Abstract:
The polarization instability inherent in laterally-oxidized VCSELs may be mitigated by employing an appropriately-shaped device aperture, a misoriented substrate, one or more cavities or employing the shaped device aperture together with a misoriented substrate and/or cavities. The laterally-oxidized VCSELs are able to operate in a single polarization mode throughout the entire light output power versus intensity curve. Combining the use of misoriented substrates with a device design that has an asymmetric aperture that reinforces the polarization mode favored by the substrate further improves polarization selectivity. Other device designs, however, can also be combined with substrate misorientation to strengthen polarization selectivity.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is a divisional of application Ser. No. 09/389,160 filed Sep. 2, 1999 which is a Continuation in Part claiming the benefit of application Ser. No. 09/364,614 filed Jul. 29, 1999 which is a Continuation in Part of application Ser. No. 08/940,867 filed Sep. 30, 1997 which claims the benefit of Provisional Application 60/037,175 filed Feb. 7, 1997. 
     
    
     FIELD OF INVENTION  
       [0002]     The present invention relates generally to semiconductor lasers. More specifically, the invention allows for the elimination of the polarization instability in laterally-oxidized vertical-cavity surface emitting lasers.  
       BACKGROUND OF INVENTION  
       [0003]     Solid state semiconductor lasers are important devices in applications such as optoelectronic communication systems and high-speed printing systems. Recently, there has been an increased interest in vertical cavity surface emitting lasers (“VCSEL&#39;s”) although edge emitting lasers are currently used in the vast majority of applications. A reason for the interest in VCSEL&#39;s is that edge emitting lasers produce a beam with a large angular divergence, making efficient collection of the emitted beam more difficult. Furthermore, edge emitting lasers cannot be tested until the wafer is cleaved into individual devices, the edges of which form the mirror facets of each device. On the other hand, not only does the beam of a VCSEL have a small angular divergence, a VCSEL emits light normal to the surface of the wafer. In addition, since VCSEL&#39;s incorporate the mirrors monolithically in their design, they allow for on-wafer testing and the fabrication of one-dimensional or two-dimensional laser arrays.  
         [0004]     A known technique to fabricate VCSEL&#39;s is by a lateral oxidation process, as schematically illustrated in  FIGS. 1 and 2 . Under this approach, a laser structure comprising a plurality of layers is formed upon substrate  10 . These layers include an active layer  12  and an AlGaAs layer  14  with a high aluminum content. The AlGaAs layer  14  is placed either above or below the active layer of a laser structure. Then, the layered structure is masked and selectively etched to form a mesa structure  22  as illustrated in  FIG. 2 . As a result of the etching, the AlGaAs layer  14  with a high aluminum content adjacent to the active layer  12  is exposed at the edges of the mesa structure  22 . To form the lasing emissive region or “aperture”, this AlGaAs layer is oxidized laterally from the edges towards the center of the mesa structure as represented by arrows A. Other layers in the structure remain essentially unoxidized since their aluminum content is lower. Consequently, their oxidation rates are also substantially lower. Therefore, only the AlGaAs layer with high aluminum content is being oxidized. The oxidized portions of the high aluminum content layer become electrically non-conductive as a result of the oxidation process. The remaining unoxidized region, which is conductive, in the AlGaAs layer forms the so-called “aperture”, a region which determines the current path in the laser structure, and thereby determines the region of laser emission. A VCSEL formed by such a technique is discussed in “Selectively Oxidized Vertical Cavity Surface Emitting Lasers With 50% Power Conversion Efficiency,” Electronics Letters, vol. 31, pp. 208-209 (1995).  
         [0005]     The current lateral oxidation approach has several disadvantages, such as large mesa, large oxidation region, and poor control of the aperture size. A key disadvantage of this approach is the difficulty in controlling the amount of oxidation. Generally, the desired device aperture is on the order of one to ten microns (μm), which means that several tens of microns of lateral oxidation will typically be required in order to fabricate the device when oxidizing in from the sides of the much larger mesa, which must typically be 50 to 100 microns in size. Since the size of the resulting aperture is small relative to the extent of the lateral oxidation regions, the devices formed generally have severe variations in aperture size as a result of non-uniform oxidation rates from wafer to wafer and across a particular wafer. The oxidation rate of AlGaAs depends strongly on its aluminum composition. Any composition non-uniformity will be reflected by changes in the oxidation rate, which in turn creates uncertainty in the amount of oxidation. The process is also relatively temperature-sensitive. As the oxidation rate varies, it is difficult to ascertain the extent to which a laser structure will be oxidized, thereby decreasing reproducibility in device performance. In short, such a process often creates various manufacturability and yield problems.  
         [0006]     Another disadvantage of a VCSEL formed by a traditional lateral oxidation approach is the difficulty it creates in forming high density laser arrays. In order to oxidize a buried layer of high aluminum content, an etching process is performed leaving a mesa. After the etching of this mesa, lateral oxidation is performed such that the oxidized regions define a laser aperture of a particular size. The use of a mesa structure, in part, limits the minimum spacing between two lasers in an array. The step height of the mesa is typically several microns because of the need to etch through a thick upper DBR mirror. Additionally, the top surface of the mesa also has to be relatively large so that a metal contact can be formed on it without covering the lasing aperture. Typically, the minimum size of an electrical contact is approximately 50×50 μm 2 . Hence, the step height of the mesa and the placement of the electrical contact on the surface make it difficult to form highly compact or high density laser arrays.  
