deposition (MOCVD) on an InP substrate and consisted of the following layers: an In0.818Ga0.182As0.4P0.6 (30 nm) separate-confinement-heterostructure (SCH) layer, a 5 pe-riod stack of In0.82Ga0.18As0.785P0.125 /In0.725Ga0.275As0.535P0.465 (60/90 Å) multiple quantum wells (MQWs), an In0.818Ga0.182As0.4P0.6 (30 nm) SCH layer, a Zn-doped InP (0.1 µm) cladding layer, an In0.818Ga0.182As0.4P0.6 (20 nm) etching-stop layer, and a Zn-doped InP (0.45 µm) buffer layer. In order to investigate the effects of ion implantation and annealing on the interdiffusion, we prepared four samples designated as A, B, C and D. Each sample with an area of 2 × 5 mm located at the near region on the same wafer. After the base structure was performed, a 400 nm thick SiO2 layer was selectively grown on the area of samples A and C to block the ion bombardment. Phos-phorous ions with a dose of 5 × 1014 (cm–2) and an energy of 100 keV were uniformly implanted on the wafer. In or-der to avoid the tunneling effect, the implantation has been done in a tilt angle of 7° and at the same time the substrate was heated up to temperature of 200 °C. Before proceeding to the RTA process, the wafer was separated into four dif-ferent pieces and the SiO2 mask layer on samples A and C was leaved off. A successive RTA process was applied to these samples at temperature of 670 °C. The annealing time applied to samples A and B is 60 s, and is 120 s for samples C and D. Finally, the three layers above the top SCH layer have been etched for the convenience of optical measurements.
The PR measurement was achieved using a 10 mW He – Ne laser, chopped at 200 Hz, as the modulating source.
The laser intensity was reduced to about 10% of its initial
value by using a neutral density filter. The monochromatic probe light was provided by a 150 W tungsten-halogen lamp filtered by a 0.25 m monochromator. The reflected light was detected by an InGaAs photodetector, and the signal was recorded from an NF model 5610B lock-in am-plifier. The PL measurements were excited by the same He – Ne laser with a power density about 100 mW/cm2, and the luminescent signal was recorded by the same detecting devices described above.
3 Results and discussion Figure 1(a) to (d) show the PL and PR spectra by the dotted and solid lines, respec-tively, taken at 300 K from the samples A, B, C and D.
Only one PL feature, which is attributed to the 11H radia-tive recombination, is observed for each sample. Compar-ing the PL spectra of samples A and B, the effect of ion implantation on the interdiffucation can be achieved. We found that the transition energy of 11H shifts from 0.796 eV (sample A) to 0.821 eV (sample B). Note that sample A has an intentionally deposited SiO2 mask layer on its top to prevent the ion bombardment, while the sam-ple B has no protection layer. Since the annealing param-eters are the same for these two samples, the shift is re-sponsible for the effect of ion-induced vacancies resulting from implantation process. The energy shift reflects the fact that the degree of intermixing has been enhanced by these vacancies, which diffuse down to the quantum well region enhancing the interdiffusion. A similar result is found in the PL spectra of samples C and D, its peak moves from 0.804 eV (sample C) to 0.848 eV (sample D).
This larger energy shift is due to the continuously interdif-fusion enhancement under longer annealing times. For each PR spectrum shown in Fig. 1, three excitronic fea-tures are observed, and these spectra have been fitted by least-square fits to the first derivative Lorentzian line shape (FDLL), as shown by the open circles. The obtained inter-subband energies of mnH(L) transitions are indicated by arrows in Fig. 1. Comparing the 11H transition energy of these four samples, it is found that for samples A and B the transition energy shifts from 0.793 eV to 0.819 eV, and for samples C and D the transition energy moves from 0.802 eV to 0.845 eV. A consistent result is observed from the transition energy of 11H extracted from PL and PR spectra. In order to analysis the degree of intermixing for these samples, it is necessary to calculate the well- and bar-rier- shapes after diffusion, and then solve the Schrödinger equation for the resulting conduction- and valence-band energy profiles. The theoretical analysis used in this paper is described as follows. However the diffusion may be af-fected by strain and defect concentraction, a constant diffu-sivity can be used in a short annealing time range. For long annealing duration a diffusion equation including the strain effect has been formulated by Ryu et al. in Ref. [7]. In this work, we assume that the interdiffusion between the well and barrier materials obeys Fick’s law. The interdiffusion of Ga (and In) atoms is characterized by a diffusion length Ld(III), which is defined as Ld(III)= DtD, where D is the dif-
Phys. Status Solidi A 206, No. 5 (2009) 793
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Figure 1 PL and PR spectra presented by the dotted and solid lines, respectively, taken at 300 K from the samples A (a), B (b), C (c) and D (d). The open circles show the least-square fits to the first derivative Lorentzian line shape.
