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Reflectivity spectra of Cd1-xMnxTe mixed crystals in the vicinity of the E1 and E1 + Δ1 transitions
~
S o l i d S~a~e Coummnica~ions, V o l . 3 6 , p p . 1 2 7 - 1 3 1 . Pergamon P r e s s L t d . 1980. P r i n t e d i n Grea~ B r i t a i n .
REFLECTIV1TT SPECTRA OF C d l _ x M n x T e ] 4 i x u ~ CRXSTALS I N THE V I C I N I T Y OF THE
11 a n d E 1 + ~ 1
TRANSITIONS
T. K e n d e l e w t o z Institute
Of Physics,
Polish ~oade~ 0 2 - 6 6 8 Warsaw,
( R a o e 4 v e d 10 J u n e
of Solenoes, Poland
AI.Lotnlk~Sw
~2/~6
1980 b y M. C a r d e r - - }
R o o m t e m p e r a t u r e a n d 85 K r e £ 1 e o t i v l t y s p e c t r a o f CdI_xM~Te ~ i x e d c r y s t a l s f o r x u p to 0 . 7 i n the e n e r g y r~n6~e x r o m 2 to ~o5 eV h a v e been i n v e s t i ~ t e d o A linear d e p e n d e n c e of the e n e r 6 i e s of E 1 + A ~ r e f l e o t l v l t y m ~ w l m a of the s h o u l d e r s c o n n e c t e d w i t h ~he E o + ~ transitions for small ~ e s e e o n o e n t r a t i o n s x w a s found. T h e c h ~ n ~ e of the v a l e n c e b a n d s p i n - o r b i t s p l i t t i n ~ at the L a n d ~- p o i n t s of the B r i l l o u l n ~ o n e is d i s o u s s e d o A n o m a l i e s i n the s h a p e s of the r e f l e o t i v i t y s p e c t r a a n d of t e m p e r a t u r e c o e f f i c i e n t s of the El and E| +/~1 t r a n s i t i o n s h a v e b e e n fouJa~d.
-orbit (SO~ intoraotiono The refieotivity structure is enhanced and sharpened due to electron-hole interaction ~3" As c a n b e s e e n f r o m F i g . 1 the doublet str~oture in Cdl ~ T e crystals is mere and mere diffused with ~owin~ maz~anese cortoentration and for man.mess-rich e|unples x ~ 0. 5 only one very broad mmorph.tc-type refleotivity peak is obset.ode Apart from the E 1 and E 1 + A 1 maxima a pronounced refleotivity line connected with the Eo exeiton at the point has been observed for all compositions at both temperatures. This peak (seen in Fi~. 1 only for m~ese-ric~ s a m p l e s ) w a s the s u b j e c t of e a r l i e r m e a s u r e m e n t s ef K h e i a n d GaJ [6] p e r f o r m e d o n s a m p l e s f r o m the same in6ots. T h e y f o u n d that at l i q u i d nitrogen temperature E O Oh~n~es aooerdin~ te Eo(X) = (1.586+l.51x)(eV) w e u s e d this r e l a t i o n as the c a l i bration curve for ooEposition determination. The composition determined in this w a y is i n e x c e l l e n t a ~ r e e m e n t w i t h that ~ I m e d at i n the c r y s t a l growth process. O n the 85 K r e f l e c t l v l t y c u r v e s an additional shoulder shown by arrows i n F i ~ . I b w a s ~ I s o o b s e r v e d o n the low e n e r g y s i d e of the E I peak. Its e n e r g y of around 2 . 5 0 eV f o r C d T e C 3 3 sug~sts that it should be aeei6ned te the EO + A o transitions - from the S0 s p l i t - o f f F 7 va..1.onoo b a n d to the U 6 conduction b~cl.. The p r e s e n t e d d a t a e n - b l e us t o investi~te the e n e r g y v ~ r i a t i o n o f
I n this p a p e r w e p r e s e n t the r e s u l t s of a s t u d y of r e f l e o t i v i t y c a r r i e d out o n C d | _ x M n x T e 8 e m i m a 6 n e t i o a l l o y s [I]. The Cd1_xMnxTe crystals have recently a t t r a c t e d eubeteuatial a t t e n t i o n b e c a u s e of their un4~que m a g n e t o - o p t i c a l propertiee [1~. These orystnls are pnurttoularly suitable for fundament~l refleotivity measurements for two reasons: 1. V e r y 6 c o d q u a l i t y o z ~ r s t a l s , Jud~in~ by eemioonduotin~ mixed crystal standards, can be prepared with a broad x~n~e of ~ e s e content. 2. In the whole rsun~e of compositions ( x .< 0 . 7 ) w h e r e the muateri~ crystallizes in the ephglerite structure flat, cleaved s u r f a c e s c a n c o o l l y be O b t L t n e d . Since £ood quality refleotivity spectra c a n be o b t a i n e d ~ we c a n 0un&lyze not o n l y the oh--nses i n the e n e r g i e s o f the ref l e o t i v i t y m a x i m a , Ms was d o n e e a r l i e r for the s i m i l a r H 6 M n T e a l l o t s [2], b u t a l s o the r e l a t i v e o h a n 6 e s of the s h a p e s of the s p e c t r a w i t h i n o r e e ~ i n ~ ~ a n ~ a nose content. T h e r o o m t e m p e r a t u r e a n d 85 K r e f l e o tivity spectra of CdMnTe o z - y s t a l o are
shown i n
F t ~ . 1. I n
the investt~ted
s p e c t r a l raJ16e we o b s e r v e t ' o r b o t h t e m peratures suad l o w m ~ n & ~ n e s e c o n c e n t r a tion samples)two distinct maxima desig-
n a t e d E 1 and E 1 + ~ 1 ,
aooorcLin~ to the
notation introduced by Cgrdoma ~3~ for zinc-blonde-type m&teriale. These maxima are connected with direct transitions at critical points o n t h e [ I | J3 d i r e c t i o n , m o s t p r o b a b l y at the L p o i n t of the B r i l l o u i n z o n e [ ~ , the doublet nature bein~ due to the spin-
127
128
Vol. 36, No. 2
REFLECTIVITY SPECTRA OF CDI-xMnxTe MIXED CRYSTALS
C~-xMnxT,
300K
Cdl-x ~ nxT~
..,'- /
85K
~
x =0,70 ;%..,..,..•..'" x =0,60
•"¢.~%,~,...-".'" /<=0.60
""~"
eoo,
x=0,50..-'*""
.
