GaAs alloys: Two layer photothermal deflection model

Journal of Alloys and Compounds 581 (2013) 358–362

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Non-radiative recombination process in BGaAs/GaAs alloys: Two layer photothermal deflection model S. Ilahi a,⇑, M. Baira b, F. Saidi b, N. Yacoubi a, L. Auvray c, H. Maaref b a Université de Carthage, Unité de Recherche de caractérisation photothermique et modélisation, Institut Préparatoire aux Etudes d’Ingénieurs de Nabeul (IPEIN), 8000 Merazka, Nabeul, Tunisia b Université de Monastir, Laboratoire de Micro-Optoélectronique et Nanostructures, Faculté des Sciences de Monastir. Avenue de l’Environnement, Monastir 5019, Tunisia c Laboratoire Multimateriaux et Interfaces, Université Claude Bernard Lyon I, 43, Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France

a r t i c l e

i n f o

Article history: Received 1 May 2013 Received in revised form 14 July 2013 Accepted 15 July 2013 Available online 22 July 2013 Keywords: Photothermal deflection technique Two layer model BGaAs/GaAs alloys

a b s t r a c t Photo-thermal deflection technique PTD is used to study the nonradiative recombination process in BGaAs/GaAs alloy with boron composition of 3% and 8% grown by metal organic chemical vapor deposition (MOCVD). A two layer theoretical model has been developed taking into account both thermal and electronic contribution in the photothermal signal allowing to extract the electronic parameters namely electronic diffusivity, surface and interface recombination. It is found that the increase of boron composition alters the BGaAs epilayers transport properties. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction A novel material based on boron incorporation in III–V binary and ternary compounds is subject of great interest due to its high-efficiency in multi-junction solar cells application [1,2], and for opto-electronic devices such as emitting laser diode in the wavelength range 1.3-1.55 lm [3–5]. Indeed, several works have been devoted to study the BGa(In)As alloys. The ternary BGaAs and the quaternary BGaInAs alloys have been successfully grown on GaAs substrates by metalorganic chemical vapor deposition MOCVD [6–11]. We also note that some previous works have shown that the addition of boron modifies some properties of the ternary GaInAs as for example the increase of the electron effective masse [12,13], an alteration of the magnetotransport properties compared with GaAs [14] and an affectation in the line shape of the fundamental band gap has been observed [15]. Recently, using the photothermal deflection spectroscopy, we have shown a decrease in the gap energy and thermal conductivity with increasing of boron composition in BGaAs/GaAs alloys [16]. In this work, we have investigated the nonradiative lifetime, electronic diffusivity, surface and interface recombination. These properties are essential for photovoltaic solar cells and electronic devices which have a profound effect on the response of semiconductors. In fact, the recombination rate increases proportionally ⇑ Corresponding author. Tel.: +216 40662557; fax: +216 72229137. E-mail address: ilehi_soufi[email protected] (S. Ilahi). 0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.jallcom.2013.07.101

with defect density, imperfection and contamination and give an important information about the surface property and quality. Indeed, the non radiative lifetime of photogenerated carrier determines the quantum efficiency of semiconductors. Then, the electronic diffusivity of a semiconductor is a very important parameter, gives in direct information about the mobility of minority carrier through the Einstein relation which determines the distance traveled by the photoexcited carriers before their recombination and depends on the scattering processes. The interface layer/substrate is another place when the recombination occurs due to the defect density in the semiconductors structures. The development of accurate theoretical models allowing to investigate the transport properties in bulk and multilayers semiconductors is highly required. Several theoretical models for bulk and multilayer semiconductors has already been reported using one of the following photothermal technique citing, photoacoustic [17,18], photoreflectance [19], photothermal radiometry [20– 22].In addition, a one layer model for photothermal deflection technique has been developed by D. Fournier et al. [23] and improved by [24] and recently by S. Ilahi et al. [25]. In the meanwhile, we have recently developed a two-layer theoretical model by means of photothermal deflection technique PTD in order to study the nonradiative recombination process in GaInAsSb/GaSb and AlGaAsSb/GaSb laser structures [26]. In this context, we report in this paper in the transport properties of BGaAs/GaAs samples having 3% and 8% of boron

