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Dielectric response of AlP by in-situ ellipsometry
Thin Solid Films 519 (2011) 8027–8029
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Dielectric response of AlP by in-situ ellipsometry Y.W. Jung a, J.S. Byun a, S.Y. Hwang a, Y.D. Kim a,⁎, S.H. Shin b, J.D. Song b a b
Nano-Optical Property Laboratory and Department of Physics, Kyung Hee University, Seoul 130-701, Republic of Korea Nano Photonics Research Center, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea
a r t i c l e
i n f o
Article history: Received 2 November 2010 Received in revised form 9 June 2011 Accepted 9 June 2011 Available online 15 June 2011 Keywords: Aluminum phosphide Dielectric response Semiconductor parametric model Molecular beam epitaxy Ellipsometry
a b s t r a c t We present and analyze pseudodielectric function data bεN = bε1N + ibε2N of AlP from 0.75 to 5.05 eV. The sample is a 1.0 μm thick AlP film grown on (001) GaAs by molecular beam epitaxy (MBE). Spectroscopic ellipsometric data were obtained before removing the sample from the MBE chamber to avoid oxidation and related artifacts. Analysis of interference oscillations and corrections for overlayer effects with a multilayer parametric model yield the closest representation to date of the intrinsic bulk dielectric response ε of AlP. From this analysis we obtain the energies of the E0′ and E1 critical points of AlP. © 2011 Elsevier B.V. All rights reserved.
1. Introduction AlP is the binary endpoint of the III–V compound-semiconductor alloys AlGaP, which are useful for optoelectronic-device applications [1–4]. Consequently, the optical properties of AlGaP have been studied extensively by many methods, including photoluminescence, cathodoluminescence, electroreflectance, and ellipsometry [5–15]. Many previous reports discussed the fundamental absorption edges and the E0 direct bandgaps [5–10], and some also treat the above-bandgap critical points (CPs) [11–15]. Here, we report data on the intrinsic dielectric response ε of AlP, and use these data to identify and obtain accurate values of the CP energies of the E0′ and E2 CPs. These data extend from 0.75 to 5.05 eV, and provide the missing endpoint of our previous work on the AlGaP alloy series [12]. These data are obtained by spectroscopic ellipsometry (SE), which is a well-known method of obtaining pseudodielectric function data bεN = bε1N + ibε2N directly without the need of Kramers–Kronig analysis [16]. However, SE data are strongly affected by overlayers such as surface oxides. Hence for bεN to provide an accurate representation of ε of any given material, it is essential to ensure the complete absence of surface overlayers [17]. This is particularly difficult for alloys with high Al concentrations, even with complex chemical processing, owing to the strong affinity of Al for oxygen. We address the reactivity issue by maintaining the AlP sample in the ultrahigh-vacuum molecular beam epitaxy (MBE) environment in which it was grown. In situ measurements have already been used to
obtain accurate values of ε for many important materials, for example AlAs and AlSb [18,19]. Using this approach along with appropriate analyses of bεN, we obtain ε data of similar accuracy for AlP. 2. Experiment Our AlP film was grown on a semi-insulating (001) GaAs substrate in a Riber compact 21E solid source MBE system with a rotating sample stage for uniform film growth. The substrate was first heated to 620 °C under As4 to remove surface oxides. A GaAs buffer layer approximately 200 nm thick was then grown at 580 °C. This was followed by the growth of an approximately 144 nm thick AlP layer at 480 °C. The substrate temperature was then increased to 590 °C during the rest of the growth of AlP. The total AlP film thickness is approximately 1.0 μm. While the reflection high energy electron diffraction pattern of the AlP grown at 480 °C was dim and spotted, that of the AlP grown at 590 °C was streaky. Since a thickness of 1.0 μm is well beyond the critical thickness of AlP for strain relaxation, the optical data obtained in this work well approximate those of bulk material. During cooldown, P2 exposure was terminated at 350 °C. When the sample had cooled to 300 K, bεN data were obtained from 0.75 to 5.05 eV using a rotatingcompensator instrument (J. A. Woollam, M-2000). Measurements were performed through strain-free windows to prevent distortion of the polarization states of the incoming and outgoing beams. The angle of incidence was 69.1°. 3. Results and discussion
⁎ Corresponding author. E-mail address: [email protected] (Y.D. Kim). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.06.015
The bεN data are shown in Fig. 1. The oscillations below about 3.8 eV are the result of interference from back-reflections from the substrate in
8028
Y.W. Jung et al. / Thin Solid Films 519 (2011) 8027–8029
30
40
AlP
30
<ε>
20
20
10
0
10
<ε1>
0 -10
<ε2>
-10 2
1
3
5
4
Energy (eV) Fig. 1. Measured pseudodielectric function spectrum bεN at 300 K for an AlP film grown on GaAs.