.........
~=o~o~"
..,"" "~w'~
'-"
], .... -o
•
x=O~O~..'/
>.
,..,"l
I-."
PJ..g'. 1 a )
spectra
b) of
composition
some important band p~r~eters. In FiK. 2 the room temperature ener~ v~rAatton of E 1 sz~ its SO o o m p o n e n t has been plotted e~a~ust -11o~ cornposition in the x~x~e o£ x for vhioh the positions of the peed~s oan be determined with suitable aoourw~y (as shown ~n the £t6~re). ~ Fig. 2 th. en.r61e, o f t h e ~ 1 ' E1 + A I '
for
85 K h a Y e
been also shown The doublet e~zrp-ene with deore•stx~ temperattLre s~zd
the re•poetize b a n d l ~ U r s J o t e r e o ~ be determined in • vldor raz~ of o~apoeltiOs~o The ener~lee of all the ro£1eotiwlty ~ obeox~red h e Y o b e e n £o~uad to ohan4~ l~J~ea:l~ vith x for x ~ 0.~ a t 85 K a n d x ~ 0o3 s t ~00 K . I n e a r lter ro£1eotiwtt 7 ~•ettr~te do~ ox~et-ls
at
~=o~.t'"
.....
" :
" /~'~....
3,0 4,0 PHOTON ENERGY (eV)
Room a n d
o tr~Dttions
/
/",/ /
-
• ";;o / I 2.0 3.0 4.0 PHOTON ENERGY (eV)
o~z H ~ l _ x ~ x x T e
.\
l " n;" /l:.l"-"~....
1/...,-:/
,t
/'-
/x=O,~S~'[" /
/
""" l" "~ /.,i ~'"" .o,s/ [/ / I"--"
a n d Eo + ~
"~,.,
%%..."
//\/~
."
oo-o"
/~_~,
/
J. x=O,30..'*""
g
"" * ~ "
x=~30~.J
/ x;~o...
.~-/
/ ~
x=0,50..
700 K~'i(~L-
85K temperature Cdl_x~?e
orb•tale
re£leotanoe o£ different
x.
ftoant departures frOm line•tit 7 o£ the 11 a~d g t +A t maxima have been found L2J. F6r both -1loTs we oannot, however, oompare our results vith oommonly used theories o f m i x e d OXTe-ill band etz~aoture e~aoe in -11 o£ them • knowledge o f t h e kazad s t z ~ o t u r e o£ the oomponente is required. The case o£ sesLtzaa~aetlo alloys is e e ~ o i - 1 1 7 d~Lffioult bee•use the oompotente, navel T CdTo or H~ro and /~zTo, havo d££ferent oxTst-1 as well as band etruoturoe ez~d;moreoYer, the band par-~etere o£ MeTe a r e n o t k n o w n v e i l enough. ~e oan, hoverer, note that the results obtained reproduce vez-y yell the basio trends in the bovJ.u~ pe~ameters of better known norun~snetio -11eye. It is olee~ that the departure from ltnearity is more pronounced ~n the merouz~/-oonte4n4n~ e~loy. This
Vol. 36, No. 2
REFLECTIVITY SPECTRA OF Cdl-xHn.xTe HT-XED CRYSTALS
129
4.05
4
4.00
E1 *Z~ 1
3.95 3.g0 3.50"
E1
3,40
3.30 @u
n~ w
3.10" 2,90 Eo"~ o
2,70 2,50 0.95" 0,90
Ao
0,65[. 0.60~ A1 ,
0
F:I.~ °
2
0.1
Variation in
of
Cd|_x~hlxTe
(cull ~iroze,) a £unotion The
/~
of
additional
Iinear
1 in
£it
to
the
O.5
refleotivity for
~d
85~ (ope~
manganese
room
temperature
oiroze.