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composition using the photothermal deflection technique. Nonradiative lifetime, electronic diffusivity, surface and interface recombination velocity have been extracted by fitting the experimental photothermal signal to the corresponding theoretical ones. 2. Theory The principle of PTD technique is shown in Fig. 1 and consists to illuminate the sample by a modulated light beam. The absorbed energy is converted into heat through a non radiative recombination processes namely carrier thermalisation, bulk and surface recombination. The generated thermal wave will propagates into the sample and surrounding media creating a temperature gradient. Then a refractive-index which causes the deflection of a laser probe beam skimming the sample surface. As the incident light is assumed to be uniform and only the sample absorbs the light with an absorption coefficient a. then, a one dimensional treatment is sufficient. A one dimensional two layer model which predicts the PTD amplitude and phase is developed allowing to investigate the transport properties in thin semiconductors. In our case, the two layers are composed of a GaSb substrate and a BGaAs epilayer. The theoretical model developed in this work is based on the minority carrier and heat diffusion equations in the different regions; substrate, layer and at the substrate–layer interface taking into consideration three fundamentals heat sources namely carrier thermalisation, bulk recombination, interface and surface recombination. The theory is based on the resolution of the minority carrier diffusion in both layer and substrate and heat equation diffusion in the different media [26].

3. Minority carrier diffusion equations The layer minority carrier diffusion equation is:

@Nlðx;tÞ @ 2 N lðx;tÞ Nlðx;tÞ ¼ Dl  þ Gl @t @x2 sl

ð1Þ

where N cðx;tÞ is the photo-generated carriers density in the layer, Dc is the electronic diffusivity and (sl) is the nonradiative lifetime of lÞ minority carriers and Gl ¼ al I0 ð1R expðal ðx  hÞÞ is the generation 2E rate carriers. I0 is the intensity of pump beam, ac is the optical absorption coefficient, Rl is the reflectivity coefficient and E is the energy of the incident beam. The substrate minority carrier diffusion equation is:

@Nsðx;tÞ @ 2 Nsðx;tÞ Nsðx;tÞ ¼ Ds  þ Gs @t @x2 ss

ð2Þ

4. Heat Equations Fig. 2 show the different media concerned by the heat diffusion. By assuming that only the sample is the absorbing medium, the one dimensional heat diffusion equation in the different media is written (Fig. 2):

@2T f  r2f T f ¼ 0 if @x2

h  x  h þ hf

ð3Þ

@2T l  r2l T l ¼ Q l @x2

if

0xh

ð4Þ

@2T s  r2s T s ¼ Q s @x2

if

@2T b  r2b T b ¼ 0 if @x2

lx0

 lb  l  x  l

ð6Þ

1=2

Di where ri ¼ ð1þiÞ is the thermal diffusion length of the li and li ¼ ðpF Þ i medium (i = f,s,l,b are respectively the fluid f, the substrate s, layer l and the backing b) and D is the thermal diffusivity. A beam energy E greater than the energy gap is susceptible to create an electron–hole pair in both layer and substrate, and after diffusion they recombine nonradiatively providing a heat. However, Ql and Qs represent the heat source term respectively in layer and substrate, each one are composed of three contributions; thermalisation component, nonradiative bulk recombination and surface recombination which are detailed elsewhere [26]. By solving theses equations taking into consideration of the continuity of temperature and heat flow allowing to obtain the expression of the periodic temperature rise at the sample surface T0 given by S. Ilahi et al. [26]:

T0 ¼

V1  V2 þ V3 þ V4 V5

ð7Þ

V 1 ¼ ðb  1Þð1 þ f Þ expðrs lÞ        al al al þ M0 1 e þ 1 þ ðz þ wÞ 1   expðrl hÞ j

rl þ ðb  1Þ expðrs lÞ

rl

Where Nsðx;tÞ is the photo-generated carriers density in the substrate, Ds is the electronic diffusion coefficient and (ss) is the non-radiative lifetime of minority carriers and Gs ¼ as I0 ð1R2El Þð1Rs Þ expðal hÞ expðas xÞ is the generation rate carriers. as is the substrate’s optical absorption coefficient, Rs is the reflectivity coefficient.

