Abstract:
A quantum-dot cascade laser which eliminates undesirable single phonon decays associated with quantum-well devices. The elimination of single phonon decays is realized by a three-dimensional confinement resulting in a several-order-of-magnitude reduction in the threshold current. Vertical radiative transitions are employed within single quantum dots contained by Bragg reflectors. Dot size, dot density and dot uniformity requirements are presented along with several embodiments.

Description:
FIELD OF THE INVENTION 
     This invention pertains to the field of semiconductor lasers, and in particular to a quantum-dot cascade laser that eliminates phonon decays associated with conventional, semiconductor cascade lasers while being highly manufacturable. 
     DESCRIPTION OF THE ART 
     Recent advances in the art such as those disclosed by J. Faist et al., in an article entitled &#34;Quantum Cascade Laser&#34;, which appeared in SCIENCE, Vol. 264, pp. 553-556, Apr. 22, 1994, have demonstrated that semiconductor lasers built from a cascade of coupled quantum wells are realizable. 
     More recently, embodiments of the above described quantum well laser devices have been described in U.S. Pat. No. 5,457,709 entitled &#34;Unipolar Semiconductor Laser&#34; issued on Oct. 10, 1995 to Capasso, et al., and U.S. Pat. No. 5,509,025 for &#34;Unipolar Semiconductor Laser&#34; which issued on Apr. 16, 1996. 
     With reference to FIG. 1, there is shown a simplified conduction-band energy diagram of a quantum-well cascade laser showing electrons making a radiative transition to a lower subband. As depicted in this Figure, photons are generated by the transition of an electron from a first excited state of energy ε 1  to a ground state of the coupled well of energy ε 0 . 
     An important characteristic of quantum-well devices is that the excited and ground states as shown in FIG. 1 are not discrete levels but form bands due to the free movement of electrons in the two dimensions transverse to the direction of conduction band energy variation, i.e., the direction of a current flow. Unfortunately, the dominant electronic decay mechanism in a quantum-well laser is nonradiative, producing an emission of an optic phonon rather than a photon. Inasmuch as the bands are continuous in energy, such transitions are always allowed. Since electron-optic-phonon coupling is much stronger than electron-photon coupling, nonradiative phonon transitions greatly outnumber radiative, photon transitions in quantum-well lasers by approximately 3000 to 1. 
     As a result of these nonradiative phonon transitions, quantum-well cascade lasers are highly inefficient, and require a large threshold current to initiate useful lasing. 
     Still more recently, U.S. patent application Ser. No. 08/625,029 filed on Mar. 29, 1996, assigned to the assignee of the present application and incorporated herein by reference, describes a quantum dot cascade laser which, while maintaining many of the advantages of the above quantum well devices, overcomes many of their noted shortcomings as well. In view of the considerable potential commercial and scientific value of such quantum dot devices, improvements to these quantum dot devices are of considerable interest. 
     SUMMARY OF THE INVENTION 
     An advance is made over the prior art in accordance with the principles of the invention wherein a semiconductor cascade laser is constructed from quantum dots. Such quantum dot cascade lasers possess the desirable characteristics of quantum-well lasers, while at the same time eliminating the very undesirable nonradiative phonon decays. In a currently preferred embodiment, vertical transitions are employed utilizing superlattice Bragg reflectors. Such lasers may be advantageously constructed utilizing only a single quantum dot. Consequently, quantum dot cascade lasers constructed according to the teachings of the present invention will exhibit tunable operating frequency, an intrinsically strong and narrow gain spectrum, low threshold current, and temperature independent operation while being highly manufacturable. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a conduction band energy diagram of a prior art cascade showing electrons making a radiative transition to a lower subband; 
     FIG. 2 is a schematic diagram of an array of pairs of coupled dots sandwiched between conducting sheets; 
     FIG. 3 is an exploded view of a quantum dot cascade laser constructed from the array sandwich of FIG. 2; 
     FIG. 4 is a conduction band energy diagram showing a vertical transition within a superlattice; 
     FIG. 5 is a conduction band energy diagram showing a vertical transition within a superlattice or an alternative embodiment of the present invention; and 