)
oonoentration
oontlnuous the
O'.6 maxima
crystals
Hgl_xHnxTe
departurel represented by the bowing parameter, is proportional to the differenoe between the ato~4o potentie~s of the J.nteroh~gtng elements of the mixed crystal~wb_tch is lar~sr for the I't~Te alloy° Seoondlyp we o a n o o m p a r e o u r d a t a with the results of similar measurements performed on better known semioonduotJ~g alloys. From the whole 6 r o u p t h e zJ~no - o o n t a i n i n g ealloys is. CdZnTo and Hgq~fre should have the ~eatest aJJmllarlty in properties to Cd~nTe a n d H~MnTe. T h £ o i s b e o a u s e f o r b o t h Z n a n d Hn t h e ~ s e l e o t r o n s
!
,
0.2 0.3 0.4 COMPOSITION X
curve
experJJmental crystals
as
x.
represents data
[2]
for
.
take part in band and bond oreation~ replao~ug the ~s or 6s electrons of Cd o r H6 a t o m s . The differenoo between both ~oups of alloys is due to different oooupation of nonbond•ng, loc~tzed ~d levels wh4oh are only half-filled f o r Mn a t o m s . Foru~lly, we oan express the atonlo potenti~ of man&~nese by:
VHn = VZn + ~ w h e r e VZn i s t h e Zn a t o m i o
potential
and ~ is a repulsive oorreotion rosultLn~ from a reduotion 4~ n u o l e a r ohar~. In the virtua~ orystal ap-
130
R.EFLECTIVITY SPECTRA OF CDl-xMnxTe MIXED CRYSTALS
proximation ['7"] t h e d i f f e r ~ e bet w e e n Z n a n d M~ a l l o y s w i t h the e a s e x value is,aooordin¢ to the above formula ~Iven by x ~ . This correction i n t h e ma~ll x l i m i t c o n be treated as a e~ll perturbation. The rouen t o m p o r a t t t r o ro£1ootlvity stu~les of H ~ Z n T o a n d of C d Z ~ r e a l l o y s w e r e p e r f o x ~ o d b y N i o u l e e o u ~ 8-[ ~ n d Sredin e t el. ) r e s p e c t i v e l y ~ " 9 ] • Nioulesou found a quadratic oham~ of the E z and E 1 + ~1 maxima with a bowi~g parmmeter of about | eV. Sredin found a linel~ dependence. A comparison shows,however, a very similar ob*-~ in the enercy 6~p8 in both oasQe • I n t h e c a s e o f t h e HgJ4nTe m i x e d crystals an extrapolation of the energy of the was made to a hypothetical M n T e w i t h a z i n c - b l o n d e - type l a t t i c e . The values obtained from such an extrap o l a t i o n , E I = 3 . 7 9 oV a n d El+ ~ I = ~.26, c a n be c o m p a r e d w i t h E 1 = ~ ) . 5 9 eV a n d El + /~ I = ~ . 1 3 o b t a i n e d f r o m the ~ O O K d a t a f o r Cd~hITe. T h e a g T e e m e n t b e t w e e n b o t h e x p e r i m e n t s is good, if we take i n t o a c c o u n t the fact that the r e f l e o t l v i t y p e a k s are d i s c e r n i b l e i n a v e r y n a r r o w r a n g e of mang~anese c o n c e n t r a tions. T h e e x t r a p o l a t e d values, e s p e o l a l l y f o r the m u c h b e t t e r q u a l i t y Cd~hITe o r T s t a l s , are also i n v e r y 6 c o d a g T e e m e n t w i t h E I = ~ . 5 8 eV a n d E | + / ~ I = = ~ . 1 4 eV o b t a i n e d by C a r d o n a a n d G r e e n a w a y f o r ZnTe c r y s t a l s ~ ~-J. T h i s r e s u l t shows that at 3 0 0 K f o r x <. 0.3 the p e r t u r b a t i o n p o t e n t i a l x ~ does not a p p r e c i a b l y e l T e o t the b a n d s that t h e i r o h a n ~ e is the same as i n n o n m a ~ n e tic c r y s t a l s . The refleotivity spectra obtained e n a b l e us a l s o to s t u d y t h e c h a n g e O f SO s p l i t t i n g of the v a l e n c e b a n d at L a n d F p o i n t s O f the B r i l l o u n i n zone. T h e r o o m t e m p e r a t u r e v a l u e s o f /% 1 a n d t h e 85K v a l u e s of ~o are shown i n Fig. 2 t o g e t h e r w i t h a n a d d i t i o n a l continuous our~e representin~ a linear fit t o the r o o m t e m p e r a t u r e /% | v a l u e s o b t a i n e d f o r HgMnTe a l l o y s ~23. T h e p o i n t s p l i t t l n ~ of C d M n T e w a s d e t e c t e d at b o t h t e m p e r a t u r e s . We d i d not, h o w ever, f o u n d a n a p p r e c i a b l e t e m p e r a t u r e d e p e n d e n c e o f its value. B o t h ~" a n d L p o i n t s p l i t t i n g s c~--nge l i n e a r l y a n d slightly decrease with increasing x. T h e o h a n ~ e of/~|, as seen f r o m the fig~re, i s m o r e r a p i d for H ~ M n T o c r y s tals. A l l these f a c t s r e p r o d u c e the basic chemical trends in 8amioonduot i n 6 alloys. T h e SO s p l i t t i n ~ o f ~F~B~ o r A~B~ s e m i c o n d u o t o r m Is g i v e n llne~u~ oo~blruatlon of the a t o m i c s p l l t t i n ~ s o f . the r e s p e c t i v e e l e m e n t s . T h e p r o p o r t l o n ~ l l t y o o e f f l o i e n t s are p r o p e r -