         [0007]     A solution to some of the problems associated with a typical mesa structure is the use of a shallow mesa. In order to use a shallow mesa, the upper mirror is not formed by an epitaxial process. Instead, the upper mirror is formed by a deposited multilayer dielectric material, which reflects light. Electrical contact is made directly onto the upper portion of the active region. Devices formed under this approach have been fabricated on mesas with widths of approximately twelve microns. However, the added complexity of depositing a dielectric material and using a liftoff process to define the contact make it difficult to optimize the devices for low threshold current and high efficiency.  
         [0008]     A VCSEL formed by a traditional lateral oxidation approach often suffers from poor mechanical or structural integrity. It is well-known that the upward pressure applied during a packaging process may cause delamination of the entire mesa since the bonding of the oxide layer to the unoxidized GaAs or AlGaAs is generally weak.  
         [0009]     Light from typical VCSELs is usually polarized along one of two orthogonal directions along the wafer surface. The dominant polarization can switch back and forth between these two orthogonal orientations as the operating current to the VCSEL is varied because there is no natural preference for either orthogonal direction. The polarization instability is a major drawback because it limits VCSELs to applications where no polarization sensitive optical elements are present. Moreover, if the VCSEL is modulated, sudden changes in polarization states can result in undesirable light intensity fluctuations that contribute to signal noise.  
         [0010]     There are several known methods for controlling VCSEL polarization. These include making devices with anisotropic mesa geometries as described by K. Choquette and R. Leibenguth in “Control of vertical-cavity laser polarization with anisotropic cavity geometries”, IEEE Photonics Technology Letters, vol. 6, no. 1, pp. 40-42, 1994, making devices with tilted etched-pillar structures as described by H. Y. Chu et al. in “Polarization characteristics of index-guided surface emitting lasers with tilted pillar structure”, IEEE Photonics Technology Letters, vol. 9, no. 8, pp. 1066-1068, 1997, use of dielectric top mirrors with coated sidewalls as described by M. Shimuzi et al. in “Polarisation control for surface emitting lasers”, Electronics Letters, vol. 27, no. 12, pp. 1067-1069, 1991, using substrates having a misoriented surface as described in Compound Semiconductor, May/June, p. 18, 1997 or milling a cavity next to a completed gain-guided device as described by P. Dowd et al. in “Complete polarisation control of GaAs gain-guided top-surface emitting vertical cavity lasers”, Electronic Letters, vol. 33, no. 15, pp. 1315-1317, 1997.  
       BRIEF SUMMARY OF INVENTION  
       [0011]     Large arrays of densely-packed VCSELs are attractive light sources for applications such as laser printbars, where there may be thousands of semiconductor lasers on a small chip operating to transfer print images at high speed. Laterally-oxidized VCSELs are of particular interest because these VCSELs operate with exceedingly low threshold currents and high efficiencies, properties that are important for densely-packed VCSEL arrays. The polarization instability inherent in laterally-oxidized VCSELs may be mitigated by employing an appropriately-shaped device aperture, a misoriented substrate, one or more cavities or employing the shaped device aperture together with a misoriented substrate and/or cavities. The laterally-oxidized VCSELs are able to operate in a single polarization mode throughout the entire light output power versus intensity curve.  
         [0012]     While a certain degree of polarization selectivity can be achieved by making devices on substrates whose surfaces are misoriented from, for example, the {100} surface, this method often does not produce sufficient polarization selectivity. A more effective solution involves combining the use of misoriented substrates with a device design that has an asymmetric aperture that reinforces the polarization mode favored by the substrate. Other device designs, however, can also be combined with substrate misorientation to strengthen polarization selectivity.  
         [0013]     An alternative device design is discussed in “Complete polarisation control of GaAs gain-guided top-surface emitting vertical cavity laser” by P. Dowd, et al. In this VCSEL, deep 1 μm wide cavities placed between 1 and 2 μm from the cavity aperture produce differential loss for the two polarization modes. The cavities are formed after device fabrication using a focus ion beam etcher. The favored polarization mode using this method is found to be in a direction perpendicular to the cavity. In this example, enhanced polarization selectivity can by achieved by fabricating the VCSEL on a misoriented substrate and aligning the cavity along a direction perpendicular to the polarization mode favored by the misoriented substrate.  
         [0014]     Another method of producing polarization selectivity involves applying an anisotropic stress either by external means or by a built in mechanism as discussed in “Engineered polarization control of GaAs/AlGaAs surface-emitting lasers by anisotropic stress from elliptical etched substrate hole” by T. Mukaihara, et al. An elliptical hole is first etched and a high thermal expansion coefficient material is then deposited on the hole. The high thermal expansion material can be a thin film, an epitaxial layer, or an adhesive. The resulting anisotropic stress produces a gain difference between the two polarization modes resulting in a favored polarization direction along the short axis of the elliptical hole. Enhanced polarization selectivity can again be achieved by fabricating the VCSEL on a misoriented substrate and aligning the short axis of the elliptical hole to the polarization direction favored by the misoriented substrate.  
         [0015]     A VCSEL employing an asymmetric etched mesa can also produce polarization preference as illustrated in “Control of vertical-cavity laser polarization with anisotropic transverse cavity geometries” by K. Choquette, et al. VCSELs utilizing dumbbell-shaped mesas have polarization preferences along the long axis of the dumbbell. The polarization preference can again be strengthened by making the device on a misoriented substrate and by positioning the long axis of the dumbbell-shaped mesa along a polarization direction favored by the misoriented substrate.  
