Abstract:
Doped diffraction gratings for use in quantum cascade lasers and mid-infrared wavelength vertical cavity surface emitting lasers can be made by introducing periodic variations in the doping levels that result in periodic refractive index variations. Doping is typically accomplished by use of an n type dopant.

Description:
BACKGROUND  
       [0001]     Quantum cascade lasers (QCL) use electronic intersubband transitions for lasing action in semiconductor superlattices. For light to be either strongly emitted or absorbed by intersubband transitions, the electric field of the light is typically perpendicular to the epitaxial layers and transverse magnetic (TM) polarized light is predominantly absorbed or emitted by intersubband transitions in quantum wells.  
         [0002]     Surface plasmons are TM polarized waves that propagate along a metal and semiconductor interface. The amplitude of surface plasmons decreases exponentially on both sides of the interface. Surface plasmons are very lossy and any coupling between the surface plasmon mode and the lasing mode is not desirable because this coupling creates an additional loss mechanism for the laser.  
         [0003]     Plasmon-waveguide structures have been introduced for transverse-mode confinement in QCLs because of the impracticality of growing cladding layers sufficiently thick to contain the long evanescent tail of the transverse mode present at the longer emission wavelengths of intersubband semiconductor lasers such as QCLs. Plasmon-waveguide structures provide optical confinement by significant lowering of the refractive index of the cladding layers by the use of high doping to increase the refractive index contrast. When the doping level is sufficiently high, the plasma frequency of the semiconductor approaches the QCL emission frequency so that the optical character of the semiconductor becomes more metal-like with a complex refractive index, n+ik, a small real component, n, and a large imaginary component, k. Adjusting the doping and thickness of the plasmon-waveguide structures allows the modal loss and the overlap with the quantum cascade gain to be optimized.  
         [0004]     The requirements for doping in the visible and near-infrared wavelengths for plasmon confinement are typically too high to be practicable. However, at the longer, mid and far infrared (IR) wavelengths typically associated with QCLs, doping levels on the order of about 10 18 /cm 3  are sufficient to reduce the refractive index of the cladding layers at the operational wavelength of the QCL to provide transverse-mode confinement.  
       SUMMARY OF THE INVENTION  
       [0005]     In accordance with the invention, doped diffraction gratings for use in QCLs and mid-IR wavelength VCSELs can be made by introducing periodic variations in the doping levels that result in periodic refractive index variations. Doping is typically accomplished by use of an n type dopant.  
         [0006]     Placement of doped diffraction gratings in the waveguide region of QCLs provides a distributed Bragg reflector (DBR) for stabilizing the emission wavelength. In accordance with the invention, doped diffraction gratings may also be used to provide a DBR for mid-IR wavelength VCSELs. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0007]      FIG. 1  shows the calculated doping dependence of the real index and the loss for InP at a wavelength of 8 μ um.  
         [0008]      FIG. 2   a  shows DBR reflectivity versus doping levels for 20, 40, 60, 80 and 100 mirror pairs in accordance with the invention.  
         [0009]      FIG. 2   b  shows DBR reflectivity versus doping levels for different semiconductor scattering times in accordance with the invention.  
         [0010]      FIG. 3   a  shows a QCL structure in accordance with the invention.  
         [0011]      FIG. 3b  shows a schematic cross-section  
         [0012]      FIG. 3   c  shows a QCL structure in accordance with the invention.  
         [0013]      FIG. 3   d  shows a VCSEL structure in accordance with the invention.  
         [0014]      FIG. 4   a  shows a method of making a doping grating in accordance with the invention.  
         [0015]      FIG. 4   b  shows a method of making a doping grating in accordance with the invention.  
         [0016]      FIGS. 5   a - c  show a method of making a doping grating in accordance with the invention. 
     
