American Journal of Applied Sciences 2 (10): , 2005 ISSN Science Publications

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1 American Journal o Applied Sciences (10): , 005 ISSN Science Publications Determination o Absorption Coeicients and Thermal Diusivity o Modulated Doped GaAlAs/GaAs Heterostructure by Photothermal Delection Spectroscopy 1 S. Aloulou, M. Fathallah, 1 M. Oueslati and 3 A. Saxi 1 Equipe de spectroscopie Raman, Faculté des sciences de Tunis Laboratoire de physique des semi-conducteurs et dispositis électroniques de Tunis 3 Laboratoire de Physique des Semi-conducteurs, Faculté des Sciences de Monastir Abstract: We report in this study theoretical and experimental studies o photothermal delection spectroscopy (PDS) or planar doped heterostructures AlGaAs/GaAs. The PDS spectra at T=300K are recorded by varying the wavelength o the excited radiation or dierent modulation requencies. They show two dierent regions related to the undamental electronic transitions rom GaAs and Si doped AlGaAs. The DX levels have been observed approximately at ev below the conduction band edge o Si doped Al 0.33 Ga 0.67 As (Eg=1.835 ev at 300 K). We give in this study a method o measuring the absorption coeicient o AlGaAs/GaAs heterostructures rom the amplitude measurement o PDS signal. The optical absorption coeicient ound was between 10 and 10 5 cm -1 in the energy range 1-.5eV or samples. The PDS data are compared with those given by conventional transmission technique. The evolution o PDS amplitude spectra by varying the modulation requency rom 5 to 100 Hz (usually called depth proile analysis) and using He-Ne laser probe beam shows that the PDS signal amplitude increases with decreasing the modulated requency. A numerical procedure is applied to it the measured amplitude o the PDS signal. The value o thermal diusivity (D s =0. 7cm s 1) shows a very good agreement with results given by spectroscopic ellipsometry. Key words: Heterostructures, AlGaAs/GaAs, photothermal delection spectroscopy INTRODUCTION Two dimensional GaAlAs/GaAs structures grown by molecular beam epitaxy (MBE) have been achieved using modulated doping techniques [1]. When a doped GaAlAs layer is grown on top o an undoped GaAs layer, a two dimensional electron gas (DEG) can be ormed at the interace []. This is due to the electron ainity dierence between the two materials. The introduction o undoped space layer separates the electron in the channel and their parent donors. Thus it reduces considerably the coulomb eects between carriers and ionized impurities and produces an increase o the mobility o the DEG in the channel. The structure studied in this work is a two δsi modulated doped GaAlAs/GaAs heterostructure elaborated according to the model proposed by Schubert et al. [3]. In the present study we report results o photo thermal delection spectroscopy (PDS) [4,5]. The aim o the PDS experiment is to determine the absorption coeicient o the thin layer structure in the visible spectral range. The absorption spectra show two maxima A (1.43 ev) and B (1.83 ev) respectively due to undamental electronic transitions rom GaAs and Ga 0.67 Al 0.33 As layers. A simpliied one dimensional model similar to Rosencwaig and Gersho (R.G) theory [6] is used or the theoretical analysis. It is solved or two layer sample. In the case o optically transparent samples (β i l i <1) and thermally thin (µ i >l i ) it is possible to divide the PDS signal in two contributions. β 1 and β are the absorption coeicient o the irst layer and the second layers o the sample. The optical absorption coeicients o GaAs and Al 0.33 Ga 0.67 As compounds vary rom 10 to 10 5 cm -1 in the energy range 1-.5eV. PDS measurements are compared with those obtained by conventional optical methods. In this study we present also a method that enables one to evaluate the thermal diusivity o the sample. This method is based on the analysis o both the measured amplitude o the PDS (recorded by varying the modulation requency rom 5 to 100Hz) and the theoretical data obtained by using an adequate model. Theoretical model: Mandelis has presented a one dimensional theory o PDS [7] using an analytical method similar to R.G theory [8]. As this theory is or thermally thick bulk samples, it is necessary to take into account the multiple relection o the incident light in the ilm. Figure 1 shows the one dimensional model used or the theoretical analysis. It is solved or three one dimensional layers o a high reractive medium, a thinilm sample and the backing material. The pumping beam is used to illuminate the sample at x=0 and L in the Fig. 1. Corresponding Author: S. Aloulou, Equipe de spectroscopie Raman, Faculté des sciences de Tunis, Fax:

