Optical properties of nanocrystalline silicon films deposited by plasma-enhanced chemical vapor deposition

Optical properties of nanocrystalline silicon films deposited by plasma-enhanced chemical vapor deposition

Optical Materials 30 (2007) 238–243 www.elsevier.com/locate/optmat Optical properties of nanocrystalline silicon films deposited by plasma-enhanced ch...

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Optical Materials 30 (2007) 238–243 www.elsevier.com/locate/optmat

Optical properties of nanocrystalline silicon films deposited by plasma-enhanced chemical vapor deposition Atif Mossad Ali

*,1

Advanced Bio-Nano Devices Laboratory, Department of Bioengineering and Robotics, Tohoku University, 6-6-01 Aza-Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan Received 28 June 2006; accepted 8 November 2006 Available online 12 January 2007

Abstract Nanocrystalline silicon (nc-Si) films were deposited by a plasma-enhanced chemical vapor deposition technique using SiF4/SiH4/H2 gas mixtures. The optical properties of the nc-Si films were examined by varying the deposition temperature (Td) under two different hydrogen flow rate ([H2]) conditions. For these films, we found two photoluminescence (PL) spectra at around 1.7–1.75 eV and 2.2– 2.3 eV. The peak energy, EPL, of the 1.7–1.75-eV PL band was found to shift as Td or [H2] changes. It was found that the decrease in Td acts to decrease the average grain size, hdi, and to increase both the optical band gap, Eopt g , and the EPL values. By contrast, the increase in [H2] decreased the hdi value, while increased the values of Eopt g , and EPL. Thus, as either Td decreases or [H2] increases, it is found that a decrease in hdi corresponds well with increases in Eopt g and EPL. As a consequence, it was suggested that an increase of EPL of the 1.7–1.75-eV PL band can be connected with an increase in Eopt g , through a decrease in hdi. However, the PL process can not be connected with the transition between both the bands, related to formation of nanocrystals. Based on these results, it was proposed that the use of both low Td and high [H2] conditions would allow to grow nc-Si films with small grains. Ó 2006 Elsevier B.V. All rights reserved. PACS: 78; 78.20.e; 78.66.w Keywords: Nanocrystalline silicon; PECVD; Deposition temperature; Photoluminescence; Quantum-size effect; Effect of hydrogen addition

1. Introduction Recently, silicon is the main material of microelectronics, but it is not widely used in optoelectronics. The reason is to due to bulk silicon has an indirect optical gap and low photoluminescence (PL) efficiency. Nanocrystalline silicon (nc-Si) have been intensively studied in the last few years, because nc-Si is expected to exhibit a quantum size effect and therefore has a potential for application to optoelectronics. Several methods of creating PL thin films containing nc-Si have been reported [1–4]. Although there is a *

Tel.: +81 22 795 6909; fax: +81 22 795 6907. E-mail addresses: [email protected], [email protected] 1 Permanent address: Department of Physics, Faculty of Science, Assiut University, Assiut 71516, Egypt. 0925-3467/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.optmat.2006.11.042

large amount of research in the recent years, the mechanism underlying the visible luminescence is still unclear. There are two mechanisms, first one is the quantum confinement model and the second is the surface model, widely discussed to know the origin of PL. Fabrication of nc-Si films, having a highly efficient quantum-size effect, requires both a reduction in the grain size, d, and an enhancement in the crystalline volume fraction, q. Then, an increase in the nucleation rate would become a key technique to be developed. It has been reported that the enhanced nucleation on the growing surface during deposition of nc-Si can be achieved by increasing the hydrogen flow rate, [H2] [5,6], or the deposition temperature, Td [7]. However, the increase in Td also caused an increase in d. Thus, the increase in [H2] leads to reduction of d [5,6], while the increase in Td should lead to increase in d [7]. Furthermore,

A.M. Ali / Optical Materials 30 (2007) 238–243

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it has been reported that formation of nc-Si is due also to higher etching activity of hydrogen radicals for the amorphous phase than the crystalline one [8,9]. In the present work, we deposited nc-Si films using a plasma-enhanced chemical vapor deposition (PECVD) method. The purpose of this work is to make clear the causes affecting the optical properties, such as the PL spectra and the optical band gap, Eopt g , in connection with a change in d.

nent) and crystalline phases (520 cm1 component). The photoluminescence spectra were also measured using the above Raman system. The vibrational spectra were measured by a FTIR spectrometer (JASCO FT/IR-610) at a normal light incident. The optical transmission spectra were measured using an UV/VIS/NIR spectrophotometer (JASCO V-570).