Fig. 2. Schematic representation of the different media.

Fig. 1. The sample constituted of one layer on a substrate is heated with a modulated normal incident light beam.

ð5Þ

Fig. 3. Experimental setup of PTD technique.

rl

S. Ilahi et al. / Journal of Alloys and Compounds 581 (2013) 358–362

Phase (°)

−7

τ l = 10 s τ l = 5 10−8s

0.5

−6

τ l = 10 s

−7

τ l = 5 10−7s

τ l = 5 10 s −7

τ l = 10 s

60

−8

τ l = 5 10 s

30

0.0

(b)

(a) 0

3

6

9

12

Square root Frequency

Normalized Amplitude

90

τ l = 10−6s

1.0

15

0

18

3

12

15

2

18

2

Dl =1cm /s

2

2

Dl =5cm /s

200

2

Dl =9,7cm /s 2

Dl =13cm /s

0.5

(c)

2

Dl =9,7cm /s 2

Dl =13cm /s

150

(d)

100

0.0 6

0

12

6

Square root Frequency (Hz1/2)

Ss =10 cm/s

60

Ss =10 cm/s Ss =100 cm/s Ss =500 cm/s Ss =1000 cm/s

1.0

12

Square root Frequency (Hz1/2)

Ss =100 cm/s

Phase (°)

Normalized Amplitude

9

Dl =1cm /s Dl =5cm /s

1.0

0

0.5

Ss =500 cm/s

50

Ss =1000 cm/s

40 30

(e)

(f)

0.0

20

0

3

6

9

12

15

18

3

6

Square root Frequency (Hz1/2)

9

12

63 Sl = 100 cm/s

1.0

15

18

Square root Frequency (Hz1/2)

Sl = 100 cm/s

56

Sl = 2000cm/s

Phase (°)

Normalized Amplitude

6

Square root Frequency (Hz1/2)

(Hz1/2)

Phase (°)

Normalized Amplitude

360

Sl = 5000cm/s Sl = 10000 cm/s

0.5

(g)

Sl = 2000cm/s Sl = 5000cm/s

49

Sl = 10000 cm/s

42 35

(h)

28

0.0

0

6

12

18

0

6

Square root Frequency (Hz1/2)

12

18

Square root Frequency (Hz1/2)

Fig. 4. Theoretical amplitude and phase of photothermal signal for four values of sl (a and b), Sl (c and d) and Ss (e and f) according to square root modulation frequency for the BGaAs /GaAs sample.

    al al V 2 ¼ ð1  f Þ expðrl hÞ j þ1 e 1

rl

rl

     al al þðz þ wÞ 1 þ  M0  2e 1 þ f expðal hÞ

rl

rl

    al al þ2j f  1 expðal hÞ þ 2ðz þ wÞ f  1 expðal hÞ

rl

rl

      as as as þ 2j1 1  þ 2ðz1 þ w1 Þ 1 þ  2M 1 þ2e1 1 þ

rs

rs

rs

   al V 3 ¼ ðb þ 1Þ expðrs lÞ ð1  f Þ expðrl hÞ j 1  rl      al al þ 1 þ ðz þ wÞ  1  M0 þe rl rl     al al expðal hÞ þ 2j f þ 1 expðal hÞ þ 2e 1  f rl rl     al as 1 þ 2ðz þ wÞ f þ 1 expðal hÞ þ 2e1 rl rs      as as þ 2ðz1 þ w1 Þ  1  2M1  2j1 1 

rs

rs

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S. Ilahi et al. / Journal of Alloys and Compounds 581 (2013) 358–362 Table 1 Electronic parameters of BGaAs/GaAs with 3% and 8% of boron composition. Dl ðcm2 =sÞ

sl  107 s

Sl ðcm=sÞ

Ss ðcm=sÞ

MSV

BGaAs with 3% of boron

1.2 (±4%)

3.2 (±4%)

11,224 (±9%)

921 (±7%)

1:4  104

BGaAs with 8% of boron

0.9 ± (3%)

2.7 (±5.5%)

12,311(±7.4)

1100 (±6.5%)

