Band offsets and electronic structures of (ZnCdHg)(SSeTe) strained superlattices

~

Pergamon

Solid.State Electromcs Vol. 37. Nos 4-6, pp. 1077-1080. 1994 Copyright (? 1994 Elsevier Science Ltd 0038-1101(93)E0015-S Printed in Great Britain. All rights reserved 0038-1101 '94 $6.00 + 0.00

BAND OFFSETS AND ELECTRONIC STRUCTURES OF (ZnCdHg)(SSeTe) STRAINED SUPERLATTICES TAKASHI NAKAYAMA Department of Physics, Faculty of Science, Chiba University, Yayoi, Inage, Chiba 263. Japan Abstract--Band offsets and electronic structures of various II-VI strained superlattices are calculated by the first-principles pseudopotential method in the local density approximation. The differences of band structures under strain between wurtzite and zinc-blende crystal structures are first analyzed. The deformation potentials are calculated for all II-VI compounds. However the strain in II-V1 superlattices is so large that nonlinear variation of energy levels with changing the magnitude of strain appears. There is a chemical trend of offset that energy levels of the heavy-hole and the electron states increase as the atomic number of anion and cation atoms increases, respectively. The calculated band offsets drastically vary with changing strain surroundings. The practical usage of the present results is illustrated.

II-VI semiconductor compounds have a high potential to opto-electronic usage, because their band gaps cover the spectral region of visible light. Recent experiments[I-3] showed that II-VI widegap superlattices (SLs) such as Zn,Cd~_,,S,.Se~_,./ Zn,.Cd,- ~S, Se I _., are one of the leading candidates for blue-light emitting devices. However, electronic structures of these systems, especially the band offsets under various strain environments, have not been understood well. In this view, in order to clarify their fundamental electronic quantities, we have calculated the band structures and band offsets of II-VI SLs made of all the combinations of II-VI compounds (from ZnS to HgTe) under various strain environments, by the first-principles theoretical method. A m o n g various characteristics seen in these systems, we concentrate on the difference of the strain effect on band-gap energy between bulks of zinc-blende and wurtzite structures, and the variation of band offsets with changing the substrate in this paper. This work is the extension of previous works on zinc-compounds SLs[4,5] to all II-VI compounds. The present theoretical calculation will help the evaluation of the quality of grown crystals and encourage the challenge to produce new types of devices. Because of the difference of lattice constant and the presence of substrate, II-VI SLs become in general strained systems. In order to determine the crystal structures of SLs, the macroscopic elastic theory[6] is employed, the details of which are described elsewhere[4]. For the band structure calculation of SLs, we have adopted the plane-wave first-principles pseudopotential method within the local density approximation[4,5]. We use pseudopotentials constructed by Bachelet et al.[7], where 3D-orbital electrons are treated as core electrons and the spin-orbit interaction is not included[4,5]. The X~t potential with = 0.7 is used for the exchange-correlation potential. From the calculated band structures, we evaluate the

band offset, the method of which is a standard one in the first-principles scheme[4,5.8]. Table 1 shows the lattice constants under no strain and the elastic constants of various II-VI compounds, which are used in this work. Before going to the calculated results of SLs, two points are discussed. At first, it should be noticed that CdS and CdSe are normally of wurtzite (WZ) structure in bulks, while they show the zinc-blende (ZB) structure when epitaxialized as SLs. Therefore we have to take into account the difference of electronic structure between W Z and ZB. Figure 1 shows the difference of the band-gap energy between WZ and ZB, as a function of strains Ei~,~~ and ~l~t~, parallel and perpendicular to the (111)direction. Comparing W Z and ZB structures, WZ has larger band-gap energy than ZB in the most strained region in Fig. I. It is generally shown that the difference of band-gap energy between W Z and ZB originates from the difference of positions of the third nearest neighboring atoms between WZ and ZB structures[10], and that all direct-gap semiconductors have larger bandgap energies in WZ forms than ZB forms[I 1]. When the lattice constant along (111) decreases: Iq~tll~[ increases in a negative region, the distance to the third nearest neighboring atoms in WZ structure becomes so short that the band-gap energy of WZ sharply increases. This fact indicates that the variation of electronic structure of ZB with changing strain surroundings is more moderate than that of WZ. However, secondly, the lattice constants of II-V1 compounds scatter in such a wide region that the strain becomes considerably large ( ~ 0. I) when 1I VI SLs are produced. Therefore, we have to examine the variation of the electronic structure under large strain. Most SLs are produced along (100) and the lattice constant perpendicular to (100) becomes equal to that of the substrate. In this case, only the diagonal