Vol. 36, No. 2
tional to the crystal ion/city. For the A 2 B 6 ~roup, to w h / o h C d T e b e l o n g s , the p o i n t s SO s p l l t t l n ~ is w e l l d e s c r i b e d b y a ~enLiempirioal r u l e ~5~:
/~SO = C(O-2Z~ z
+ 0.8
~'a)
T h e meuse r u l e , w i t h d i f f e r e n t C, c a n elsO b e a p p l i e d to represent the L point splitting. It follows from th/s formule that in CdTe and even in I~Te, the valence band ~0 splitting is mainly determined b y t h e SO s p l i t t J n ~ of the 5P electrons of Te and the same is true for the investigated alloys. This explains why only a slight x depende n o e o f t h e SO s p l i t t ! n ~ s i s observed. Tn the C d M n T e a l l o y A A m a y be replaoed by (1-x~c d + x~N n and beoause the atomic splitting is proportional to the atomic number)we may anticipate a decrease of the splittin~ value. This decrease should be more pronounced i n ~EMnTe b e c a u s e of the larger difference in the atomic splittings. The above dissousion shows that room temperature band parameters of semimagnetlo alloys in the region of X where distinct reflectlvity maxima are o b s e r v e d is w e l l d e s o r l b e d by the 8emiempirloal rules appropriate for n o n m a ~ l e t i o alloys. In s e m i m a g n @ t i o a l l o y s w e o b s e r Y e ~ h o w e v e r , some a n o m a l i e s w h i c h a r e not o b s e r v e d i n 6~od quality nonmagnetlo semioondusting mixed crystals. F i r s t l y , there is a s y s t e m a t i c d i f f u s i o n of the E| a n d E | + /~ 1 refleotivity structures. Secondlyl there is a r a p i d d e c r e a s e of tempera t u r e c o e f f i c i e n t s , as o b t a i n e d l'rom our 300 a n d 85 K m e a s u r e m e n t s as s e e n i n Fig. 2. T h e l a t t e r l'act s h o w s that e v e n at l o w m a n ~ a n e s e conc e n t r a t i o n s , the i r ~ l u e n c e of ma~neti o a l l y a c t i v e e l e c t r o n s oE the u n f i l l e d n~u1~anese 3d shell a f f e c t s the l o w t e m p e r a t u r e a l l o y b a n d s t r ~ o ture. The smearln~ of the r e f e l e c t i v i t y s t r u c t u r e i n the v i c i n i t y of the E| a n d E1 + /~ 1 18 a v e r y i n t e r e s t i n ~ p r o p e r t y o £ CdMnTe" a l l o y s we c a n n o t e that s u c h d i f f u s i o n is not o b s e r v e d in the c a s e of the E 0 e x o i t o ~ r e f l e c t i v i t y s t r u c t u r e . T h l e p o i n t w i l l be dlsoussed in detail in a subsequent p a p e r ; i n w h i c h the vaoutul u l t r a v i o l e t r e f l e o t i v l t y s p e c t r a of C d M n T e c r y s t a l s w i l l be p r e s e n t e d . Acknowledgements - The author would llke to t h a n k D r . R . R . G a l q z k a Dr.E.Kierzek-Pecold f o r 8 t i ~ u / a t i n ~ dlscussions and enoour~e~ente thtou~out this work. T~--ks ~e also due to U . D ~ b s k a / I F PAN, W a r s a w / for Erowin~ the c r y s t a l s i n Y e e t i ~ t e d i n this study.
Vol. 36. No. 2
REFLECTIVITY SPECTRA OF Cdl-xMnxTe MIXED CRYSTALS
REFERENCES I.
2. 94. 56. 7. 8. 9.
~ , R . R . , ]Proo. l t t t h T n t e r ~ v ~ t . C o n f . PI:~s. Semioolaclt., F_xtii:lbctr~l:l 1978, ed. VTI-~ON, B . L . H . , Inst. P h T s . C o n t . S e t . No 4 3 , 13~ 1978 • ~]~¢DRIRWICZ, T., K I E R ~ - P E C O L D , E., Solid State Commun. 25, 579 1978 • CARDONA, M., C~RRMA¥£T, D.L., Phys. Rev. I_/!, 98 1963 • CwRITKOWSKX, J.R., CONEN, M.L., P~Ts. Re'w.---~ I~, 556 1976 . CARDONA, k., Solid. State Phys. Suppl. 11 I~9 • wwOI, T.N., GAJ, J.A., ~hys. stat. sol.--b 8/, K133 1977 . P ~ , R.H., Phys. R e v . 97, 587 1955 . NICb'LF~CU, D., J. Phys. CI PToo. Phys. Soo. Ser. 2, 80~ 1968 SPT~nIN, N.G., PASZK0¥SKIJ, M.W., YASILINA~ Z.S.~ JEWTIGNIEJEW, A.I., F i z . TeEh. P o l u p r . 7, 2354 1973 .