2. Experimental

3.1. Results

Nc-Si films were deposited on Corning 7059 glass, (1 0 0) Si and fused quartz substrates by PECVD using a SiF4/ SiH4/H2 gas mixture. For SiF4, we used a SiF4 gas diluted with helium (95% He + 5% SiF4). In this paper, we represent the net flow rates of the SiF4 gas as [SiF4]. The substrates were cleaned for 20 min using nitrogen plasma and subsequently for 20 min using hydrogen plasma, just before deposition of nc-Si films. The samples were deposited on 0.3-mm-thick glass substrates for measurements of X-ray diffraction (XRD) and Raman scattering, on 0.3-mm-thick n-type (1 0 0) Si substrates with high resistivity of 1000–3000 X cm for measurements of Fourier transform infrared (FTIR) absorption, and on 0.3-mm-thick fused quartz substrates for measurements of PL and optical absorption. The films with two different series of thickness values were prepared by adjusting the deposition time: The thickness of one series was fixed at 0.37 (±0.03) lm for measuring the XRD, the Raman scattering, the PL, and the FTIR. In another series, we adopt a fixed value of 0.73 (±0.03) lm for measuring the optical absorption. The deposition temperature, Td, was varied from 95 °C to 250 °C. Other deposition conditions are summarized in Table 1. The average value, hdi, of the grain size d was estimated from the spectral width of the XRD using Scherrer’s formula [10], which will reflect those in the depth direction of the films. The Raman spectra were measured by a Raman spectrometer having a double monochrometer (Jobin Yvon RAMANOR HG 2S) coupled with a cooled photo-multiplier tube (Hamamatsu R649S) and having an Ar–ion laser light at 488 nm. The observed Raman spectra were divided into amorphous phase (480 cm1 compo-

Fig. 1 shows the peak frequency, ER, of the Raman signal arising from the crystalline Si (c-Si) phase for the nc-Si films, as a function of Td. As shown in Fig. 1, with an increase in Td, the ER increases and approaches a value around 522 cm1, which was observed for single c-Si by using the same Raman system with that in the present work. In addition, the increase in [H2] is found to increase the ER toward 522 cm1. Then, a decrease of ER in the range lower than 522 cm1 will reflect a change in d. Fig. 2 shows the deposition rates, Rd, for nc-Si films, as a function of the reciprocal values of Td. The Rd value increases with an increase in Td but decreases with an increase in [H2]. As revealed in Fig. 2, the relationship between Rd and Td can be expressed as follows:   DE Rd ¼ A exp  ; ð1Þ RT d

Feed gas Substrates [SiH4] [SiF4] [H2] Deposition temperature, (Td) Total gas pressure RF power (PRF)

SiF4/SiH4/H2 Glass (Corning 7059), Si (1 0 0) and fused quartz 0.60 sccm 0.38 sccm 30 or 46 sccm 95–250 °C 0.3 Torr 20 W

where A is a constant, DE the activation energy for film growth, and R the gas constant. Based on the results shown in Fig. 2, we find DE = 1.2 eV for [H2] = 30 sccm and DE = 3.3 eV for [H2] = 46 sccm. The Rd value can be controlled by a change in the self-diffusion coefficient of Si atoms. The high self-diffusion coefficient, which will increase with increasing Td under a given condition of the host-network, is expected to increase Rd. For self-diffusion in amorphous Si, the DE value has been reported to be

522

Peak Frequency, ER, (cm-1)

Table 1 Deposition parameters for growth of nc-Si films using PECVD method

3. Results and discussion

Single c-Si 521 520 519 518 [H2] = 30 sccm

517

[H2] = 46 sccm 516 80

100

120

140

160

180

200

220

240

260

Deposition Temperature (oC) Fig. 1. Peak frequency, ER, of the Raman signal arising from crystalline Si phases for nc-Si films, as a function of Td. Dashed line shows the value of ER for single c-Si. Solid lines are drawn as a visual guide.

A.M. Ali / Optical Materials 30 (2007) 238–243

2.5

1.2 eV

ln RD

2.0

3.3 eV 1.5

[H2] = 30 sccm [H2] = 46 sccm

1.0 1.8

2.2

2.0

2.4

2.6

2.8

-1

1000/Td (K ) Fig. 2. Logarithmic deposition rate, ln Rd, for nc-Si films, as a function of the reciprocal value of Td. The solid lines were drawn, using a method of the least square. The values shown on each solid line show the activation energy, DE, in film growth, obtained using Eq. (1).