the energy region where the film is transparent. These oscillations are well defined, confirming the quality of the film and its interfaces. To obtain the dielectric response of AlP directly, we first constructed a representation of ε using the parametric-model (PM) approach [20]. In the PM, ε is written as the summation of m energybounded, Gaussian-broadened polynomials, with P additional poles to account for index-of-refraction effects caused by absorption outside the region being modeled: ε ðωÞ = ε 1 ðωÞ + iε2 ðωÞ m
E max
= 1 + i ∑ ∫E j=1
m + P + 1 ∑ Wj ðEÞΦ ℏω; E; σj + j=m + 1
min
Aj ðℏωÞ2 −Ej2
: ð1Þ
Here, W(E) includes the joint density of states. The complex broadening function Ф is typically either Lorentzian or Gaussian. Each CP is described by 9 parameters, as depicted in Fig. 2 for the imaginary part of ε of a single CP. EC is the CP energy, while EL and EU are the end points. ELM and EUM are two control points for establishing the asymmetric characteristics of the lineshape. ALM, A, and AUM are the respective amplitudes at ELM, EC, and EUM. To construct the lineshape of a given CP, second- and fourth-order polynomials were used for the energy regions (I, IV) and (II, III), respectively, with the constraints that the lines connect smoothly and with values forced to zero at the boundaries EL and EU. Therefore, the PM can describe asymmetric behavior not only at the direct band gap of the E0 edge but also at higher CPs without generating negative values of bε2N. The corresponding real part of ε is obtained by a Kramers–Kronig transform of the result, with an extra parameter used for the baseline. A detailed discussion is given in Ref. [20].
Fig. 3a shows the PM spectrum (solid line) obtained as a best fit to the data (open circles) in the energy range above 3.8 eV. For clarity, only one out of every 10 data points is shown. Four CPs, with contributions indicated by the dashed lines, were used in the model. According to Ref. [21], the lowest absorption edge of AlP is indirect. This is supported by the unusually long energy range between the onset of attenuation of the interference oscillations and their extinction. We represented this absorption tail by an asymmetric CP, which we label “unassigned CP”. It serves the function of describing optical absorption in the region between the indirect edge and the first strong CPs, which occur at 4.5 and 4.7 eV, respectively. As AlP is the III–V analog of Si, these should occur some 1 eV above the equivalent transitions of Si [22]. The lowestenergy strong CPs in Si are at 3.33 and 3.41 eV, and are due to E0′ and E1 transitions, respectively. Thus we make the corresponding assignments for AlP. The next strong transitions are due to the E2 CP cluster, which occurs near 4.24 eV in Si and thus should appear near 5.5 eV in AlP. For this reason we assign the 5.48 eV CP to E2, although because the actual structure lies outside our accessible energy range the actual energy is uncertain. However, the assignment is consistent with the data reported in Refs. [23] and [24]. Owing to their small oscillator strengths, we do not expect to observe the E0 and E0 + Δ0 CPs, which again by analogy to Si are expected to occur in a spectral region where absorption is already very strong [25]. Although there are several reported band-structure calculations of AlP [21,26–28], the CP assignments vary and are not always consistent with ours. A critical test of these band structures is their ability to reproduce the known CP data for Si, and there are numerous differences here as well. The discrepancy between our CP assignments here and the extrapolated assignments obtained by regression analysis in Ref.
a
b
A
AUM
ALM
I EL
II III IV ELM EC EUM
EU
E (eV) Fig. 2. Unbroadened CP structure described by 4 component polynomials I, II, III, and IV.