fusion coefficient, and tD is the diffusion time. On the other hand, the interdiffusion of P (and As) atoms is character-ized by another diffusion length Ld(V). Due to the intermix-ing across the well and barrier materials, the compositional profile is changed from a square into an error function curve, therefore the strain profile and the bandgap energy are also modified. Assuming that the diffusion obeys Fick’s law, the constituent atoms compositional profile in the growth direction has been modeled using an error
func-tion. Using the Ga composition profile as an example, which can be given by: is the number of barriers, erf (y) denotes the error function, z ⭌ 0 is the growth axis of the MQW layers, ai and bi are the left and right interface positions, respectively, of the i-th as-grown barrier within the MQWs, while c1 and c2 are that at the two end positions of the as-grown MQWs. Simi-larly the As composition profile after intermixing can also be described by Eq. (1) as a function of Ld(V). The parame-ter kd is defined as kd = Ld(V)/Ld(III), so that when kd < 1 the interdiffusion rate on the group-V sublattice is less than the interdiffusion rate on the group-III sublattice, and vice versa.
The strain-dependent energy difference between the conduc-tion band and heavy- and light-hole bands are given by:
C,HH 0 ( ) ,
E =E + aα-bβ ε (2)
C,LH 0 ( ) ,
E =E + aα+bβ ε (3)
where E0 is the direct band gap of unstrained InGaAsP, a and b are the interband deformation potentials, ε is the strain, and α and β are functions of the elastic-stiffness constants Cij:
The physical parameters such as lattice constant, effective mass, elastic constants and deformation potentials for In1–xGaxAsyP1–y are determined by Eq. (6)
Using the material parameters in Ref. [8]. and assum-ing that kd = 0.315, the potential profiles of a five-period MQW structure with different values of Ld(III) are shown in Fig. 2. It can be seen that the potential profiles change gradually from an abrupt one to broaden error function profiles as the interdiffusion length is increased.
The electron- and hole-subband energies can be de-duced by solving the appropriated Schrodinger equation, using the envelope function scheme with an effective mass approximation. The one-electron Schrödinger equation for the intermixed QW can be written by:
2
794 D. Y. Lin et al.: Interdiffusion in InGaAsP multiple-quantum-well structures
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physica
p s s
statusFigure 2 Confinement profiles of the conduction, heavy- and light-hole bands of MQW structure calculated at different diffu-sion lengths.
where z is the growth direction, ψrl( )z is the envelope func-tion, m* is the effective mass, Er1 is the quantized energy level with respect to the subband energy zeroed at the bot-tom of the QW, and r = c, hh or lh refers to the electron, heavy- or light-hole band, respectively. This equation is solved numerically to obtain the quantized energy levels and the envelope wavefunctions. Figure 3 shows the transi-tion energy of 11H as a functransi-tion of diffusing length of Ld(III). The four curves present the calculated results using different kd parameter increasing from 0.3 to 0.9. As de-scribed above, the composition profile after interdiffusion is characterized by a diffusion length Ld= Dt where D D, is the diffusion coefficient and tD is the diffusion time, i.e.