1077

TAKASHI NAKAYAMA

1078

ZnS

T a b l e 1+ L a t t i c e c o n s t a n t s a a n d elastic c o n s t a n t s C , a n d C~2 o f v a r i o u s I I - V I c o m p o u n d s used in this w o r k

ZnS ZnSe ZnTe CdS CdSe CdTe HgS HgSe HgTe

4

a [au]

Cl~

C,z

10.208 10.694 11.509 10.991 11.420 12.228 I 1.040 11.479 12.191

10.462 8.720 7.130 8.470 7.490 5.380 8.130 6.900 5.361

6.533 5.240 4.070 5.450 4.609 3.740 6.220 5.190 3.660

All v a l u e s are t a k e n f r o m Ref. [9]. E l a s t i c c o n s t a n t s are in 1 0 m N / m 2 unit.

components of strain tensor exist[4], which have the following relation in the linear elastic theory, El,<~m=-2C~2/CHEj.uoo). Establishing the strained structures of II-VI bulks based on this formula, the band-gap energies are calculated from the first-principles, which are shown in Fig. 2, as a function of the lattice constant of the substrate. Here the band gap corresponds to the transition from the heavy-hole state to the lowest conduction-band state at the center of the Brillouin zone. Though the band structure calculation in the local density theory underestimates the band-gap energy, the variation of energy levels with changing strain surroundings is well described by the calculation. Thus the calculated band-gap energies are constantly shifted in order to coincide with observed values[9] only for the unstrained cases, e.g. by +0.400 (ZnS), +0.691 (ZnSe) and +0.500 eV (ZnTe). Most striking feature seen in Fig. 2 is that the band-gap energy of each material has the largest value and the slowest variation with changing the substrate, in the region near the unstrained lattice constant. However, far away from this region, though the strain of crystal is treated in the linear theory, the band-gap energy rapidly decreases in a non-linear manner. As seen in Fig. 2, though the deformation potential seems to be a well-defined quantity only around the

0.1

Z

-0.1

0

........... 0 , 0 7 0 .......... O. 1 7 6 .......... 0 . 0 0 1

. . . . . . . . . . O, 1 5 0 .......... 0 . 0 4 4 .......... 0 . 0 1 4

...........

0 . 0 4 8 .......... 0 . 0 2 5

'-'-0.1 . . . .

0

........... 0 . 0 2 7

. . . .

011'

'~ I! (111)

Fig. 1. Contour-map plot of the difference of band-gap energy between wurtzite and zinc-blende CdSe. as a function of the strain ~,uut) and ~l.m.

>(5

'

ZnSe CdS CdSe

'

~

~''

CdTe

'I"

'

' '~

Se

'

'

HgTe

c

Z I<~

CdTe ,-"

0

,'

HgSe

,' (

10

-LCS----"--:-:.--.-.~

.~ .....

/

/ " ~ H gT..9o- ~ + e

,

,

.¢

i

,

,

,

A I

11 asubstrat e

~

,

i

i

12 [a.u.]