Fig. 3. (a) Parametric model fit (solid line) to the bε2N data (open circles) of Fig. 1, assuming four CPs. The contributions of the individual CPs are shown as the dashed lines. (b) Model calculations (solid lines) to the bε1N (closed circles) and bε2N (open circles) data in the region of interference oscillations.
Y.W. Jung et al. / Thin Solid Films 519 (2011) 8027–8029 Table 1 Parameters of the 4 CPs that construct bεN of AlP. CP no.
Unassigned CP
E0 ′
E1
E2
Ec (eV) A EL (eV) EU (eV) B (meV) ELM (eV) ALM EUM (eV) AUM
4.105 1.740 2.578 4.594 37.665 0.034 0.006 0.265 0.280
4.594 35.316 4.105 4.711 74.021 0.987 0.291 0.427 0.024
4.711 39.036 4.594 5.481 145.067 0.353 0.964 0.617 0.327
5.481 57.432 4.711 5.500 238.712 0.596 0.425 0.700 0.400
[12] is also interesting. Owing to the high reactivity of Al these were based on dielectric-function data of AlxGa1 − xP alloys for x ≤ 0.52. They were also obtained by assuming a linear variation of CP energies with x. In fact the energy dependences are quite nonlinear, as seen for example for the E1 transition of AlxGa1 − xAs [29]. Although for x b 0.5 linear fits are reasonable, extrapolations to AlP are obviously not as accurate as those obtained directly from data. Returning to the intrinsic dielectric function of AlP, our model spectrum allows us to compensate for overlayer effects and to analyze the interference oscillations to obtain information about the indirect edge. We fit these oscillations using a four-phase (ambient/roughness/ film/substrate) model, where the film thickness is used as an adjustable parameter. Surface roughness was modeled by the effective-medium approximation (EMA): N ε−εh ε −εh = ∑ fi i : ε + 2εh εi + 2εh i=0
ð2Þ
Here, εi and fi are the dielectric function and volume fraction of the i th constituent, and ε and εh are the effective dielectric functions of the mixture and host materials. In the Bruggeman EMA [30] εh = ε, and we assume that the surface-roughness layer can be treated as an equal mixture (f = 0.5) of AlP and void. This is the standard approach for describing the dielectric response of a rough surface. Fig. 3b shows that the resulting calculation of bεN (solid lines) follows the bε1N (closed circles) and bε2N (open circles) data exactly. This demonstrates both the validity of the model and the quality of the fit. The calculated thickness of the roughness layer is 14 Å, a meaningful result for epitaxial thin films. The parameters obtained from Fig. 3 are listed in Table 1. The values ELM and EUM do not represent absolute energy positions but are rather differences relative to EC. B corresponds to the full-width-halfmaximum broadening parameter of harmonic-oscillator lineshapes. The intrinsic dielectric response of AlP extracted from our data, taking the rough surface into account, is given as the solid line in Fig. 4. In
the inset, bε2N below 3.2 eV is enlarged to give a better indication of the absorption edge. We note that the 2.6 eV estimate that we obtain for the indirect gap is similar to theoretical estimates reported in Refs. [21,26,27]. However, our value is obtained by minimizing differences between the parametric model and data. We believe that the present results represent the best currently available approximation to the bulk dielectric function of AlP. 4. Conclusions We report the intrinsic dielectric response ε of AlP, obtained from the analysis of in situ SE data of an AlP thin film grown on GaAs. The spectral range is 0.75 to 5.05 eV. Oxidation artifacts were avoided by performing our measurements before the sample was removed from the MBE growth chamber. Optical modeling was used to extract ε from interference oscillations in the region of transparency. We obtained the energies of the E0′ and E1 CPs of AlP from this analysis. Parameters describing CPs are also reported so values of the dielectric function may be obtained at arbitrary wavelengths. Acknowledgment This work was supported by the National Research Laboratory (NRL) through the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (2010-008026) and the Mid-career Researcher Program (MEST) (2010-000508). We thank D. E. Aspnes for useful discussions. The researchers in KIST acknowledge the support from Institutional program of KIST. References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
15
40
1
[20]
2
[21] [22] [23]
10
30
5
x20 0 0.8
1.4
2.0
2.6
[24]
3.2
20
[25] [26] [27] [28] [29]
1
10 2
0 3.2
[30]
3.8
4.4
5.0
Energy (eV) Fig. 4. ε1 and ε2 of AlP obtained from the 4-phase (ambient/roughness/AlP/GaAs) model. The spectral dependence of ε2 below 3.2 eV is enlarged in the inset.
