Ellipsometric investigation of optical constant and energy

band gap of Zn1�xMnxSe/GaAs (1 0 0) epilayers

D.-J. Kim a, Y.-M. Yu a, Y.D. Choi a,*, J.-W. Lee b

a Department of Optical & Electronic Physics, Mokwon University, 800, Doan-Dong, Seo-ku, ,

Daejeon 302-729, Republic of Koreab Department of Materials Engineering, Hanbat National University, Daejeon 305-719, Republic of Korea

Received 30 January 2005; received in revised form 15 May 2005; accepted 25 July 2005

Available online 8 September 2005

www.elsevier.com/locate/apsusc

Applied Surface Science 252 (2006) 5745–5751

Abstract

Zn1�xMnxSe/GaAs (1 0 0) epilayers were grown using a hot-wall epitaxy method. The spectroscopic ellipsometry was used

to determine the optical dielectric constant. The obtained pseudodielectric function spectra revealed the distinct structures at

energies of E0, E0 + D0, E1, E1 + D1, E2 and E00 + D0 critical points (CPs) at lower Mn composition range. These critical points

were determined by analytical line-shapes fitted to numerically calculated derivatives of their pseudodielectric functions. The

peak characteristics were changed with the change in Mn composition. The spectral dependence of pseudodielectric function heiwas used to obtain the fundamental energy gaps E0 including a unique relation with Mn composition. Also, the shifting and

broadening of the CPs were observed with increasing Mn composition.

# 2005 Elsevier B.V. All rights reserved.

Keywords: Hot-wall epitaxy; ZnMnSe; Spectroscopic ellipsometer; Pseudodielectric constant

1. Introduction

Diluted magnetic semiconductors (DMS) are the

class of semiconductor materials formed by randomly

replacing some of the cations in a compound semi-

conductor with transition metal ions [1]. ZnMnSe is

one of the most extensively studied DMS and has

attracted considerable attention both for basic research

* Corresponding author. Tel.: +82 42 829 7552;

fax: +82 42 823 0639.

E-mail address: ydchoi@mokwon.ac.kr (Y.D. Choi).

0169-4332/$ – see front matter # 2005 Elsevier B.V. All rights reserved

doi:10.1016/j.apsusc.2005.07.037

and for the application in optoelectronic devices,

such as a spin aligner [2–4]. Recently, the studies of

Zn1�xMnxSe/GaAs (1 0 0) epilayers have been con-

centrated especially on magneto-optical characteriza-

tion in order to promote their applicability to spin-

dependent electric devices [5,6]. High quality epilayer

growth and the precise information on the optical,

magnetic and electrical properties of the samples are

critical for this material to be applicable to magneto-

optical devices. To date, the reflectance spectroscopy,

photoluminescence (PL) spectroscopy and Raman

scattering spectroscopy of Zn1�xMnxSe have been

.

D.-J. Kim et al. / Applied Surface Science 252 (2006) 5745–57515746

primarily studied [7,8]. Since the above investigations

were limited mainly to the Brillouin zone center,

however, a number of optical parameters appearing in

the high-energy region could not be obtained. There-

fore, the study on the high photon energy region is of

considerable necessity.

The purpose of this article is to determine the

optical properties of Zn1�xMnxSe/GaAs (1 0 0)

epilayers by spectroscopic ellipsometry (SE) mea-

surement for the wide photon energy range of 2.5–

8.5 eV. In particular, the spectral dependence of

pseudodielectric function spectra hei = he1i + ihe2i of

Zn1�xMnxSe was observed in this study. The funda-

mental energy band gap E0 represents an anomalous

behavior by the strong sp–d exchange interaction with

an increase of Mn composition. The shifting and

broadening of the critical points, namely E0, E0 + D0,

E1, E1 + D1, E2 and E00 + D0, are investigated in

relation to Mn composition. It is also shown that the

SE technique is the reliable new tool to obtain the E0

gap of all the semiconductor epilayers of direct

interband transition type.