131
S o l i d S~a~e Coummnica~ions, V o l . 3 6 , p p . 1 2 7 - 1 3 1 . Pergamon P r e s s L t d . 1980. P r i n t e d i n Grea~ B r i t a i n .
REFLECTIV1TT SPECTRA OF C d l _ x M n x T e ] 4 i x u ~ CRXSTALS I N THE V I C I N I T Y OF THE
11 a n d E 1 + ~ 1
TRANSITIONS
T. K e n d e l e w t o z Institute
Of Physics,
Polish ~oade~ 0 2 - 6 6 8 Warsaw,
( R a o e 4 v e d 10 J u n e
of Solenoes, Poland
AI.Lotnlk~Sw
~2/~6
1980 b y M. C a r d e r - - }
R o o m t e m p e r a t u r e a n d 85 K r e £ 1 e o t i v l t y s p e c t r a o f CdI_xM~Te ~ i x e d c r y s t a l s f o r x u p to 0 . 7 i n the e n e r g y r~n6~e x r o m 2 to ~o5 eV h a v e been i n v e s t i ~ t e d o A linear d e p e n d e n c e of the e n e r 6 i e s of E 1 + A ~ r e f l e o t l v l t y m ~ w l m a of the s h o u l d e r s c o n n e c t e d w i t h ~he E o + ~ transitions for small ~ e s e e o n o e n t r a t i o n s x w a s found. T h e c h ~ n ~ e of the v a l e n c e b a n d s p i n - o r b i t s p l i t t i n ~ at the L a n d ~- p o i n t s of the B r i l l o u l n ~ o n e is d i s o u s s e d o A n o m a l i e s i n the s h a p e s of the r e f l e o t i v i t y s p e c t r a a n d of t e m p e r a t u r e c o e f f i c i e n t s of the El and E| +/~1 t r a n s i t i o n s h a v e b e e n fouJa~d.
-orbit (SO~ intoraotiono The refieotivity structure is enhanced and sharpened due to electron-hole interaction ~3" As c a n b e s e e n f r o m F i g . 1 the doublet str~oture in Cdl ~ T e crystals is mere and mere diffused with ~owin~ maz~anese cortoentration and for man.mess-rich e|unples x ~ 0. 5 only one very broad mmorph.tc-type refleotivity peak is obset.ode Apart from the E 1 and E 1 + A 1 maxima a pronounced refleotivity line connected with the Eo exeiton at the point has been observed for all compositions at both temperatures. This peak (seen in Fi~. 1 only for m~ese-ric~ s a m p l e s ) w a s the s u b j e c t of e a r l i e r m e a s u r e m e n t s ef K h e i a n d GaJ [6] p e r f o r m e d o n s a m p l e s f r o m the same in6ots. T h e y f o u n d that at l i q u i d nitrogen temperature E O Oh~n~es aooerdin~ te Eo(X) = (1.586+l.51x)(eV) w e u s e d this r e l a t i o n as the c a l i bration curve for ooEposition determination. The composition determined in this w a y is i n e x c e l l e n t a ~ r e e m e n t w i t h that ~ I m e d at i n the c r y s t a l growth process. O n the 85 K r e f l e c t l v l t y c u r v e s an additional shoulder shown by arrows i n F i ~ . I b w a s ~ I s o o b s e r v e d o n the low e n e r g y s i d e of the E I peak. Its e n e r g y of around 2 . 5 0 eV f o r C d T e C 3 3 sug~sts that it should be aeei6ned te the EO + A o transitions - from the S0 s p l i t - o f f F 7 va..1.onoo b a n d to the U 6 conduction b~cl.. The p r e s e n t e d d a t a e n - b l e us t o investi~te the e n e r g y v ~ r i a t i o n o f
I n this p a p e r w e p r e s e n t the r e s u l t s of a s t u d y of r e f l e o t i v i t y c a r r i e d out o n C d | _ x M n x T e 8 e m i m a 6 n e t i o a l l o y s [I]. The Cd1_xMnxTe crystals have recently a t t r a c t e d eubeteuatial a t t e n t i o n b e c a u s e of their un4~que m a g n e t o - o p t i c a l propertiee [1~. These orystnls are pnurttoularly suitable for fundament~l refleotivity measurements for two reasons: 1. V e r y 6 c o d q u a l i t y o z ~ r s t a l s , Jud~in~ by eemioonduotin~ mixed crystal standards, can be prepared with a broad x~n~e of ~ e s e content. 2. In the whole rsun~e of compositions ( x .< 0 . 7 ) w h e r e the muateri~ crystallizes in the ephglerite structure flat, cleaved s u r f a c e s c a n c o o l l y be O b t L t n e d . Since £ood quality refleotivity spectra c a n be o b t a i n e d ~ we c a n 0un&lyze not o n l y the oh--nses i n the e n e r g i e s o f the ref l e o t i v i t y m a x i m a , Ms was d o n e e a r l i e r for the s i m i l a r H 6 M n T e a l l o t s [2], b u t a l s o the r e l a t i v e o h a n 6 e s of the s h a p e s of the s p e c t r a w i t h i n o r e e ~ i n ~ ~ a n ~ a nose content. T h e r o o m t e m p e r a t u r e a n d 85 K r e f l e o tivity spectra of CdMnTe o z - y s t a l o are
shown i n
F t ~ . 1. I n
the investt~ted
s p e c t r a l raJ16e we o b s e r v e t ' o r b o t h t e m peratures suad l o w m ~ n & ~ n e s e c o n c e n t r a tion samples)two distinct maxima desig-
n a t e d E 1 and E 1 + ~ 1 ,
aooorcLin~ to the
notation introduced by Cgrdoma ~3~ for zinc-blonde-type m&teriale. These maxima are connected with direct transitions at critical points o n t h e [ I | J3 d i r e c t i o n , m o s t p r o b a b l y at the L p o i n t of the B r i l l o u i n z o n e [ ~ , the doublet nature bein~ due to the spin-
127
128
Vol. 36, No. 2
REFLECTIVITY SPECTRA OF CDI-xMnxTe MIXED CRYSTALS
C~-xMnxT,
300K
Cdl-x ~ nxT~
..,'- /
85K
~
x =0,70 ;%..,..,..•..'" x =0,60
•"¢.~%,~,...-".'" /<=0.60
""~"
eoo,
x=0,50..-'*""
.