Fig. 2. Calculated band-gap energies of various II-VI compounds, as a function of the lattice constant of the substrate. Positions of unstrained lattice constants are denoted by arrows around the upper line. Solid line corresponds to Zn-compound, dotted line to Cd-compound and dashed line to Hg-compound.

unstrained lattice constant, it becomes the measure of energy-level variation. Without the spin-orbit interaction, the band-gap energy between the heavy-hole and the lowest conduction-band electron states E c - E h h and the splitting energy between the light and the heavy-holes E m - Ehh are given as follows: Ec - E b b = a (2~±,0m + Ellu0o))- b (~±,0m - Eli,00)) and E m - E h h = 3b (~±u0m- Ell,0m). Fitting the calculated results to these formulas, we obtain the deformation potentials a and b in Table 2. Then we consider the calculated results of II-VI strained SLs. Most features of electronic structures of various II-VI SLs are similar to those in case of zinc-compounds SLs in previous calculations[5]. Thus, at first, we shortly comment on this. By examining the layer-thickness dependence of bandgap energies of SLs and the manner of charge distribution of respective band-edge state of SLs in constituent layers, it is concluded that the quantum well picture is well applicable to the states around the fundamental gap in all II-V1 strained SLs. This result allows us to define the band offset. T a b l e 2. C a l c u l a t e d d e f o r m a t i o n pot e n t i a l s for v a r i o u s II VI c o m p o u n d s in eV

ZnS ZnSe ZnTe CdS CdSe CdTe HgS HgSe HgTe

a

h

-6.95 -4.73 - 5.91 - 3.77 -4.64 -4.13 -4.64 -3.66 -4.22

- 1.25 - 1.23 - 1.3 I - 1.07 - 1.14 -I.13 - 1.24 -I.16 - 1.22

1079

Band offsets and electronic structures of II-VI structures i

i

i

I

I

i

i

i

I

~

i

i

i

i

[

i

i

i

e,.

I.L

HgTe

I.L O

CoTe

..

I,LI

-~

O 1 -'1-"

III

ZnTe

"~'--~ "

-~

HgSe

I"--

CdSe ZnSe HgS

~-

"1-

"

* . . . . . . . . . . . . . °. . . . . . . 0

" i

-.

" i

i

[

[

10.5

i

CdS

' i

[

I

i

i

[

I

[

ZnS i

i

be included a posteriori [5] when we use the observed values of spin-orbit splitting energies A0 in experiments[9]; 0.064, 0.42 and 0.42 eV for ZnS, ZnSe and CdSe, respectively, The calculated offset for the heavy-hole state of ZnSe/ZnS on ZnSe substrate is evaluated as follows: AE (ZnSe/ZnS) = 0.69 +-~ x (0.42 - 0.064) = 0.809 eV.

(I)

Similarly, because the band offset linearly depends on the strain as shown in Fig. 3, the offset of Zn075Cd0.:sSe/ZnS on ZnSe is estimated as:

i

11

11.5 asubstrate [a.u.]

Fig. 3. Calculated band offsets for the heavy-hole state between various II-VI compounds and ZnS as a function of the lattice constant of the substrate. Solid line corresponds to Zn-compound, dotted line to Cd-compound and dashed line to Hg-compound.

AE (Zn075Cd0.25Se/ZnS) = 0.75 x (0.69 + ½x (0.42 - 0.064)) + 0.25 x (0.90 + ½x (0.42 - 0.064)) = 0.861 eV.

(2)

Using both values, we obtain: AE (Zno.75Cd0.25Se/ZnSe)

