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EFFECT OF AN APPLIED ELECTRIC FIELD ON INTERSUBBAND TRANSITIONS IN STRAINED In xGa 1¹xAs/InP COUPLED DOUBLE STEP QUANTUM WELLS T.W. Kim* and J.H. Kim Department of Physics, Kwangwoon University, 441-1 Wolgye-dong, Nowon-ku, Seoul 139-701, Korea (Received 3 August 1998; accepted 1 September 1998 by C.N.R. Rao) A new approach has been introduced for the fabrication of light-modulation and switching devices with the goal of producing the large Stark effect. A large tunability of the intersubband transition energy under an applied electric field is observed in the strained In xGa 1¹xAs/InP coupled double step quantum well consisting of a shallow In 0.63Ga 0.37As quantum well and a deep In 0.75Ga 0.25As quantum well. The electronic subband energies and the corresponding wavefunctions in the In xGa 1¹xAs/InP double step quantum wells without and with applied electric fields are calculated by a transfer matrix method taking into account strain effects. The transition energy and Stark shift of the In xGa 1¹xAs/InP coupled double quantum well are much more sensitive to the applied electric field than those of the In xGa 1¹xAs/InP single step quantum well and the behavior of the double step quantum well is followed by the physical properties of the coupled double quantum well rather than those of the single step quantum well. These results indicate that the large Stark shifts can be achieved for the strained In xGa 1¹xAs/InP coupled double step quantum wells and that the double step quantum wells may hold promise for potential applications such as new types of modulators and two-color infrared photodetectors. 䉷 1998 Elsevier Science Ltd. All rights reserved

Many studies on the quantum-confined Stark effect utilizing artificial quantum structures have been performed with a great deal of interest from both the scientific and technological points of view [1–15]. The energy shifts of the interband and the intersubband transitions under applied electric fields in a rectangular quantum well are not relatively sensitive [3]. Even though the Stark shifts in a coupled double quantum well are large than those in a rectangular quantum well, the oscillator strengths in the coupled double quantum well are small [16, 17]. The possibility for both large Stark shifts and large oscillator strength in a single step quantum well has been suggested [18]. Recently, the effect of an applied electric field on electronic subbands in Cd xZn 1¹xTe/ZnTe asymmetric step quantum wells has been studied [19] and the experimental and theoretical Stark shifts in the step quantum wells are much larger than those in single rectangular quantum

* Corresponding author.

well. In xGa 1¹xAs/InP coupled double step quantum wells have attracted a great deal of interest because of the possible enhancement of Stark shifts and oscillator strengths utilizing the physical advantages of the step and coupled quantum wells. However, to the best of our knowledge, a study on the investigation of the possibility for producing new kinds of optoelectronic devices utilizing In xGa 1¹xAs/InP coupled double step quantum wells have not been investigated until now. Furthermore, pseudomorphic In xGa 1¹xAs/InP quantum well structures have emerged as excellent candidates for the fabrication of high-speed field-effect transistors, electrically pumped intersubband lasers and long-wavelength communication devices as a consequence of the relatively smaller energy gap and electron effective masses. This communication reports on the effect of an applied electric field on the intersubband transitions in strained In xGa 1¹xAs/InP coupled double step quantum wells. A transfer matrix method is introduced for the calculations of the energy levels and the energy wavefunctions in an In xGa 1¹xAs/InP coupled double step

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quantum well in the presence of an electric field. The effective-mass difference and the strain effect due to the lattice mismatch between In xGa 1¹xAs and InP are taken into account. The In xGa 1¹xAs/InP coupled double step quantum well structures used in this study consisted of the follow˚ In 0.63Ga 0.37As shallow ing structures: two sets of a 50-A ˚ In 0.75Ga 0.25As deep step wells bounded by and a 50-A ˚ InP two thick InP barriers are separated by a 30-A embedded potential barrier. To determine the subband energies and the corresponding energy wavefunctions, a transfer matrix method taking into account the strain effects was used [17, 18]. The dielectric constants of both the InP and the In xGa 1¹xAs were taken to be 13.5 [20] and the electron effective-mass values of the InP barrier, the In 0.75Ga 0.25As well and the In 0.63Ga 0.37As well were 0.079, 0.033 and 0.0348 m e, respectively [20, 21]. Even though the magnitudes of the band offsets at the heterointerfaces of a coupled double step quantum well are not well-established yet, the conduction bandedge discontinuities at the InP/In 0.75Ga 0.25As, the In 0.75Ga 0.25As/In 0.63Ga 0.37As and the In 0.63Ga 0.37As/InP heterointerfaces, taking into account the strain effects, were assumed to be 1086, 707 and 755 meV, respectively [21–23]. Figure 1 shows the electronic subband energy structure of an In xGa 1¹xAs/InP coupled double step quantum well under zero electric field. Detailed analytic dispersion relations for a single step quantum well and coupled double quantum well were described in other literatures [17, 18]. The calculated magnitudes of the three electronic eigenenergies, measured from the top of the In 0.75Ga 0.25As/InP valence band, were 775, 778 and