annealing time. The annealing time of sample C is twice of that for sample A, so the diffusion length of sample C should be in a factor of 2 the diffusion length of sample A. As illustrated in Fig. 3, the 11H transition energies of samples A and C deduced from PR spectra are indicated by open and solid squares, respectively. Following this crite-rion, we found that the experimental data match well to the theoretical curve with kd = 0.3 at the diffusion length of 13 Å and 18 Å for samples A and C, respectively. This analysis is also applied on samples B and D, we find that a well match between PR data, shown by open and solid tri-angles, and theoretical calculation is found on the curve with kd = 0.7. The diffusion length of group-III atoms is in-creased to 16 Å and 23 Å for samples B and D. Due to complex mechanisms of intermixing in quantum well structure, the diffusion length can be affected by dielectric capping materials and thickness, quantum well composi-tions, implantation and annealing conditions. A dielectric capping layer such as SiO2 or SiNx will enhance the diffu-sion by increased vacancies. In this study low-energy P+ ions were used to create point defects well above the active region. So the amount of defects is strongly correlated to the amount of diffusion length. Under the effect of low-
Figure 3 11H transition energies in a function of diffusion length calculated at different ratios of diffusion length between group III and group V atoms. The experimental data are shown by sym-bols.
energy ion implantation the diffusion length of group-III elements has been enhanced. Based on our knowledge, the diffusion length with the similar implantation and anneal-ing conditions has not been reported. Compared to the data reported in Ref. [9], the diffusion length of group-III elements in InGaAsP/InP multiquantum-well structure changes from 5 Å to 20 Å for different annealing times.
From the amount of PL blueshift of 11H transition ob-served in our study, the diffusion length has been estimated quite reasonably. It is worth to point out that the increase of kd implies the interdiffusion rate of the group-V sublattice has been enhanced through P+ ions implantation process.
Concerning to the PR spectra in Fig. 1, besides the 11H ground state transition, we also found two additional reso-nances located at higher energies, which were attributed to
0 5 10 15 20 25 30
Figure 4 Energy difference between 11L and 11H as a function of the diffusion length calculated at different ratios of diffusion length between group III and group V atoms. The experimental data are shown by symbols.
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the 12H and 11L transitions. The 11H and 11L features correspond to the transitions originating from the ground state of heavy- and light-hole bands to the same ground state of conduction band, respectively. For the as-grown sample, the lattice constant of barrier materials is nearly matched to InP substrate while the lattice constant of well materials is larger than that of InP substrate. A compres-sive strain exists in the well material and produces energy splitting between heavy- and light-hole bands. If the strain in the well material is relaxed, the energy gaps between the heavy- and light-hole bands will be changed. Since the ef-fective mass does not strongly depends on the strain, so the energy difference between the 11H and 11L transitions can be used as a sensitive parameter to monitor strain varia-tions. During the interdiffusion process, the Ga and P at-oms were diffused into the well material and the As and In atoms were moved out of the well material. The compo-sitional broadening due to QWI will induce a strain-redistribution and make a change in the splitting energy between heavy- and light-hole bands. Figure 4 shows the energy difference between the 11H and 11L transitions as a function of diffusion length. In Fig. 4 the solid lines show the calculated results as a function of diffusion length of group III atoms using different values of kd. For as-grown structure the energy difference between 11L and 11H is about 115 meV. Due to the compositional broadening and strain effect, when the interdiffusion length increases, the transition energies of 11H features shift faster than that of 11L transitions. As we can see in Fig. 4, the solid line (kd = 0.3) shows that for the energy difference between 11L and 11H decreases to 108 meV and 102 meV as the diffusion length increases to 13 Å and 18 Å, respectively.
The open and solid squares in Fig. 4 show the energy dif-ference between 11L and 11H transitions for samples A and C, respectively. It is observed that the experimental data match well with the calculated line with kd = 0.3. As shown in Fig. 4, the open and solid triangles, respectively, which represent the energy difference between 11L and 11H transitions of samples B and D, indicate a larger de-crease than the shift observed in samples A and C. A good agreement between the PR data and calculation results is achieved using kd = 0.7. Because the samples B and D do not have SiO2 mask on their top to block the implantation ions, the implantation induce vacancies make an enhanced diffusion length and kd, hence a broadened composition distribution is observed. On the basis of the good
agree-ments observed in Figs. 3 and 4, we concluded that the dif-fusion coefficients and the ratio of difdif-fusion rates between the group-V and group-III atoms has been enhanced due to the P+ ion implantation.
4 Conclusions The effect of compositional