Abstract:
The performance characteristics of ridge waveguide QCL may be improved in accordance with the invention by replacing the insulating dielectric layers such as SiO 2 , Si 3 N 4  or SiC with p-type InP overgrowth layers as well as p-type AlInAs or InGaAsP overgrowth layers, for example.

Description:
BACKGROUND  
       [0001]     Conventional ridge waveguide quantum cascade lasers (QCL) typically have dielectric layers deposited around the ridge structure as shown in  FIG. 1  to provide optical confinement and current blocking. Prior art QCL structure  100  has upper electrode  160  and lower electrode  110 , n-type lower cladding layer  120 , n-type upper cladding layer  140 , QC active region  130 , upper separate confinement heterostructure (SCH) layer  135 , lower separate confinement heterostructure (SCH) layer  125 , ridge region  145  and insulating dielectric layers  150  deposited around ridge region  145 .  
       SUMMARY OF THE INVENTION  
       [0002]     The performance characteristics of ridge waveguide QCL may be improved in accordance with the invention by replacing the insulating dielectric layers such as SiO 2 , Si 3 N 4  or SiC with p-type InP overgrowth layers as well as p-type AlInAs or InGaAsP overgrowth layers, for example. The substitution of p-type non-insulating overgrowth layers for insulating dielectric layers around the ridge structure of a QCL improves lateral mode discrimination and allows high temperature operation by providing lower thermal resistance The doping, etch depth and waveguide width may be selected to provide modal discrimination such that the fundamental lateral mode experiences relatively small loss compared to the higher order modes. Hence, higher order modes are effectively filtered out.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0003]      FIG. 1  shows a prior art ridge waveguide quantum cascade laser.  
         [0004]      FIG. 2  shows an embodiment of a quantum cascade laser in accordance with the invention.  
         [0005]      FIG. 3  shows doping dependence of the real part of the refractive index and absorption loss in accordance with the invention.  
         [0006]      FIG. 4  shows the computed refractive index versus thickness of the upper cladding layer in accordance with the invention.  
         [0007]      FIG. 5  shows a structure in accordance with the invention for performing a one-dimensional slab waveguide simulation.  
         [0008]      FIG. 6  shows the lateral optical confinement factor as a function of ridge width for various doping levels in accordance with the invention.  
         [0009]      FIG. 7  shows mode loss calculations in accordance with the invention.  
         [0010]      FIG. 8  compares fundamental lateral mode loss with first order mode loss in accordance with the invention. 
     
    
     DETAILED DESCRIPTION  
       [0011]     In accordance with the invention, p-type overgrowth layers in ridge waveguide QCL comprised of, for example, InP:Zn or InP:Mg provide lower thermal resistance and better lateral mode selectivity in comparison to the use of dielectric layers. For AlGaAs-based QCLs, AlAs:C, AlAs:Zn or AlAs:Mg as well as AlGaAs:C, ALGaAs:Zn or AlGaAs:Mg p-type overgrowth layers may be used. For GaAsSb—InAs or GaAs based QCLs, GaSb:C, GaSb:Zn or GaSb:Mg p-type overgrowth layers may be used.  
         [0012]      FIG. 2  shows QCL structure  200  in accordance with the invention. QCL structure  200  includes lower electrode  210  and upper electrode  260 , n-doped substrate  215 , n-type lower cladding layer  220 , n-type upper cladding layer  240 , QC active region  230 , upper separate confinement heterostructure (SCH) layer  235 , lower separate confinement heterostructure (SCH) layer  225 , ridge region  245  and p-type overgrowth layers  250 . Note that n-doped substrate  215  is typically more heavily doped than n-type lower cladding layer  220  which is typically grown over n-doped substrate  215 . The presence of free holes in p-type overgrowth layers  250  contributes to free carrier absorption loss in the guided mode. However, the modal loss may be controlled by adjusting waveguide width w, etch depth h and the p-doping concentration in p-type overgrowth layers. Adjustment of the p-doping concentration, the waveguide width w and the etch depth h allows modal discrimination such that the fundamental lateral mode experiences relatively small loss compared to higher order modes. P-type doping concentrations in the range from about 10 18  to about 10 19  cm −3  are typically adequate to achieve the desired results in accordance with the invention.  