         [0016]     There are various means of producing a polarization preference by different VCSEL designs. However, most VCSEL designs do not produce sufficient polarization selectivity to completely suppress the non preferred polarization mode. The polarization selectivity can be significantly improved by fabricating these devices on misoriented substrates and designing the VCSELs so that their favored polarization direction reinforces the polarization preference that is inherent in the misoriented substrate.  
         [0017]     The advantages and objects of the present invention will become apparent to those skilled in the art from the following detailed description of the invention, its preferred embodiments, the accompanying drawings, and the appended claims.  
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0018]      FIGS. 1 and 2  illustrate a prior art approach to the formation of a laser aperture in a VCSEL structure.  
         [0019]      FIG. 3  illustrates a side sectional view of a semiconductor structure which is used to form the preferred embodiment of the present invention.  
         [0020]      FIG. 4  is a top view of a portion of a mask which may be applied to the semiconductor structure shown in  FIG. 1  under the present invention.  
         [0021]      FIG. 5  is a partial side sectional view of the semiconductor structure of  FIG. 1  with a cavity etched therein.  
         [0022]      FIG. 6  is a simplified top view of a portion of an oxidation layer, wherein the layers above it have been removed.  
         [0023]      FIG. 7  is a cross-sectional view taken substantially along line  7 - 7  in  FIG. 6  and in  FIG. 9 .  
         [0024]      FIG. 8  is a cross-sectional view taken substantially along line  8 - 8  in  FIG. 6  and in  FIG. 9 .  
         [0025]      FIG. 9  is a top view of two adjacent VCSEL structures showing a non-transparent top contact.  
         [0026]      FIG. 10  is a top view of two adjacent VCSEL structures showing a transparent top contact.  
         [0027]      FIG. 11  shows a laser structure whose aperture is defined by a triangular bounding pattern of cavities.  
         [0028]      FIG. 12  shows an array of lasers which is formed by repeating the triangular bounding pattern shown in  FIG. 11 .  
         [0029]      FIG. 13  shows a laser structure whose aperture is defined by a bounding pattern of four cavities arranged in a square pattern.  
         [0030]      FIG. 14  shows an array of lasers which is formed by repeating the square bounding pattern shown in  FIG. 13 .  
         [0031]      FIG. 15  shows another array of lasers which is formed by repeating the square bounding pattern shown in  FIG. 13 .  
         [0032]      FIG. 16  shows a laser structure whose aperture is defined by a bounding pattern of six cavities arranged in an hexagonal pattern.  
         [0033]      FIG. 17  shows an array of lasers which is formed by repeating the hexagonal bounding pattern shown in  FIG. 16 .  
         [0034]      FIG. 18  shows another array of lasers which is formed by an alternative repeating of the hexagonal bounding pattern shown in  FIG. 16 .  
         [0035]      FIG. 19  shows a typical planar laterally oxidized VCSEL.  
         [0036]      FIG. 20  shows a light output power versus current plot for a typical planar laterally oxidized VCSEL.  
         [0037]      FIG. 21  shows an embodiment of a planar laterally oxidized VCSEL in accordance with the invention.  
         [0038]      FIG. 22  shows a light output power versus current plot for the embodiment shown in  FIG. 21 .  
         [0039]      FIG. 23  shows a misoriented substrate relative to standard crystallographic orientations.  
         [0040]      FIG. 24  shows the orientation of the electric field vector relative to misoriented substrate.  
         [0041]      FIG. 25  shows gain anisotropies for a misoriented substrate.  
         [0042]      FIG. 26  shows an embodiment of a planar laterally oxidized VCSEL in accordance with the invention.  
         [0043]      FIG. 27  shows an embodiment of a planar laterally oxidized VCSEL in accordance with the invention. 
     
    
     DETAILED DESCRIPTION  
       [0044]      FIG. 3  illustrates a semiconductor structure which is used to form the preferred embodiment of the present invention. The structure illustrated includes a number of semiconductor layers, which can be used to form a vertical cavity surface emitting laser. As will be apparent, the layers are illustrated schematically only and bear no relationship to the relative thicknesses each to the other. As shown in  FIG. 3 , an n-type GaAs buffer layer  102  of approximately 200 nanometers is grown on an n-type GaAs substrate  100  using an epitaxial deposition process known as metal-organic chemical vapor deposition (“MOCVD”). The doping level of the n-type GaAs substrate and GaAs buffer are typically around the range of 3×10 18  cm −3  to 7×10 18  cm −3  so that a reasonably low resistance can be achieved in these layers. The semiconductor layers may also be deposited on a substrate by liquid phase epitaxy (“LPE”), molecular beam epitaxy (“MBE”), or other known crystal growth processes.  
         [0045]     Above the GaAs buffer layer  102  is a superlattice structure for forming a lower distributed Bragg reflector (“DBR”)  104  which provides a portion of the necessary internal reflection in a VCSEL structure. The lower DBR  104  is typically formed by multiple pairs of an AlGaAs layer with a high aluminum content (approximately 86% aluminum) and another AlGaAs layer with a low aluminum content (approximately 16% aluminum). After the growth of a number of layer pairs (typically 35 Si doped pseudoparabolically graded DBR pairs), a final AlGaAs layer with a high aluminum content is deposited before growing the first cladding layer  106  of the optical cavity. A typical thickness of each layer pair is approximately 120 nanometers for a laser emitting at 820 nanometers. The total thickness of each layer pair is designed to be equal to one half of the optical wavelength at the intended wavelength of laser operation. The thickness of the final high aluminum content layer is designed to be a quarter of the optical wavelength at the intended wavelength of laser operation. The AlGaAs layer with a high aluminum content contains approximately 86% aluminum. The aluminum content of the AlGaAs layer with a high aluminum content should be sufficiently high to provide for a low refractive index, but not so high as to oxidize easily. The AlGaAs layer with a low aluminum content has an aluminum content of approximately 16%. The composition of the AlGaAs layer with a low aluminum content should typically have sufficient aluminum so that it is non-absorptive at the lasing wavelength.  