8029
J.N. Baillargeon, K.Y. Cheng, K.C. Hsieh, G.E. Stillman, J. Appl. Phys. 68 (1990) 2133. V.A. Odnoblyudov, C.W. Tu, Appl. Phys. Lett. 89 (2006) 191107. T.E. Zipperian, L.R. Dawson, J. Appl. Phys. 54 (1983) 6019. M.E. Overberg, G.T. Thaler, R.M. Frazier, C.R. Abernathy, S.J. Pearton, R. Rairigh, J. Kelly, N.A. Theodoropoulou, A.F. Hebard, R.G. Wilson, J.M. Zavada, J. Appl. Phys. 93 (2003) 7861. J.L. Merz, R.T. Lynch, J. Appl. Phys. 39 (1968) 1988. M.R. Lorenz, R. Chicotka, G.D. Pettit, P.J. Dean, Solid State Commun. 8 (1970) 693. B. Monemar, Solid State Commun. 8 (1970) 1295. H.G. Grimmeiss, W. Kischio, A. Rabenau, J. Phys. Chem. Solid 16 (1960) 302. H. Sonomura, T. Nanmori, T. Miyauchi, Appl. Phys. Lett. 24 (1974) 77. B. Monemar, Phys. Rev. B 8 (1973) 5711. J.M. Rodríguez, G. Armelles, J. Appl. Phys. 69 (1991) 965. S.G. Choi, Y.D. Kim, S.D. Yoo, D.E. Aspnes, D.H. Woo, S.H. Kim, J. Appl. Phys. 87 (2000) 1287. J.M. Rodríguez, G. Armelles, P. Salvador, J. Appl. Phys. 66 (1989) 3929. D.P. Bour, J.R. Shealy, A. Ksendzov, F. Pollak, J. Appl. Phys. 64 (1988) 6456. A. Onton, R.J. Chicotka, J. Appl. Phys. 41 (1970) 4205. R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarized Light, North-Holland, New York, 1977. D.E. Aspnes, A.A. Studna, Appl. Phys. Lett. 39 (1981) 316. 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. 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. B. Johs, C.M. Herzinger, J.H. Dinan, A. Cornfeld, J.D. Benson, Thin Solid Films 313 (1998) 137. M.-Z. Huang, W.Y. Ching, J. Phys. Chem. Solids 46 (1985) 977. A. Daunois, D.E. Aspnes, Phys. Rev. B 18 (1978) 1824. T.J. Kim, J.J. Yoon, S.Y. Hwang, D.E. Aspnes, Y.D. Kim, H.J. Kim, Y.C. Chang, J.D. Song, J. Appl. Phys. 95 (2009) 111902. T.J. Kim, J.J. Yoon, Y.W. Jung, S.Y. Hwang, T.H. Ghong, Y.D. Kim, H.J. Kim, Y.C. Chang, J. Appl. Phys. 97 (2010) 171912. D.E. Aspnes, A.A. Studna, Solid State Commun. 11 (1972) 1375. A.S. Poplavnoi, Fiz. Tverd. Tela 8 (1966) 2238 Sov. Phys.-Solid State 8 (1967) 1179. Y.F. Tsay, A.J. Corey, S.S. Mitra, Phys. Rev. B 12 (1975) 1354. D.J. Stukel, R.N. Euwema, Phys. Rev. 186 (1969) 754. Y.W. Jung, T.J. Kim, J.J. Yoon, Y.D. Kim, D.E. Aspnes, J. Appl. Phys. 104 (2008) 013515. D.E. Aspnes, Thin Solid Films 89 (1982) 249.