2. Experiments

Zn1�xMnxSe/GaAs (1 0 0) epilayers were grown by

hot-wall epitaxy (HWE). ZnSe (5N) and Mn (5N)

powders were used as source materials. In order to

control the Mn composition of the Zn1�xMnxSe

epilayers, ZnSe and Mn powders were placed in

different sections and heated independently. The

specific procedure to find the optimum growth

conditions for the Zn1�xMnxSe epilayer is described

Table 1

Peak position energy of the critical point in optical spectra of ZnSe (Mn

Energy gap (eV) E0

(M0CP)

E0 + D0

(M0CP)

E1

(M1CP)Workers Growth

Walter and Cohen EPM 2.90 – 4.75

Adachi and Taguchi RTHM 2.67 3.10 4.75

Kim et al. MBE 2.69 3.11 4.83

Dahmani et al. MBE 2.68 3.12 4.40

Kim and Sivananthan MBE 2.76 3.21 4.72

Kim et al. MBE 2.70 3.10 4.80

Kvietkova et al. MBE 2.70 3.11 4.95

This work HWE 2.70 3.08 4.72

in Ref. [8] in detail. The thickness of most epilayers

was about 1 mm, as determined by the reflectance

measurements using a spectrophotometer. The misfit

strain due to the difference in lattice constants of the

epilayer and the substrate was assumed to be almost

entirely relaxed. The growth rate of epilayer was 1–

3 A/s. Prior to the SE measurements the samples were

rinsed by being flushed with methanol. And during the

SE measurements, the dried nitrogen gas of high

purity flowed continuously onto the sample surface to

prevent the oxidation and contamination by air. The

pseudodielectric function spectra, which indicate the

optical properties of Zn1�xMnxSe epilayers, were

measured at room temperature for the wide photon

energy range of 2.5 and 8.5 eV using an automatic

spectroscopic rotating analyzer ellipsometer (Wool-

lam VUV-VASE system) with 300 W xenon and 70 W

deuterium lamps at an incident angle of 708. In this SE

experiment, the elliptical azimuth C and phase angle D

determined with respect to the polarized components,

which vibrate perpendicular (s) and parallel (p) to the

incident plane, can be measured precisely. Therefore,

the complex pseudodielectric function hei of the

epilayer can be determined in the two-phase model by

heðEÞi ¼ eaðEÞ�

sin2fþ sin2f tan2f

�ð1� rÞð1� rÞ

�2�

(1)

where r = tanCeiD; ea ¼ n2a ¼ 1 and f are the dielec-

tric constant of the ambient medium and the incident

angle of the probing light, respectively. Since the

corrections of the overlayers and surface roughness

have not been made, the dielectric function spectra

composition x = 0) at 300 K

E1 + D1

(M1CP)

E2

(M1CP)

D5!1

(M0CP)

E00 + D0

(M0CP)

Reported

years

5.05 6.63 7.25 8.28 1969 [11]

5.05 6.70 – – 1991 [9]

5.10 – – – 1993 [21]

4.75 6.90 – – 1994 [14]

5.00 6.50 – – 1996 [10]

5.10 – – – 1998 [17]

5.24 – – – 2004 [15]

5.06 6.30 7.06 8.26 2005

D.-J. Kim et al. / Applied Surface Science 252 (2006) 5745–5751 5747

derived from ellipsometric data can be treated as

‘pseudodielectric function’ hei.

Fig. 1. The pseudodielectric constant e1(E) spectra of Zn1�xMnxSe/

GaAs (1 0 0) epilayers obtained from SE measurement as a function

of Mn composition. The inset represented the oscillation region

below 3.0 eV.

3. Results and discussion

Table 1 shows the critical points determined by a

number of investigators on ZnSe. In the present

study on SE measurement, we have assumed that the

transition occurs in the G-point of Brillouin zone in

ZnSe. It is known that the critical points vary to some

extent according to the crystal growth method. As

delineated in Table 1, our experimental results are

similar to those reported by Adachi and Taguchi [9] at

below 5 eV and those reported by Kim and Siva-

nanthan [10] at above 5 eV. Also, comparing the

CPs reported by Walter and Cohen [11] with those

observed in the present study, the latter yielded the

lower peak position energy values than those of Walter

et al. in entire photon energy range from 2.5 to 8.5 eV.

Also, it is worthy of note that the CPs appearing near

7.0 and 8.26 eV are observed only in our study, as

shown in Table 1.