         [0046]     Under this embodiment, since light is outcoupled through the top surface of the semiconductor sample, the reflectivity of the lower DBR  104  should be as close to 100% as possible in order to achieve high internal reflection. High internal reflection generally reduces the threshold current of a laser. It is well-known that the reflectivity of the lower DBR  104  is generally a function of the difference in the refractive indices between the two AlGaAs layers of the superlattice and the number of layer pairs in the structure. The greater the difference in the refractive indices, the fewer number of pairs are required to obtain a given reflectivity. For example, 30 to 40 pairs of AlGaAs layers may be used to form the lower DBR structure  104 .  
         [0047]     After the lower DBR structure  104  has been deposited epitaxially, an AlGaAs cladding layer  106  is deposited. This lower AlGaAs cladding layer  106  has an aluminum content of about 58% and is n-type with a doping level of 1×10 18  cm −3  to 5×10 18  cm −3 . Its thickness is approximately 100 nanometers. Above this AlGaAs cladding layer  106  is the active layer  108  of the laser structure which comprises four InAlGaAs quantum wells with a thickness of about four to ten nanometers, typically about four nanometers, along with five Al 0.35 Ga 0.65 As barriers with a thickness of about two to eight nanometers, typically about six nanometers. Depending upon the desired output wavelength of the laser structure, pure GaAs or AlGaAs with a low aluminum content may be also used to form the quantum well structures. Nothing in this invention prevents the use of a single quantum well or other multiple quantum well (“MQW”) structures to form the active layer  108 .  
         [0048]     Above the active layer  108  is an upper AlGaAs cladding layer  110 , which is structurally similar to the lower AlGaAs cladding layer  106  except for the polarity of its dopants. This upper cladding layer  110  has an aluminum content of about 58% but is p-type with a doping level of 1×10 18  cm −3  to 4×10 18  cm −3 . Similar to the lower AlGaAs cladding layer  106 , the thickness of top cladding layer  110  is also about 100 nanometers. These two AlGaAs cladding layers,  106  and  110 , along with the active layer  108  generally form the optical cavity in which the desired optical gain can be attained. The total optical thickness of layers  106 ,  108 , and  110  is adjusted to be equal to an integer multiple of the intended wavelength of laser operation.  
         [0049]     Above the upper AlGaAs cladding layer  110  is an oxidation layer  112 , which is used to form the laser aperture. The laser aperture controls the current flow and thus the lasing location in the active layer  108 . Under this embodiment, this oxidation layer  112  is above the upper AlGaAs cladding layer  110 . Nothing in this invention prevents the placement of this oxidation layer  112  in another location either further above or below the active layer  108 . Typically, this oxidation layer  112  has an aluminum content of approximately 95% and a thickness of about 70 nanometers. Typically, this oxidation layer  112  constitutes the first layer of an upper DBR mirror and contains a p-type dopant.  
         [0050]     After the oxidation layer  112  has been formed, the remainder of an upper DBR mirror  114  which contains p-type doping is deposited. The upper DBR mirror  114  is structurally similar to the lower DBR mirror  104  except for the polarity of its dopants. Additionally, the mirror layer closest to each side of the active region generally has a high aluminum content. In this embodiment, this high aluminum content layer is also the oxidation layer  112 . In this embodiment, the reflectivity of the upper DBR  114  is typically 98% to 99% because light will be outcoupled through the surface of the semiconductor sample. Typically, 20 to 25 pairs of alternate AlGaAs layers are used to form this upper DBR mirror  114 . Typically, a p-AlGaAs current spreading layer and a final 22 nanometer thick p +  GaAs layer are grown above top DBR mirror  114 .  
         [0051]      FIG. 4  is a top view of a portion of a mask which may be applied to the semiconductor structure shown in  FIG. 3  under the present invention. First, as is conventional, a uniform layer of silicon nitride will be deposited over the entire semiconductor sample. Then, a photoresist layer  118  is deposited over the silicon nitride layer and is formed into the mask shown in  FIG. 4  by a photolithographic process which removes photoresist material from four circular areas  120 . The circular areas  120  form a pre-determined bounding pattern which will later be used to define the resulting aperture of a laser structure.  
         [0052]     As illustrated in  FIG. 5 , the sample then undergoes an etching process during which cylindrical cavities  126  are formed in the semiconductor structure through the four exposed circular areas  120 . The etching is performed by a process such as reactive ion etching which provides for the formation of a deep depression with vertical sidewalls. The depth of each cylindrical cavity should extend at least into the oxidation layer  112 , as shown in  FIG. 5 . After the formation of the cylindrical cavities and the removal of any photoresist on the surface, the semiconductor sample undergoes an oxidation. The sample is typically oxidized with water vapor in a nitrogen environment at elevated temperatures, in excess of 350° C. During the oxidation process, the oxidation layer  112  is exposed to the ambient through each cylindrical cavity, as indicated by arrows A. Thus, the oxidation layer  112 , which comprises of AlGaAs with a high aluminum content, is oxidized radially outwards from each cavity  126 , typically until the oxidized regions  124  surrounding each cavity approach one another and overlap, as can be seen in  FIG. 6 . However, a small non-oxidized gap between the oxidized regions may be permissible so long as electrical and optical fields are adequately confined. Although the cross section of each cavity has been described as being cylindrical, any suitable cross section may be used.  