Contents lists available at ScienceDirect
Thin Solid Films j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / t s f
Dielectric response of AlP by in-situ ellipsometry Y.W. Jung a, J.S. Byun a, S.Y. Hwang a, Y.D. Kim a,⁎, S.H. Shin b, J.D. Song b a b
Nano-Optical Property Laboratory and Department of Physics, Kyung Hee University, Seoul 130-701, Republic of Korea Nano Photonics Research Center, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea
a r t i c l e
i n f o
Article history: Received 2 November 2010 Received in revised form 9 June 2011 Accepted 9 June 2011 Available online 15 June 2011 Keywords: Aluminum phosphide Dielectric response Semiconductor parametric model Molecular beam epitaxy Ellipsometry
a b s t r a c t We present and analyze pseudodielectric function data bεN = bε1N + ibε2N of AlP from 0.75 to 5.05 eV. The sample is a 1.0 μm thick AlP film grown on (001) GaAs by molecular beam epitaxy (MBE). Spectroscopic ellipsometric data were obtained before removing the sample from the MBE chamber to avoid oxidation and related artifacts. Analysis of interference oscillations and corrections for overlayer effects with a multilayer parametric model yield the closest representation to date of the intrinsic bulk dielectric response ε of AlP. From this analysis we obtain the energies of the E0′ and E1 critical points of AlP. © 2011 Elsevier B.V. All rights reserved.
1. Introduction AlP is the binary endpoint of the III–V compound-semiconductor alloys AlGaP, which are useful for optoelectronic-device applications [1–4]. Consequently, the optical properties of AlGaP have been studied extensively by many methods, including photoluminescence, cathodoluminescence, electroreflectance, and ellipsometry [5–15]. Many previous reports discussed the fundamental absorption edges and the E0 direct bandgaps [5–10], and some also treat the above-bandgap critical points (CPs) [11–15]. Here, we report data on the intrinsic dielectric response ε of AlP, and use these data to identify and obtain accurate values of the CP energies of the E0′ and E2 CPs. These data extend from 0.75 to 5.05 eV, and provide the missing endpoint of our previous work on the AlGaP alloy series [12]. These data are obtained by spectroscopic ellipsometry (SE), which is a well-known method of obtaining pseudodielectric function data bεN = bε1N + ibε2N directly without the need of Kramers–Kronig analysis [16]. However, SE data are strongly affected by overlayers such as surface oxides. Hence for bεN to provide an accurate representation of ε of any given material, it is essential to ensure the complete absence of surface overlayers [17]. This is particularly difficult for alloys with high Al concentrations, even with complex chemical processing, owing to the strong affinity of Al for oxygen. We address the reactivity issue by maintaining the AlP sample in the ultrahigh-vacuum molecular beam epitaxy (MBE) environment in which it was grown. In situ measurements have already been used to
obtain accurate values of ε for many important materials, for example AlAs and AlSb [18,19]. Using this approach along with appropriate analyses of bεN, we obtain ε data of similar accuracy for AlP. 2. Experiment Our AlP film was grown on a semi-insulating (001) GaAs substrate in a Riber compact 21E solid source MBE system with a rotating sample stage for uniform film growth. The substrate was first heated to 620 °C under As4 to remove surface oxides. A GaAs buffer layer approximately 200 nm thick was then grown at 580 °C. This was followed by the growth of an approximately 144 nm thick AlP layer at 480 °C. The substrate temperature was then increased to 590 °C during the rest of the growth of AlP. The total AlP film thickness is approximately 1.0 μm. While the reflection high energy electron diffraction pattern of the AlP grown at 480 °C was dim and spotted, that of the AlP grown at 590 °C was streaky. Since a thickness of 1.0 μm is well beyond the critical thickness of AlP for strain relaxation, the optical data obtained in this work well approximate those of bulk material. During cooldown, P2 exposure was terminated at 350 °C. When the sample had cooled to 300 K, bεN data were obtained from 0.75 to 5.05 eV using a rotatingcompensator instrument (J. A. Woollam, M-2000). Measurements were performed through strain-free windows to prevent distortion of the polarization states of the incoming and outgoing beams. The angle of incidence was 69.1°. 3. Results and discussion
⁎ Corresponding author. E-mail address: [email protected] (Y.D. Kim). 0040-6090/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2011.06.015
The bεN data are shown in Fig. 1. The oscillations below about 3.8 eV are the result of interference from back-reflections from the substrate in
8028
Y.W. Jung et al. / Thin Solid Films 519 (2011) 8027–8029
30
40
AlP
30
<ε>
20
20
10
0
10
<ε1>
0 -10
<ε2>
-10 2
1
3
5
4
Energy (eV) Fig. 1. Measured pseudodielectric function spectrum bεN at 300 K for an AlP film grown on GaAs.