Transmittance (r.u.)

2.8 eV [11], which is close to that found for the films with [H2] = 46 sccm. However, the value of DE = 1.2 eV, observed for [H2] = 30 sccm, appears to be too small for interpreting in terms of only a change in the self-diffusion coefficient. Fig. 3 illustrates the IR absorption spectra over the range 400–4000 cm1, which were measured under vacuum for nc-Si films with different Td and [H2] values. These spectra were measured within 2 days after deposition. As seen in Fig. 3, the absorption bands were observed at around 650, 800–900 and 2100 cm1, which are assigned to the wagging, bending and stretching motions of Si–H bonds, respectively. For the SiH stretching band, we can find three satellite lines at around 2090, 2100, and 2140 cm1. The intensity ratio of these three satellite lines is found to be independent of the deposition conditions of both [H2] and Td (=95 °C and 180 °C). Origins of these three lines are unknown, though the absorption band around

o

X 3.5

[H2] = 46 sccm, Td = 250 C

X 2.5

[H2] = 30 sccm, Td = 250o C

2100 cm1 is known to arise from dihydrides (Si–H2) [12]. The intensity of the spectra around 2100 cm1 is likely to decreases with increasing Td and/or [H2]. These Si–H2 bonds should exist in the grain boundary regions. We have proposed that Si–H2 bonds would be occupied in microvoid-like boundaries formed in nc-Si films, in a previous article [13]. The PL spectra observed for (a) nc-films with [H2] = 30 sccm and for (b) those with [H2] = 46 sccm under different Td conditions, as a function of photon energy, are plotted in Fig. 4. These spectra were observed at room temperature. In addition, the hd(1 1 1)i and hd(1 1 0)i values were shown for comparison. As seen in Fig. 4, the PL spectra have two separated lines at the peak energy, EPL, of 1.7–1.75 eV and 2.2–2.3 eV. The observed EPL values are similar to those found by Zhao et al. [14] and Edelberg et al. [4]. As demonstrated in previous works [13,15], the spectrum with EPL = 1.7–1.75 eV may be ascribed to nanometer size grains in nc-Si films [4], and that with EPL = 2.2– 2.3 eV may be due to defects related to oxygen [16], or to SiH-related bonds [17]. Fig. 5 shows (a) the optical band gap, Eopt g , and (b) EPL of the 1.7–1.75-eV band observed for nc-films, as a function of Td. The Eopt were deterg values pffiffiffiffiffiffiffiffiffiffiffi mined by drawing the Tauc plots, ðahmÞ versus ðhm  Eopt g Þ, using the optical absorption coefficient, a,

(δ <110>) = 18 nm

[H2] = 46 sccm, Td = 180 C

X2

[H2] = 30 sccm, Td = 180o C

X 1.5

[H2] = 46 sccm, Td = 95 C

X1

[H2] = 30 sccm, Td = 95o C

Td = 95 oC

19.7 nm

250 oC

14.3 nm (δ <111>) =

14.3 nm

180 oC

[H2 ] = 46 sccm

(δ <110>) = 17 nm

7.5 nm

Td = 95 oC

o

(Si-H) ben

2000

12.8 nm

18.2 nm 1.6

3000

180 oC

10.6 nm

(Si-H) str

(Si-H) wag 4000

9 nm

11.4 nm

o

X3

(δ <111>) = [H2 ] = 30 sccm

16 nm

PL Intensity (a.u.)

240

1000

400

Wavenumber (cm-1) Fig. 3. IR absorption spectra over the range 400–4000 cm1, which were measured under vacuum for nc-Si films with different Td and [H2] values.

1.8

2.0

2.2

250 oC 2.4

Photon Energy (eV) Fig. 4. Photoluminescence (PL) spectra for nc-Si films with (a) [H2] = 30 sccm and (b) [H2] = 46 sccm under different Td conditions, as a function of photon energy.