.........
~=o~o~"
..,"" "~w'~
'-"
], .... -o
•
x=O~O~..'/
>.
,..,"l
I-."
PJ..g'. 1 a )
spectra
b) of
composition
some important band p~r~eters. In FiK. 2 the room temperature ener~ v~rAatton of E 1 sz~ its SO o o m p o n e n t has been plotted e~a~ust -11o~ cornposition in the x~x~e o£ x for vhioh the positions of the peed~s oan be determined with suitable aoourw~y (as shown ~n the £t6~re). ~ Fig. 2 th. en.r61e, o f t h e ~ 1 ' E1 + A I '
for
85 K h a Y e
been also shown The doublet e~zrp-ene with deore•stx~ temperattLre s~zd
the re•poetize b a n d l ~ U r s J o t e r e o ~ be determined in • vldor raz~ of o~apoeltiOs~o The ener~lee of all the ro£1eotiwlty ~ obeox~red h e Y o b e e n £o~uad to ohan4~ l~J~ea:l~ vith x for x ~ 0.~ a t 85 K a n d x ~ 0o3 s t ~00 K . I n e a r lter ro£1eotiwtt 7 ~•ettr~te do~ ox~et-ls
at
~=o~.t'"
.....
" :
" /~'~....
3,0 4,0 PHOTON ENERGY (eV)
Room a n d
o tr~Dttions
/
/",/ /
-
• ";;o / I 2.0 3.0 4.0 PHOTON ENERGY (eV)
o~z H ~ l _ x ~ x x T e
.\
l " n;" /l:.l"-"~....
1/...,-:/
,t
/'-
/x=O,~S~'[" /
/
""" l" "~ /.,i ~'"" .o,s/ [/ / I"--"
a n d Eo + ~
"~,.,
%%..."
//\/~
."
oo-o"
/~_~,
/
J. x=O,30..'*""
g
"" * ~ "
x=~30~.J
/ x;~o...
.~-/
/ ~
x=0,50..
700 K~'i(~L-
85K temperature Cdl_x~?e
orb•tale
re£leotanoe o£ different
x.
ftoant departures frOm line•tit 7 o£ the 11 a~d g t +A t maxima have been found L2J. F6r both -1loTs we oannot, however, oompare our results vith oommonly used theories o f m i x e d OXTe-ill band etz~aoture e~aoe in -11 o£ them • knowledge o f t h e kazad s t z ~ o t u r e o£ the oomponente is required. The case o£ sesLtzaa~aetlo alloys is e e ~ o i - 1 1 7 d~Lffioult bee•use the oompotente, navel T CdTo or H~ro and /~zTo, havo d££ferent oxTst-1 as well as band etruoturoe ez~d;moreoYer, the band par-~etere o£ MeTe a r e n o t k n o w n v e i l enough. ~e oan, hoverer, note that the results obtained reproduce vez-y yell the basio trends in the bovJ.u~ pe~ameters of better known norun~snetio -11eye. It is olee~ that the departure from ltnearity is more pronounced ~n the merouz~/-oonte4n4n~ e~loy. This
Vol. 36, No. 2
REFLECTIVITY SPECTRA OF Cdl-xHn.xTe HT-XED CRYSTALS
129
4.05
4
4.00
E1 *Z~ 1
3.95 3.g0 3.50"
E1
3,40
3.30 @u
n~ w
3.10" 2,90 Eo"~ o
2,70 2,50 0.95" 0,90
Ao
0,65[. 0.60~ A1 ,
0
F:I.~ °
2
0.1
Variation in
of
Cd|_x~hlxTe
(cull ~iroze,) a £unotion The
/~
of
additional
Iinear
1 in
£it
to
the
O.5
refleotivity for
~d
85~ (ope~
manganese
room
temperature
oiroze.