         [0053]     During the oxidation process, other layers in the structure remain essentially unoxidized since their aluminum content is lower. The oxidation rate of AlGaAs increases with the aluminum content in a generally exponential manner at constant temperature. The time duration of the oxidation process depends upon the aluminum content in the oxidation layer  112  and the oxidation temperature. A desirable, controllable oxidation duration would be a few tens of minutes. Therefore, the layer that is being oxidized is the AlGaAs which has a high aluminum content of close to 95%. The portion of the AlGaAs layer which remains unoxidized controls the current path through the active layer  108 .  
         [0054]      FIG. 6  is a largely simplified top view of the oxidation layer  112  shown in  FIG. 3  assuming that all the layers above it have been removed. The shaded region  122  represents the laser aperture in oxidation layer  112  which determines the region of laser emission by active layer  108 . It is formed by the oxidation process of the present invention. During the oxidation process, the oxidation fronts emanate through the oxidation layer from the pattern of four cavities  126 , and the shaded region  122  is formed by the intersection of the boundaries of the oxidized regions  124 . The oxidation fronts emanating from the cylindrical cavities  126  are also generally cylindrical, resulting in overlapping oxidized regions  124 . The center of the overlapping regions  124  remains unoxidized. This unoxidized region forms the shaded area  122 , which is the aperture of the laser structure. After the oxidation process, an ion implantation process, which is next described, is used to form isolation region  130  to isolate the laser structure from its neighbor.  
         [0055]     After the oxidation process, the areas  124  are oxidized and the unoxidized portion  122  forms the aperture which controls the current path through the active layer  108 . Current flow through that portion of the active layer  108  which lies below the aperture  122  results in an injected density of p-type and n-type carriers, resulting in optical amplification. At sufficiently high current flow, this optical amplification, in combination with feedback from the DBR mirrors,  104  and  114 , will result in laser oscillation and emission from the active layer within the region defined by aperture  122  in oxidation layer  112 .  
         [0056]     Isolation region  130  (illustrated in  FIGS. 6, 7  and  8 ), which is formed by using an ion implantation isolation process, is highly resistive. The typical implantation energies used in such a process are 50 KeV, 100 KeV, 200 KeV and 310 KeV. The dose is typically 3×10 15  cm −2  at each energy level. The ion used to form the isolation region  402  is typically hydrogen.  
         [0057]     After the isolation process, metal contacts  132  and  134  are formed on the top surface and the bottom surface of the semiconductor structure, respectively, for biasing the laser, as illustrated in  FIGS. 7, 8  and  9 . A typical material used for forming the contacts is a titanium/gold bilayer film.  
         [0058]      FIG. 9  shows a top view of a VCSEL structure formed in accordance to the present invention after a typical metallization process to form the top contact  132 . Views in the direction of section lines  7 - 7  and  8 - 8  in this Figure are also as illustrated in  FIGS. 7 and 8 . The top contact  132  is of a generally keyhole shape, including a circular portion  134  and an extension portion  136 . The circular portion lies inboard of the cavities  126  and overlies the laser aperture  122 . Since it is non-transparent it is made annular in shape so as to allow light to be coupled out of the laser through its central opening. The width “W” of the annular circular portion  134  is usually limited by the minimum line width achievable under the processing technology used, thus setting a lower limit on the pitch between adjacent VCSEL structures Thus, a typical pitch between the centers of two adjacent VCSEL apertures  122  would be “4W.” However, if a transparent conductor is used (e.g. see  FIG. 10 ), the pitch between adjacent VCSEL structures could be further reduced to be on the order of “2W” because the top contact could overlie the laser aperture  122 . Moreover, the contact arrangement provides a direct current path to the optical mode at the center of aperture  122  and may be useful in applications where reduced mode partition noise is desired.  
         [0059]     A typical transparent conductor is indium tin oxide (“ITO”) which is deposited by a sputtering process prior to etching cavities  126  as described above. This procedure is self-aligned and greatly simplifies fabrication and is enabled by the stability of ITO during the lateral oxidation process (see “Low-threshold InAlGaAs vertical-cavity surface-emitting laser arrays using transparent electrodes” by C. L. Chua et al. in Applied Physics Letters, vol. 72, no. 9, 1001, which is incorporated by reference in its entirety). A half-wavelength thick ITO film is first deposited over the p +  GaAs contact layer overlying p-AlGaAs current spreading layer which is grown over DBR layer  114 . The ITO film is then successively rapid thermal annealed at 300 and at 600° C. for 2 min each in a nitrogen ambient. The low-temperature anneal crystallizes the deposited amorphous ITO film, while the second, higher-temperature anneal induces ohmic contact formation between the ITO film and the p +  GaAs contact layer. The transparent ITO film attains a post anneal contact resistance of 2×10 −5  ohm cm 2 , a sheet resistivity of 5×10 −4  ohm cm, and a power transmission coefficient of 98% at an emission wavelength of 817 nanometers.  
         [0060]     Next a set of cavities  126 , typically having a diameter of 2 μm delineating laser aperture  122  is patterned as shown in  FIG. 10  for example. The ITO and underlying DBR layers  114  are then dry etched using chemically assisted ion beam etching in two successive self-aligned steps to form cavities  126  that reach oxidation layer  112 , typically Al 0.94 Ga 0.06 As. Oxidation layer  112  is oxidized for 45 minutes at 415° C. in flowing steam. Oxidized regions  124  progress laterally outwards from each cavity  126 , and on merging define laser aperture  122 . Apertures  122  may typically range from 5 μm to 43 μm in diameter.  