A.M. Ali / Optical Materials 30 (2007) 238–243 2.3

[H2] = 30 sccm

[ H2] = 46 sccm

2.1

g

E opt (eV)

2.2

2.0

EPL (eV)

1.75

1.74

1.73 100

150

200

Deposition Temperature

250

(oC)

Fig. 5. (a) Optical band gap, Eopt g , and (b) the peak energy, EPL, of the 1.7– 1.75-eV PL band observed for nc-Si films, as a function of Td. Solid lines are drawn as a visual guide.

observed at photon energy of hm. In these experiments, we used 0.73 (±0.03)-lm-thick films to eliminate an affection of thinner thickness. As revealed in Fig. 5, an increase in EPL corresponds well with an increase in Eopt g with varying Td or [H2], though the rates in the increase of EPL is considerably smaller than that of Eopt g . This result suggest that the radiative recombination between excited electron and hole pair, may be caused by states other than those at both the band edges. This will be discussed at a later stage again. In Fig. 4, we also notice that the absolute values of EPL = 1.7–1.75 eV and EPL = 2.2–2.3 eV are higher than the band gap for c-Si (1.12 eV at RT), though the values of both hd(1 1 1)i and hd(1 1 0)i for almost films are larger than 10 nm and 7 nm, respectively. Such large grains will have a characteristic similar to that of c-Si. As revealed in Figs. 4 and 5b, EPL of the 1.7–1.75-eV band increases with a decrease in Td, and appears to increase with increasing [H2]. On the other hand, the intensities of both the PL bands increase with a decrease in Td or an increase in [H2]. Thus, the dependence of EPL on Td or [H2] for the 1.7–1.75eV band is close to that of the PL intensity. This is because the oscillator strength of the 1.7–1.75-eV band may increase with a decrease in d, as shown theoretically by Stevens Kalceff and Phillips [18], that is, small grains will cause a relatively large PL spectrum, under a fixed density of grains. This supports an assignment that the 1.7–1.75-eV band may be ascribed to nanometer size grains in nc-Si films as stated above. Indeed, as seen in Figs. 4 and 5, the decrease in hdi is found to correspond well with an increase in EPL of the 1.7–1.75-eV band, along with an

241

increase in Eopt g . Thus, the characteristics of the 1.7–1.75eV PL band appear to be closely connected with a change in hdi, in agreement with a model proposed by Edelberg et al. [4]. This result implies a contribution of a quantum size effect to the PL spectra. Furthermore, note that the surface of small grains should be defined well, in order to obtain a PL emission from the small grains related to a quantum size effect. However, the values of EPL are larger than those inferred from the hdi values, as stated above. Next, we will discuss the origins causing such large EPL. The intensity of the emitted PL light should be obtained as the product of the number of grains and their respective oscillator strength values. If the PL process is controlled by small grains, the oscillator strength would increase with a decrease in d as stated above. On the other hand, grains with different d values will be distributed in the films. Then, the size of grains effective in the PL process should be smaller than the values of the average in d. Furthermore, in a previous article [15], we assumed a result that grains with smaller d values preferentially may exist in shallower layer of the films, then the above-mentioned relationship between hdi and EPL values is easy to be explained. The hdi values in Fig. 4 were estimated from the width values of the XRD spectra (Section 2). In the present work, since ˚ is used, the an X-ray light with the wavelength of 1.54 A penetration depth of the X-ray for Si is approximately 13 lm. On the other hand, the XRD signal from grains smaller than 3 nm can not be detected because of broadening of the spectrum. Therefore, the hdi values in Fig. 4 will give an average size of grains larger than 3 nm over the entire positions in 0.37-lm-thick films used (Section 2). This may also be one of reasons causing the observed values of hdi larger than those inferred from the EPL values as stated above. On the other hand, the penetration depth of a 488-nm Ar ion laser light, used for both the PL measurements and the Raman scattering, was approximately 0.5 lm. 3.2. Band gap based on simple theory As discussed in Section 3.1, the values of d contributing to the EPL and Eopt values are larger than the hdi values g obtained through the XRD measurements, because the former will become effective in smaller grains than those for the latter. In this section, we will discuss the band gap estimated using the shifts of the Raman spectra that will reflect the characteristics of the whole grains with different size as well as the PL and the optical absorption measurements. As shown in Fig. 1, the Raman peak arising from crystalline phases shifts toward a low frequency side with decreasing Td. Supposing that the peak shift is due only to the confinement of optical phonons in spherical nanocrystals, we can estimate the crystallite size in diameter, DR, as [4]: rffiffiffiffiffiffi B DR ¼ 2p ; ð2Þ Dm