)
oonoentration
oontlnuous the
O'.6 maxima
crystals
Hgl_xHnxTe
departurel represented by the bowing parameter, is proportional to the differenoe between the ato~4o potentie~s of the J.nteroh~gtng elements of the mixed crystal~wb_tch is lar~sr for the I't~Te alloy° Seoondlyp we o a n o o m p a r e o u r d a t a with the results of similar measurements performed on better known semioonduotJ~g alloys. From the whole 6 r o u p t h e zJ~no - o o n t a i n i n g ealloys is. CdZnTo and Hgq~fre should have the ~eatest aJJmllarlty in properties to Cd~nTe a n d H~MnTe. T h £ o i s b e o a u s e f o r b o t h Z n a n d Hn t h e ~ s e l e o t r o n s
!
,
0.2 0.3 0.4 COMPOSITION X
curve
experJJmental crystals
as
x.
represents data
[2]
for
.
take part in band and bond oreation~ replao~ug the ~s or 6s electrons of Cd o r H6 a t o m s . The differenoo between both ~oups of alloys is due to different oooupation of nonbond•ng, loc~tzed ~d levels wh4oh are only half-filled f o r Mn a t o m s . Foru~lly, we oan express the atonlo potenti~ of man&~nese by:
VHn = VZn + ~ w h e r e VZn i s t h e Zn a t o m i o
potential
and ~ is a repulsive oorreotion rosultLn~ from a reduotion 4~ n u o l e a r ohar~. In the virtua~ orystal ap-
130
R.EFLECTIVITY SPECTRA OF CDl-xMnxTe MIXED CRYSTALS
proximation ['7"] t h e d i f f e r ~ e bet w e e n Z n a n d M~ a l l o y s w i t h the e a s e x value is,aooordin¢ to the above formula ~Iven by x ~ . This correction i n t h e ma~ll x l i m i t c o n be treated as a e~ll perturbation. The rouen t o m p o r a t t t r o ro£1ootlvity stu~les of H ~ Z n T o a n d of C d Z ~ r e a l l o y s w e r e p e r f o x ~ o d b y N i o u l e e o u ~ 8-[ ~ n d Sredin e t el. ) r e s p e c t i v e l y ~ " 9 ] • Nioulesou found a quadratic oham~ of the E z and E 1 + ~1 maxima with a bowi~g parmmeter of about | eV. Sredin found a linel~ dependence. A comparison shows,however, a very similar ob*-~ in the enercy 6~p8 in both oasQe • I n t h e c a s e o f t h e HgJ4nTe m i x e d crystals an extrapolation of the energy of the was made to a hypothetical M n T e w i t h a z i n c - b l o n d e - type l a t t i c e . The values obtained from such an extrap o l a t i o n , E I = 3 . 7 9 oV a n d El+ ~ I = ~.26, c a n be c o m p a r e d w i t h E 1 = ~ ) . 5 9 eV a n d El + /~ I = ~ . 1 3 o b t a i n e d f r o m the ~ O O K d a t a f o r Cd~hITe. T h e a g T e e m e n t b e t w e e n b o t h e x p e r i m e n t s is good, if we take i n t o a c c o u n t the fact that the r e f l e o t l v i t y p e a k s are d i s c e r n i b l e i n a v e r y n a r r o w r a n g e of mang~anese c o n c e n t r a tions. T h e e x t r a p o l a t e d values, e s p e o l a l l y f o r the m u c h b e t t e r q u a l i t y Cd~hITe o r T s t a l s , are also i n v e r y 6 c o d a g T e e m e n t w i t h E I = ~ . 5 8 eV a n d E | + / ~ I = = ~ . 1 4 eV o b t a i n e d by C a r d o n a a n d G r e e n a w a y f o r ZnTe c r y s t a l s ~ ~-J. T h i s r e s u l t shows that at 3 0 0 K f o r x <. 0.3 the p e r t u r b a t i o n p o t e n t i a l x ~ does not a p p r e c i a b l y e l T e o t the b a n d s that t h e i r o h a n ~ e is the same as i n n o n m a ~ n e tic c r y s t a l s . The refleotivity spectra obtained e n a b l e us a l s o to s t u d y t h e c h a n g e O f SO s p l i t t i n g of the v a l e n c e b a n d at L a n d F p o i n t s O f the B r i l l o u n i n zone. T h e r o o m t e m p e r a t u r e v a l u e s o f /% 1 a n d t h e 85K v a l u e s of ~o are shown i n Fig. 2 t o g e t h e r w i t h a n a d d i t i o n a l continuous our~e representin~ a linear fit t o the r o o m t e m p e r a t u r e /% | v a l u e s o b t a i n e d f o r HgMnTe a l l o y s ~23. T h e p o i n t s p l i t t l n ~ of C d M n T e w a s d e t e c t e d at b o t h t e m p e r a t u r e s . We d i d not, h o w ever, f o u n d a n a p p r e c i a b l e t e m p e r a t u r e d e p e n d e n c e o f its value. B o t h ~" a n d L p o i n t s p l i t t i n g s c~--nge l i n e a r l y a n d slightly decrease with increasing x. T h e o h a n ~ e of/~|, as seen f r o m the fig~re, i s m o r e r a p i d for H ~ M n T o c r y s tals. A l l these f a c t s r e p r o d u c e the basic chemical trends in 8amioonduot i n 6 alloys. T h e SO s p l i t t i n ~ o f ~F~B~ o r A~B~ s e m i c o n d u o t o r m Is g i v e n llne~u~ oo~blruatlon of the a t o m i c s p l l t t i n ~ s o f . the r e s p e c t i v e e l e m e n t s . T h e p r o p o r t l o n ~ l l t y o o e f f l o i e n t s are p r o p e r -