    
     DETAILED DESCRIPTION  
       [0017]     Heavy doping levels on the order of about 10 18 /cm 3  are sufficient to produce appreciable refractive index reductions in InP layers. In  FIG. 1 , plot  101  shows that for a QCL operating at 8 μ m with InP cladding layers, if the doping level is increased from 1-2×10 17 /cm 3  to 5×10 18 /cm 3  this corresponds to a reduction of real refractive index from about 3.1 to about 2.6. Plot  102  in  FIG. 1  shows the increased loss as a function of the doping level.  
         [0018]     In accordance with the invention, a periodic variation of the doping can be used to produce a diffraction grating. The typical period for the doping variation, L, is given by L =λ/2n eff  where n eff  is the effective refractive index and λ is the wavelength. A typical value for the period for the doping is on the order of 1 μ m. Alternatively, higher order gratings can be defined by using odd multiples of λ/2n eff  (2m+1)λ/2n eff  where m is a positive integer. If this diffraction grating is appropriately positioned in the waveguide region of the QC laser such as, for example, the InP cladding layers or the waveguide core, the diffraction grating can be used as a distributed Bragg reflector (DBR) to control the emission wavelength.  
         [0019]     The grating strength may be controlled by the doping concentration and thickness of the heavily doped regions as well as the proximity from the waveguide core. The doping induced reduction in refractive index at the long wavelengths typically associated with QCLs is comparable to or greater than is typically achieved by conventional, shorter wavelength structures that rely on compositional variation to achieve variation of the refractive index. However, the large refractive index step achieved is associated with large absorption losses. Both absorption losses and refractive index steps increase as doping levels are increased. Hence, there is a trade-off between having desirable large refractive index steps and undesirable large absorption losses.  
         [0020]     In accordance with the invention,  FIG. 2   a  shows the peak reflectivity, R, for DBRs with differing numbers of mirror pairs as a function of the doping level, Lo, in units of 1×10 18 /cm 3 . Plots 205, 210, 215, 220, 225 and 230 correspond to 20, 40, 60, 80 and 100 mirror pairs, respectively. From  FIG. 2   a,  it is apparent that the reflectivity, R, typically saturates to a peak reflectivity of about 0.9 over a wide range of doping levels, Lo. For example, plot  205  which represents 20 mirror pairs, saturates to a peak reflectivity of about 0.9 at a doping level Lo of about 5×10 18 /cm 3  and plot  230  which represents 100 mirror pairs, saturates to a peak reflectivity of about 0.9 at a doping level Lo of about 1×10 18 /cm 3 . This shows that while higher doping levels, Lo, increase the refractive index step, the absorption loss is increased such that the peak reflectivity is limited. From  FIG. 2   a,  it is apparent that the design details for the DBR are relatively insensitive to the precise doping level and the particular number of mirror pairs selected.  
         [0021]     Ultimately, however, the absorption loss limits the quality of the DBR that can be achieved. Plots  205 ,  210 ,  215 ,  220 ,  225  and  230  shown in  FIG. 2   a  assume a scattering time of 0.1 ps for the semiconductor Drude model used to calculate them.  FIG. 2   b  shows how variation of the scattering time affects DBR reflectivity in accordance with the invention for a DBR having 50 mirror pairs. Plots  235 ,  240 ,  245  and  250  correspond to scattering times of 0.05 ps, 0.1 ps, 0.15 ps and 0.2 ps, respectively. Plots  235 ,  240 ,  245  and  250  indicate that a larger scattering time typically results in a higher peak reflectivity for the DBR in accordance with the invention. Therefore, using materials having larger scattering times will typically result in better DBRs. For example, for InP materials the scattering time is typically about 0.1 ps at a doping level, Lo, of about 1×10 18 /cm 3.    
         [0022]     The results shown in  FIGS. 2   a - b  do not take into account the overlap of the DBR region with the waveguide mode. There is typically a 10% to 20% confinement of the waveguide mode in the upper cladding layer of the waveguide in typical InP QCL  350  (see  FIG. 3   a ). Hence, if the DBR is formed in the entire upper cladding layer, the strength of the DBR may be reduced by an order of magnitude from the results shown in  FIGS. 2   a - b . The reflectivity R, is defined as:
 
 R=tan h   2 κL   (1) 
 
 where κ, is defined as 
 
κ=2ΓΔn/λ  (2) 
 
 where Δ n is the refractive index step between the mirror pairs of the DBR. The overlap Γ in Eq. (2), of the cross-section of DBR  354  with waveguide mode cross-section  399  (see  FIG. 3   b ), is given by:  
             Γ   =         ∫   DBR     ⁢            E        2     ⁢     ⅆ   A             ∫     waveguide   ⁢           ⁢   mode       ⁢            E        2     ⁢     ⅆ   A                   (   4   )             
 
 where the integrals are over the cross-sectional area of the waveguide normal to the propagation direction. 
 
