Dielectric function and critical points of AlP determined by spectroscopic ellipsometry

Journal of Alloys and Compounds 587 (2014) 361–364

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Dielectric function and critical points of AlP determined by spectroscopic ellipsometry S.Y. Hwang a, T.J. Kim a, Y.W. Jung a, N.S. Barange a, H.G. Park a, J.Y. Kim a, Y.R. Kang a, Y.D. Kim a,⇑, S.H. Shin b, J.D. Song b, C.-T. Liang c, Y.-C. Chang c a b c

Nano-Optical Property Laboratory and Department of Physics, Kyung Hee University, Seoul 130-701, Republic of Korea Center for Opto-Electronic Convergence Systems, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea Research Center for Applied Sciences, Academia Sinica, Taipei 115, Taiwan

a r t i c l e

i n f o

Article history: Received 18 June 2013 Received in revised form 24 October 2013 Accepted 27 October 2013 Available online 4 November 2013 Keywords: Ellipsometry AlP Dielectric function Critical point

a b s t r a c t We report the room-temperature dielectric function e of AlP from 0.74 to 6.54 eV obtained by in situ spectroscopic ellipsometry. Measurements were done on a 1.2 lm thick film grown on (0 0 1) GaAs by molecular beam epitaxy, with e extracted using a multilayer parametric model. Critical point energies of features in the e spectra were obtained from numerically calculated second-energy-derivatives, and their Brillouin-zone origins identified by band-structure calculations done using the linear augmented Slatertype orbital method. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction The AlGaP alloy series has received much attention because it is useful for many applications, for example heterojunction bipolar transistors (HBTs) [1], light emitting diodes (LEDs) [2], and waveguides [3]. To properly design these devices, it is important to know the optical properties of materials, such as dielectric function e and critical point (CP) energies. Several experimental studies of the optical properties of AlP have been reported [4–8]. The fundamental (indirect) absorption edge [4–7] and the lowest direct band gap (E0) [7] of AlP are known. Grimmeiss et al. [4] measured reflectance and transmittance from 2 to 3.5 eV, Lorenz et al. [5] performed transmittance measurements from 2 to 3 eV, and Monemar measured transmittance [6] and photoluminescence [7] below 3.1 eV and from 2 to 3.5 eV, respectively. However, these previous reports presented the CP information of AlP only over the limited spectral range E<  3.5 eV. We had previously reported e of AlP from 0.75 to 5.05 eV obtained with spectroscopic ellipsometry (SE) [8]. However, the investigation of CPs, which were obtained by parametric model (PM) analysis and identified by comparing them to the CPs of silicon, can be improved [8]. In particular, the spectral range was insufficient to access the CPs above 5 eV that were predicted by band-structure calculations [9–11]. These calculations include those of Stukel et al. [9], Tsay et al. [10], and Huang et al. ⇑ Corresponding author. Tel.: +82 2 961 0525; fax: +82 2 957 8408. E-mail address: [email protected] (Y.D. Kim). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.10.205

[11], who used the self-consistent orthogonalized-plane-wave model, the empirical pseudopotential method, and the semi-ab initio orthogonalized linear combination of atomic orbital method, respectively. In this work we use in situ SE to determine e of AlP over the significantly wider spectral range of 0.74–6.54 eV. We extract e and identify the indirect band gap and the direct CPs E0, E00 , E1, E01 , E2, and E02 . We obtain accurate energies of these CPs by lineshape fitting of numerically calculated second-energy-derivatives. We identify each CP from the AlP band-structure calculated by the linear augmented Slater-type orbital (LASTO) method. However, we observe two CP features whose origins cannot be identified. 2. Experiment Owing to its high reactivity, removing oxides and preventing reoxidation of any Al-containing material is very difficult, even with complex chemical processing. However, by maintaining as-deposited materials in their original ultrahigh-vacuum (UHV) environments, in situ SE measurements provide a way around these difficulties. In situ SE measurements have been used to obtain accurate e spectra of many important materials, for example AlAs and AlSb [12,13]. Here, we take advantage of in situ SE measurements to obtain SE data on a film grown by molecular beam epitaxy (MBE), where the film was prepared and maintained in UHV. The AlP film was grown under conditions reported in our previous work [8], although to a greater thickness (1.2 lm) to ensure complete strain relaxation. Consequently, our optical data well approximate those of bulk material. Briefly, the AlP film was grown on a semi-insulating (0 0 1) GaAs substrate using by MBE. A GaAs buffer layer was first deposited. The AlP film was then grown at a temperature of 590 °C. The layers exhibited streaky reflection-high-energy-electron-diffraction (RHEED) patterns during growth, indicating that growth was laminar.