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892 meV, respectively. The ground-state energy is located near the first-excited state energy, its wavefunction is strongly localized in each In xGa 1¹xAs step quantum well. The first and second excited subband wavefunctions oscillate globally in the In xGa 1¹xAs/InP coupled double step quantum well. In particular, the electronic subband wavefunction of the second subband in the double step quantum well structure with an ˚ was embedded InP potential-barrier width of 30 A clearly coupled over the In xGa 1¹xAs quantum well. Each wavefunction can be engineered by the each step potential to have a localized ground state and delocalized excited states [18]. Figure 2 shows the electronic subband energy structure of In xGa 1¹xAs/InP coupled double step quantum well under þ60 kV/cm. The calculated magnitudes of three electronic eigenenergies, measured from the top of the In 0.75Ga 0.25As valence band, were 803, 884 and 934 meV, respectively. The subband energy levels and the corresponding wavefunctions in the In xGa 1¹xAs/InP double step quantum well are strongly dependent on the electronic fields. When the electric fields are applied to the In xGa 1¹xAs/InP double step quantum well, since the coupled double step quantum well has symmetric properties, the firstexcited subband energy moves closer to the secondexcited energy, independent of the direction of the applied electric field. It is intuitive to relate the energy eigenvalues and the energy wavefunctions of the double step well coupling case to the single step eigenvalues and eigenfunctions. While the interwell transition indicates that the intersubband transition between an initial state and a final state originates from different wells, the

Fig. 1. The electronic subband energy structure of an In xGa 1¹xAs/InP double step quantum well without an applied electric field. The dashed lines indicate the energy wavefunctions.

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Fig. 2. The electronic subband energy structure of an In xGa 1¹xAs/InP double step quantum well under þ60 kV/cm. The dashed lines indicate the energy wavefunctions. intrawell transition is considered to be the transition between two states in the same well. A strong dependence of the energy states under the applied electric field might be related to the interwell transition. The electric-field dependence of the transition energy states in In xGa 1¹xAs/InP coupled double step quantum wells and in single step quantum wells are shown in Fig. 3. The solid lines and the dashed line represent transition energies in an In xGa 1¹xAs/InP double step quantum well and an In xGa 1¹xAs/InP single step quantum well, respectively. Figure 3 indicates that shift of the intersubband transition energy between the ground state and the first excited state (E 1 –E 2) in the double step quantum well under an applied electric field are much larger than that in the single step quantum well case. In the spatially indirect transition under applied electric fields, while the electrons of the E 1 level are localized in the left-band step quantum well, those of the E 2 level are localized in the right-band step quantum well, as shown in Fig. 2. This behavior enhances the magnitude of the transition energy corresponding to the (E 1 –E 2) in the double step quantum well. In contrast to the single quantum well, since the In xGa 1¹xAs/InP coupled double step quantum well breaks the intersubband selection rule, the intersubband transition between the ground state and the second excited state (E 1 –E 3) together with the (E 1 –E 2) and the transition between the first excited state and the second excited state (E 2 –E 3) are allowed [18]. Therefore, even though (E 1 –E 3) in a square quantum well is forbidden, three kinds of intersubband transitions under applied electric fields, which are (E 1 –E 3), (E 2 –E 3) and (E 1 –E 3), are feasible for a double step quantum well [18]. The transition possibility of the (E 1 –E 3) in the

Fig. 3. The electric-field dependence of the intersubband transition energy states for an In xGa 1¹xAs/InP double step quantum well and a single quantum well. The solid lines and the dashed line represent an In xGa 1¹xAs/InP double step quantum well and an In xGa 1¹xAs/InP single step quantum well, respectively and the E i –E j and the (E i –E j) indicate the intersubband transition of the double step quantum well and that of the single step quantum well, respectively.

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In summary, the energy levels, the energy wavefunctions, the transition energies and the intersubband Stark shifts in the In xGa 1¹xAs/InP double step quantum well have been calculated using a transfer matrix method taking into account the strain effect. The calculated results show that the transition energy and the Stark shift corresponding to the (E 1 –E 2) transition in the In xGa 1¹xAs/InP double step quantum well is much larger than that in the single step quantum well and the behavior of the double step quantum well is followed by the properties of the coupled double quantum well rather than those of the single step quantum well. These present observations can help improve understanding of the new kind of applications in low-current and high-speed optoelectronic switching devices utilizing the unique intersubband transitions of the In xGa 1¹xAs/InP double step quantum well. Acknowledgements—This work was supported by the Korean Science and Engineering Foundation (Contract No. 971-0209-038-1). REFERENCES Fig. 4. The Stark shift as a function of the applied electric field. The solid lines and the dashed line represent an In xGa 1¹xAs/InP double step quantum well and an In xGa 1¹xAs/InP single step quantum well, respectively and the E i –E j and the (Ei –E j) indicate the intersubband transition of the double step quantum well and that of the single step quantum well, respectively. double step quantum well originates from the strong interwell transition. The Stark shift as a function of the applied electric field in the In xGa 1¹xAs/InP double step quantum wells and in single quantum wells are represented in Fig. 4. The Stark shift corresponding to the (E 1 –E 2) transition in the In xGa 1¹xAs/InP double step quantum well is much larger than that in the In xGa 1¹xAs/InP single step quantum well. In particular, the Stark shifts corresponding the (E 1 –E 2) and (E 2 –E 3) transitions in the In xGa 1¹xAs/InP double step quantum well are more sensitive than that of (E 1 –E 3) transition. The enhancement of the Stark shift of the (E 1 –E 2) intersubband transition in the In xGa 1¹xAs/InP double step quantum well compared with that in the single step quantum well are associated with recombinations of electrons concentrated mostly in the left-hand step quantum well and electrons concentrated mostly in the right-hand step quantum well. This result indicates the feasibility of the presented quantum wave function approach to obtaining desirable optical properties in the double step quantum well.

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