2 Am. J. Appl. Sci., (10) : , 005 α I 0 ( 1 R 0 ) Q = K e ( α σ s ) σ ( )( ) sd σ r 1 b 1 e ( r 1)( b 1) e sd ( b r ) e α d σ ( g 1)( b 1) e sd σ ( g 1)( b 1) e sd + + (3) Fig. 1: Geometry o one-dimensional theoretical model or PDS In a one dimensional geometry case, the expression o the PDS signal S is given [9] : S L dn dt e = n0 dt dz z0 where, 1 dn n dt 0 iπν t (1) is the relative index inreraction change 1 dn with temperature o the delecting medium, is n0 dt larger or CCl 4 (510-4 K -1 ) than or air (10-6 K -1 ), L the interaction length, ν the modulation requency and z 0 the distance o the probe beam rom the sample surace. The temperature distribution in the delecting medium T (z) is complex and given by the equation (): T (z) = Qexp( σ z) () where, σ = (1 + j)( πν / D ) = (1 + j) / µ. µ i is the 1/ i i i thermal diusion length and D i the thermal diusion constant. Here the index I take the subscripts, and b or the ilm sample, luid and backing material respectively. Q is the complex temperature rise above the average temperature on the sample surace and its expression is obtained by solving the one dimensional heat equation in the dierent environments sample, luid and packing material and assuming a continuity o the temperature and the heat lux at the dierent interace. In the case o homogeneous optically absorbing sample and or a sample made o one layer the expression o Q is given by [10] : where, α is the optical absorption coeicient, K i the thermal conductivity and R 0 the reraction actor: g = K µ S / KSµ, b = K bµ S / KSµ b, σ S = (1 + j) / µ S et αµ s r = (1 j) Q is a complex parameter depending on the optical and thermal proprieties o the sample. The amplitude A and the phase ϕ o the PDS signal are inally given [9] : dn L 1/ A = ( Qr + Qi ) e n dt µ 0 Q z π Q 4 1 i 0 φ = tg r µ z0 µ (4) (5) where, Q r and Q i are the real and imaginary part o Q respectively. Saadallah [11] introduced a general orm or the expression o the periodic temperature surace o a semi conducting multilayer sample, deposited on a substrate and heated using a modulated light beam. It showed a good agreement with the experimental data when the sum o the thickness o all layers is much smaller than the thickness o the substrate. McGahan [1] introduced an analytical expression or the surace temperature based on Green s unctional treatment o heat condition equation. In this work we used the expression o T given by equation (4) o re [9] in the many layer case, determined without any assumption on the value o the layer thickness. This expression was obtained by resolving the heat equation in the dierent media with suitable boundary conditions. It showed a very good agreement with data obtained using GaAs and AlGaAs/GaAs hetero structures. Table 1 lists the physical constants used in our calculations. Samples and experimental setup: The samples used in this study are GaAs compound and three AlGaAs/GaAs modelled doped hetero structure grown by molecular beam epitaxy on semi-insulating GaAs (001) substrate and elaborated according to the model proposed by Schubert et al. [13]. Heir structures are illustrated in Fig.. Two delta doping monolayer were incorporated. The irst planar doping δ 1 Si (N D δ1 = 10 1 cm - ) is introduced in a plateau (Sample S 1, x=0. 33), in a narrow QW (Sample S x=0. 4), or in a barrier (Sample S 3 x=0. 41) as it is shown in Fig

3 Am. J. Appl. Sci., (10) : , 005 Table 1: Physical constants used in theoretical calculations [14] Thermal conductivity K (W/cm K) Density ρ (g/cm 3 ) Speciic heat C (J/g K) Thermal diusivity D=K/ρC (cm /s) GaAs Al xga 1-xAs x +.48x x x x +1.46x CCl Fig. : Schematic cross section o sample Fig. 4: PDS spectra o 375µm GaAs compound This deviation is measured by using a position photodetector attached to a look in ampliier. The PDS spectra are normalized by to the lux o incident photons. Fig. 3: The sel consistent calculation o the conduction band structure, the levels energy and the corresponding wave unctions, or samples S 1 (a), S (b) and S 3 (c) The second planar δ Si (N D δ=10 13 cm - ) is placed in Al 0.33 Ga 0.67 As at 150Å rom the cap layer in order to compensate the electrical charge needed or surace depletion. The sample is heated using a 1000W halogen lamp placed behind the slot o a monochromator. Light coming out o the monochromator is chopped using a mechanical chopper. The optical