Optoelectronics Materials and Techniques Part 13 docx

An Analytical Solution for Inhomogeneous Strain Fields Within Wurtzite GaN Cylinders Under Compression Test 349 to constant strain without end friction and 1 α = . Fig. 4 shows the normalized axial strain 0 / zz zz εε versus the normalized vertical distance z/h for various values of α for r/R=0.0 and r/R=0.5, and 0 zz ε is the axial strain of the cylinder under compression without end friction and can be calculated according to (7). Fig.4 shows that the axial strain is also inhomogeneous, and the maximum values can be more than 40% and 30% for r/R=0.0 and r/R=0.5 respectively, comparing to that without end friction. Fig. 5 shows the normalized strain 0 / H H εε versus the normalized vertical distance z/h for various values of α for r/R=0.0 and r/R=0.5, and 0 H ε is the strain of the cylinder under compression without end friction and can be calculated according to (58). Fig.5 shows that the normalized strain 0 / H H εε is quite inhomogeneous, and the maximum values can be 100% and 53% more than those without end friction for r/R=0.0 and r/R=0.5 respectively. Overall, the inhomogeneous strain distributions are induced in the cylinder as long as friction exists between the end surface and the loading platens, and the larger the friction on the end surfaces, that is, the smaller the value of β , the more non-uniform inhomogeneous strain is induced within the cylinder. 9.2 The strain distributions within cylinder for different shape of cylinder All of the numerical calculations given above are for / 2.0hR= . In order to investigate the shape effect on the strain distribution within cylinder under compression with end friction, Figs. 6-8 plot the normalized strains 0 / rr rr εε , 0 / θθ θθ εε and 0 / zz zz εε versus the normalized vertical distance z/h from the center of the cylinder for various values of h/R for r/R=0.0 and 0.0 β = . Figs. 6-8 show that a larger deviation may be induced for shorter cylinder. For example, 35% error in 0 / H H εε can be induced even at the center of the cylinder for h/R=0.5. But the strain distributions for long cylinders are more homogeneous, especially the strains are relatively uniform at the central part of the cylinder if / 2 hR≥ . So a relatively long cylinder should be suggested for compression test. Fig. 6. The normalized strain 0 / rr rr εε versus the normalized distance z/h along the axis of loading for various ratios of h/R Optoelectronics - Materials and Techniques 350 Fig. 7. The normalized strain 0 / θθ θθ εε versus the normalized distance z/h along the axis of loading for various ratios of h/R Fig. 8. The normalized strain 0 / zz zz εε versus the normalized distance z/h along the axis of loading for various ratios of h/R 10. The effect of strain on the valence-band structure of wurtzite GaN The band structure of wurtzite GaN deserves attention since the valence bands, such as the heavy-hole, light-hole and split-off bands are close each other. The strain effects on wurtzite GaN are less understand (Chuang & Chang, 1996). Based on the deformation potential theory of Luttinger-Kohn and Bir-Pikus (Bir & Pickus, 1974), the valence-band structure of the strained wurtzite GaN can be described by a 6x6Hamiltonian according to the envelope- function method, and the basis function for wurtzite GaN can be written as An Analytical Solution for Inhomogeneous Strain Fields Within Wurtzite GaN Cylinders Under Compression Test 351 * * * * * * 1()() 22 2()() 22 3 4()() 22 5() () 22 6 XiY XiY XiY XiY ZZ XiY XiY XiY XiY ZZ αα ββ ββ αα ββ ββ =− + ↑ + − ↓ =− − ↑ − + ↓ =↑+↓ =− + ↑ − − ↓ =−↑++↓ =− ↑ + ↓ (59) where (3 /4 3 /2) ( /4 /2) (1/ 2) , (1/ 2 ) ii ee πφ πφ αβ ++ ==and 1 tan ( / ) y x kk φ − = . The 6x6 Hamiltonian is obtained as 33 33 () 0 () 0() U L Hk Hk Hk × × ⎡ ⎤ ⎢ ⎥ = ⎢ ⎥ ⎣ ⎦ (60) and 33 tt t U tt t ttt FK iH HKG iH iH iH λ × − ⎡ ⎤ ⎢ ⎥ =Δ− ⎢ ⎥ ⎢ ⎥ Δ+ ⎣ ⎦ (61) 33 tt t L tt t ttt FK iH HKG iH iH iH λ × ⎡ ⎤ ⎢ ⎥ =Δ+ ⎢ ⎥ ⎢ ⎥ −Δ− ⎣ ⎦ (62) 12ttt F λθ =Δ +Δ + + (63) 12ttt G λθ =Δ −Δ + + (64) 2 222 12 12 0 [()] () 2 ttztx y zz xx yy Ak A k k D D m λεεε =+++++ = (65) 2 222 34 34 0 [()] () 2 ttztx y zz xx yy Ak A k k D D m θεεε =+++++ = (66) 2 22 5 0 () 2 ttx y KAkk m =+ = (67) Optoelectronics - Materials and Techniques 352 2 221/2 6 0 () 2 ttx y z HAkkk m =+ = (68) 3 2Δ= Δ (69) where 3421 2 tttt AAAA=− = − (70) 35 6 42 tt t AA A+= (71) 32 Δ=Δ (72) The valence-band structure can be determined by det[ ( ) ] 0Hk EI−= (73) which leads to 32 2 210 ()0 ttt ECECEC+++= (74) where 2 () tttt CFG λ =− + + (75) 22 2 1 2 ttttttt t t CFGG F K H λλ =++−Δ−− (76) 033 det[ ] U CH × =− (77) so we obtained HH t EF= (78) 2 2 () 22 tt tt LH GG E λλ +− =+ +Δ (79) 2 2 () 22 tt tt SO GG E λλ +− =− +Δ (80) where HH E , LH E and so E are the energies for the heavy-hole the light-hole and split-off bands, respectively. 