfI napaMeTp1,i pemeTxri. C IIOMOmb~o na6mo- ~eHI4~ MyapoBbIX IIOJIOC HCC~e~yeTC~ l~OCJle~IOBaTeJlbHOCTb rpyr/I1HpoBaHI4~ IIOJ'IHTHI]OB.

(*) l'lepeaec)eHo pec)aKque~.