         [0061]     Positioning of cavities  126  is typically selected so that lateral oxidation needs to proceed by only a few micrometers from the perimeters of cavities  126 . This reduced path of oxidation compared to typical etched pillar devices reduces the sensitivity of laser aperture  126  to variations in oxidation rates. The aluminum content of oxidation layer  112  is relatively low in order to lengthen the oxidation time so that transients are minimized. As noted above, the ITO film is not effected by the oxidation process.  
         [0062]     An alternative embodiment of the top contact is shown in  FIG. 10  and is identified by numeral  138 . It comprises a transparent conductive contact finger  140  and contact pad  142 , the contact finger overlying the laser aperture  122 . After the formation of an electrical contact on the top surface, the bottom electrode  134  is formed by depositing metal on the bottom surface of the substrate  100  and is typically an evaporated eutectic Ge/Au metal.  
         [0063]      FIGS. 11 , and  12 ,  13 ,  14  and  15 , and  16 ,  17  and  18  illustrate alternative packing arrangements for forming an array of lasers formed by the method of the present invention. In the laser device of  FIG. 11  and an array of such devices shown in  FIG. 12 , each laser structure includes an aperture  222  defined by oxidized regions  224  surrounding a bounding pattern of three cylindrical cavities  226  positioned at the apexes of an equilateral triangle. The spacing between the centers of any two cavities is “S.” As stated previously, during the oxidation process, an embedded AlGaAs layer with a high aluminum content will be oxidized radially outwardly from the cylindrical cavities  226  until the oxidized regions  224  overlap to form the unoxidized laser aperture  222 . The packing arrangement shown in  FIG. 11  may be repeated to form a laser array as shown in  FIG. 12 . If the spacing between the centers of two cylindrical cavities is “S,” a typical linear spacing “L” between two laser apertures is approximately “S/2.” 
         [0064]     In the laser device of  FIG. 13  and the arrays of  FIGS. 14 and 15 , the square bounding pattern of cylindrical cavities  126  is illustrated. Oxidized regions  124  will overlap to form the unoxidized laser aperture  122 . This packing arrangement shown in  FIG. 13  may be repeated to form a laser array as shown in  FIG. 14  or  15  If a packing arrangement such as  FIG. 14  is used and the spacing between the centers of two adjacent cylindrical cavities is “S,” a typical linear spacing “L” between two laser apertures is approximately “S.” If an arrangement such as  FIG. 15  is used and the spacing between the centers of two cylindrical depressions is “S,” a typical linear spacing “L” between two laser apertures is approximately “{square root}2×S.” 
         [0065]     In the laser device of  FIG. 16  and the arrays of  FIGS. 17 and 18  an hexagonal bounding pattern of cylindrical cavities is illustrated. It should be apparent that the cavities  326  may also be arranged at the vertices of any other polygon. As in the previously described embodiments, the laser aperture is formed by the unoxidized region  322  defined by the oxidized regions  324 . The packing arrangement shown in  FIG. 16  may be repeated to form a laser array as shown in  FIG. 17  or  18 . If an arrangement such as  FIG. 17  is used and the spacing between the centers of two adjacent cylindrical cavities is “S,” a typical linear spacing “L” between two laser apertures is approximately “1.5S.” If an arrangement such as  FIG. 18  is used, the closest linear spacing “L” between two laser apertures is approximately “{square root}3×0.5S.” 
         [0066]     The composition, dopants, doping levels, and dimensions given above are exemplary only, and variations in these parameters are permissible. Additionally, other layers in addition to the ones shown in the figures may also be included. Variations in experimental conditions such as temperature and time are also permitted. Lastly, instead of GaAs and GaAlAs, other semiconductor materials such as GaAlSb, InAlGaP, or other III-V alloys may also be used.  
         [0067]     The planar laterally-oxidized (PLO) VCSELs described above utilize holes or cavities  126 ,  226  or  326  to penetrate upper DBR mirror  114 . Cavities  126 ,  226  or  326  serve to expose buried high aluminum layer  112  that is then selectively oxidized. Cavities  126 ,  226  or  326  may be arranged at the vertices of a polygon such that upon oxidation, the oxidized regions, such as oxidized regions  124  of cavities  126  border VCSEL aperture  122 . Because oxidized regions  124  bordering aperture  122  have a refractive index lower than the refractive index of aperture  122  and are electrically insulating, oxidized regions  124  form a good lateral waveguide that also functions to confine current to aperture  122 . The planar surface areas between cavities  126  allows electrical contacting and routing to be established in a planar manner. Inter-device isolation is accomplished using ion implantation.  
         [0068]      FIG. 19  shows planar laterally oxidized (PLO) VCSEL  400 . Typically, cavities  426  have a 2 μm diameter and cavities  426  are placed at the vertices of a regular octagon. Cavities  426  are typically positioned with a center to center spacing of about 5 μm. Oxidation regions  424  extend by about 3.5 μm from the edges of cavities  126 , typically leaving aperture  422  with a 4 μm width. Light is emitted from aperture  422  of VCSEL  400  through ITO electrode  438 .  