11. Conclusions The exact analytical solution for the inhomogeneous strain field within a finite and transversely isotropic cylinder under compression test with end friction is derived. The method employed Lekhnitskii's stress function in order to uncouple the equations of An Analytical Solution for Inhomogeneous Strain Fields Within Wurtzite GaN Cylinders Under Compression Test 353 equilibrium. It was found that the end friction leads to a very inhomogeneous strain distribution within cylinder, especially in the area near the end surface. Numerical results show that all of the strain components, including the axial, radial, circumferential and shear strains, are inhomogeneous, both in distribution pattern and magnitude, the maximum value of the strain concentration near the end surfaces can be 100% higher than the constant strain in the case without end friction. However, the strain distributions are relatively uniform at the central parts of long cylinders, say in the area of 0.5 0.5hz h−<< , the magnitude of the strains can be more than 2% of that without end friction. The method for analyzing the effect of the strain and end friction on the band structure of wurtzite GaN is discussed, end friction has effect on the shape of constant energy surfaces of valence bands and the band gaps between the heavy-hole, light-hole and split-off bands of wurtzite GaN. 12. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant No. 11032003 and 10872033) and the State Key Laboratory of Explosion Science and Technology. 13. References Bir, G. L. & Pickus, G. E. (1974). Symmetry and Strain Induced Effects in Semiconductors, John Wiley, New York, USA Chau K. T. & Wei, X. X(1999). Finite solid circular cylinders subjected to arbitrary surface load: part I. Analytic solution. International Journal of Solids and Structures, Vol. 37, pp. 5707-5732 Choi, S. W. & Shah, S. P. (1998). Fracture mechanism in cement-based materials subjected to compression. Journal of Engineering Mechanics ASCE, Vol. 124, pp. 94-102 Chuang, S. L. & Chang, C. S. (1996), k⋅p method for strained wurtzite semiconductors. Physical Review B, Vol. 54, pp. 2491-2504 Goroff, I. & Kleinman, L. (1963). Deformation potentials in silicon. III. effects of a general strain on conduction and valence levels. Physical Review, Vol. 132, pp. 1080-1084 Hasegawa, H. (1963). Theory of cyclotron resonance in strained silicon crystals. Physical Review, Vol. 129, pp. 1029-1040 Hussein, A & Marzouk, H(2000). Finite element evaluation of the boundary conditions for biaxial testing of high strength concrete. Material Structure, Vol. 33, pp. 299-308 Jiang, H. & Singh, J. (1997). Strain distribution and electronic spectra of InAs/GaAs self- assembled dots: An eight-band study. Physical Review B, Vol. 56, pp. 4696-4701 Lekhnitskii, S. G(1963). Theory of elasticity of an anisotropic elastic body, English translation by P. Fern , Holden~Day Inc., San Francisco, USA Mathieu, H. ; Mele, P. and Ameziane, E. L., et al (1979). Deformation potentials of the direct and indirect absorption edges of GaP. Physical Review B, Vol. 19,pp. 2209-2223 Pollak, F. H. & Cardona, M. (1968). Piezo-Electroreflectance in Ge, GaAs, and Si. Physical Review, Vol. 172, pp 816-837 Pollak, F. H. (1990). In Strained-Layer Superlattices, edited by T. Pearsall, Semiconductors and Semimetals, Academic, Boston, , USA Suzuki, K. & Hensel, J. C. (1974). Quantum resonances in the valence bands of germanium. I. Theoretical considerations. Physical Review B, Vool. 9, pp 4184-4218 Optoelectronics - Materials and Techniques 354 Singh, J. (1992). Physics of Semiconductors and Their Heterostructures, McGraw~Hill Higher Education, New York, USA Torrenti, J.M. ; Benaija, E. H. & Boulay, C. (1993). Influence of boundary conditions on strain softening in concrete compression test. Journal of Engineering