Intersubband (IS) transitions in semiconductor heterostructures with large band offset have recently seen a surge in interest. See, e.g., N. Suzuki et al., “Feasibility Study on Ultrafast Nonlinear Optical Properties of 1.55-μm Intersubband Transition in AlGaN/GaN Quantum Wells,” Jpn. J. Appl. Phys., 36, pp. L1006-L1008 (1997); N. Suzuki et al., “Effect of polarization Field on Intersubband Transition in AlGaN/GaN Quantum Wells,” Jpn. J. Appl. Phys., 38, pp. L363-L365 (1999); N. Iizuka et al., “Ultrafast Intersubband Relaxation (≦150 fs) In AlGan/GaN Multiple Quantum Wells,” Appl. Phys. Lett., 77, pp. 648-650 (2000); C. P. Garcia et al., “1.26 cm Intersubband Transitions In In0.3Ga0.7As/AlAs Quantum Wells,” Appl. Phys. Let., 77, pp.3767-3769 (2000); R. Akimoto et al., “Short-Wavelength Intersubband Transitions Down To 1.6 μm In ZnSe/BeTe Type-II Superlattices,” Appl. Phys. Lett., 78, pp. 580-583 (2001), each of which is incorporated herein by reference. This fuels attempts to extend the wavelength range of IS-based optical devices to the fiber-optics wavelength range around 1.55 μm. GaN/AlGaN-based heterostructures are of particular interest due to their large effective electron mass (m*˜0.2˜0.3 m0, with m0 being the electron rest mass) and large longitudinal optical (LO) phonon energy (ELO˜90 meV). Both are essential to achieve ultra fast electron relaxation at large transition energies, i.e. short wavelengths. GaN/AlGaN quantum wells with IS transition wavelengths as short as 1.4 μm have been demonstrated. See, e.g., C. Gmachl et al., “Intersubband Absorption at λ˜1.55 μm In Well- and Modulation-Doped GaN/AlGaN Multiple Quantum Wells With Superlattice Barriers,” Appl. Phys. Lett., 77, pp.3722-3724 (2000), which is incorporated herein by reference. In addition, the IS electron relaxation time has been measured as 150 fs and 370 fs for IS-transitions at 4.5 μm and 1.7 μm wavelength, respectively, as described in N. Iizuka et al.,(2000) cited above, and C. Gmachl et al., “Sub-picosecond Electron Scattering Time for λ˜1.55 μm Intersubband Transitions in Gan/AlGaN Multiple Quantum Wells,” Electron. Lett., 37, pp. 378-380 (2001), which are incorporated herein by reference. So far, however, IS-transitions have been experimentally studied in stacks of isolated single quantum wells.
More complex devices will require multiple active quantum wells and inter-well electron transfer to produce a pumpable population inversion for laser action. To that aim, the large effective electron mass becomes a hindrance when very thin barriers are necessary for efficient energy tunneling between wells. In addition, large intrinsic piezo- and pyro-electric fields have been reported in GaN type devices. See, e.g., N. Grandjean et al., “Built-in Electric-field Effects in Wurtzite AlGaN/GaN Quantum Wells,” J. Appl. Phys., 86, pp. 3714-3719 (1999) and F. Bernardini et al., “Spontaneous Polarization and Piezoelectric Constants of III-V Nitrides,” Phys. Rev. B, 56, pp. R10024-R10027 (1997), each of which is incorporated herein by reference. The exact strength of such fields in large AlN-mole fraction materials that are used for barrier layers is largely unknown and are not easily determined from IS measurements. In addition, coupling quantum wells produces Stark-shifts that produce further uncertainties in relative locations of energy levels of adjacent quantum wells.
In order for electrons to tunnel resonantly between quantum wells, the height of the energy levels must be substantially equivalent. In addition, in order to generate light of a certain wavelength, the energy level of the quantum well must be known to effectively calculate the change in energy level when the light is emitted. However, as stated above, the generation of large electric fields when using multiple quantum wells can skew the energy levels of the quantum wells, making the energy levels unknown.
To produce optical devices based on coupled quantum wells, there exists a need for a method of eliminating uncertainties between relative values of energy levels even in the presence of these intrinsic internal electric fields.
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