1:6  104

Theoretical curve BGaAs with 8% of boron BGaAs with 3% of boron

1.0

Theoretical curve BGaAs with 8% of boron BGaAs with 3% of boron

160 140 120

0.8

Phase (°)

Normalized Amplitude

1.2

0.6

100 80 60

0.4 40

(a)

0.2 0

(b)

20 6

12

18

0

6

12

18

Square root Frequency (Hz1/2)

Square root Frequency (Hz1/2)

Fig. 5. Experimental (dots) and theoretical amplitude phase of the photothermal signal according to square root modulation frequency for BGaAs/GaAs with 3% and 8% of boron.

   as  b expðas lÞ  4j1 þ b expðas lÞ þ 4ðz1 rs rs   as þ w1 Þ  b expðas lÞ

V 4 ¼ 4e1



as

rs

V 5 ¼ ð1 þ gÞð1 þ f Þðb  1Þexpðrl hÞexpðrs lÞ þ ð1  gÞð1  f Þðb  1Þ expðrl hÞexpðrs lÞ þ ð1 þ gÞð1  f Þðb þ 1Þexpðrl hÞexpðrs lÞ þ ð1  gÞð1 þ f Þðb þ 1Þ expðrl hÞexpðþrs lÞ The expression of probe beam deflexion given as follow:

w¼

L dn rf T 0 expðrf x0 Þ n dT

ð8Þ

n is the refractive index, L is the sample length, w is complex number written as w ¼ jwj expð/Þ where jwj is the amplitude and / the phase. x0 is the distance between the probe beam axis and the sample surface. 5. Results and discussion The growth of BGaAs layers has been performed at atmospheric-pressure by the technique (MOVPE) in a T-shape horizontal reactor. The layers were deposited on (0 0 1) GaAs substrates misoriented 1° off (±0.05°) towards (1 1 0) direction. Triethylgallium (TEG) and diborane (B2H6) were used as group III precursors. Arsine (AsH3) was used for the arsenic source as group V precursor. Hydrogen was used as carrier gas. Diborane flow-rate was kept constant. We used high V/III ratios in order to favor BGaAs alloy stabilization in order of 62%. The boron gas-phase concentration was quantified by the initial molar flow-rate ration: H6  Xv ¼ 2½B22H½B62þ Prior to BGaAs growth, a GaAs buffer layer of ½TEG

approximately 0.1 lm thick was grown at the same temperature as the epilayers. Post growth Boron composition is measured by DDX [8].The thicknesses of the GaAs substrate and BGaAs epilayer are respectively 400 lm and 0.1 lm. The PTD experimental setup is described elsewhere [25–27] and shown in fig. 3, where the sample is heated by mechanically

chopped light produced by a halogen lamp. He–Ne laser probe beam of 100 lm diameter skimming the sample surface at x0 distance is deflected. The deflection is detected by a position photodetector linked to a lock in amplifier. The obtained photothermal signal has two compounds: amplitude and phase. A computer reads the values of amplitude and phase and draws their variation versus square root frequency. As well known the PTD technique is able to study the transport properties in bulk semiconductors. The first theoretical model was proposed by Fournier et al. [23]. In this work we have developed a theoretical model in the case of a layer deposed on a substrate where the Eq. (28) allows to investigate the transport properties in both layer and substrate by means of PTD technique. We have varied one of the nonradiative lifetime sl ,electronic diffusivity Dl ,surface recombination Sl and interface recombination velocity Ss and Keeping the other constants in order to show their impact on the PTD signal. We have plotted on Figs. 4(a–h) are respectively plotted the amplitude and phase of the photothermal signal for different values sl, Dl, Sl and Ss. However, the great sensitivity of PTD signal to the electronic parameters sl, Dl, Sl and Ss according to the square root frequency is clearly shown in Fig. 3.In other hand, the dependence in the amplitude and phase on the frequency is described in detail in the one layer model reported by [23,24]. Moreover, two regimes are identified by the first is purely thermal behavior occurs at low frequency regime <100 Hz and described by rapid decrease in the amplitude of the PTD signal explained by the carrier thermalization .Then, the second is electronic behavior occurs in the high frequency >100 Hz described by a slow decrease in the amplitude which high sensitive to the carrier lifetime and surface recombination. The multiparameters fitting is detailed elsewhere [26], to ensure the uniqueness of the extracted values we have fitted simultaneously the amplitude and phase of PTD signal by minimizing the mean square variance (MSV). The others parameters used for the fit procedure in reported elsewhere [16–18]. The extracted values are listed on Table 1 for two BGaAs with 3% and 8% of boron composition. Thus, on Fig. 5 are plotted the