Mechanics ASCE, Vol. 119, pp. 2369-2384 Wei, X. X. ; Chau, K. T. & Wong, R. H. C. (1999). A new analytic solution for the axial point load strength test for solid circular cylinders. Journal of Engineering Mechanics, Vol. 125, pp. 1349-1357 Wei, X. X(2008). Non-uniform strain field in a wurtzite GaN cylinder under compression and the related end friction effect on quantum behavior of valence-bands. Mechanics of Advanced Materials and Structures, Vol. 15, pp. 612-622 Wright, A. F(1997). Elastic properties of zinc-blende and wurtzite AlN, GaN, and InN. Journal of Applied Physics, Vol. 82, pp. 2833-2839 0 Application of Quaternary AlInGaN- Based Alloys for Light Emission Devices Sara C. P. Rodrigues 1 , Guilherme M. Sipahi 2 ,LuísaScolfaro 3 and Eronides F. da Silva Jr. 4 1 Departamento de Física - Universidade Federal Rural de Pernambuco 2 Instituto de Física de São Carlos - Universidade de São Paulo 3 Department of Physics - Texas State University 4 Departamento de Física - Universidade Federal de Pernambuco 1,2,4 Brazil 3 USA 1. Introduction Excellent progress has been made during the past few years in the growth of III-nitride materials and devices. Today, one of the most important application of novel o ptoelectronic devices is the design and engineering of light-emitting diodes (LEDs) working from ultraviolet (UV) through infrared (IR), thus covering the whole visible spectrum. Since the pioneer works of Nakamura et al. at Nichia Corporation in 1993 (Nakamura et al. (1995)) when the blue LEDs and pure green LEDs were invented, an enormous progress in this field was observed which has been reviewed by several authors (Ambacher (1998); Nakamura et. al. (2000)). The rapid advances in the hetero-epitaxy of the group-III nitrides (Fernández-Garrido et al. (2008); Kemper et al. (2011); Suihkonen et al. (2008)) have facilitated the production of new devices, including blue and UV LEDs and lasers, high temperature and high power electronics, visible-blind photodetectors and field-emitter structures (Hirayama (2005); Hirayama et al. (2010); Tschumak et al. (2010); Xie et al. (2007); Zhu et al. (2007)). There has been recent interest in the Al x In 1−x−y Ga y N quaternary alloys due t o potential application in UV LEDs and UV-blue laser diodes (LDs) once they present high brightness, high quantum efficiency, high flexibility, long-lifetime, and low power consumption (Fu et al. (2011); Hirayama ( 2005); Kim et al. ( 2003); Knauer et al. (2008); Liu et al. (2011); Park et al. (2008); Zhmakin (2011); Zhu et al. (2007)). The availability of the quaternary alloy offers an extra degree of freedom which allows the independent control of the band gap and lattice constant. Another i nteresting feature of the AlGaInN alloy is that it gives rise to higher emission intensities than the ternary AlGaN alloy with the absence of In (Hirayama (2005); Wang et al. (2007)). An important issue is r elated to white light emission, which can be obtained by mixing emissions in different wavelengths with appropriate intensities (Roberts (1997); Rodrigues et al. (2007); Xiao et al. (2004)). Highly conductive p-type III-nitride layers are of crucial importance, in particular, for the production of LEDs. Although the control of p-doping in these materials is still subject of discussion, remarkable progress has been achieved (Hirayama (2005); Zhang et al. (2011)) and 14 2 Will-be-set-by-IN-TECH recently reported e xperimental results point towards acceptor doping concentration high as ≈ 10 19 cm −3 (Liu et al. (2011); Zado et al. (2011); Zhang et al. (2011)). The group-III nitrides crystallize in both, the stable wurtzite (w) phase and the metastable cubic (c) p h ase. Unlike for the hexagonal w-structure, the growth of cubic GaN is more complicated due to the thermodynamically unstable nature of the structure. In hexagonal GaN inherent spontaneous and piezoelectric polarization fields are present along the c-axis because of the crystal symmetry. Due to these fields, non-polar and semi-polar systems have attracted interest. One method to produce real non-polar materials is the growth of the c-phase. Considerable advances in the growth of c-nitrides, with the aim of getting a complete understanding of the c-nitride-derived heterostructures have been observed (As (2009); Schörmann et al. (2007)). Successful growth of