Figs. 1 and 2 show the pseudodielectric function

spectra hei of Zn1�xMnxSe/GaAs (1 0 0) epilayers

obtained from SE measurement as a function of Mn

composition x. In figures, the arrows represent the

notation of Cardona and Greenaway. The insets of

Figs. 1 and 2 show the shift of E0 peak position in the

oscillation for the photon energy range below 3.0 eV.

The interval of y-axis is widened to observe with

accuracy the shift of E0 peak position. The strong

interference oscillations appearing at the energy below

the energy band gap, E0, are due to the multiple

internal reflections of the light beam in the transparent

epilayer. As listed in Table 1, although there have been

many reports on an E0 peak in Zn1�xMnxSe system

[12,13–15], the data on E0 peak measured by SE as a

function of Mn composition x have not been reported

to date. The optical transitions occurring near G-point

(k = 0) are well known as the E0 gap (G v8!G c

6).

Generally, the energy for direct interband transitions

in semiconductors corresponds to optical energy band

gap, which appears at the right end of oscillation

regions, as shown in Figs. 1 and 2. Choi et al. and Kim

et al. reported the systematic blue-shifting of the E0

gap of Al1�xGaxP and Zn1�xMgxSe as a function of

composition x [16,17]. They also observed the strong

oscillations in the energy region below the E0 gap. In

the same manner, Kim and Sivananthan and Dahmani

et al. reported that the E0 peak in ZnSe appeared at the

right end of oscillation regions [10,14]. The E0 and

E0 + D0 peaks in ZnSe are displayed in the lower

photon energy range and may be related to 3D M0CP

[10]. As shown in Figs. 1 and 2, the E0 gap of pure

ZnSe (x = 0) is 2.70 eV and the E0 for x = 0.05 is

2.67 eV. The E0 + D0 peak by G v7!G c

6 transition

caused by spin–orbit interaction splits near G-point is

distinctly presented at 3.08 eV, especially with lower

Mn composition. However, it was weakened at Mn

composition x = 0.24 and somewhat red-shifted with

increasing Mn composition, and thereafter disap-

peared. Although an intrinsic splitting energy D0 of

approximately 0.4 eVexists in ZnSe, the interval of E0

and E0 + D0 became increasingly smaller owing to the

increased Mn composition [9,12]. Also, the E1 and

E1 + D1 peaks by Lv4;5!Lc

6 and Lv6!Lc

6 transitions

D.-J. Kim et al. / Applied Surface Science 252 (2006) 5745–57515748

Fig. 2. The pseudodielectric constant e2(E) spectra of Zn1�xMnxSe/

GaAs (1 0 0) epilayers obtained from SE measurement as a function

of Mn composition. The inset represented the oscillation region

below 3.0 eV.

occurring along the L direction near the L-point were

observed near 4.72 and 5.06 eV, respectively. They

can be explained by 3D M1CP type. The peaks show

the red-shifting and broadening with increasing Mn

composition, as shown in Figs. 1 and 2. They were

weakened for higher Mn composition. These results

are qualitatively in good agreement with those

reported by other investigators. Generally, the E1

and E1 + D1 peaks are formed by contribution of

strong 2D exciton in II–VI compounds. However, the

excitons are localized because of the crystalline

degradation or the sp–d hybridization, as the Mn

composition increases [18]. Therefore, the amplitude

of E1 + D1 peak caused by spin–orbit interaction splits

at near L-point decreases to some extent at x = 0.05,

and it merges into a E1 peak as the Mn composition

further increases, shifting the peak to lower energies.

These observations are clearly shown in Figs. 1 and 2.

In general, the splitting energy D1 is known to be

0.3 eV, and our results show the good agreement with

this value [9]. The E2 peak occurred along the S-

direction near the X-point at 6.30 eV, as shown in

Figs. 1 and 2, and is characterized by a damped

harmonic oscillator (DHO) such as the classical

Lorentzian line shape model applied in Adachi’s

report [9]. The E2 peak energy can also be

characterized by strength and damping parameter.

Note that our E2 peak energy value is smaller than that

reported in many other studies [9–11,14]. With

increasing Mn composition x, the rapid decreasing

and red-shifting of the E2 peak intensity was observed,

and then the E2 peak ultimately disappeared above

x = 0.24. The E00 + D0 peak at 8.26 eV caused by 3D

excitons disappeared as Mn composition increased.