absorption is generated in the sample a thermal wave which propagates until the CCl 4 luid and creates a temperature gradient causing a reractive index gradient, hence a deviation o the probe laser beam. RESULTS AND DISCUSSION The Fig. 4 shows the PDS amplitude spectra (curve S(E)) o a thick GaAs compound (375µm) used as a substrate or the elaboration o our heterostructures, at the modulated requency =13Hz. The thermal diusion length µ s or this sample GaAs is large compared to his thickness at this modulated requency (µ s = 871µm). So we considerate the sample as thermally thin. The PDS spectrum has been normalized by the saturated intensity just beore the onset o a sudden decrease. The phase inormation is obtained rom both calculations and experiments. The phase spectra, however, indicate only a constant value because the sample is thermally thin. Thereore the α dependences o the phase shit contain little inormation. The optical absorption coeicients α were derived rom the PDS amplitude spectrum by comparison with the theoretical analysis. For a GaAs sample o thickness L=375 µm and or the modulated requency =13Hz, we plot the theoretical PDS amplitude calculated rom Eqs (4) and (5) o re [9] (by setting l 1 =l =0 ) as a unction o the optical absorption coeicient α. The theoretical curve S(α) in Fig. 5 shows the dependence o the normalized amplitude o the PDS signal on the optical absorption coeicient. In the low- α range the delection amplitude increases with increasing α; but in the large -α range the signal saturates to a constant value. This saturation occurs or optically opaque and thermally thin (µ s >L>1/α) sample. 1414

4 Am. J. Appl. Sci., (10) : , 005 Fig. 5: Determination o the absorption curve α c (ђω) Fig. 6: Transmission and relection spectrum o GaAs compound Fig. 8: PDS spectrum o S 1, S and S 3 samples We have measured the optical transmission coeicient and relection coeicient o the ultra polished GaAs sample. The thickness is determined by using an electronic microscope (d= 5µm). We present in Fig. 6 the relectance R and transmittance T spectra obtained or the same GaAs sample. We present in Fig. 7 the absorption coeicient α 0 GaAs calculated by using the ollows equation [14] : Fig. 7: The adjusted photodelexion spectrum and the absorption curve α ( ħω ) C deduced rom PDS measure and theoreticthe resultslts agree with results obtained by Casey From the measured PDS spectrum we determine the absorption coeicient α c (E) by corresponding the theoretical normalized curve S (α) and the experimental curve S (E) or each value o excitation energy E (Fig. 5). The results obtained appear in Fig. 7 (curve α c ), and they can be compared with that deduced rom optical measures. 1 ( 1 R ) ( 1 R 1 ) α o = Log + R + d T T We report also in Fig. 7 the absorption curve α c (E) deduced rom PDS measure and experimental results obtained by Casey [15] From spectroscopic ellipsometry measurement. We notice a good agreement between these spectra or 1.3eV < E < 1.45eV. That shows the best choice o the model o calculation used. It is possible to see that photo delection spectroscopy gives the absorption spectra over the undamental gap. To make a comparative study with classical optics it would be necessary to use much thinner samples, but it would be diicult to obtain suiciently good optical polishes. 1415

5 Am. J. Appl. Sci., (10) : , 005 Table : Values o thermal diusivity, thermal diusion lengths calculated rom the requency =13Hz and thickness d i o each layers constituting the sample Layers Thickness (µ m) Thermal diusivity cm /s Thermal diusion length (µm) Capsule GaAs Al 0.33Ga 0.67As GaAs Fig. 9: Optical absorption spectra o the thick sample S 1 We report on the Table values o thermal diusivity, thermal diusion lengths calculated rom the requency =13Hz and thickness d i o each layer constituting the sample. The thermal diusion lengths µ i = (D i /π ) 1/ or use modulated requency (Table ) is large compared to the thickness o each layer. So we considerate the sample as thermally thin. Yasuhiro et al. [16] treated the multi-layer model in which the incident light was assumed to be entirely absorbed at the surace o the sample. The approximate ormula o the PDS signal in this case indicates the possibility o investigating two optical absorption coeicients o the irst and second layers o the sample. So the PDS signal is the sum o two contributions coming respectively rom GaAs and Si doped Al 0.33 Ga 0.67 As layers: I µ 0 b s = (1 j) α i li = s1 + s a k b i = 1 Fig.10: PDS amplitude