quaternary c-Al x In 1−x−y Ga y Nlayers lattice matched to GaN has been reported (Kemper et al. (2011); Schö rmann et al. (2006)). The absence o f polarization fields in the c-III nitrides may be advantageous for s ome device applications. Besides, it has been shown that these quaternary alloys can be doped easily as p-type, and due to the wavelength localization the optical transition energies are higher in the alloys than in GaN (Wang et al. (2007)). However, the exact nature of the optical processes involved in the alloys with In is a subject of controversy. Different mechanisms have been proposed for the origin of the carriers’ localized states in the quantum well devices. One is related to the low solubility of InN in GaN, leading to the presence of nanoclusters inside the alloy, which can be suppressed by biaxial strain as predicted and me asured in c-InGaN samples (Marques et al. (2003); Scolfaro et. al. (2004); Tabata et al. (2002)). The s econd mechanism proposes that the recombination occurs through the quantum confined states (electron-hole pairs or excitons) inside the well. In this chapter we show the results of detailed studies of the theoretical photoluminescence (PL) and absorption spectra for several systems based on nitride quaternary alloys, using the  k ·p theory within the framework of effective mass approximation, in conjunction with the Poisson equation for the charge distribution. E xchange-correlation effects are also included within the local density approximation (Rodrigues et al. (2002); Sipahi et al. (1998)). All systems are assumed to be strained, so that the optical transitions are due to confinement effects. The theoretical method will be described in section 2. Through these calculations the possibility of obtaining light emission from undoped (see section 3) and p-doped (see section 4)quaternary Al X In 1−X−Y Ga Y N/Al x In 1−x−y Ga y N superlattices (SLs) is addressed. By properly choosing the x and y contents in the wells and the acceptor doping concentration N A as well X and Y in the barriers, it is shown to be possible to achieve light emission which covers the visible spectrum fr om violet to red. The investigation is also extended to double quantum wells (DQWs), as described i n section 5 , confronting the results with experimental data reported on these systems (Kyono et al. (2006)). The results are co mpared with regard to the PL emissions f or the different systems , also when an external electric field i s present. Finally it is shown that by adopting appropriated combinations of SLs is possible to obtain the best conditions in order to get white-light emission. This fact is fundamental in the design of new optoelectronic devices. 2. Theoretical band structure and luminescence spectra calculations During the last few years, the super-cell  k ·p method has been adapted to quantum wells and superlattices (SLs) ( Rodrigues et al. (2002); Sipahi et al. (1996)). Using this approach, one can self-consistently solve the 8 ×8 Kane multiband effective mass equation (EME) for the charge 356 Optoelectronics - Materials and Techniques Application of Quater nary AlInGaN- Based Alloys for Light Emission Devices 3 distribution ( Sipahi et al. (1998)). The results below are calculated assuming an infinite SL of squared wells along <001> direction. The multiband EME is represented with respect to plane waves with vectors K= (2π/d )l ( l being an integer and d the SL period) equal to the reciprocal SL vector. The rows and columns of the 8 ×8 Kane Hamiltonian refer to the Bloch-type eigenfunctions |jm j  k) of Γ 8 heavy- and light-hole bands, Γ 7 spin-orbit-split-hole band and Γ 6 conduction band;  k denotes a vector in the first SL Brillouin zone (BZ). By expanding the EME with respect to plane waves (z|K) one is able t o represent this equation with respect to Bloch functions (r|jm j  k + Ke z ). For a Bloch-type eigenfunction (z|E  k) of the SL of energy E and wavevector  k, the EME takes the form: ∑ j  m  j K   jm j  kK | H 0 + H ST + V HET + V A + V H + V XC | j  m  j  kK   j  m  j  kK  |E  k  = E(  k)  jm j  kK|E  k  ,(1) where H 0 is the effective kinetic energy operator, generalized for a heterostrucures H ST is the strain operator originated from the lattice mismatch, V HET is the potential that arises from the band offset at the interfaces, which