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When the film was thick enough, the sample was cooled to 300 K. SE data were then obtained using a rotating compensator ellipsometer [14]. The angle of incidence is 69.64°.

(a)

3. Results and discussion Fig. 1 shows our pseudodielectric-function hei data of AlP. The major CP structures E1 and E00 are easily seen. The oscillations in the energy region below about 3.7 eV are interference fringes resulting from back reflections from the substrate, a consequence of the fact that the film is essentially transparent below its fundamental E0 direct gap. We can see that the oscillation amplitude decreases above the indirect band gap energy. The magnitude of these oscillations confirms the quality of the film and its interfaces. To obtain e and determine the indirect band gap and CP energies more precisely, we constructed a multilayer model consisting of surface roughness, the AlP film, and the substrate. We used wellknown standard e values for GaAs substrate [15], while the PM [16] was applied for the analysis e of AlP film. Fig. 2(a) shows the PM spectrum (solid line) obtained as a best fit to the he2i data (open circles) above the semitransparent region. Seven CP components were used, as indicated by the dashed lines. Fig. 2(b) shows that the hei spectrum calculated in the multilayer model exactly follows the real (open circles) and imaginary (closed circles) hei data in the region of interference oscillations below the E0 direct gap due to the transparent characteristics of the AlP film in this spectral range. For clarity, the number of data points is reduced appropriately in both Fig. 2(a) and (b). The agreement proves the quality of the fit, verifying that the fitted thickness value of 1203 lm (±4.4 lm) for the AlP film agrees with the expected value (1.2 lm) during the growth. A fitted thickness of 1.25 lm (±1.09 lm) for the rough surface is also reasonable. Fig. 3 presents our final e spectrum of AlP. The CP energy parameters obtained from the PM are shown in Table 1. We enhance accuracy and better resolve the CP structures above the E0 feature by numerically calculating second-energyderivatives d2 hei/ dE2 of hei in Fig. 1 using the 11-point linear filtering algorithm of Savitzky and Golay [17]. We work here with hei rather than e to avoid possible modeling artifacts, noting that we have shown previously that CP energies obtained in this way are relatively unaffected by overlayers [18]. The calculated derivatives are then fit to the standard analytic CP expression [19,20].

1

0

(b)

Fig. 2. (a) Parametric model fit (solid line) to the he2i data (open circles) of Fig. 1 with seven CPs. The individual CP contributions are shown as the dashed lines. (b) Model calculations (solid lines) to the he1i (open circles) and he2i (closed circles) data in the region of interference oscillations below the E0 direct gap.

2

n2

d e=dx2 ¼ nðn  1ÞAei/ ðx  E þ iCÞ ¼ Aei/ ðx  E þ iCÞ

2

n–0 ð1Þ

The exponent n has the value 1, 1/2, 0, and 1/2 for excitonic, one-, two-, and three-dimensional CPs. E is energy, C is the broadening parameter, A is the amplitude, and / is the phase angle of the CP. Fig. 4 shows the calculated second-derivative spectra from 4 to 6.3 eV along with the best fits. The open circles are values determined from the he1i data, while the solid and dashed lines are the best fits to d2 h e1i/dE2 and d2 he2i/dE2, respectively. For clarity, the number of points for d2 he1i/dE2 is reduced appropriately and those for d2 he2i/dE2 are not shown. Six structures are resolved, and these are best represented by the excitonic lineshape (n = 1). The resulting CP energies are shown in Table 1. To confirm the Brillouin-zone (BZ) origins of these CPs, we performed band-structure calculations using the LASTO method [21,22] within the local density approximation. Self-energy corrections are included by the empirical tight-binding formula

kcv ðkÞ ¼ k0 þ k1

X X ð1Þ ð2Þ ejkRi þ k2 ejkRi i

ð1Þ

Fig. 1. Pseudodielectric function hei of the AlP film on GaAs at 300 K as determined by SE. The sample thickness is approximately 1.2 lm, which is well beyond the critical thickness of AlP for strain relaxation.