the energy region where the film is transparent. These oscillations are well defined, confirming the quality of the film and its interfaces. To obtain the dielectric response of AlP directly, we first constructed a representation of ε using the parametric-model (PM) approach [20]. In the PM, ε is written as the summation of m energybounded, Gaussian-broadened polynomials, with P additional poles to account for index-of-refraction effects caused by absorption outside the region being modeled: ε ðωÞ = ε 1 ðωÞ + iε2 ðωÞ m
E max
= 1 + i ∑ ∫E j=1
m + P + 1 ∑ Wj ðEÞΦ ℏω; E; σj + j=m + 1
min
Aj ðℏωÞ2 −Ej2
: ð1Þ
Here, W(E) includes the joint density of states. The complex broadening function Ф is typically either Lorentzian or Gaussian. Each CP is described by 9 parameters, as depicted in Fig. 2 for the imaginary part of ε of a single CP. EC is the CP energy, while EL and EU are the end points. ELM and EUM are two control points for establishing the asymmetric characteristics of the lineshape. ALM, A, and AUM are the respective amplitudes at ELM, EC, and EUM. To construct the lineshape of a given CP, second- and fourth-order polynomials were used for the energy regions (I, IV) and (II, III), respectively, with the constraints that the lines connect smoothly and with values forced to zero at the boundaries EL and EU. Therefore, the PM can describe asymmetric behavior not only at the direct band gap of the E0 edge but also at higher CPs without generating negative values of bε2N. The corresponding real part of ε is obtained by a Kramers–Kronig transform of the result, with an extra parameter used for the baseline. A detailed discussion is given in Ref. [20].
Fig. 3a shows the PM spectrum (solid line) obtained as a best fit to the data (open circles) in the energy range above 3.8 eV. For clarity, only one out of every 10 data points is shown. Four CPs, with contributions indicated by the dashed lines, were used in the model. According to Ref. [21], the lowest absorption edge of AlP is indirect. This is supported by the unusually long energy range between the onset of attenuation of the interference oscillations and their extinction. We represented this absorption tail by an asymmetric CP, which we label “unassigned CP”. It serves the function of describing optical absorption in the region between the indirect edge and the first strong CPs, which occur at 4.5 and 4.7 eV, respectively. As AlP is the III–V analog of Si, these should occur some 1 eV above the equivalent transitions of Si [22]. The lowestenergy strong CPs in Si are at 3.33 and 3.41 eV, and are due to E0′ and E1 transitions, respectively. Thus we make the corresponding assignments for AlP. The next strong transitions are due to the E2 CP cluster, which occurs near 4.24 eV in Si and thus should appear near 5.5 eV in AlP. For this reason we assign the 5.48 eV CP to E2, although because the actual structure lies outside our accessible energy range the actual energy is uncertain. However, the assignment is consistent with the data reported in Refs. [23] and [24]. Owing to their small oscillator strengths, we do not expect to observe the E0 and E0 + Δ0 CPs, which again by analogy to Si are expected to occur in a spectral region where absorption is already very strong [25]. Although there are several reported band-structure calculations of AlP [21,26–28], the CP assignments vary and are not always consistent with ours. A critical test of these band structures is their ability to reproduce the known CP data for Si, and there are numerous differences here as well. The discrepancy between our CP assignments here and the extrapolated assignments obtained by regression analysis in Ref.
a
b
A
AUM
ALM
I EL
II III IV ELM EC EUM
EU
E (eV) Fig. 2. Unbroadened CP structure described by 4 component polynomials I, II, III, and IV.
Fig. 3. (a) Parametric model fit (solid line) to the bε2N data (open circles) of Fig. 1, assuming four CPs. The contributions of the individual CPs are shown as the dashed lines. (b) Model calculations (solid lines) to the bε1N (closed circles) and bε2N (open circles) data in the region of interference oscillations.
Y.W. Jung et al. / Thin Solid Films 519 (2011) 8027–8029 Table 1 Parameters of the 4 CPs that construct bεN of AlP. CP no.
