Photothermal investigations of doping effects on opto-thermal properties of bulk GaSb

Journal of Alloys and Compounds 484 (2009) 772–776

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Photothermal investigations of doping effects on opto-thermal properties of bulk GaSb Sameh Abroug, Faycel Saadallah ∗ , Noureddine Yacoubi Photothermal Laboratory, Nabeul, Tunisia

a r t i c l e

i n f o

Article history: Received 16 December 2008 Received in revised form 6 May 2009 Accepted 9 May 2009 Available online 18 May 2009 PACS: 71.55.Eq 78.20.Ci 78.20.Nv

a b s t r a c t GaSb is a direct gap semiconductor (0.72 ev) having good carriers motility and significant electro-optical potential in the near IR range. As substrate or active layer, GaSb can be employed in conjunction with many semiconductors such as (AlGa)Sb or In(AsSb) and has interesting hetero junction potential for detectors, lasers and quantum well structures. The aim of this work is to investigate the influence of doping on the opto-thermal properties (optical absorption, refractive index and thermal diffusivity) of doped and undoped GaSb bulk throw, the phothermal deflection and spectroscopic reflectivity. It is found that absorption below the gap and thermal diffusivity increases with doping concentration. © 2009 Elsevier B.V. All rights reserved.

Keywords: Semiconductors Heat conduction Light absorption and reflection Impurities in semiconductors

1. Introduction Gallium antimonide GaSb is widely used in [1–3] many opto-electronic devices such as laser diodes, photodetectors and photocells. Non-intentionally doped (n.i.d.) GaSb is naturally of P type because it includes residual acceptors. However, intentional doping of GaSb may affect its properties. Many authors have shown that doping changes both optical and electronic behavior of semiconductors [4,5] due to the injected free carriers. In this work, photothermal deflection [6–11] and spectroscopic reflectivity are used in order to study the influence of doping on thermal and optical properties of bulk GaSb. For this purpose, absorption spectrum, gap energy, refractive index and thermal diffusivity are measured and doping effects are highlighted. 2. Photothermal measurements Photothermal deflection technique is used in order to study GaSb optical and thermal characteristics near its bandgap energy.

∗ Corresponding author. Tel.: +216 98248252; fax: +216 72220181. E-mail address: [email protected] (F. Saadallah). 0925-8388/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2009.05.040

The experimental setup has been described in detail in [7]. When a sample (Fig. 1) is irradiated with modulated and monochromatic beam radiation, the absorbed energy is converted into heat through different relaxation processes. The generated thermal wave diffuses in the material and in the surrounding fluid (CCl4 ). The temperature variations in the fluid lead to a refractive index gradient causing the deflection of a probe laser beam (He–Ne 4 mW) skimming the sample surface. This deflection is detected by a position photosensor linked to a lock in amplifier. The obtained photothermal signal has two compounds: amplitude and phase. The principle of this technique is shown in Fig. 2. The probe beam deflection is given by [9]: = L/n(dn/dT) f T0 exp(− f x0 ) where n is the fluid refractive index, x0 is the distance between probe beam and the sample surface, and L is the sample length.  D/F is thermal diffusion length in the  f = (1 + j)/f and f = fluid, D the thermal diffusivity and F is the modulation frequency of the heating beam. We notice that deflection is proportional to the complex temperature T0 at the sample surface. This temperature is calculated by solving the one dimension heat equation in the sample, the backing and the surrounding fluid (Fig. 1): ∂Tf ∂x2

=

1 ∂Tf Df ∂t

for x ≥ 0

(1)

S. Abroug et al. / Journal of Alloys and Compounds 484 (2009) 772–776

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Fig. 1. Schema of the sample.

Fig. 3. Normalized amplitude of photothermal signal versus wavelength for Zn doped (circles), Te doped (triangle) and n.i.d. (squares) GaSb.

Fig. 2. Schema of photothermal deflection principle.

∂Te 1 ∂Te − Aexp(˛x)(1 + exp(jωt) = De ∂t ∂x2 1 ∂Tb ∂Tb = Db ∂t ∂x2

for − h ≤ x ≤ 0

(2)

for − h − lb ≤ x ≤ −h

(3)

These equations are solved while taking into account of the boundary conditions at different interfaces. The obtained surface temperature is given by: T0 =

˛I0 2ke (˛2 −  2 )

On the other hand, the value of the amplitude minimum is much larger for doped than for the undoped samples due to free carriers’ contribution to optical absorption below the gap [9,10]. Therefore, we can use this minimum value to determine free carrier concentration [10]. Even for undoped sample which is naturally of P type, we obtain a high minimum value (∼0.45) due to residual hole absorption. From the comparison of experimental and theoretical slopes of the normalized amplitude (Fig. 4a and b), we can deduce the absorption spectrum in the near gap region.

 (r − 1)(b + 1)exp( h) − (r + 1)(b − 1)exp(− h) + 2(b − r)exp(−˛h)  e e (g + 1)(b + 1)exp(e h) − (g − 1)(b − 1)exp(−e h)

All thermal and optical parameters that appear in the above expression are given in reference [10]. For this study we have used several samples of doped and undoped bulk GaSb, and their characteristics are reported in Table 1. Near gap absorption and thermal diffusivity are obtained from the comparison between the signal phase (or amplitude) and the phase (or modulus) of the theoretical surface temperature T0 .

