Quantum cascade lasers (QCLs) are semiconductor lasers that emit in the infrared portion of the electromagnetic spectrum and were first demonstrated during the mid-1990's. Unlike typical interband semiconductor lasers that emit electromagnetic radiation through the recombination of electron-hole pairs across the material band gap, QCLs are unipolar and laser emission is achieved through the use of intersubband transitions in a superlattice.
QLCs are important because of their ability to produce coherent radiation in the near to mid-IR through the terahertz frequency bands. At the same time, a weakness of the QCL is that it is a two terminal n+-i-n semiconductor device with current injection into the cascade region limited by the resistance of the structure and the applied voltage. Because a field is required in the cascade region of a QCL to overcome the quasi-static electric field associated with the bandgap grating between cascade regions, the devices tend to operate at higher voltages than standard semiconductor diode lasers. Direct modulation at high speed is therefore a greater challenge for QCL lasers.
The conventional two-terminal QCL relies on an induced field in the cascade region for operation yet has no independent way to decouple field from current. Field variation affects the transitions that produce gain in the cavity. More specifically, in one of the common embodiments of the QCL, basic operation of the device relies on a transition from an electron in a high-energy quantum state in a narrow first quantum well to a lower energy state in a wider adjacent quantum well. This is illustrated in FIG. 1, in which an electron is represented as transitioning from a high energy quantum state to a lower energy quantum state. The electric field across the well effects the bending of the bands. As the magnitude of the field changes, as would occur under modulation, the location of the energy levels in the quantum wells also changes. This is illustrated in FIG. 2, which is a depiction of the fundamental QCL electron transition under two bias conditions illustrating the change in band bending and transition energy. In this illustration, a higher electric field would be present across the structure in case (b). The graph (c) shows the exemplary points of (a) and (b) on an I-V plot. As a secondary effect, the magnitude of the probability density function ψ*ψ of an electron in the higher energy well in the spatial location of the lower energy well, which affects transition probability, will also be modified by applied field and, by direct relation, the modulation voltage.
Free carrier absorption is a significant parameter in the operation of quantum cascade lasers. The general formula for free-carrier absorption is:
                              α          f                =                                            Nq              2                        ⁢                          λ              2                                                          m              *                        ⁢            8            ⁢                                                  ⁢            π            ⁢                                                  ⁢                          nc              3                        ⁢            τ                                              (        1        )            where N is the carrier concentration, n is the index of refraction, and τ is the relaxation time. (See e.g. Pankkove, “Optical Processes In Semiconductors”, Dover, N.Y., 1975). As can be seen from this general expression, free carrier absorption is directly proportional to the carrier concentration and proportional to the square of the wavelength. The graphs of FIG. 3, including the Table thereof, show the absorption coefficient for n-GaAs as a function of doping (see Spitzer and Whelan, Phys. Rev. 114, 59). This data shows the strong influence of doping density and wavelength on absorption in the mid-IR. The significant increase in absorption that occurs starting near a wavelength of 3 μm illustrates the need to minimize the overlap of the optical field with doped regions. Another point to note is that sample 1, which is undoped and has a carrier concentration less than 5E14 cm−3, shows the typical increase in absorption at the band edge but has no measurable absorption at wavelengths longer than 1.0 μm.
A number of papers on Quantum Cascade Lasers (QCLs) discuss free carrier absorption. Developments that have improved QCL performance in recent years have included waveguide structures to limit overlap of the optical mode with doped regions of the n+-i-n structure, as well as to improve thermal management. Other improvements have been associated with structures that inject and remove carriers from the upper and lower energy states in the cascade region more efficiently. Reference can be made, for example, to the following publications.
Faist, et. al. (Science, V264, April 1994, pp. 553) measured a threshold current density of ˜14 kA/cm2, and estimated an internal loss of ˜9 cm−1 from a combination of free carrier absorption, waveguide scattering loss, and plasmon losses in from the electrical contact. (Other key parameters were a gain of 9 cm−1 kA−1 cm−2, emission wavelength of 4.26 μm, and a mirror reflectivity of 27%.) No specific attempts were made to control internal loss other than the use of an n+-i-n structure.
Sirtori et. al. (APL, V75, N25, December 1999, pp. 3911) discusses contributions to internal optical loss, and uses doping density changes to provide optical confinement. Threshold current densities of ˜4.7 kA/cm2 and cavity losses of 20 cm−1 were measured for devices operated at 77 K having a wavelength of 9 μm. He also points out that the optical absorption in the n+ region of their device is 1740 cm−1, which still contributes 14 cm−1 of loss when multiplied by the confinement factor Γ in that region. This reinforces the need to minimize optical overlap with doped regions.
Giehler, et. al. (J. Appl. Phys. V96, N9, Nov. 2004, pp. 4755) discusses the effect of free carrier absorption on the threshold current density of QCLs. This work confirms the contribution of free carrier losses in regions outside of the cascade region to the threshold current density and provides further detail on the use of the confinement factor Γ to estimate the contribution of free carrier loss to total loss on a layer-by-layer basis.
Yu, et. al. (APL, V88, 091113, 2006) shows cw, room temperature operation of a 9.5 μm QCL with a threshold current density of 1.57 kA/cm2. Minimization of free carrier absorption through structure, process, and waveguide design coupled with thermal management are highlighted as the key techniques for improving performance.
Diehl, et. al. (APL, V88, 201115, 2006) shows operation to 204 mW at 300 K at an emission wavelength of 8.38 μm. Internal waveguide loss was ˜8.3 cm−1. Threshold current densities at room temperature were 1.9 kA/cm2. The structure was designed to minimize optical overlap with regions having a higher doping density (free carrier loss) or plasmon-related loss.
Lyakh, et. al. (APL, V95, 141113, 2009) shows 3 W cw, room temperature operation at an emission wavelength of 4.6 μm. Threshold current density was 0.86 kA/cm2, and wallplug efficiency was 12.7%. The key improvement was in the design of the cascade region, but the paper also mentions “doping level was empirically adjusted so that roll over current density of the optical power vs. current characteristic was approximately equal to 3 kA/cm2.” Waveguide losses were measured to be 2.6 cm−1.
Faist (APL, V90, 253512, 2007) provides a generalized analytical treatment of wall plug efficiency. This paper highlights the role of in-plane scattering (layer interface roughness) and free carrier absorption in limiting wall plug efficiency.
Liu, et. al. (Nature Photonics, V4, February 2010, pp. 95) discusses improvements in wall plug efficiency through more efficient transport of electrons into the laser active region. The paper also mentions the susceptibility of the tunneling rate to changes in bias.
The QCL has a higher operating voltage than diode lasers, and requires a larger drive current. This is illustrated in FIG. 4 which shows the current-voltage characteristics from typical commercially available QCLs. Curve (a) shows the I-V characteristic for a QCL emitting at a wavelength of 5 μm, while curve (b) is for a device engineered to emit at 10 μm. These I-V characteristics highlight the fact that high power dissipation creates the need for good thermal management solutions, as heat generation will ultimately limit optical power. From a modulation perspective, driving large currents at higher voltages requires high power RF or microwave sources. Viability of applications where direct modulation of a conventional QCL is required would therefore be limited by size, weight, and power of the total system.
It is among the objects of the present invention to overcome disadvantages and limitations of existing quantum cascade lasers and techniques, as just described, and to set forth light emitting devices and methods that exhibit various operational advantages, as will be described.
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