is diagonal with r espect to jm j , j  m  j , V XC is the exchange-correlation potential for carriers taken within Local Density Approximation (LDA), V A is the ionized acceptor charge distribution potential, and V H is the Hartree potential or one-particle potential felt by the carrier from the carriers charge density. So the Coulomb potential, V C given by contribution of V A and V H potentials, can be obtained by means of the self-consistent procedure, where the Poisson equation stands, in the reciprocal space as, ( K | V C   K   = 4πe 2 ε 1 |K −K  | 2  ( K | N A (z)   K   − ( K | p(z)   K   ,(2) with ε being the dielectric constant, e the electron charge, N A (z) the ionized acceptors concentration, and p (z) being the holes charge distribution, which is given by p (z)= ∑ jm j  k∈ em pty states    ( zs | jm j  k)    2 ,(3) where s is the spin coordinate. The next term in the Hamiltonian is the strain potential, V ST . The kind of strain in these systems is biaxial, so it c an be decomposed into two terms, a h ydrostatic term and an uniaxial term ( Rodrigues et al. (2001)). Since the hydrostatic term changes the gap energy, thus not affecting the valence band potential depth, only the uniaxial strain component will be considered ( Rodrigues et al. (2001)). This latter may be calculated by the following expression:  = −2/3D u  xx (1 + 2C 12 /C 11 ),(4) where −2/3 D u is the shear deformation potential, C 11 and C 12 are the elastic constants, and  xx is the lattice mismatch which is given by:  xx =(a barrier − a wel l )/a wel l ,(5) 357 Application of Quaternary AlInGaN- Based Alloys for Light Emission Devices 4 Will-be-set-by-IN-TECH with a barrier and a wel l being the lattice parameters of the barrier and well materials, respectively. Through these definitions one can calculate the Fourier coefficients of the strain operator ( K | (z) | K  ) and express the strain term of the Hamiltonian V ST as follows:  jm j  kK    H S T    j  m  j  kK   = ( K | (z)   K   M j  m  j jm j ,(6) where M j  m  j jm j is defined as M j  m  j jm j = ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ 10 00 0 0 0 −100−i √ 20 00 −10 0 −i √ 2 00 01 0 0 0 i √ 200 0 0 00i √ 20 0 0 ⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ .(7) Exchange-correlation effects can be taken into account in the local density approximation, by adopting a parameterized expression for an inhomogeneous hole gas, applying the exchange interaction only for identical particles and the correlation for all of them ( Enderlein et al. (1997)). The band shift potential V HET is diagonal with respect to jm j , j  m  j ,andisdefinedby  jm j  kK    V HET | j  m  j  kK   = ( K | V HET | K   δ jj  δ m j m  j (8) where ( K | V HET | K  ) are the Fourier coefficients of V HET along the growth direction. From the calculated eigenstates, one can determine the luminescence and absorption spectra of the SL by using the following general expression ( Sipahi et al. (1998)) I (ω)= 2¯h ω 3 c e 2 m 0 c 2 ∑  k ∑ n e ∑ n q , q =hh,lh,so f n e n q (  k)N n e  k  1 − N n q  k  × γ π  E n e (  k) − E n q (  k) −¯hω  2 + γ 2 ,(9) where m 0 is the electron mass, ω is the incident radiation frequency, γ is the emission broadening (assumed as constant and equal to 10 meV), E n e and E n q are the energies associated to n e and n q , respectively, the electron and hole states involved in the transition. The occupation functions N n e  k and [1 − N n q  k ] are the Fermi-like occupation functions for states in the conduction- and valence-band, respectively. For the calculation of luminescence (absorption) spectra, the s um in Eq. ( 9) is performed over the occupied states in the conduction (valence) band, and unoccupied states in the valence (conduction) band ( Sipahi et al. (1998)). The oscillator strength, f n e n q (  k),isgivenby f n e n q (  k)= 2 m 0 ∑ σ e σ q     n e σ e  k    p x    n q σ q  k     2 E n e (  k) −E n q (  k) , (10) 358 Optoelectronics - Materials and Techniques [...]