     FIG. 6 is a conduction band energy diagram showing a vertical transition within a superlattice for a second alternative embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION 
     In order to fully appreciate the quantum-dot cascade laser which is the subject of the present invention, it is useful to compare it with a prior art quantum-well laser. With further reference to FIG. 1, there are shown two electronically coupled dots or alternatively, two electronically coupled wells. Photons are generated by the transition of an electron from the first excited state to the ground state of the coupled dots or coupled wells. In both cases, electrons are injected directly into the excited state by a current tunneling through the upstream barrier. Once an electron is de-excited, it escapes quickly through the downstream barrier so that photon absorption is negligible. 
     A significant distinction between the quantum-dot laser and prior-art quantum-well lasers is that in the quantum-dot laser, the excited and ground electronic levels as shown in FIG. 1 represent truly discrete states while in the case of a quantum-well laser, the excited and ground electronic levels shown in FIG. 1 represent the bottom of a continuous band of states. Specifically, in the quantum-well laser, electrons form bands due to their free movement in the two dimensions transverse to the direction of conduction-band energy variation shown in FIG. 1 (i.e., the direction of current flow). Consequently, the dominant electronic decay mechanism in the quantum wells is nonradiative, involving emission of an optic phonon rather than a photon. Since the bands are continuous in energy, such transitions are always allowed. Furthermore, since the electron-optic-phonon coupling is much stronger than the electron-photon coupling such nonradiative transitions will always dominate the radiative ones. 
     In a sharp contrast, the rate of radiative decay dominates the nonradiative rate in the quantum-dot laser. Inasmuch as the excited and ground states of the coupled dots are discrete levels, nonradiative decays involve emission of a phonon at the difference energy ε 1  -ε 0 . In general, phonon energies form a continuous band so that such one-phonon decays are allowed. However if the difference energy ε 1  -ε 0  is larger than the largest phonon energy (e.g., the optic phonon energy at ω LO  =36 meV in GaAs) then no single phonon can carry away the electronic energy. Multiphonon decay processes are still allowed but the rate of these is negligible (except in certain narrow energy bands). The dominant decay mechanism in quantum dots therefore is photon emission. 
     The size of each of the coupled dots is strongly constrained by the requirement that the energy difference between the excited and ground states exceed the optic-phonon energy ω LO . The resulting maximum dot size L can be estimated from the energy spacing in a square well of size L, ##EQU1## For GaAs, with an effective mass m *  =0.067 m, dots smaller than L=20 nm in all three dimensions are required. 
     With reference to FIG. 2, there is shown a basic structure (sandwich) of an array of double quantum dots, suitable for the construction of a laser. It includes conducting sheets 60, which provide the basic structural support for the array of double quantum dots and provide conductive pathways to other sandwiches of quantum dots stacked above and below the sandwich. In a preferred embodiment, the conducting sheets may be made of n-doped GaAs, although those skilled in the art can readily appreciate that the other materials made from Group III-Group V Elements, or Group II-Group VI elements, could be substituted from the GaAs. 
     Positioned between the conducting sheets, is an array of quantum dots, spaced to provide a dot density that is effective for lasing. Preferable, and as shown in FIG. 2, the quantum dots 62 are completely separated by, and sandwiched between barrier layers 64. While it is not explicitly shown in FIG. 2, the barrier material completely surrounds each of the double dots on each side, i.e., above, below and in space between adjacent dots. Those skilled in the art will readily appreciate that quantum dots 62 may be made from any suitable material, i.e., GaAs or other Group III-Group V; Group II-Group VI materials, where Group III is B, Al, Ga, In, TI; Group V is N, P, As, Sb, Bi; Group II is Zn, Cd, Hg; and Group VI is O, S, Se, Te, Po and that the barrier layers are likewise made from a suitable barrier material, i.e., AlGaAs. 
     Laser action will only occur if the gain coefficient γ(ω) exceeds the distributed loss, 
     