         [0013]     The modal loss associated with p-type overgrowth layers  250  may be quantified by using waveguide simulations which incorporate the Drude model for the dielectric function of doped semiconductors. For example, for the InP material system, curve  310  in  FIG. 3  shows the doping dependence of the real part n real  of the refractive index and Curve  330  in  FIG. 3  shows the doping dependence of the absorption loss a at a wavelength of about 10 μm for p-type overgrowth layers  250  with a scattering time of τ of about 0.03 psec. Even for moderate p-doping levels in the range of about 10 17  cm −3 , curve  330  shows the absorption loss a becomes relatively large. The absorption loss α actually increases more rapidly than is indicated by curve  330  because the scattering time τ decreases as the doping level increases. Including the dependence of scattering time τ on the doping level increases the absorption loss α for a doping level of about 10 18  cm −3  from about 70 cm −1  with a scattering time τ of about 0.03 psec as shown in  FIG. 3  to about 86 cm −1  with a scattering time τ of about 0.024 psec.  
         [0014]     The effective index method is used to determine the lateral waveguiding of QCL structure  200  using the Drude model to establish the refractive index of p-type overgrowth layers  250  in  FIG. 2 . Table 1 shows the values for layers of QCL  200  in an embodiment in accordance with the invention for a wavelength of about 10 μm. Note p-InP overgrowth layer InP layer  250  and n-InP lower cladding layer  220  are taken to be semi-infinite for computational purposes. The thickness of n-type lower cladding layer  220  typically depends on the operational wavelength of QCL structure  200  and the substrate doping level. Typically, n-type lower cladding layer  220  must be grown sufficiently thick so that free-carrier loss from the more heavily n-doped substrate  215  is minimized which means that n-type lower cladding layer  220  must be thick enough to minimize the mode penetration into n-doped substrate  215 . Typically, the required thickness is on the order of several microns but also depends on the particular wavelength and doping level of n-doped substrate  215 . For the case of n-doped substrate  215  being heavily doped, in the range of 5×10 18  cm −3 , a typical thickness for n-type lower cladding layer  220  would be on the order of 2-3 μm for QCL structure  200  operating at about 5 μm and increased to a thickness on the order of 4-5 μm for QCL structure  200  operating at about 10 μm. For n-doped substrate  215  being lightly doped, in the range of 5×10 17  cm −3 , a typical thickness of n-type lower cladding layer  220  is typically on the order of 1 μm or less. Similar reasoning applies to the thickness of n-type upper cladding layer  240  where the loss is associated with upper electrode  260  which must be placed sufficiently far from the waveguide core which includes lower SCH layer  225 , active region  230 , and upper SCH layer  235 . Hence, typical thicknesses for n-type upper cladding layer  240  and  245  are on the order of several microns and p-type overgrowth layer  250  is also several microns thick to planarize the top surface of QCL structure  200 .  
                                                   doping level           layer   layer thickness   (cm −3 )   refractive index                   p-InP overgrowth layer 250   semi-infinite   1 × 10 18     3.07 + 0.00659i               3 × 10 18     3.00 + 0.02002i               1 × 10 19     2.87 + 0.1600i        n-InP upper cladding layer 240   h   1 × 10 17     3.08       n-InGaAs upper SCH layer 235   0.5 μm   5 × 10 16     3.37       n-AlInAs/GaInAs active region 230   1.5 μm   2 × 10 16     3.28       n-InGaAs lower SCH layer 225   0.5 μm   5 × 10 16     3.37       n-InP lower cladding layer 220   semi-infinite   1 × 10 17     3.08                  
 
         [0015]     For computational purposes, the fundamental TM 0  transverse mode effective index is first evaluated using a one-dimensional slab waveguide simulation using the structure shown in  FIG. 5  with p-InP overgrowth layer  550  displaced a distance h from upper SCH  235 .  FIG. 4  shows the computed refractive index values versus the thickness h of n-InP upper cladding layer  240  where imaginary component  480  of the transverse fundamental mode&#39;s complex refractive index corresponds to intensity loss. Real component  470  of the transverse fundamental mode&#39;s complex refractive index corresponds to the transverse effective index. Intensity loss values for imaginary component  480  are shown by curves  440 ,  450  and  460  which correspond to p-type doping levels of 1×10 19  cm −3 , 3×10 18  cm −3  and 1×10 18  cm −3 , respectively. The transverse effective index values correspond to real component  470  and are shown by curves  410 ,  420  and  430  which correspond to p-type doping levels of 1×10 19  cm −3 , 3× 10   18  cm −3  and 1×10 18  cm −3 , respectively.  