Unassigned CP
E0 ′
E1
E2
Ec (eV) A EL (eV) EU (eV) B (meV) ELM (eV) ALM EUM (eV) AUM
4.105 1.740 2.578 4.594 37.665 0.034 0.006 0.265 0.280
4.594 35.316 4.105 4.711 74.021 0.987 0.291 0.427 0.024
4.711 39.036 4.594 5.481 145.067 0.353 0.964 0.617 0.327
5.481 57.432 4.711 5.500 238.712 0.596 0.425 0.700 0.400
[12] is also interesting. Owing to the high reactivity of Al these were based on dielectric-function data of AlxGa1 − xP alloys for x ≤ 0.52. They were also obtained by assuming a linear variation of CP energies with x. In fact the energy dependences are quite nonlinear, as seen for example for the E1 transition of AlxGa1 − xAs [29]. Although for x b 0.5 linear fits are reasonable, extrapolations to AlP are obviously not as accurate as those obtained directly from data. Returning to the intrinsic dielectric function of AlP, our model spectrum allows us to compensate for overlayer effects and to analyze the interference oscillations to obtain information about the indirect edge. We fit these oscillations using a four-phase (ambient/roughness/ film/substrate) model, where the film thickness is used as an adjustable parameter. Surface roughness was modeled by the effective-medium approximation (EMA): N ε−εh ε −εh = ∑ fi i : ε + 2εh εi + 2εh i=0
ð2Þ
Here, εi and fi are the dielectric function and volume fraction of the i th constituent, and ε and εh are the effective dielectric functions of the mixture and host materials. In the Bruggeman EMA [30] εh = ε, and we assume that the surface-roughness layer can be treated as an equal mixture (f = 0.5) of AlP and void. This is the standard approach for describing the dielectric response of a rough surface. Fig. 3b shows that the resulting calculation of bεN (solid lines) follows the bε1N (closed circles) and bε2N (open circles) data exactly. This demonstrates both the validity of the model and the quality of the fit. The calculated thickness of the roughness layer is 14 Å, a meaningful result for epitaxial thin films. The parameters obtained from Fig. 3 are listed in Table 1. The values ELM and EUM do not represent absolute energy positions but are rather differences relative to EC. B corresponds to the full-width-halfmaximum broadening parameter of harmonic-oscillator lineshapes. The intrinsic dielectric response of AlP extracted from our data, taking the rough surface into account, is given as the solid line in Fig. 4. In
the inset, bε2N below 3.2 eV is enlarged to give a better indication of the absorption edge. We note that the 2.6 eV estimate that we obtain for the indirect gap is similar to theoretical estimates reported in Refs. [21,26,27]. However, our value is obtained by minimizing differences between the parametric model and data. We believe that the present results represent the best currently available approximation to the bulk dielectric function of AlP. 4. Conclusions We report the intrinsic dielectric response ε of AlP, obtained from the analysis of in situ SE data of an AlP thin film grown on GaAs. The spectral range is 0.75 to 5.05 eV. Oxidation artifacts were avoided by performing our measurements before the sample was removed from the MBE growth chamber. Optical modeling was used to extract ε from interference oscillations in the region of transparency. We obtained the energies of the E0′ and E1 CPs of AlP from this analysis. Parameters describing CPs are also reported so values of the dielectric function may be obtained at arbitrary wavelengths. Acknowledgment This work was supported by the National Research Laboratory (NRL) through the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (2010-008026) and the Mid-career Researcher Program (MEST) (2010-000508). We thank D. E. Aspnes for useful discussions. The researchers in KIST acknowledge the support from Institutional program of KIST. References [1] [2] [3] [4]
[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
15
40
1
[20]
2
[21] [22] [23]
10
30
5
x20 0 0.8
1.4
2.0
2.6
[24]
3.2
20
[25] [26] [27] [28] [29]
1
10 2
0 3.2
[30]
3.8
4.4
5.0
Energy (eV) Fig. 4. ε1 and ε2 of AlP obtained from the 4-phase (ambient/roughness/AlP/GaAs) model. The spectral dependence of ε2 below 3.2 eV is enlarged in the inset.
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