n¼0

ð2Þ

ð2Þ

i

where Ri and Ri run through the first and second nearest-neighbor lattice sites, respectively. The three adjustable parameters k0 , k1 , and k2 are determined by requiring that kcv ðkÞ at the C-, L-, and Xpoints of the BZ agree with data. The parameters used in this calculation are 0.449, 1.155, and 1.263 eV, respectively. Fig. 5 shows the calculated band-structure of AlP. The resulting CP energies are also listed in Table 1, together with results obtained by previous theoretical methods. It should be noted that in our LASTO calculations, we have included the spin–orbit interaction (even though it is not significant) and we have adopted an

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Table 1 CP energies (in eV) of AlP at 300 K obtained by various methods. Previously reported values are also listed. Values obtained from the LASTO band-structure calculations agree well with those obtained from the PM and from second-energy-derivatives of the e data itself. CP

Indirect band gap (C15t?X1c)

E0 A (C15t?C1c)

E1 (L3t?L1c)

E2 (X5t?X1c)

B E00 (C15t?C15c)

E02 (X5t?X3c)

E01 (L3t?L3c)

PM-derived 2nd-derivative analysis Band-structure calculation Previous experimental results

2.691 – 2.711 2.42(293 K)4) 2.45(300 K)5 2.52(6 K)5) 2.49(4 K)6) 2.41(300 k)6) 2.505(4 K)7) 2.149) 2.4910) 2.5111)

3.681 – 3.681 3.63(4 K)7)

4.126 4.105 – –

4.611 4.574 4.574 –

4.732 4.824 4.824 –

4.921 5.099 4.915 –

– 5.352 – –

5.778 5.901 5.741 –

6.587 – 6.643 –

3.279) 3.6010) 3.7411)

–

3.759) 4.1510) 4.3711)

4.229) 4.7510) 4.7811)

4.799) 5.6010) 5.0911)

–

4.969) 6.089) 5.2510)6.5711) 6.6510)7.2111)

Previous theoretical results

(a)

6

30 4

L

E 1' E2'

2

Energy (eV)

20

<εε1>

L

10

0

This work Ref. 8

E1

0

band gap

E2

L

-2 -4 -6

-10

-8

123456 (b)

eV

30

-10 L

<εε2>

E0

E0' indirect

Γ

Χ

K

Γ

AIP

20

Fig. 5. Energy band-structure of AlP calculated by the LASTO method. The CPs identified in the optical spectra are indicated by arrows.

10 This work Ref. 8 0 1

2

3

4

5

6

eV Fig. 3. Solid lines: (a) e1 and (b) e2 of AlP. The dashed lines show the result from Ref. [8].

E1

E2

4. Conclusions

E0'

B

We report SE data of AlP over the spectral range of 0.74– 6.54 eV, which is much wider than in previous work. We extract e and identify the indirect band gap and the direct critical points E0, E00 , E1, E01 , E2, and E02 . We observe two CP features, however, whose BZ origins cannot be identified. These results will be useful in a number of contexts, including the design of optoelectronic devices based on AlP for industrial purpose. A more detailed understanding of the band-structure of AlP has also been achieved.

E2'

2

d <εε>/dE

2

A

4

empirical k-dependent self-energy correction, which fits the experimental data at U-, L-, and X-points. Consequently, the CP energies obtained by our model have better over-all agreement with experimental values at all CPs than previous calculations. Four CPs above E0 are identified as E00 , E1, E2, and E02 , respectively. However, the BZ locations of the CPs found at 4.105 and 5.352 eV could not be determined from the current LASTO band-structure calculation. Similar cases have been reported previously [23–26]. Accordingly, we simply labeled these CPs as A and B. Further studies are needed to identify their BZ origins.

5

6

eV Fig. 4. Open circles: second-energy-derivative spectrum from 4 to 6.3 eV numerically calculated from the he1i data. The solid and dashed lines represent best-fit second-energy-derivatives to he1i and he2i, respectively.