         [0069]      FIG. 20  shows the light output power versus current characteristics of an embodiment of VCSEL  400 . Curve  2071  shows the light from VCSEL  400  with no polarization filter applied. Curve  2072  shows the light from VCSEL  400  having a polarization along direction  2320  (see  FIG. 23 ) inclined at an angle of about 4.1 degrees relative to the [011] crystallographic direction. Curve  2073  shows light from VCSEL  400  having a polarization along the [01 1 ] crystallographic direction.  FIG. 20  shows that the light from VCSEL  400  is initially polarized along direction  2325  which is the [01 1 ] direction but that the polarization switches abruptly to direction  2320  (see  FIG. 23 ) when the current reaches approximately 0.8 mA as is indicated by the sudden drop in curve  2073  and the corresponding rise in curve  2072 . Curve  2073  rises again at currents above about 1.25 mA indicating the reappearance of a [01 1 ] polarized lasing mode. However, curve  2072  remains greater than curve  2073  between about 1.25 mA and 2.25 mA, which shows that the dominant polarization mode is along direction  2320  in this current range. The dominant polarization mode switches to direction  2325  beyond about 2.25 mA.  
         [0070]     Embodiments of VCSEL  400  that are seemingly identical may behave differently with respect to the polarization direction and polarization switching as shown in “Anisotropic apertures for polarization-stable laterally oxidized vertical-cavity lasers” by Chua et al., Applied Physics Letters vol. 73, no. 12, pp. 1631-1633 which is incorporated by reference in its entirety. This is indicative of the polarization instability inherent in conventional devices such as, for example, VCSEL  400 .  
         [0071]     A stable polarization can be achieved if the symmetry between two orthogonal axes is broken by a sufficiently large perturbation. In an embodiment in accordance with the invention,  FIG. 21  shows this symmetry breaking may be created by making aperture  522  asymmetric by arranging holes or cavities  426  at the vertices of a distorted octagon. The distorted octagon is compressed by, for example, about 1.5 μm along the [01 1 ] direction and elongated by 1.5 μm along direction  2320  (see  FIG. 23 ). Upon oxidation, oval-like aperture  522  is formed. Ion implantation is performed outside of ellipsoidal region  531  consistent with the discussion above.  
         [0072]     During oxidation, AlGaAs layer  124  surrounding aperture  122  contracts and the change in thickness of layer  124  results in mechanical stresses at the boundary between layer  124  and aperture  122  (see  FIG. 7 ). The anisotropic stress resulting from oval-like aperture  522  removes the polarization modal gain degeneracy. Hence, a significant polarization preference is established along one of the two orthogonal axes resulting in stable polarization independent of the current level in the operating range. The difference in gain available to the two orthogonal polarization states is due to the differential gain that develops with the asymmetric stress and the different modal gain resulting from stress-induced birefringence.  
         [0073]      FIG. 22  shows polarization-resolved light output power versus current curves obtained from an embodiment of VCSEL  500  in accordance with the present invention. Curve  2271  shows the light output power without polarization filter. Curve  2272  shows that laser output in direction  2320  (see  FIG. 23 ) is completely suppressed throughout the operating regime. Curve  2273  shows that VCSEL  500  displays stable polarization along the [01 1 ] direction throughout the operating regime. The polarization suppression ratio is 18 dB for curve  2272  relative to curve  2273  at a current level of about 2.5 mA where peak light output power is reached.  
         [0074]     Asymmetric apertures  522  on VCSELs  500  that are rotated ±90° from the orientation shown in  FIG. 25  exhibit an enhanced output with polarization in direction  2320  relative to symmetric aperture  422  but laser light polarized in the [01 1 ] direction is not completely suppressed if the substrate orientation favors the [01 1 ] polarization direction. Suppression of laser light polarized in all but the desired polarization direction is possible if both the substrate orientation and the aperture asymmetry favor laser light polarized in the desired polarization direction.  
         [0075]     Substrate  2300  (see  FIG. 23 ) used in one embodiment of VCSEL  500  in accordance with the present invention has the characteristics as shown in  FIG. 22  with a substrate surface cut in a crystal plane that is tilted toward the [011] crystallographic axis.  FIG. 23  shows misoriented substrate  2300  with surface vector  2310  misoriented relative to [100] direction  2305  of a (100) oriented substrate surface. The misorientation is by angle of rotation β about [01   1   ] direction  2325  toward [011] direction  2315 . Misorientation relative to any of the &lt;111&gt; axes also results in anisotropic polarization selectivity. The &lt;111&gt; axes are oriented at an angle θ relative to the &lt;100&gt; axes where sin 2  θ=⅔. For the embodiment of  FIG. 22 , angle of rotation β is about 4.1 degrees. Groups of VCSEL  500  may be made in arrays resulting, for example, in arrays similar to those shown in  FIGS. 17 and 18  with printer and other applications.  
         [0076]      FIG. 24  shows the orientation of electric field vector E at polarization angle α′ with respect to axis  2320  of an embodiment of misoriented substrate  2300  in accordance with this invention for light exiting substrate  2300 .  FIG. 25  shows the corresponding gain that is achieved in arbitrary units versus the polarization angle α′ for an embodiment of misoriented substrate  2300 . The gain is seen to vary with polarization angle α′ in a periodic manner. The gain is higher for E fields polarized along ±[01 1 ] direction  2325 . Therefore, misoriented substrate  2300  favors laser light polarized in ±[01 1 ] direction  2325  over laser light polarized in ±direction  2320 .  
         [0077]     However, substrates that are misoriented along a different direction and by different angles can also produce gain anisotropies. Since standard (100)-oriented substrates have crystal symmetries that belong to the D 4th  point group, their gain properties are isotropic in the substrate plane as a function of angle. Misoriented substrates, however, can have symmetries that produce gain anisotropies leading to directional gain dependencies as shown, for example, in  FIG. 25  for an embodiment of substrate  2300 .  