Figure 3 shows the calculated band offsets at (various II-VI semiconductors)/ZnS interface for the heavy-hole state as a function of the lattice constant of the substrate. As seen in this figure, band offsets drastically vary with changing the substrate, i.e. changing strain strength. These variations are caused by the competition between the energy-level shift by strain and the charge transfer at the interface[5]. There appears a chemical trend that the offsets for the heavy-hole state of Te-compounds are large, while those of S-compounds are small. This is because the top of the valence-band states mainly consists of p-orbital of cation atom, and because the energy of cation p-orbital is higher for Te than for S. On the other hand, as for the calculated results of the electron state, the energy position is high for Zn-compounds and low for Cd- and Hg-compounds. This is the reflection from the magnitude of band-gap energies of these materials, and is explained by the fact that the lowest conduction-band state at the center of the Brillouin zone is the anti-bonding state of cation s-orbitals. HgSe and HgTe are metals, which have negative band-gap energies as shown in Fig. 1 even in the strained structures. Thus their energy positions of electron states are extremely low. In order to clarify the relative position of the band-edge states among II-VI compounds, the band offsets on the ZnSe substrate are shown in Fig. 4. From this figure, it is easily concluded, for example, that ZnS/ZnSe SL is of type I, while ZnTe/CdSe and ZnSe/CdSe SLs are of type II, which is in good agreement with experimental observations[12,13]. Then we compare the calculated offsets with experiments. The ZnSe/Sn075Cd0.25Se superlattice coherently grown on ZnSe[14] is considered, for example. Though the spin-orbit interaction is absent in the present first-principles calculation such an effect can

= 0.861 - 0.809 = 0.052 eV.

(3)

This value is in good agreement with estimated value (0.055 eV) from experiments by Pelekanos et all14]. It should be noticed here that, in the above evaluation, we used the fact that band offset is transitive for the combination of materials; A E ( A / B ) = A E ( A / C ) + A E ( C / B ) , as long as SLs are grown on the substrate of the same lattice constant. This property is approximately satisfied in all the present II-VI SLs because the charge transfer across the interface is additive for each combination of II-VI compounds[5]. Finally, we make remarks on the effect of atomic configuration at the interface on the band offset. For multinary SLs such as ZnS/CdSe, there exist two kind of clean interfaces S/Cd and Zn/Se. Table 3 shows the calculated band offsets for the heavy-hole states at cation/Se and anion/Zn interfaces. The calculated band offset differs by _+20 meV between these interfaces, due to the difference of charge distribution at

ZnTe ZnS ZnSe[ >-

I CdS •"'

CdTe CdSe HgS r----1

rr IxI Z iii

Fig. 4. Calculated band alignment of the top of valence bands and the bottom of conduction bands, for various II-VI compounds on the ZnSe substrate, in eV.

1080

TAKASHI NAKAYAMA Table 3. Calculated band offset for the heavy-hole state at multinary (II-VI compounds);ZnSe interfaces on the ZnSe substrate, in eV C A CdS -0.513 -0.499 HgS -0.259 -0.239 CdTe 1.409 1.428 HgTe 1.543 1.572 C and A indicate the interfaces cation/Se and anion/Zn, respectively.

the interface. T h o u g h this variation is small, such difference will become i m p o r t a n t when the configuration of interface a t o m s is controlled, which is not clear in experiments in the present stage. In summary, we have calculated electronic structures and b a n d offsets of various I I - V I strained superlattices by the first-principles pseudopotential m e t h o d in the local density a p p r o x i m a t i o n . It is shown that the variation of the b a n d - g a p energy with changing strain surroundings is more m o d e r a t e in zinc-blende structure than in wurtzite one. The deform a t i o n potentials are calculated for all I I - V I compounds. However, the variation of energy levels is not limited to the linear variation due to the large strain in I I - V I superlattices. The calculated b a n d offsets for the heavy-hole states drastically vary with changing strain strength. There is a chemical trend that the energy position of the heavy-hole state is high for T e - c o m p o u n d s a n d low for S-ones, while that the energy position of the lowest c o n d u c t i o n - b a n d state is high for Z n - c o m p o u n d s a n d low for Hg-ones. F o r multinary superlattices such as ZnS/CdSe, the dependence of the band offset on the kind o f a t o m s at the interface is small. We d e m o n s t r a t e the usage of

the calculated experiments.

band

offsets by c o m p a r i n g

with

Acknowledgements--We are pleased to thank Miss Misao Murayama for preparing the manuscript. This work is supported by a Grand-in-Aid from the Ministry of Education, Science and Culture, Japan. REFERENCES

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