This result is due to the low contribution of 3D

excitons of atoms as Mn composition increases. From

the SE measurement in this study, we discovered that

the peak observed around 7.0 eV for the pure ZnSe

epilayer (x = 0) is due to D5!1 transition [11]. This

peak was described in our previous report [8], but it

was not defined in detail. This transition gradually

decreased and completely disappeared at x = 0.24.

Note that the peak is presented in another form near

7.0 eV as the Mn composition x approaches 0.39. This

peak is to due to the spin exchange splitting energy of

Mn 3d+ and the peak increases more distinctly as the

Mn composition x approaches 0.63 [19]. Thus, the

shift and disappearance of these peaks are closely

related to the increase of Mn composition.

Fig. 3 shows the E0 CPs energies determined by the

second derivative spectra and their fits to Eq. (2) of

pseudodielectric function hei. The results are fitted

using the line shape formula developed by Aspnes

et al. [13]. The solid and dotted lines represent the best

fits and resulting parameters are shown in Table 2.

Note that good agreement between the experimental

data and the fitted data is obtained. These results,

especially, can certify the validity of E0 indicated by

arrows in the inset of Figs. 1 and 2. Also, it can

convince that the energy for direct interband transi-

tions in semiconductors corresponds to optical energy

band gap, which appears at the right end of oscillation

regions.

Fig. 4 compares the peak position energy E0

obtained from SE with the peak position energy E0

determined from electro-reflectance (ER) and wave-

length-modulated reflectivity (WMR) measurements

D.-J. Kim et al. / Applied Surface Science 252 (2006) 5745–5751 5749

Fig. 3. Open squares and circles represent the experimental data for

d2e1/dE2 and d2e2/dE2, respectively. The real (solid lines) and

imaginary (dash-dotted lines) parts of the pseudodielectric function

of Zn1�xMnxSe are obtained from fits to the second derivatives.

Fig. 4. Comparison between the peak position energy E0 obtained

from SE and the peak position energy E0 determined from electro-

reflectance (ER) and wavelength-modulated reflectivity (WMR) as

well as reflection spectra measurements.

by Stankiewicz and Fermin [12] and reflection spectra

by X. Wang et al. [20]. In a Zn1�xMnxSe/GaAs (1 0 0)

system, contrary to expectations, the fundamental

energy band gap E0 decreases at first and then

increases again with increasing Mn composition x

[12,18,20]. Kim et al. suggested an sp–d exchange

interaction model that could explain the band gap

energy of Zn1�xMnxSe/GaAs (1 0 0) epilayers. They

also conducted a limited investigation into the band

Table 2

Critical point parameters of ZnSe (Mn composition x = 0) epilayer

fitted by Eq. (2)

E0 E0 + D0 E1 E1 + D1 E2 E00 + D0

A (eV) 0.18 0.159 4.30 1.31 3.84 1.25

F (8) 21.89 30 �9.40 �8.50 21.82 21.80

E (eV) 2.70 3.08 4.72 5.06 6.30 7.06

G (eV) 0.034 0.112 0.175 0.115 0.213 0.239

gap energy E1 and E1 + D1 measured from SE at lower

Mn content (x = 0.144) [21]. The main goal of the

aforementioned research was to analyze the G-point

band gap. It should be noted that the systematical

investigation of the fundamental energy band gap E0

and the higher band gap (>5 eV) in ZnSe with higher

Mn composition was not undertaken. As shown in

Fig. 4, the E0 gap slowly decreases to near x = 0.13,

and subsequently begins to increase. It can be seen that

the guideline of the fundamental energy band gap E0

formed a bow region below x = 0.39 and a straight line

above x = 0.39. Our results on the shift of the E0 gap,

obtained for the first time by SE for Zn1�xMnxSe

epilayers, showed the good agreement with the results

obtained by ER and WMR. From the above results, it

is clear that the ellipsometric measurements as a

function of composition could be used as a powerful

tool to observe changes of the energy band gap.

Fig. 5 shows the numerically calculated second

derivatives spectra of the pseudodielectric function heiof ZnSe (x = 0) epilayers for a further analysis of the

critical points. The fitted data are expressed as

analytical line-shapes with two-dimensional critical

points [22,23]

eð�hvÞ ¼ C � A lnð�hv� E � iG ÞexpðiFÞ: (2)

This numerical formula is made up of four

parameters for each point; energy, E, broadening, G,

amplitude, A and phase angle F. As mentioned earlier,

the solid and dotted lines represent the best fits and

D.-J. Kim et al. / Applied Surface Science 252 (2006) 5745–57515750

Fig. 6. Dependence of the peak position energy of critical points Mn

composition.