spectra o the sample S 1 as a unction o wavelength and or various modulated requencies The PDS thus appears particularly interesting because the experiment has been perormed without any particular sample preparation with unpolished suraces. Figure 8 shows the photo thermal delection signal obtained rom S 1, S and S 3 samples at room temperature and at =13Hz as a unction o photon energy. The three spectra present the same appearance but they are so dierent in amplitude. The peaks A (1.44 ev), B (1.67eV) and C (1.894 ev) dominate S 1, S and S 3 spectra, correspond respectively to optical transition band-band in GaAs, valence band-dx centre and door-acceptor in Si-doped Al 0.33 Ga 0.67 As. PDS measurements show that the presence o the DX center in Al 0.33 Ga 0.67 As barrier can control the electron population in GaAs channel. The DX central eects are reduced when the irst δ-doping plane is introduced in a thin quantum well QW (Sample S ) To determine the absorption spectra o S 1, we adjust the corresponding PDS spectrum to the absorption spectrum o GaAs substrate. We obtain thus absorption spectra o the sample S 1 represented in Fig. 9. Figure 10 shows the PDS amplitude spectra o the sample S 1 and or dierent modulated requencies (13Hz, 53Hz and 93Hz). It is pointed out that the shit o the absorption curves is due to the dierence in the thickness o thermal active layers at the sample which has an inluence on the photo thermal delection signal since µ s > L s. The procedure or inding the thermal diusivity coeicient o the sample is as ollows. First the PDS spectrum o the sample was recorded by varying the modulated requency rom 10 to 100Hz. The excitation radiation, used was 63.8nm He-Ne. For this requency range and this excitation energy where the sample is thermally thin (σ s d<<1) and optically opaque (α>>1) the equation (3) can be written as: L dn A = n dt 0 ( ) ( + ) I 1 R D π exp( z ) K b g D D 0 0 s 0 e (7) The simple orm o A that correspond to the sample used in this work: 4 A Ds exp( 0.68z0 ) = (8)

6 Am. J. Appl. Sci., (10) : , 005 Fig. 11: Fitting results o the PDS amplitude as unction o the modulated requency As the relationship between the PDS amplitude and the modulated requency we it the experimental data. The best it curve, is shown in Fig. 11. The good agreement between the experimental and theoretical results demonstrates the reliability o the adopted theoretical approach. From the experimental results we can deduce by comparison with the corresponding theoretical variation in Fig. 11. The value o D s (D s =0.7 cm /s). This D s value is in good agreement with previous work [17,18]. CONCLUSION In this work, we have presented a method to determine quantitatively the optical absorption spectra o thin ilms using the high sensitive technique o photo thermal delection spectroscopy. In addition the PDS measurement enables us to evaluate the thermal diusivity o the sample. REFERENCES 1. Saxi, L., L. Bouzaine and H. Maare, Microelectronics J., 30: Aloulou, S., M. Oueslati, A. Metah, L. Saxi, H. Maare and R. Chtourou, 000. J. Maghrébin de Phys. 1: Schubert, E.F., J.E. Cunningham, W.T. Tsang, G.L. Timp, Appl. Phys. Lett., 51: Fournier, D. Boccara and A.C. Badoz, J. Appl. Phys. Lett., 36: Jackson, W.B., N. Amer, M. Boccara and A.C. Fournier, Appl. Optics, 0: Rosencwaig, A. and A. Gersho, J. Appl. Phys., 47: Mandelis, A., In: Photoacoustic and Thermal Wave Phenomena in Semiconductors. Edit. A. Mandelis, North Holand, New York. 8. Rosencwaig, A., Photoacoustics and Photoacoustic Spectroscopy. Wiley, New York. 9. Zammit, U., M. Marinelli and R. Pizzoerrato. J. Appl. Phys., 69: FESQUET, J., B. Girault and M.D.M. Razaindrandriatsimany, Appl. Optics, 3: Fernelius, N.C., Extension o Rosencwaig- Ghessho uturistic spectroscopy theory to include the eect o a sample coating. J. Appl. Phys., 51: Glorieux, C., J. Fivez and J. Thoen, Photoaccoustic investigation o the thermal properties o layered materials: Calculation o the orward signal and numerical inversion procedure. J. Appl. Phys., 73:. 13. Aloulou, S., H. Ajlani, A. Metah, M. Oueslati, L. Saxi and H. Maare, 00. Materials Science and Engineering B., 96: Oueslati, M., C. Hirlimam and M. Balkanski, J. Phys., 4: Casey, M.C., D.D. Sell et K.W. Wecht, J. Appl. Phys., 46: Fujii, Y., A. Moritani and J. Nakai, Jap. J. Appl. Phys., 0: Rtolotti, V.D., G. L. Liakhou, R. Li Voti, S. Paoloni and C. Sibilia, Rev. Sci. Instrum., 64: Boltz, R.E. and G.L. Tuve (Eds.), Book o Tables or Applied Engineering Science. nd Ed., 5CRC Press, Boca Raton, Florida, pp: