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Optical properties of Sulfur doped InP single crystals M.M. El-Nahass, S.B. Youssef, H.A.M. Ali ∗ Department of Physics, Faculty of Education, Ain Shams University, Roxy 11757, Cairo, Egypt

highlights • • • • •

Optical properties of InP:S single crystals were investigated. Absorption data analysis revealed direct allowed and direct forbidden transitions. Dielectric functions and some of the dispersion parameters were calculated. Energy positions of the structures for InP:S single crystal were determined. S dopants into InP crystals increase the ionicity of it.

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Article history: Received 2 April 2011 Received in revised form 18 January 2013 Available online 6 February 2014 Keywords: Sulfur doped InP Optical constants Dispersion parameters Dielectric functions

abstract Optical properties of InP:S single crystals were investigated using spectrophotometric measurements in the spectral range of 200–2500 nm. The absorption coefficient and refractive index were calculated. It was found that InP:S crystals exhibit allowed and forbidden direct transitions with energy gaps of 1.578 and 1.528 eV, respectively. Analysis of the refractive index in the normal dispersion region was discussed in terms of the single oscillator model. Some optical dispersion parameters namely: the dispersion energy (Ed ), single oscillator energy (Eos ), high frequency dielectric constant (ε∞ ), and lattice dielectric constant (εL ) were determined. The volume and the surface energy loss functions (VELF & SELF) were estimated. Also, the real and imaginary parts of the complex conductivity were calculated. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Indium Phosphide is one of the promising semiconductors of the III–V group, suitable for the development of X - and γ -ray radiation detectors for their application mainly in medicine, on-line monitoring of industrial processing special experiments, radioactive waste management and security [1]. However, at the end of 1980s, due to the large value of the atomic number of In (49), high electron mobility (∼4000 cm2 /Vs) and relatively wide band gap (1.34 eV) at room temperature 300 K [2], high radiation hardness and good heat-conducting properties, InP is widely being used for manufacturing microwave devices, high-frequency devices and optoelectronic integrated circuits which are indispensable for wireless technology and satellite communications [3]. Also, owing to its remarkable photoluminescence and optical properties, InP is used in light emitting diodes, light detectors and solar cells [4]. As is well known, impurity diffusion in semiconductors has a technological importance in the fabrication of these devices [5]. The technology of doping for these materials is of considerable importance due to their effect on the electrical and optical properties of them. Dopant elements are normally incorporated into InP single crystals produce particular electrical characteristics, e.g. n-conducting, p-conducting or semi-insulating properties [6]. Effect of impurities such as Zn, Sn, Fe, and

∗

Corresponding author. E-mail address: [email protected] (H.A.M. Ali).

http://dx.doi.org/10.1016/j.physa.2014.01.069 0378-4371/© 2014 Elsevier B.V. All rights reserved.

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Fig. 1. The spectral distribution of transmittance, T (λ), and reflectance, R(λ), of InP:S single crystal.

S on the electrical properties of InP have been extensively investigated [7]. Impurities of sulfur (S) are well known to form shallow donors in InP [8]. Also, it can effectively reduce the dislocation density generated in these crystals during the growth process [9]. Dislocation-free InP crystals are very useful as substrates to fabricate devices such as lasers, photodiodes and microwave transistors with high reliability and high performance [10]. Thus, the characterization of InP single crystals doped with Sulfur is important and a subject for study. The aim of the present paper is to investigate the optical properties of InP single crystals doped with Sulfur (InP:S) in the wavelength range from 200 to 2500 nm using spectrophotometer measurements for the transmittance and reflectance. Also, to determine optical constants, dielectric functions and some of the dispersion parameters. 2. Experimental work InP:S single crystals with a (100) surface orientation were supplied from Spectra chemical industries. The samples exhibited n-type conductivity with a carrier concentration of 3 × 1018 cm−3 at room temperature as given by sample information. The sample have dimensions of 9 × 8.5 × 0.5 mm3 and has mirror-like plane parallel surfaces; hence, there was no need for mechanical polishing. The surfaces were cleaned from chemical impurities and contaminations with chromic acid before the measurements. The transmittance T (λ) of InP:S crystals, at normal incidence, as well as the reflectance R (λ), at an incident angle of 5°, were measured in the spectral range 200–2500 nm by using a double beam spectrophotometer (JASCO, V-570 UV–VIS–NIR). 3. Results and discussion 3.1. The spectral distribution of T (λ) and R(λ) The spectral distribution of the transmittance, T (λ), and reflectance, R(λ), for InP:S single crystal (0.5 mm thick as representative example), is shown in Fig. 1 in the spectral wavelength range of 200–2500 nm. As observed, the transmittance spectrum rises abruptly at 770–790 nm then decreases until λ of 930 nm and increases again with increasing wavelength up to 2500 nm. The abruptly raise in the transmittance forms the position and the shape of the absorption-edge, that the information on the nature of the transition from band to band can be investigated. The reflectance spectrum is characterized by a sharp structures at λ < 1000 nm, which associated with high energy transitions from the valence band to the conduction band with energies E0 , E1 and E2 . Their values are tabulated in Table 1. At λ > 1000 nm, the reflectance decreases with increasing the wavelength. 3.2. The absorption coefficient (α) Fig. 2 represents the spectral distribution of the absorption coefficient (α) of InP:S crystal, which calculated according to the following equation [16]:

α = (1/d) ln{(1 − R)2 /2T + [((1 − R)4 /4T 2 ) + R2 ]1/2 }

(1)

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M.M. El-Nahass et al. / Physica A 402 (2014) 216–223 Table 1 Inter-band transition corresponding to peak positions in the reflectance spectrum of InP:S single crystal. Identification

E0 (eV)

E1 (eV)

E2 (eV)

Transitions [11]

Γ15ν − Γ1c

Λ3 − Λ1

X5ν − X1c

Present data (InP:S)

1.531

3.246

5.438

Energy values for pure InP

1.335 (Exp.) [12] 1.357 (Exp.) [13] 1.42 (Th.) [14] 1.35 (Th.) [15]

3.148 [12] 3.162 [13] 3.18 [14] 3.10 [15]

4.7 [12] 4.68 [13] 4.76 [14] 4.7 [15]

Fig. 2. The spectral distribution of absorption coefficient, α(λ), for InP:S single crystal.

where d is the sample thickness in cm, T and R the values of transmittance and the reflectance of the sample at the same wavelength (λ), respectively. To determine the energy gap (Eg ) and the type of optical transition, the absorption due to band-to-band transition can be described using the following relation [17,18]:

(α hυ) = B(hυ − Eg )r

(2)

where B is a constant, h is Planck’s constant, Eg is the energy band gap and r is a parameter takes the values: 1/2, 2, 3/2 and 3 which related to allowed direct, allowed indirect, forbidden direct and forbidden indirect optical transitions, respectively. So, the dependence of (α hυ)1/r on energy (hυ) of InP:S single crystal was checked. Two best straight lines are obtained for r = 1/2 and 3/2, as shown in Fig. 3, indicating that InP:S single crystal exhibits allowed and forbidden direct transitions. The intersections of the two lines with hυ -axis at (α hυ)2 and (α hυ)2/3 = 0 gave the values of the energy gaps for the allowed and the forbidden transitions, which were found to be 1.578 and 1.528 eV, respectively. According to them, doping with sulfur atoms into InP crystals leads to the increase of the bandwidth value incomparable with that for pure InP (1.34 eV [2]). 3.3. Refractive index (n) The spectral distribution of the refractive index, n, can be determined by knowing the values of the reflectance, R, and the absorption index, k (=αλ/4π ), at the same wavelength, for different wavelengths using the following equation [19]: n = [(1 + R)/(1 − R)] + [(4R/(1 − R)2 ) − k2 ]1/2 .

(3)

The spectral distribution of (n) for InP:S single crystal is shown in Fig. 4. It is characterized by sharp structure due to valence to conduction band transitions with the energies E0 , E1 and E2 at (hυ) > 1.24 eV in the refractive index spectrum. Fig. 4 also presents the spectral dependence of (n) for InP samples measured by Cardona in the spectral range of 200–885 nm, and by Pettit and Turner in the spectral range of 925–2000 nm. These data are taken from Ref. [11, Tables 16, 17]. As illustrated from Fig. 4, the values of (n) corresponding to the peaks of InP:S are larger than those for InP crystals. This difference may be attributed to: the effect of surface conduction, the effect of free carriers injected and/or a change in the bonding and accordingly the polarizability of the material [20].

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Fig. 3. Plot of (α hυ)2 and (α hυ)2/3 against (hυ) for InP:S and InP single crystals.

Fig. 4. The spectral distribution of the refractive index, n, for InP:S and InP single crystals as a function of (hυ). Data of InP are taken from Ref. [11].

Also, the spectral distribution of (n) has a normal dispersion in the spectral range of 1.24–0.49 eV for InP:S, in which the single oscillator model can be applied. According to this model, the dispersion curve of the refractive index can be expressed by using Wemple and DiDomenico relation [21,22]:

(n2 − 1)−1 = (Eos /Ed ) − (1/Eos Ed ) (hυ)2

(4)

where Eos is the oscillator energy and Ed is the dispersion energy. The values of Eos and Ed can be determined by plotting a relation between (n2 − 1)−1 and (hυ)2 as shown in Fig. 5. From the slope and the intercept of the extrapolated straight line, the values of Eos and Ed were calculated and were found to be 2.86 and 25.03 eV, respectively. The intercept of the extrapolated straight line with ordinate axis at (hυ)2 = 0 yields the value of the dielectric constant at infinite frequency (ε∞ ) which was found to be 9.75. The dispersion energy, Ed , which is a measure of the intensity of the inter-band optical transition, does not depend significantly on the band gap. The dispersion energy is related to other physical parameters of material through the empirical formula [23] as: Ed = β Nc Za Ne

(5)

where Nc is the coordination number of the cation nearest neighbor to the anion, Za is the formula chemical valence of the anion, Ne is the effective number of valence electrons per anion and β is a parameter between 0.26 ± 0.04 eV for Ionic materials and 0.37 ± 0.05 eV for covalent materials. Using the calculated value of Ed for InP:S crystal and the values of

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Fig. 5. The variation of (n2 − 1)−1 against (hυ)2 for InP:S single crystal.

Fig. 6. The variation of n2 against λ2 for InP:S single crystal.

Nc = 4, Za = 3 and Ne = 8 [24,25], the value of the parameter β was found to be 0.261. The obtained result indicates that InP:S has more ionic character than InP crystals. From viewpoint of the bonding nature, it is noted that InP has 11% ionic bonding [26] and the sulfur dopant has a large Pauling’s electronegativity than phosphorus [27]. Thus, S dopants increase the ionicity of the material. The refractive index, n, of InP:S crystal can be also analyzed to determine the lattice dielectric constant (εL ). It can be expressed as a function of the wavelength (λ) by the following equation [28]: n2 = εL − (e2 /π c 2 )(N/m∗ )λ2

(6)

where e is the electronic charge, c is the light speed and N/m is the ratio of carrier concentration to its effective mass. The dependence of n2 on λ2 is linear at longer wavelength for InP:S crystal as shown in Fig. 6. The values of εL and N/m∗ are calculated from the slope and extrapolation of the linear part to the ordinate at λ2 = 0 and listed in Table 2. ∗

3.4. Complex dielectric functions The complex dielectric constant (ε ∗ = ε ′ + iε ′′ ) characterizes the optical properties of a material. It can be estimated if the refractive index and extinction coefficient are known. The real (ε ′ ) and imaginary (ε ′′ ) parts of dielectric constants were