Vol. 36, No. 2
tional to the crystal ion/city. For the A 2 B 6 ~roup, to w h / o h C d T e b e l o n g s , the p o i n t s SO s p l l t t l n ~ is w e l l d e s c r i b e d b y a ~enLiempirioal r u l e ~5~:
/~SO = C(O-2Z~ z
+ 0.8
~'a)
T h e meuse r u l e , w i t h d i f f e r e n t C, c a n elsO b e a p p l i e d to represent the L point splitting. It follows from th/s formule that in CdTe and even in I~Te, the valence band ~0 splitting is mainly determined b y t h e SO s p l i t t J n ~ of the 5P electrons of Te and the same is true for the investigated alloys. This explains why only a slight x depende n o e o f t h e SO s p l i t t ! n ~ s i s observed. Tn the C d M n T e a l l o y A A m a y be replaoed by (1-x~c d + x~N n and beoause the atomic splitting is proportional to the atomic number)we may anticipate a decrease of the splittin~ value. This decrease should be more pronounced i n ~EMnTe b e c a u s e of the larger difference in the atomic splittings. The above dissousion shows that room temperature band parameters of semimagnetlo alloys in the region of X where distinct reflectlvity maxima are o b s e r v e d is w e l l d e s o r l b e d by the 8emiempirloal rules appropriate for n o n m a ~ l e t i o alloys. In s e m i m a g n @ t i o a l l o y s w e o b s e r Y e ~ h o w e v e r , some a n o m a l i e s w h i c h a r e not o b s e r v e d i n 6~od quality nonmagnetlo semioondusting mixed crystals. F i r s t l y , there is a s y s t e m a t i c d i f f u s i o n of the E| a n d E | + /~ 1 refleotivity structures. Secondlyl there is a r a p i d d e c r e a s e of tempera t u r e c o e f f i c i e n t s , as o b t a i n e d l'rom our 300 a n d 85 K m e a s u r e m e n t s as s e e n i n Fig. 2. T h e l a t t e r l'act s h o w s that e v e n at l o w m a n ~ a n e s e conc e n t r a t i o n s , the i r ~ l u e n c e of ma~neti o a l l y a c t i v e e l e c t r o n s oE the u n f i l l e d n~u1~anese 3d shell a f f e c t s the l o w t e m p e r a t u r e a l l o y b a n d s t r ~ o ture. The smearln~ of the r e f e l e c t i v i t y s t r u c t u r e i n the v i c i n i t y of the E| a n d E1 + /~ 1 18 a v e r y i n t e r e s t i n ~ p r o p e r t y o £ CdMnTe" a l l o y s we c a n n o t e that s u c h d i f f u s i o n is not o b s e r v e d in the c a s e of the E 0 e x o i t o ~ r e f l e c t i v i t y s t r u c t u r e . T h l e p o i n t w i l l be dlsoussed in detail in a subsequent p a p e r ; i n w h i c h the vaoutul u l t r a v i o l e t r e f l e o t i v l t y s p e c t r a of C d M n T e c r y s t a l s w i l l be p r e s e n t e d . Acknowledgements - The author would llke to t h a n k D r . R . R . G a l q z k a Dr.E.Kierzek-Pecold f o r 8 t i ~ u / a t i n ~ dlscussions and enoour~e~ente thtou~out this work. T~--ks ~e also due to U . D ~ b s k a / I F PAN, W a r s a w / for Erowin~ the c r y s t a l s i n Y e e t i ~ t e d i n this study.
Vol. 36. No. 2
REFLECTIVITY SPECTRA OF Cdl-xMnxTe MIXED CRYSTALS
REFERENCES I.
2. 94. 56. 7. 8. 9.
~ , R . R . , ]Proo. l t t t h T n t e r ~ v ~ t . C o n f . PI:~s. Semioolaclt., F_xtii:lbctr~l:l 1978, ed. VTI-~ON, B . L . H . , Inst. P h T s . C o n t . S e t . No 4 3 , 13~ 1978 • ~]~¢DRIRWICZ, T., K I E R ~ - P E C O L D , E., Solid State Commun. 25, 579 1978 • CARDONA, M., C~RRMA¥£T, D.L., Phys. Rev. I_/!, 98 1963 • CwRITKOWSKX, J.R., CONEN, M.L., P~Ts. Re'w.---~ I~, 556 1976 . CARDONA, k., Solid. State Phys. Suppl. 11 I~9 • wwOI, T.N., GAJ, J.A., ~hys. stat. sol.--b 8/, K133 1977 . P ~ , R.H., Phys. R e v . 97, 587 1955 . NICb'LF~CU, D., J. Phys. CI PToo. Phys. Soo. Ser. 2, 80~ 1968 SPT~nIN, N.G., PASZK0¥SKIJ, M.W., YASILINA~ Z.S.~ JEWTIGNIEJEW, A.I., F i z . TeEh. P o l u p r . 7, 2354 1973 .
131