... efficiencies are predicted ( Rodrigues et al (2005)) 362 8 Optoelectronics - Materials and Techniques Will-be-set-by-IN-TECH Fig 4 Theoretical normalized PL (solid line) and electroluminescence (dashed line) spectra for strained undoped In0.1 Ga0.9 N/Al x Gay In1− x −y N SLs, with x = 0.03, 0.10, and 0.20, and y = 0.50, respectively, barrier width d1 = 8 nm and well width d2 = 3 nm The electric field used for... E1 and second occupied heavy-hole level HH2) for N A = 0 and 5 × 1018 cm−3 This behavior is directly related to the transition probabilities in such systems and the potential profile due to the charges distribution The later is determined by the balance between the Coulomb and exchange-correlation potentials contribution which defines the potential bending 364 10 Optoelectronics - Materials and Techniques. .. implantation of Si+ (Iwayama et al., 1994), cosputtering of silicon and silicon dioxide (Zhang et al., 1995), and plasma-enhanced chemical vapor deposition (Inokuma et al., 1998) 376 Optoelectronics - Materials and Techniques On the other hand, for the visible luminescence properties of nanocrystalline silicon, control of the size distribution and surface condition of nanocrystalline silicon with reproducibility... emission in the 366 12 Optoelectronics - Materials and Techniques Will-be-set-by-IN-TECH Fig 10 Calculated PL and absorption spectra, at T = 2 K, for a p-doped (Al0.20 In0.05 Ga0.75 )N/(Al x In1− x −y Gay )N SL, which emits in the blue region (see Table II), for N A = 0 (undoped), NA = 5 × 1018 cm−3 , and NA = 1 × 1019 cm−3 blue region, for NA = 0 (undoped), NA = 5 × 1018 cm−3 , and NA = 10 × 1018 cm−3... spike width is fixed in 4 nm and the well width is varied Application of Quaternary Alloys for Light Emission Devices Application of Quaternary AlInGaN- Based AlInGaN- Based Alloys for Light Emission Devices 367 13 Fig 11 Schematic diagram for the conduction and valence bands of the DQW structure investigated here dw and ds are the well and the spike widths, respectively The interband transition is also... nm the DQW is in an interacting regime and at dw = 5 nm it reaches the changing point from interacting 368 14 Optoelectronics - Materials and Techniques Will-be-set-by-IN-TECH regime to isolated QWs For larger wells, the spike width loses its importance and above dw = 5 nm it occurs a blue-shift in the energy due to the confinement effects for isolated wells Fig 13 presents calculated PL spectra for... p-doped c-Al0.25 In0.05 Ga0.70 N/ Al0.08 In0.37 Ga0.55 N/ Al0.10 In0.10 Ga0.80 N DQWs, for well and spike widths equal to 4 nm and doping N2D = 2 × 1012 cm−2 (dashed-dot line), 4 × 1012 cm−2 (dashed line), 8 × 1012 cm−2 (dotted line), and undoped (solid line) for comparison 370 16 Optoelectronics - Materials and Techniques Will-be-set-by-IN-TECH Fig 15 Theoretical normalized PL spectra at 2 K for strained... 0553-1.05/10/APQ), and FAPESP LS also acknowledges partial support from the Materials Science, Engineering and Commercialization Program of Texas State University 8 References Ambacher, O (1998) Growth and applications of Group III-nitrides Journal of Physics D: Applied Physics, Vol 31, No 20, (October 1998) pp 2653- 2710, ISSN 136 1-6463 As, D J (2009) Cubic group-III nitride-based nanostructures basics and applications... confinement and strain effects, which become stronger as the In content increases As the results described above are from systems where InGaN represents the barriers and the quaternary alloy is in the wells, one can change the picture and start analyzing systems where the barriers correspond to the quaternary alloys while the InGaN alloy forms the wells 360 6 Optoelectronics - Materials and Techniques. .. normal light incident and under vacuum, using a bare silicon wafer as reference in the range of 400 – 4000 cm-1 The optical transmission spectra were measured using an UV/VIS/NIR spectrophotometer (JASCO V-570) 378 Optoelectronics - Materials and Techniques 3 Film structure and morphology In order to further improve properties of hydrogenated nanostructured silicon thin films and performances of related . bands of germanium. I. Theoretical considerations. Physical Review B, Vool. 9, pp 4184-4218 Optoelectronics - Materials and Techniques 354 Singh, J. (1992). Physics of Semiconductors and. |jm j  k) of Γ 8 heavy- and light-hole bands, Γ 7 spin-orbit-split-hole band and Γ 6 conduction band;  k denotes a vector in the first SL Brillouin zone (BZ). By expanding the EME with respect. width is fixed in 4 nm and the well width is varied 366 Optoelectronics - Materials and Techniques Application of Quater nary AlInGaN- Based Alloys for Light Emission Devices 13 Fig. 11. Sche matic