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Table 2 The dispersion parameters of InP:S single crystal. Parameters

ε∞

Eos (eV)

Ed (eV)

εL

N/m∗ (cm−3 g−1 )

InP:S InP [11] InP [29] InP [30]

9.75 9.6 – 9.5

2.86 – 3.39 –

25.03 – 28.91 –

10.64 12.6 – 12.3

6.99 × 1046 – – –

Table 3 Energy positions (in eV) of the structures for InP:S single crystal. Energy positions in (eV) obtained from the figure of n

ε′

ε ′′

σ′

σ ′′

5.439 3.263 1.545

5.425 3.261 1.518

5.239 3.212 1.554

5.486 3.267 1.544

5.479 3.265 1.549

Identification [11] E2 (X5ν − X1c ) E1 (Λ3 − Λ1 ) E0 (Γ15ν − Γ1c )

Fig. 7. The variation of ε ′ and ε ′′ as a function of (hυ) for InP:S single crystal.

determined by using the following relations [25,31]:

ε ′ = n2 − k2 and ε ′′ = 2nk.

(7)

The photon energy dependence of both ε and ε is illustrated in Fig. 7, which is characterized by the existence of the same sharp structure associated with the valence to conduction band transitions (E0 , E1 and E2 ) having the values mentioned in Table 3. The dissipation factor (tan δ) can be calculated according to the following equation [32]: ′

tan δ = ε ′′ /ε ′ .

′′

(8)

The variation of dissipation factor as a function of energy for InP:S crystal is shown in Fig. 8. This figure shows that the dissipation factor almost decreases increasing photon energy. It is also possible to calculate the volume and surface energy loss functions (VELF and SELF), which relate to the real and imaginary parts of the dielectric constant according to the following relations [33,34]: VELF = ε ′′2 /[ε ′2 − ε ′′2 ]

(9)

SELF = ε /[(ε + 1) + ε ]. ′′2

′

2

′′2

(10)

The distribution of the volume and the surface energy loss function of InP:S crystal as a function of the photon energy is shown in Fig. 9. Both VELF and SELF showed the same behavior by increasing the photon energy, but the SELF values are slightly higher than the VELF values. The complex conductivity σ ∗ (ω) consists of a real part denoted as σ ′ (ω) and an imaginary part denoted as σ ′′ (ω) [35]:

σ ∗ = σ ′ + iσ ′′

(11)

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Fig. 8. The variation of tan δ as a function of (hυ) for InP:S single crystal.

Fig. 9. The variation of VELF and SELF as a function of (hυ) for InP:S single crystal.

where σ ′ = ωεo ε ′′ and σ ′′ = ωεo (1 − ε ′ ). Fig. 10 shows the spectral distribution of both σ ′ and σ ′′ as a function of photon energy. As observed from the figure that σ ′ reflects the sharp structure associated to the valence band transitions (E0 , E1 and E2 ) with energy values determined and tabulated in Table 3 and confirms the previously obtained value of Eg . 4. Conclusion Optical transmittance and reflectance of InP:S crystals were measured in the spectral range of 200–2500 nm in order to derive the absorption coefficient and refractive index. The analysis of the absorption data revealed the existence of direct allowed and direct forbidden transitions for InP:S crystals with energy gaps of 1.578 and 1.528 eV, respectively. The obtained results indicate that doping impurity (sulfur atoms) into InP crystals increases the width of the band gap. The refractive index dispersion data were analyzed using the Wemple–DiDomenico single oscillator model. As a result, the oscillator energy, dispersion energy, lattice dielectric constant, and zero-frequency refractive index parameters were determined. Graphical representation of both the surface and volume energy loss functions and the complex conductivity as a function of photon energy supports the existence of the mentioned optical transitions. The obtained results indicate that S dopants into InP crystals increase the ionicity of the material.

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Fig. 10. The variation of the real and imaginary parts (σ ′ and σ ′′ ) of the complex conductivity as a function of (hυ) for InP:S single crystal.

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