         [0016]     When the thickness h of n-InP upper cladding layer  240  is taken to be large in the context of the effective index method,  FIG. 4  shows that the p-InP layers are far from the guided mode so that the mode loss extrapolates to zero (imaginary component  480  at h=5 μm) and the transverse effective index extrapolates to about 3.182 (real component  470  at h=5 μm). Taking h˜5 μm corresponds to evaluating the fundamental TM 0  transverse mode effective index in the plane bisecting ridge structure  245  in  FIG. 2 . As the thickness h of n-InP upper cladding layer  240  decreases the guided mode starts to overlap lossy p-InP overgrowth layer  550  which has a lower refractive index than n-InP upper cladding layer  240 . Decreasing h corresponds to evaluating the fundamental TM 0  transverse mode effective index as one moves out laterally from the plane bisecting ridge structure  245  in  FIG. 2 . The effective index is reduced and the loss is increased. The loss and the refractive index difference between lossy p-InP overgrowth layer  550  and n-InP upper cladding layer  240  are the greatest for a p-type doping level of 1×10 19  cm −3 . For h˜0 μm, which corresponds physically to the case where p-InP overgrowth layer  250  is grown directly on upper SCH layer  235 , the refractive index decreases by about 0.01 and the refractive index decreases by more than about 0.02 for p-doping levels of 3×10 18  cm −3  and 1×10 · cm −6 , respectively. This shows that QCL structure  200  forms a positive index guide where the refractive index difference between the middle of QCL structure  200  and the outer parts of QCL structure  200  may be relatively high.  
         [0017]      FIG. 4  shows that the reduction of refractive index due to the high p-doping levels results in a positive refractive index step lateral waveguide. As the p-doping concentration is increased, the refractive index decreases yielding a better lateral waveguide.  FIG. 6  shows lateral optical confinement factor Γ lateral  as a function of ridge width w and h˜0 μm (see  FIG. 2 ) for p-doping level curves  604   605  and  606  corresponding to 1×10 19  cm −3 , 3×10 18  cm −3  and 1×10 18  cm −3 , respectively. Γ lateral  is the highest for doping level curve  604  and Γ lateral  is lowest for doping level curve  606 . Γ lateral  for doping level curve  606  is typically too low for applications and the required p-doping levels are typically on the order of about 3×10 18  cm −3  or higher to create an acceptable waveguide for low threshold operation, typically about 2-3 kA/cm 2 . For low threshold operation, the fundamental mode loss needs to be sufficiently low, typically less than about 10 to about 20 cm −1  and the high lateral optical confinement factor, Γ lateral , needs to approach unity.  
         [0018]      FIG. 7  shows mode-loss calculations in accordance with the invention. The ridge width w of the lateral fundamental mode loss is shown for four cases. Curve  720  shows the lateral fundamental mode loss for h˜0 μm at a p-doping level of 1×10 19  cm −3  as a function of w. Curve  730  shows the lateral fundamental mode loss for h˜1 μm at a p-doping level of 1×10 19  cm −3  as a function of w. Curve  740  shows the lateral fundamental mode loss for h˜0 μm at a p-doping level of 3×10 18  cm −3  as a function of w. Curve  750  shows the lateral fundamental mode loss for h˜1 μM at a p-doping level of 3×10 18  cm −3  as a function of w. The calculations presented in  FIG. 8  show that the fundamental mode loss decreases as either the p-doping levels are reduced from 1×10 19  cm −3  to 3×10 18  cm −3  or h is increased which increases the distance between p-Inp overgrowth layers  250  which function as guiding layers and active region  230 . With a suitable choice such as 1 μm for the thickness h of n-InP upper cladding layer  240  and more than 15 μm for ridge width w it is possible to achieve acceptable loss values α that are less than 10 cm −1  even at p-doping levels as high as about 1×10 19  cm −3 .  
         [0019]     Additionally, embodiments in accordance with the invention such as QCL structure  200  provide excellent mode discrimination.  FIG. 8  compares fundamental lateral mode loss with first order lateral mode loss. Curve  810  represents the fundamental lateral mode loss as a function of ridge width w for h˜0 μm at a p-doping level of 3×10 18  cm −3 , curve  820  represents the fundamental lateral mode loss as a function of ridge width w for h˜1 μm at a p-doping level of 1×10 19  cm −3  and curve  830  represents the fundamental lateral mode loss as a function of ridge width w for h˜0 μm at a p-doping level of 1×10 19  cm −3 ; all at λ=10 μm. Curve  840  represents the first order lateral mode loss corresponding to the parameters of curve  810 , curve  850  represents the first order lateral mode loss corresponding to the parameters of curve  820  and curve  860  represents the first order lateral mode loss corresponding to the parameters of curve  830 . As can be seen from  FIG. 8 , the first order lateral mode loss represented by curve  840 , curve  850  and curve  860  is many times greater than the fundamental lateral mode loss represented by curve  810 , curve  820  and curve  830 , respectively.  
         [0020]     While the invention has been described in conjunction with specific embodiments, it is evident to those skilled in the art that many alternatives, modifications, and variations will be apparent in light of the foregoing description. Accordingly, the invention is intended to embrace all other such alternatives, modifications, and variations that fall within the spirit and scope of the appended claims.