         [0023]     Achieving the reflectivity values, R, shown in  FIGS. 2   a - b  would then require an increase in the mirror pairs of the DBR by an order of magnitude. For example, if the entire upper cladding layer is used to create a DBR having 200 mirror pairs with a doping level, Lo, of 5×10 18 /cm 3 ,  FIGS. 2   a - b  indicate that a DBR with a reflectivity of about 0.8 to 0.9 may be achieved. A DBR having less overlap with the waveguide mode would require a proportionately longer grating to achieve 0.8 to 0.9 reflectivity.  
         [0024]      FIG. 3   a  shows QCL  350  with waveguide mode  399 , an embodiment in accordance with the invention. DBR mirror pair  357  containing DBR elements  356  and  355  forms part of DBR  354  located in cladding region  360 . DBR element  356  differs from DBR element  355  in doping level. The difference in doping level between DBR elements  355  and  356  results in a refractive index difference between DBR element  356  and DBR element  355  at the emission wavelength. DBR  354  functions as the back mirror for QCL  350 . Region  361  functions as the waveguide core. Together, cladding region  360  and waveguide core  361  form waveguide layer  362 .  
         [0025]      FIG. 3   b  shows the overlap Γ as defined in Eq. (4) above between the cross-section of DBR  354  and waveguide mode cross-section  399  in the x-direction.  
         [0026]      FIG. 3   c  shows QCL  351  in accordance with the invention. DBR mirror pair  359  containing DBR elements  347  and  348  forms part of DBR  344  located in waveguide core  361 . DBR element  347  differs from DBR element  348  in doping level. The difference in doping level between DBR elements  347  and  348  results in a refractive index difference between DBR element  347  and DBR element  348  at the emission wavelength. DBR functions as the back mirror for QCL  351 .  
         [0027]     In accordance with the invention, doping level variations may be used to create DBRs for vertical cavity surface emitting lasers (VCSELs). Although lasing transitions in QC lasers are typically TM-polarized and not applicable to VCSELs, transverse electric (TE) polarized intersubband transitions exist. For example, TE transitions have been observed in the valence band of Si/SiGe QC lasers where there are two bands, the heavy and light hole bands. Transitions occurring between the heavy and light hole bands of the valence band allow TE-polarized transitions whereas transitions within the same band do not allow TE-polarized transitions.  
         [0028]      FIG. 3   d  shows an embodiment in accordance with the invention of epitaxial VCSEL structure  300  with waveguide mode  325 . In epitaxial VCSEL structure  300  with laser cavity  375  and active region  380 , modulation of the doping levels between about 1×10 17 /cm 3  and 1×10 18 /cm 3  in alternating layers  310  and  315 , respectively, of DBR  335  allows homogeneous DBR  335  with a high index contrast to be constructed. Each of layers  310  and  315  is typically an odd multiple of a quarter wavelength thick.  FIGS. 2   a - b  show that peak reflectivies of about 0.8 to 0.9 can be achieved for DBR  335  with as few as 20 mirror pairs if doped layers  315  are doped to a level of about 5×10 18 /cm 3 . Because DBR  335  is not made of different bandgap materials, interfacial potential barriers are absent and series resistance for perpendicular current flow is typically less than a few ohms at a few kA/cm 2  current density. As noted above, as the index contrast is increased through increased doping levels, the layer absorption is increased. Thus, the transparency of DBR  335  approaches zero. Therefore, a doped DBR such as DBR  335  is typically used only as the back reflector for VCSEL 300 and not as the output coupler mirror.  