Fig. 5. The second derivative spectra of the pseudodielectric con-

stant e1(E) and e2(E) of ZnSe (x = 0) epilayers, which is numerically

calculated using the Eq. (2).

resulting parameters are shown in Table 2. We

determined the critical points of epilayers by taking

the zero-crossing of the second derivative spectra of

the imaginary parts of their pseudodielectric function

hei. The line shapes were smoothed by applying the

binomial filtering procedure [24]. As can be seen from

Fig. 5, all the peaks are clearly resolved.

Fig. 6 shows the change of the peak position energy

of E0, E0 + D0, E1, E1 + D1, E2 and E00 + D0 as a

function of Mn composition. The respective peak

position energies are changed with Mn composition.

In particular, the peak position energies of E0, E0 + D0

and E2 are increased with increasing Mn composition,

but the peak position energies of E1 and E1 + D1 are

decreased. Also, peak position energies of E00 + D0 are

maintained constant. As mentioned above, the E0

and E0 + D0 decreases at lower Mn composition

(x < 0.13), thereafter it increases again. These results

agree well with the previously reported result on

Zn1�xMnxSe [18]. The transition energies of E1 and

E1 + D1 decrease with increasing Mn composition.

Kim et al. studied for hybridization effect of the

Zn1�xMnxSe by perturbative semi-empirical tight-

binding calculations at lower Mn composition and

assumed that the correlation between the localized d

states can be ignored [25]. A linear term proportional

to Mn composition was added to account for the

normal alloying effect. In this study, we extended the

experimental range to high Mn composition (x = 0.63)

and found that the E1 and E1 + D1 peak position

energies decrease almost linearly with increasing Mn

composition through the entire range of the Mn

composition studied. The E1 and E1 + D1 energies

obtained in our study thus agree quite well with the

experimental data of Kim et al. The E2 peak energy

occurred along the S-direction near the X-point is

increased with Mn composition and the E00 + D0 peak

at 8.26 eV caused by 3D excitons maintain the

constant value.

4. Conclusions

Zn1�xMnxSe epilayers used in this optical study

were grown on GaAs (1 0 0) substrates by the hot-wall

epitaxy method. In order to determine optical

properties of the epilayers, the spectroscopic ellipso-

metry was carried out in a photon energy range of

2.5–8.5 eV at 300 K. The unique relation between the

fundamental band gap energy E0 of Zn1�xMnxSe

epilayers and the Mn composition was observed. The

E0 + D0 peak caused by 3D excitons at 3.08 eV

D.-J. Kim et al. / Applied Surface Science 252 (2006) 5745–5751 5751

appeared weakly and then disappeared. The E1 peak

formed at 4.72 eV by the contribution of strong 2D

excitons red-shifted. Also, the weak E1 + D1 peak was

observed at 5.06 eV. The E2 peak caused by DHO at

6.30 eV disappeared as Mn composition x increased.

The E00 + D0 peak located at 8.26 eV was due to 2D

excitons. A peak at approximately 7.0 eV was also

found. This peak due to a D5!1 transition at lower Mn

composition completely disappeared with increasing

Mn composition x. With increasing Mn composition,

another peak caused by the spin exchange splitting

energy of Mn 3d+ showed up near 7.0 eV. Our results

on the shift of the E0 gap determined by SE as a

function of Mn composition x corresponded closely

with the results obtained by ER and WMR. Therefore,

from the SE measurement performed for the first time

in this study for the Zn1�xMnxSe epilayers, it was

clearly seen that the ellipsometric measurements

could be used as a powerful new tool to observe

changes of the energy band gap.

Acknowledgment

This work was supported by a Korea Research

Foundation grant (KRF-2002-070-C00036).

References

[1] J.K. Furdyna, J. Appl. Phys. 64 (1988) 29.

[2] R. Fiederling, M. Keim, G. Reuscher, W. Ossau, G. Schmidt,

A. Waag, L.W. Molenkamp, Nature 402 (1999) 787.

[3] B.T. Jonker, Y.D. Park, B.R. Bennett, H.D. Cheong, G. Kio-

seoglou, A. Petrou, Phys. Rev. B 62 (2001) 8180.