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experimental amplitude (fig. (a)) and phase (fig. (b)) of the photothermal signal and the corresponding theoretical ones. Moreover, the non radiative lifetime sl in BGaAs is greater compared to that reported for GaAs layer in GaAs substrate using photoacoustic technique [28]. This behavior may be attributed to the localized states induced by the non-uniform insertion and the clustering of the boron atoms in BGaAs which formed non radiative centers in the layer resulting decreases of sl. Through the high density of defects and the nonradiative recombination centers increase with increasing the boron content. In this context, preview report [8] indicates that the BGaAs epilayers does not give luminescence at room temperature; due to the presence of the nonradiative centers in these structures. In fact, we can see in Table 1, sl becomes faster when increasing the boron composition which is a good agreement with the reported prediction. Moreover, the measured value of Dl listed in Table 1 is smaller than the values reported in [28] for the GaAs layer. We can deduce a decrease in the mobility of minority carrier caused by the boron incorporation. Furthermore, it was found that Dl decreases with increasing the boron composition. These results agree well with that presented by Teubert et al. [14] where the decrease of the mobility in n-type (B,Ga,In) as compared to n-type GaAs has been attributed to the boron cluster states. An alteration in the BGaAs lattice parameter compared to GaAs mainly due to the large size between B,Ga and As, and electronegativity difference between B and Ga isolated B atoms, and B–B pair are originate of the cluster and localized states [29,30], this defect at the interface improve the recombination rate. These reported explanations are a good agreement with our reported results for the interface recombination velocity. We have shown that the interface recombination velocity Ss is enhanced when increasing the boron composition which explained by the boron cluster state at interface layer substrate, moreover, the disorder in the crystal lattice caused by the difference between the boron, gallium, and arsenic atoms sizes has a great effect in the increase of recombination rate. Furthermore, the obtained values shown for the surface recombination velocities listed in Table 1 for both BGaAs epilayer correspond to a nonpassivated surface (free surface) which could be contaminated and oxidized by the contact with the surrounding air. We remark that the values of Sl for both epilayer are relatively higher. Using the atomic force microscopy AFM. Studies [31,32] have shown the roughness and imperfection of the surface which are associated to the boron surface segregation. Thus, Sl increases when increasing the boron composition, which is traditionally explained by the increase of the defect density acting as traps for the photogenerated carrier. In summary, a Two layer theoretical model applied for photothermal deflection technique has been developed in order to extract the non-radiative lifetime, electronic diffusivity, surface and interface recombination velocity by fitting the experimental curves