Acknowledgments This work was supported by the World Class University program through the Korea Science and Engineering Foundation funded by the Ministry of Education, Science, and Technology (MEST) under Grant R33-2008-0000-10118-0 and by the Basic Sci-

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ence Research Program through the National Research Foundation of Korea (NRF) funded by the MEST (2010-0005640). This work was also supported by the NRF grant funded by the Korea government (MSIP) (2013-016297). J.D.S acknowledges support from the KIST institutional program including dream project, partially by 2012K001280, and by the GRL Program through MEST. Y.C.C was supported by Grant NSC-101-2112-M-001-024-MY3 of the Republic of China. We thank D.E. Aspnes for useful discussions. References [1] T.E. Zipperian, L.R. Dawson, J. Appl. Phys. 54 (1983) 6019–6025. [2] V.A. Odnoblyudov, C.W. Tu, Appl. Phys. Lett. 89 (2006) 191107. [3] T. Tanabe, K. Suto, T. Saito, T. Kimura, Y. Oyama, J. Nishizawa, J. Appl. Phys. 93 (2003) 43–46. [4] H.G. Grimmeiss, W. Kischio, A. Rabenau, J. Phys. Chem. Solid 16 (1960) 302– 309. [5] M.R. Lorenz, R. Chicotka, G.D. Pettit, P.J. Dean, Solid State Commun. 8 (1970) 693–697. [6] B. Monemar, Solid State Commun. 8 (1970) 1295–1298. [7] B. Monemar, Phys. Rev. B 8 (1973) 5711–5718. [8] Y.W. Jung, J.S. Byun, S.Y. Hwang, Y.D. Kim, S.H. Shin, J.D. Song, Thin Solid Films 519 (2011) 8027–8029. [9] D.J. Stukel, R.N. Euwema, Phys. Rev. 186 (1969) 754–757.

[10] Y.F. Tsay, A.J. Corey, S.S. Mitra, Phys. Rev. B 12 (1975) 1354–1357. [11] M.-Z. Huang, W.Y. Ching, J. Phys. Chem. Solids 46 (1985) 977–995. [12] C.M. Herzinger, H. Yao, P.G. Snyder, F.G. Celii, Y.-C. Kao, B. Johs, J.A. Woollam, J. Appl. Phys. 77 (1995) 4677–4687. [13] Y.W. Jung, T.H. Ghong, J.S. Byun, Y.D. Kim, H.J. Kim, Y.C. Chang, S.H. Shin, J.D. Song, Appl. Phys. Lett. 94 (2009) 231913. [14] M2000 DI™, J.A. Woolam, Co. Inc., USA. [15] D.E. Aspnes, A.A. Studna, Phys. Rev. B 27 (1983) 985–1009. [16] B. Johs, C.M. Herzinger, J.H. Dinan, A. Cornfeld, J.D. Benson, Thin Solid Films 313 (1998) 137–142. [17] A. Savitzky, M.J.E. Golay, Anal. Chem. 36 (1964) 1627–1639. [18] Y.W. Jung, T.H. Ghong, Y.D. Kim, D.E. Aspnes, Appl. Phys. Lett. 91 (2007) 121903. [19] M. Cardona, Modulation spectroscopy, in: F. Seitz, D. Turnbull, H. Ehrenreich (Eds.), Supplement 11 of Solid State Physics, Academic, New York, 1969. [20] D.E Aspnes, Handbook on semiconductors, in: M. Balkanski (Ed.), vol. 16, North Holland, Amsterdam, 1980, p. 109. [21] J.W. Davenport, Phys. Rev. B 29 (1984) 2896–2904. [22] Y.-C. Chang, R.B. James, J.W. Davenport, Phys. Rev. B 73 (2006) 035211. [23] S. Zollner, M. Garriga, J. Humlicˇek, S. Gopalan, M. Cardona, Phys. Rev. 43 (1991) 4349–4360. [24] P. Lautenschlager, S. Logothetidis, L. Vina, M. Cardona, Phys. Rev. 32 (1985) 3811–3818. [25] S. Zollner, M. Garriga, J. Kircher, J. Humlicˇek, M. Cardona, Phys. Rev. 48 (1993) 7915–7929. [26] S. Logothetidis, J. Petalas, M. Cardona, T.D. Moustakas, Phys. Rev. 50 (1994) 18017–18029.