         [0078]     Gain curves for a given substrate orientation can be determined by first calculating the quantum wave functions using the multiband effective mass theory for the valence band and Kane&#39;s model (e.g., see E. O. Kane, in Journal of Physics and Chemistry of Solids, v. 1, p. 249, (1957), incorporated by reference in its entirety) for the conduction band. In the multiband effective mass theory, the valence band Hamiltonian for a (100) substrate consists of the Luttinger-Kohn Hamiltonian (e.g., see J. M. Luttinger and W. Kohn in Physical Review, v. 97, p. 869 (1955), incorporated by reference in its entirety) and a strain-orbit potential term if the active layer is under stress. Details regarding the strain-orbital term may be found in G. E. Pikus and G. L. Bir in Soviet Physics-Solid State, vol. 1, 1502 (1960) incorporated by reference in its entirety.  
         [0079]     Several sources of stress exist. First, stress on active layer  108  (see  FIG. 3 ) occurs because of the lattice mismatch between active layer  108  and GaAs substrate  100  resulting in a stress ranging from 0.01% to 1%, and typically about 0.5% compressive stress for the embodiment shown in  FIGS. 21 and 22 . The amount and type of built-in active layer stress, if any, depends on the particular alloy chosen for the quantum wells in active layer  108 . Possible alloys for quantum wells include InAlGaAs, AlGaInP, InGaAsN and AlGaAsSb. Second, reduction in the thickness of AlGaAs layer  112  during the oxidation process also produces stress. Third, cavities may be used to induce stress.  
         [0080]     The Hamiltonians for arbitrary wafer orientations may be obtained by performing a unitary transformation on the (100) Hamiltonians: H′=U(θ,φ,γ) H U t (θ,φ,γ), where U(θ,φ,γ) is the rotation operator corresponding to the Euler angles θ, φ, and γ of the substrate relative to the (100) orientation. Once the Hamiltonians are determined, the energy band structure may be solved for numerically. The gain curve as a function of direction is then obtained by calculating the density of states and evaluating the relevant optical matrix elements.  
         [0081]     The substrate orientation necessary to produce a desired gain versus polarization angle dependency can be investigated, for example, by using the PICS3D software program available from Crosslight Software, Inc. at 5450 Canotek Road, Unit 56, Gloucester, Ontario, Canada K1J9G4.  
         [0082]      FIG. 26  shows VCSEL  400  with etched cavities  2601  and  2602  in accordance with an embodiment of this invention. Aperture  422  is not asymmetric but cavities  2601  and  2602  are etched on either side of VCSEL  400 , typically placed as close as possible to aperture  422 , to induce an asymmetry on active region of VCSEL  400 . One cavity or more than two cavities may also be used to generate differential loss and/or stress on VCSEL  400 . Typically, cavities  2601  and  2602  are etched at the same time and using the same process as cavities  426 . Hence, the depth of cavities  2601  and  2602  is about the same as the depth of cavities  426 . However, cavities  2601  and  2602  can also be formed at a different time and using a different process from cavities  426 . For example, cavities  2601  and  2602  in an embodiment in accordance with the invention may be formed using focused ion beam milling subsequent to fabrication of VCSEL  400 . Cavities  2601  and  2602  may be filled with a filler material having a coefficient of thermal expansion different from substrate  100  to enhance the function of cavities  2601  and  2602  (see  FIG. 3 ). For example, cavities  2601  and  2602  may be filled with a metal, semiconductor or dielectric material. The filler material is deposited at temperatures well in excess of the operating temperature of VCSEL  400  so that as the filler cools a stress is induced in VCSEL  400 .  
         [0083]     If VCSEL  400  is grown on misoriented substrate  2300 , cavities  2601  and  2602  may be oriented perpendicular to the direction of polarization reinforced by misoriented substrate  2300  to further suppress the polarization instability for VCSEL  400 .  
         [0084]      FIG. 27  shows VCSEL  500  with etched cavities  2701  and  2702  in accordance with an embodiment of this invention. Aperture  522  is asymmetric and cavities  2701  and  2702  are etched on either side of VCSEL  500 , typically placed as close as possible to aperture  522 , to reinforce the asymmetry on the active region of VCSEL  500 . One cavity or more than two cavities may also be used to generate differential loss and/or stress on VCSEL  500 . Typically, cavities  2701  and  2702  are etched at the same time and using the same process as cavities  426 . Hence, the depth of cavities  2701  and  2702  is about the same as the depth of cavities  426 . However, cavities  2701  and  2702  can also be formed at a different time and using a different process from cavities  426 . For example, cavities  2701  and  2702  in accordance with an embodiment the invention may be formed using focused ion beam milling subsequent to fabrication of VCSEL  500 . Cavities  2701  and  2702  may be filled with a filler material having a coefficient of thermal expansion different from substrate  100  to enhance the function of cavities  2701  and  2702  (see  FIG. 3 ). For example, cavities  2701  and  2702  may be filled with a metal, semiconductor or dielectric material. The filler material is deposited at temperatures well in excess of the operating temperature of VCSEL  500  so that as the filler cools a stress is induced in VCSEL  500 .  
         [0085]     If VCSEL  500  is grown on misoriented substrate  2300 , cavities  2701  and  2702  and the major axis of aperture  522  may be oriented perpendicular to the direction of polarization reinforced by misoriented substrate  2300  to further suppress the polarization instability for VCSEL  500 .  
         [0086]     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 such alternatives, modifications, and variations that fall within the spirit and scope of the appended claims.