of the phase and normalized amplitude of the photothermal signal by the corresponding theoretical for two BGaAs with 3% and 8% of boron composition. The increase of the boron composition induces a localized state, clusters at interface layer/substrate and roughness and imperfection of the surface which are the mainly reasons for the transport properties altering in BGaAs epilayer. References [1] J.F. Geisz, D.J. Friedman, et al. in: the Twenty-Eighth IEEE Photovoltaic Specialists Conference, Anchorage, USA, 2000. [2] G. Leibiger, C. Krahmer, et al., J. Cryst. Growth 272 (2004) 732–738. [3] J.F. Geisz, D.J. Friedman, J.M. Olson, S.R. Reedy, A.B. Swartzlander, B.M. Keyes, A.G. Norman, Appl. Phys. Lett. 76 (2000) 1443. [4] G. Leibiger, C. Krahmer, J. Bauer, H. Hernberger, V. Gottschalch, J. Cryst. Growth 272 (2004) 732–738. [5] G.L.W. Hart, A. Zunger, Phy. Rev. B 62 (2000) 13522. [6] Q. Wang, X. Ren, F. Wang, J. Feng, J. Lv, J. Zhou, S. Cai, H. Huang, Y. Huang, J. Microelectron. 39 (2008) 1678–1682. [7] Q. Wang, X. Ren, H. Huang, Y. Huang, S. Cai, in: J. Microelectron. 40 (2009) 87– 91. [8] R. Hamila, F. Saidi, P.H. Rodriguez, L. Auvray, Y. Monteil, H. Maaref, J. Alloys Comp. 506 (2010) 10–13. [9] F. Saidi, R. Hamila, H. Maaref, Ph. Rodriguez, L. Auvray, Y. Monteil, J. Alloys Comp. 491 (2010) 45–48. [10] J.F. Geisz, D.J. Friedman, S. Kurtz, J.M. Olson, A.B. Swartzlander, R.C. Reedy, A.G. NormanJ, Cryst. Growth 225 (2001) 372–376. [11] J.F. Geisz, D.J. Friedman, J.M. Olson, S.R. Reedy, A.B. Swartzlander, B.M. Keyes, A.G. Norman, Appl. Phys. Lett. 76 (2000) 1143–1145. [12] T. Hofmann, M. Schubert, G. Leibiger, V. Gottschalch, Appl. Phys. Lett. 90 (2007) 182110. [13] A. Lindsay, E.P. O’Reilly, Phys. Rev. B 76 (2007) 075210. [14] J. Teubert, P.J. Klar, A. Lindsay, E.P. O’Reilly, Phys. Rev. B 83 (2011) 035203. [15] T. Sander, J. Teubert, P.J. Klar, A. Lindsay, E.P. O’Reilly, Phys. Rev. B 83 (2011) 235213. [16] S. Ilahi, F. Saidi, R. Hamila, N. Yacoubi, L. Auvray, H. Maaref, Curr. Appl. Phys. 13 (2013) 610–613. [17] I. Riech, M.L. Gomez-Herrera, P. Dıaz, J.G. Mendoza-Alvarez, J.L. Herrera-Perez, E. Marin, Appl. Phys. Lett 79 (2001) 964. [18] I. Reich, P. Dıaz, T. Prutskij, J. Mendoza, H. Vargas, E. Marin, J. Appl. Phys. 86 (1999) 6222. [19] B.C. Forget, D. Fournier, V.E. Gusev, Appl. Surf. Sci. 63 (1993) 159–255. [20] A. Mandelis, A. Othonos, C. Christofides, J. Boussey-Said, J. Appl. Phys. 80 (1996) 9. [21] M. Nestoros, Y. Karmiotis, C. Christofides, J. Appl. Phys. 82 (1997) 15. [22] Bincheng Li, Derrick Shaughnessy, Andreas Mandelis, Jerias Batista, J. Appl. Phys. 95 (2004) 7832. [23] D. Fournier, C. Boccara, A. Skumanich, N.M. Amer, J. Appl. Phys. 59 (1986) 787. [24] Anita R. Warrier, Tina Sebastian, C. Sudha Kartha, K.P. Vijayakumar, J. App. phys 107 (2010) 073701. [25] S. Ilahi, F. Saadalah, N. Yacoubi, Appl. Phys. A 110 (2013) 459–464. [26] S. Ilahi, N. Yacoubi, F. Genty, J. App. Phys. 113 (2013) 183705. [27] Imen Gaied, Aymen Amara, Noureddine Yacoubi, Taher Ghrib, J. App. optics 47 (2008). [28] Sajan D George, Dilna S.P. Radhakrishnan, C.P.G. Vallabhan, V.P.N. Nampoori, Phys. stat. sol. (a) 195 (2003) 416–421. [29] A. Lindsay, E.P. O’Reilly, Phys. Stat. Sol. 5 (2008) 454–459. [30] A. Lindsay, E.P. O’Reilly, Phys. Rev. B. 76 (2007) 075210. [31] P. Rodriguez, L. Auvray, H. Dumont, J. Dazord, Y. Monteil, J. Cryst. Growth 298 (2007) 81. [32] H. Dumont, L. Auvray, Y. Monteil, F. Saidi, F. Hassen, H. Maaref, Opt. Mater. 24 (2003) 303.