[4] R.M. Stroud, A.T. Hanbicki, Y.D. Park, G. Kioseoglou, A.G.

Petukhov, B.T. Jonker, G. Itskos, A. Petrou, Phys. Rev. Lett. 89

(2002) 166602.

[5] W.M. Chen, I.A. Buyanova, G.Yu. Rudko, A.G. Mal’shukov,

K.A. Chao, A.A. Toropov, Y. Terent’ev, S.V. Sorokin, A.V.

Lebedev, S.V. Ivanov, P.S. Kop’ev, Phys. Rev. B 67 (2003)

125313.

[6] A.A. Toropov, A.V. Lebedev, S.V. Sorokin, D.D. Solnyshkov,

S.V. Ivanov, P.S. Kop’ev, I.A. Buyanova, W.M. Chen, B.

Monemar, Physica E 17 (2003) 352.

[7] T. Matsumoto, A. Ota, K. Nakamura, A. Fujita, Y. Nabetani, T.

Kato, Phys. Status Solidi (c) 1 (2004) 933.

[8] Y.M. Yu, D.J. Kim, K.J. Lee, Y.D. Choi, B.O.K.S. Lee, I.H.

Choi, M.Y. Yoon, J. Vac. Sci. Technol. A 22 (2004) 1908.

[9] S. Adachi, T. Taguchi, Phys. Rev. B 43 (1991) 9569.

[10] C.C. Kim, S. Sivananthan, Phys. Rev. B 53 (1996) 1475.

[11] J.P. Walter, M.L. Cohen, Phys. Rev. 183 (1969) 763.

[12] J. Stankiewicz, J.R. Fermin, J. Appl. Phys. 63 (1988) 3300.

[13] Y.D. Kim, S.L. Cooper, M.V. Klein, B.T. Jonker, Appl. Phys.

Lett. 62 (1993) 2387 (references therein; D.E. Aspnes, in: M.

Balkanski (eds), Handbook on Semiconductors, North-Hol-

land, Amsterdam, 1980, vol. 2, p. 109).

[14] R. Dahmani, L. Salamanca-Riba, N.V. Nguyen, D. Chandler-

Horowitz, B.T. Jonker, J. Appl. Phys. 76 (1994) 514.

[15] J. Kvietkova, B. Daniel, M. Hetterich, M. Schubert, D. Spe-

mann, Thin Solid Films 455–456 (2004) 228.

[16] S.G. Choi, Y.D. Kim, S.D. Yoo, D.E. Aspnes, D.H. Woo, S.H.

Kim, J. Appl. Phys. 87 (2000) 1287.

[17] K.J. Kim, M.H. Lee, J.H. Bahng, C.Y. Kwak, E. Oh, Solid State

Commun. 95 (1997) 17.

[18] W.K. Hung, M.Y. Chern, Y.F. Chen, W.C. Chou, C.S. Yang,

C.C. Cheng, J.L. Shen, Solid State Commun. 120 (2001) 311.

[19] H. Sato, T. Mihara, A. Furuta, Y. Ueda, H. Namatame, M.

Taniguchi, J. Electron Spectrosc. Relat. Phenom. 78 (1996) 87.

[20] X. Wang, X. Chen, J. Liu, C. Chen, J. Wang, Z. Ling, X. Wang,

S. Wang, S. Lu, Solid State Commun. 95 (1995) 525.

[21] Y.D. Kim, S.L. Cooper, M.V. Klein, B.T. Jonker, Phys. Rev. B

49 (1994) 1732.

[22] C.S. Cook, S. Zollner, M.R. Bauer, P. Aella, J. Kouvetakis, J.

Menendez, Thin Solid Films 455–456 (2004) 217.

[23] L. Vina, S. Logothetidis, M. Cardona, Phys. Rev. B30 (1984)

1979.

[24] R. Kellner, J.M. Mermet, M. Otto, H.M. Widmer (Eds.),

Analytical Chemistry, Wiely-Vch, Weinheim, 1998.

[25] Y.D. Kim, S.L. Cooper, M.V. Klein, Phys. Rev. B 48 (1993)

17770.