In this way, from experimental amplitude (Fig. 3) obtained with the three GaSb samples we have determined their spectra shown in Fig. 5. These spectra show that absorption decreases more rapidly near the gap than in the transparency region [12,13]. 2.2. Determination of the gap energies

2.1. Near gap absorption spectrum Fig. 3 shows the experimental curves of the normalized amplitude for the studied samples: undoped (n.i.d.), Te and Zn doped GaSb. The amplitude presents a saturation for energies above the gap ( < 1.7 ␮m). Below the gap, the amplitude decreases towards a minimum corresponding to the transparency region. According to Burstein–Moss effect, the absorption edge shifts to higher energies due to doping. This effect is confirmed for GaSb(Te), but not for GaSb(Zn) where a shift to lower energies is observed. Table 1 Electronic characteristics of GaSb samples. Sample

Type of doping

Dopants

Mobility (cm2 /V s)

Dopant density (cm−3 )

Thickness (␮m)

GaSb GaSb GaSb

P N P

n.i.d. Tellurium Zinc

654 3190 361

1.37 × 1017 9.62 × 1017 1.85 × 1018

605 550 600

In order to obtain the gap energy Eg from optical spectra, we have used the Tauc method [14,15]. For energies E = h higher than Eg , the quantity (˛E)n should have linear variations with E, following the Tauc law: (˛ E)n = ˇ (E − Eg ) where ˛ is the absorption coefficient and ˇ is the slope of the curve. For direct bandgap semiconductor such as GaSb: n = 2. The curves of (˛E)2 versus E are shown in Fig. 6. The obtained gap energy Eg values are reported in Table 2. We notice a bandgap shift of about 24 mev for P type and 33 mev for the N type GaSb. The higher value obtained for N type sample is due to the increase of free carrier mobility (Table 1). Indeed, the conduction band filling induces a fusion of the Fermi level, leading to a bandgap shift to higher energies as expected by Burstein–Moss [16,17]. 2.3. Thermal diffusivity The phase of photothermal signal saturates in both high and low absorption regions. In the case of a bulk semiconductor, the

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S. Abroug et al. / Journal of Alloys and Compounds 484 (2009) 772–776

Fig. 4. Determination of absorption spectrum by comparison of the experimental amplitude (a) to theoretical one (b) for the n.i.d. GaSb.

Fig. 5. Absorption spectra of Zn doped (circles), Te doped (triangle) and n.i.d. (squares) GaSb.

Fig. 7. Photothermal phase versus wavelength for Zn doped (circles), Te doped (triangle) and n.i.d. (squares) GaSb.

phase difference between the two saturations is related to thermal diffusivity. In our case, the experimental phase difference decreases when increasing dopant concentration. This is probably due to the improvement of thermal diffusion. Thermal diffusivity values obtained while comparing experimental and theoretical phase differences (Fig. 7) are reported in Table 2. Thermal diffusivity is affected by both carrier and phonon diffusions. Firstly, the heat diffusion is improved by additional free carrier absorption. However, the diffusion of phonons by lattice defects reduces thermal diffusivity. For all GaSb samples, free carrier absorption has more influence than phonon diffusion (Table 2). Indeed, the thermal diffusivity D has increased with dopant concentration. Although, a relative great

Table 2 Gap energy and thermal diffusivity of GaSb Zn and Te doped and undoped (n.i.d.).

2

Fig. 6. (˛E) versus energy E near the bandgap of Zn doped (circles), Te doped (triangles) and undoped (squares) GaSb.

Sample

GaSb n.i.d.

GaSb Zn doped

GaSb Te doped

Gap energy (eV) Thermal diffusivity × 10−5 (m2 s−1 )

0.698 2.3

0.722 2.65

0.733 2.9

S. Abroug et al. / Journal of Alloys and Compounds 484 (2009) 772–776

Fig. 8. Experimental reflectivity versus wavelength obtained for Te doped (dashed), Zn doped (dotted) and n.i.d. (solid line) GaSb.

( D = 0.6 m2 s−1 )

variation GaSb ( D = 0.35 m2 s−1 ).

is noticed for N-GaSb compared to P-

3. Reflectivity measurements Reflectivity measurements are carried out in order to determine the real part of refractive index as well as absorption spectra above the gap for the three GaSb samples. As the samples are optically thick, the reflectivity is given by a simple expression:

   (n˜ e − 1) 2  (n˜ + 1)

R=

e

n˜ e is the complex refractive index given by: n˜ e = ne + iqe

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Fig. 10. Real part of refractive index “ne ” obtained for Te doped (dashed), Zn doped (dotted) and n.i.d. (solid line) GaSb.

ne , qe = ˛e /4 and ˛e are real refractive index, extinction coefficient and absorption coefficient. Then reflectivity becomes : R =

(ne − 1)2 + (˛/4) 2

(ne + 1) + (˛/4)

2 2

The reflectivity obtained with the above expression is compared to experimental curves shown in Fig. 8. We notice that reflectivity increases with dopant concentration. Absorption spectra (Fig. 9) and the real part of refractive index “ne ” (Fig. 10) are obtained while fitting theoretical curves to experimental ones. According to Fig. 9, doped samples have lower absorption than the n.i.d. one in the above gap region. This behavior is inverted for wavelengths below 0.62 ␮m which corresponds to a maximum of refractive index. Moreover, we notice that N type GaSb has higher refractive index than P type sample; nevertheless they have almost the same doping concentration. The same effect has been revealed for GaAs [18]. However, doping does not affect the shape of reflectivity curve or the position of its maximum. 4. Conclusion Two techniques, photothermal deflection and spectroscopic reflectivity, are carried out in order to investigate doping effects on optical and thermal behavior of three bulk GaSb samples. Photothermal deflection is used to measure thermal diffusivity and absorption spectra near and below the gap. As a result, we notice an additional absorption that increases with doping concentration. We also notice that N and P doping does not lead to the same bandgap shift. However, reflectivity is used to show doping-induced changes of refractive index and optical absorption above the gap. References [1] [2] [3] [4]

Fig. 9. Absorption spectra above the gap for Te doped (dashed), Zn doped (dotted) and n.i.d. (solid line) GaSb.

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