242

A.M. Ali / Optical Materials 30 (2007) 238–243

where B is 2.24 cm1 nm2, and Dm the frequency shift in unit of cm1, which was defined as the difference between the observed peak-frequency value and 522 cm1. The latter value was observed for single crystal Si as described in Section 3.1. Fig. 6 shows a relationship between hd(1 1 1)i and hd(1 1 0)i, and DR. When we compared the results obtained under a given crystal direction and a given [H2], we can find a close correlation between the hdi and DR values. However, it is found that the absolute values of hdi observed are considerably larger than DR values and the rate in the increase of hdi are faster than that of DR, Furthermore, based on the results shown in Fig. 6, we find a relationship of hdi = 3.69DR  7.28 (nm) for the films with [H2] = 30 sccm and of hdi = 3.56DR  11.89 for the films with [H2] = 46 sccm, in the measurements under a direction of the h1 1 0i axis that is the dominant texture in the films. On the other hand, for the h1 1 1i texture, we find a relationship of hdi = 2.61DR + 4.48 for [H2] = 30 sccm and hdi = 2.64DR + 0.05 for [H2] = 46 sccm. These formulas were obtained by fitting the values of hdi vs. DR to a linear relationship, using a method of the least squares. As seen in these results, the linear relationships of hdi as a function of DR appear to be characterized by the crystal axis of grains, that is, the slope (3.63 ± 0.07) for the h1 1 0i texture is steeper than that (2.63 ± 0.02) for the h1 1 1i texture. In addition, as shown in Figs. 4 and 6, the sizes of the h1 1 0i grains are smaller than that of the h1 1 1i grains. As described in Section 3.1, the size of grains effective the XRD spectra, whose width determines the hdi values, would be larger than those inferred from the shifts of the Raman spectra, which reflect the characteristics of the whole grains with different d values. This is because grains smaller than 3 nm would be insensitive to the XRD spectra as stated above. This result may also explain the observation of a large intercept in the linear relationship of hdi vs. DR, as seen in Fig. 6.

Using the values of DR for the individual samples, we can evaluate the lowest excitation energy, E, under a simple confinement theory for electron and hole [4,19,20], as follows: E ¼ Eg þ

2p2 h2 3:572 e2  þ 0:284ERy ; er D R mr D2R

ð3Þ

where Eg is the energy gap of c-Si (1.12 eV at RT), mr is the reduced effective mass of an electron-hole pair, er is the dielectric constant, and ERy is the Rydberg energy for the bulk semiconductor. The value of E correspond to the band gap of the films. In the later two terms, 3.572e2/erDR corresponds to the coulomb term and 0.284ERy gives the spatial correlation energy. The later two terms are minor corrections, so we neglected them in the calculation used in this work, because the contribution of these two terms to the total energy will be less than 5% [4]. Fig. 7 shows the E values (a solid curve) obtained based on Eq. (3), as a function of R. In Fig. 7, the experimental values of Eopt g (closed symbols) and EPL (open symbols) shown in Fig. 5a and b, respectively, are also shown for comparison, as a function of R (R = DR/2 is the radius of crystals), through the values of DR obtained using the experimental Dm values along with Eq. (2). As shown in Fig. 7, we can find a qualitative agreement between the observed Eopt values (closed triangles and g closed circles) and a solid curve calculated using Eq. (3), though the former values are considerably larger than the latter. Furukawa and Miyasato [21] have found also similar

2.4

2.1

E, E g or EPL (eV)

1.8

<111>, [H2] = 30 sccm

24

<111>, [H2] = 46 sccm <110>, [H2] = 46 sccm

18

1.2

opt

Average Grain Size (nm)

<110>, [H2] = 30 sccm 21

1.5

0.9

Eq. (3) opt

E g at [H2] = 30 sccm

15

0.6

12

E opt at [H2] = 46 sccm g

EPL at [H2] = 30 sccm

0.3

EPL at [H2] = 46 sccm

9 0.0 0

6

1

2

3

4

5

6

7

R (nm) 0

2

4

6

8

DR (nm) Fig. 6. Relationship between the average grain size, hd(1 1 1)i and hd(1 1 0)i, as a function of the diameter of grains, DR, calculated using Eq. (2). The solid lines were drawn, using a method of the least square.

Fig. 7. Lowest excitation energy, E, as a function of radius of crystals R (a solid curve), obtained based on Eq. (3). In this diagram, the experimental values of Eopt values (closed symbols) and EPL (open g symbols) values, which were shown in Figs. 5a and 5b, respectively, are also shown for comparison, as a function of R (=DR/2) through the DR values obtained using the experimental Dm values along with Eq. (2).