         [0029]     To implement doping-grating structures in the waveguide of a QCL, standard photolithography or e-beam lithography may be used to pattern photoresist on the surface of the semiconductor to form a pattern of lines and spaces having a typical pitch of about 1μ m or an odd multiple of 1μ m. In accordance with the invention,  FIG. 4   a  shows patterned photoresist mask  420  used in conjunction with ion implantation of dopant species  425  such as Si or Zn, for example in the fabrication of QCL  401 . The doping level and depth of the doping profile are typically controlled by the implant dose and ion implant energy, respectively. Typical dose values are on the order of about 1×10 14   1 /cm 2  to about 1×10 15 /cm 2  and typical ion implant energies of about 0.5 MeV to about 2 MeV are used to create highly doped regions  455  in a portion of the waveguide of QCL  401  that is patterned into a grating structure. If more implant protection is required than patterned photoresist mask  420  can provide, patterned photoresist mask  420  may be transferred into a hard mask of, for example, metal or dielectric using wet or dry etching techniques or standard lift-off.  
         [0030]     In accordance with the invention,  FIG. 4   b  shows a method of creating a doping-grating through solid source diffusion of dopant species  445  into semiconductor wafer  402 . The photoresist pattern (not shown) can be transferred onto thin film mask  446 , for example, an Si thin film mask, on the semiconductor surface using standard wet or dry etching methods. Semiconductor wafer  402  can then be placed in a diffusion oven having a temperature in the range from about 700° C. to 900° C. where the dopant, for example, Si in the case of an Si thin film mask, will diffuse out of thin film mask  446  into semiconductor wafer  402 .  FIG. 4   b  shows diffusion profiles  448  in semiconductor wafer  402  for diffusion times in the range of 1 to 8 hours.  
         [0031]     Another example of solid-source diffusion has thin film mask  446  made of, for example, Ge-Au or similar n contact metal onto which the grating pattern has been transferred from the photoresist pattern (not shown) using standard lift-off or wet or dry etching methods. Standard annealing of the Ge-Au n contact metal at about 400° C. to 450° C. for about 10 to 300 seconds in a nitrogen or other inert gas ambient drives the Ge into semiconductor wafer  402  to create diffusion profiles  448 .  
         [0032]     Vapor diffusion may also be used to create the doping-grating in accordance with the invention and is typically carried out in a closed-quartz tube ampule. In using vapor diffusion, thin film mask  446  is typically made from silicon dioxide and is not the source of the dopant. Thin film mask  446  acts to block the vapor-phase dopant such as Zn, for example, from diffusing into semiconductor wafer  402 . Hence, vapor phase diffusion creates a doping profile that is the negative of that shown in  FIG. 4   b.  The vapor phase dopant diffuses into the openings of thin film mask  446  and is blocked from diffusing by thin film mask  446  elsewhere.  
         [0033]      FIGS. 5   a - c  show the use of selective growth of doped regions to define a doping grating in accordance with the invention.  FIG. 5   a  shows patterned layer  510 , typically SiO 2  or Si 3 N x , that is typically transferred from a patterned photoresist (not shown) through wet or dry etching methods. When high doped layer  511  is regrown over patterned layer  510 , typically SiO 2  or Si 3 N x , high doped layer  511  will grow only on the exposed portions  509  of semiconductor wafer  500  and not on patterned layer  510  resulting in patterned high-doped layer  511 . Patterned layer  510 , typically SiO 2  or Si 3 N x , is then removed from semiconductor wafer  500  using wet or dry etching methods and semiconductor wafer  500  can be regrown with low-doped material to bury patterned high doped layer  511  inside low-doped burying layer  515  as shown in  FIG. 5   c . This allows a buried doping-grating to be created.  
         [0034]     Alternatively, high-doped layer  511  can be grown first on semiconductor wafer  500  and patterned layer  510 , typically SiO 2  or Si 3 N x , is deposited over high-doped layer  511 . Exposed portions of high-doped layer  511  not protected by patterned layer  510  are then removed by wet or dry etching methods. Patterned layer  510 , typically SiO 2  or Si 3 N x , can then be removed by wet or dry etching methods and semiconductor wafer  500  can be regrown with low-doped burying layer  515 . This allows a buried-doping grating to be created. Note that the steps shown in  FIGS. 5   a - 5   c  may be modified to create a buried-doping grating below waveguide core  550  by using regrowth prior to growth of waveguide core  550 .  
         [0035]     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.