         γ(ω)&gt;α.sub.I +α.sub.M,             (2) 
    
     where α I  is the bulk loss and α m  =(1/L)log(1/R) is the loss through mirrors. Relation (2) jointly constrains the minimum density of dot pairs and the uniformity of dot sizes. The gain is proportional to the three-dimensional density of coupled dots and is given by: 
     
         γ(ω)=ƒNσ(ω),              (3) 
    
     where ƒ is the fraction of coupled dots with an electron in the excited state (we neglect the small fraction of dots with an electron in the ground state) and σ(ω) as the product of an oscillator strength S and a normalized lineshape function g(ω), 
     
         σ(ω)=Sg(ω)                               (4) 
    
     In the dipole approximation the oscillator strength is given by: ##EQU2## where α=e 2  /c=1/137 is the fine structure constant, n is the index of refraction, and ω fi  is the transition frequency between initial and final states. The dipole matrix element between initial and final state &lt;ƒ|r·e|i&gt; projects the polarization direction e on the dipole moment. In the coupled dot, the transition dipolemoment lies purely along the current direction so the radiation will be polarized in that direction. In the sec ond line of Equation (5), the dipole matrix element is approximated by the product of the distance between the dots d and interdot hybridization t/ω fi , where t is the tunnel coupling between dots. The remaining factor is the normalized lineshape function g(ψ). It is assumed that inhomogeneous broadening due to disorder will determine the lineshape. Taking, for convenience, a Lorentzian lineshape with FWHM disorder broadening of Δψ, one finds a peak gain coefficient of: ##EQU3## 
     By equating the peak gain to the total loss, a joint requirement on density and uniformity for a quantum-dot laser can be stated. As described by Salch and Teich in Fundamentals of Photonics, published by Wiley, New York 1991, the distributed loss for a semiconductor injection laser is at least 10 cm -1 . The interdot hybridization t/ω fi  must be sufficiently small such that the spontaneous emission rate ω sp  dominates the leakage rate from the excited state through the downstream barrier. In turn, the spontaneous emission rate must be smaller than the escape rate from the ground state. Assuming a fixed escape rate Γ through the downstream barrier, these inequalities require: 
     
         (t/ω.sub.ƒi).sup.2 Γ&lt;ω.sub.sp &lt;Γ,(7) 
    