A.M. Ali / Optical Materials 30 (2007) 238–243

discrepancy between the theoretical and experimental results, and interpreted the discrepancy in terms of a difference in the surface shape of grains as boundary conditions in both the theoretical and experimental process. On the other hand, the change of EPL as a function of R is considerably smaller than those of E and Eopt g though the trend of the changes for EPL agreed with that for Eopt as shown in g Fig. 5. This result indicates that the PL process of the 1.7–1.75-eV band can not be connected with the transition between both the band edges, related to formation of nanocrystals. 4. Conclusions We prepared nc-Si films by a PECVD method using SiF4/SiH4/H2 gas mixtures. The optical properties of the nc-Si films were examined by decreasing Td from 250 to 95°C under [H2] = 30 and 46 sccm. We found two PL spectra at around 1.7–1.75 eV and 2.2–2.3 eV. The peak energy, EPL, of the 1.7–1.75-eV PL band was found to shift as Td or [H2] changes. It was found that the increase in Td causes the increases in hdi, and the decreases in both the Eopt g and EPL. By contrast, the increase in [H2] decreases the hdi, while increases the Eopt and EPL. Thus, as Td decreases or g [H2] increases, it was suggested that EPL increases with an increase in Eopt g , in good correspondence to a decrease in hdi. However, the observed hdi values were found to be considerably larger than the values of d inferred from the EPL and Eopt values, and some models for interpreting g the causes were proposed. Based on these results, it was suggested that the use of both low Td and high [H2] conditions would allow us the preparation of nc-Si films with small grains.

243

Acknowledgement The author is pleased to thanks Professor S. Hasegawa for using his laboratory to do this work. References [1] J.H. Kim, K.A. Jeon, G.H. Kim, S.Y. Lee, Opt. Mater. 27 (2005) 991. [2] S. Veprek, T. Wirschem, M. Ruckschloß, H. Tamura, J. Oswald, Mater. Res. Soc. Symp. Proc. 358 (1995) 99. [3] G. Cicala, G. Bruno, P. Capezzuto, L. Schiavulli, V. Capozzi, G. Perna, Mater. Res. Soc. Symp. Proc. 452 (1997) 809. [4] E. Edelberg, S. Bergh, R. Naone, M. Hall, E.S. Aydil, J. Appl. Phys. 81 (1997) 2410. [5] D. Milovzorov, T. Inokuma, Y. Kurata, S. Hasegawa, J. Electrochem. Soc. 145 (1998) 3615. [6] S.K. Kim, K.C. Park, J. Jang, J. Appl. Phys. 77 (1995) 5115. [7] H.J. Lim, B.Y. Ryu, J.I. Ryu, J. Jang, Thin Solid Films 289 (1996) 227. [8] I. Solomon, B. Drevillon, H. Shirai, N. Layadi, J. Non-Cryst. Solids 164–166 (1993) 98. [9] S. Oda, M. Odobe, Mater. Res. Soc. Symp. Proc. 358 (1995) 721. [10] B.D. Cullity, Elements of X-Ray Difffraction, Addison-Wesley, Reading, 1978, p. 102. [11] R.B. Iverson, R. Reif, J. Appl. Phys. 62 (1987) 1675. [12] D.V. Tsu, G. Lucovsky, B.N. Davidson, Phys. Rev. B 40 (1989) 1795. [13] A.M. Ali, T. Inokuma, Y. Kurata, S. Hasegawa, Jpn. J. Appl. Phys. 38 (1999) 6047. [14] X. Zhao, O. Schoenfeld, Y. Aoyagi, T. Sugano, Appl. Phys. Lett. 65 (1994) 1290. [15] A.M. Ali, T. Inokuma, Y. Kurata, S. Hasegawa, Mater. Sci. Eng. C 15 (2001) 125. [16] A.J. Kenyon, P.F. Trwoga, C.W. Pitt, J. Appl. Phys. 79 (1996) 9291. [17] X. Zhao, O. Schoenfeld, J. Kusano, Y. Aoyagi, T. Sugano, Jpn. J. Appl. Phys. 33 (1994) L649. [18] M.A. Stevens Kalceff, M.R. Phillips, Phys. Rev. B 52 (1995) 3122. [19] Al.L. Efros, A.L. Efros, Sov. Phys. Semicond. 16 (1982) 772. [20] Y. Kayanuma, Phys. Rev. B 38 (1988) 9797. [21] S. Furukawa, T. Miyasato, Phys. Rev. B 38 (1988) 5726.