     which clearly limits the hybridization to (t/ω fi ) 2  &lt;1/10. Further assuming a transition energy of 100 meV, interdot spacing of d=10 nm, and index refraction n=3, it is found that lasing requires an excited coupled-dot density to broadening energy ration of: ##EQU4## 
     Hence at 10% disorder broadening of the transition energy (5% nonuniformity), and an excited fraction near f=1, requires a minimum density of one coupled dot pair per (180 nm) 3  volume. 
     To achieve this average density of coupled dots throughout the region occupied by the lasing mode requires a three-dimensional structure. One such preferred structure, as shown in FIG. 3, is a layered structure, comprising a stack of two-dimensional arrays of coupled quantum dots (See FIG. 2) with an overall density for the gain requirements. 
     Finally, the threshold current for such a quantum-dot device can be determined. Since radiative decays dominate, the current flowing through each pair of dots need only be adequate to replenish losses due to spontaneous emission. The total spontaneous emission rate is given by: ##EQU5## 
     Using the same parameters as above, a threshold current of J t  =ew sp   25  16 pA per coupled dot pair is obtained. For a uniform array of dots in three dimensions, this gives a current density of 4.9 mA/cm 2 . This threshold current density of the quantum-dot device is six-and-a-half orders of magnitude lower than the 14 kA/cm 2  required for the quantum-well cascade laser. 
     With reference to FIG. 3, there is shown an embodiment of a quantum-dot laser constructed according to the teachings of the present invention so far described. Specifically, substrate 702 provides the basic structural support for the laser. The substrate typically is a monocrystalline wafer whose lattice parameters are well suited for growing thereover the various functional layers needed for laser operation while maintaining a high degree of monocrystallinity free from dislocations or defects. 
     Overlying the substrate 702 is the cladding layer 704 which is suitably reflective of photons generated within double dot array layers 714 and which are constructed as shown previously in FIG. 2. 
     While only three such double-dot array layers 714 are shown, those skilled in the art can readily appreciate that the number of such layers can be varied to realize effective double-dot density depending upon the particular materials utilized for each layer. 
     Additionally, it may be desirable to have opposite edges of cladding layer 704 to be highly reflective of emitted radiation, although at least one of the two edges, 712a, 712b should be partially transmissive for laser light to exit. 
     It is also desirable to provide electrical contacts 708, 710 to substrate 702 and contact layer 706, respectively, to provide a current flow through the structure sufficient to support the lasing. 
     Finally, it should be readily apparent to those skilled in the art that additional downstream barrier(s) may be advantageously utilized such that escape from the excited state of energy, by tunneling is eliminated, thereby enhancing the overall efficiency of the quantum-dot cascade laser. 
     The dimensions of the various layers are chosen in accordance with known laser design principles. 
     A variety of known techniques are available for the production of structures of the kind described, such as molecular beam epitaxy (MBE) or alternatively, chemical vapor deposition (CVD). 
     At this point those skilled in the art will appreciate that the requirement for a pair of quantum dots imposed upon the invention as described to this point is solely to prevent leakage via tunneling from the excited state. Consequently, if this tunneling can be prevented via some other means such as &#34;bandstructure engineering&#34;, e.g., by placement of a superlattice with a forbidden band at the excited-state energy, then the invention can be embodied in a laser in which the lasing transition takes place within a single dot or single &#34;vertical transition&#34;. 
     With reference now to FIG. 4, there it shows a portion of the conduction band diagram of the quantum dot, vertical transition laser according to the invention. Specifically, forbidden miniband 408 and allowed miniband 409 are associated with superlattice Bragg reflector 410 and indicate energy regions in which the superlattice is, respectively, relatively transparent and relatively opaque to electrons. Upstream active region 411 and downstream active region 421 are shown upstream and downstream, respectively, from quantum dot 405 which is shown by wavy arrow 406 emitting a photon when a vertical transition from a excited, high energy state to a final, low energy state occurs. 
     As can be readily appreciated by those skilled in the art, with this geometry, there are no allowed final states at the energy of the excited state of the quantum dot in the region immediately downstream of the quantum dot. Since an excited electron cannot escape by tunneling, it can only decay--preferably by photon emission to a lower energy state of the quantum dot. Consequently, this avoids the need for a second quantum dot or double dot, however, at the cost of a superlattice Bragg reflector downstream of the single quantum dot. 
     A further refinement to the above vertical transition quantum dot laser can take advantage of the inherent phonon emission. With reference now to FIG. 5, there it shows the vertical transition quantum dot energy transition diagram of FIG. 4, having an additional quantum dot 419. Specifically, photon emission transition 406 is further enhanced with phonon emission 407 to the additional quantum dot 419. Including this second dot having an energy level tuned sufficiently below the lower lasing level allows relatively quick depopulation of this lower lasing level. 
     Finally, those skilled in the art will quickly appreciate that the principles diagrammed in FIGS. 4 and 5 could be combined into a single dot structure having three energy levels. With reference now to FIG. 6, there it shows a conduction band diagram for the combined device constructed from the principles discussed in FIGS. 4 and 5. As can be seen from this conduction band diagram showing a vertical transition within a single quantum dot 405, a photonic emission results when an electron transition takes place from level 3, (413) to level 2 (415). Resonant phonon emission occurs from level 2 to level 1 (417). Advantageously, the energy difference between level 2 and level 1 is engineered such that this phonon transition occurs readily. Preferably, level 1 is the ground state of the quantum dot. 
     While there has been described and illustrated a quantum dot cascade laser, it will be apparent to those skilled in the art that modification and variations are possible without deviating from the broad principle and spirit of the invention which shall be limited solely by the scope of the claims appended hereto.