REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application is a divisional application of U.S. application Ser. No. 10/811,112, entitled “METHOD FOR PRODUCING A VERTICALLY EMITTING LASER”, that was filed on Mar. 26, 2004, the entirety of which is hereby incorporated by reference in its entirety. 
     
    
     FIELD OF THE INVENTION  
       [0002]     The invention relates to a method for producing a vertically emitting laser, in particular a VCSEL laser (VCSEL: Vertical Cavity Surface Emitting Laser).  
       BACKGROUND OF THE INVENTION  
       [0003]     The document “Transverse Mode Selection in Large-Area Oxide-Confined Vertical-Cavity Surface-Emitting Lasers Using a Shallow Surface Relief” (H. Martinsson, J. A. Vukusic, M. Grabherr, M. Michalzik, R. Jager, K. J. Ebeling, A. Larsson; IEEE Photonics Technology Letters, Vol. 11, No.  12 , December 1999, pages 1536-1538) describes a method for producing a VCSEL laser, in which a so-called “semiconductor relief” is produced on the surface of the VCSEL laser. The function of the semiconductor relief is to suppress higher modes of the light generated in the active zone of the laser and to leave only the fundamental mode of the light as far as possible uninfluenced. In essence, the functioning of the semiconductor relief is based on the fact that higher modes have a field distribution in the case of which the light is guided principally at the edge of the radiation lobe of the light. In contrast thereto, the fundamental mode has a radiation behavior in the case of which the light is situated principally in the inner region of the radiation lobe of the light. The semiconductor relief thus preferably suppresses higher modes, so that principally or exclusively the fundamental mode of the VCSEL laser is coupled into optical components arranged downstream of the VCSEL laser.  
         [0004]     In the case of the VCSEL laser in accordance with the already cited document “Transverse Mode Selection in Large-Area Oxide-Confined Vertical-Cavity Surface-Emitting Lasers Using a Shallow Surface Relief”, the semiconductor relief is arranged on the top side of the VCSEL laser, that is to say above the upper mirror or mirror stack of the VCSEL laser. The semiconductor relief is thus separated from a current aperture of the VCSEL laser by the upper mirror layer of the laser. In the case of the VCSEL laser shown in the document, the current aperture has an area size with a diameter of 15.5 μm. In this case, the area size of the semiconductor relief is understood to be the area size of the inner raised region of the semiconductor relief. The current aperture arranged below the upper mirror layer of the VCSEL laser has an area size (or a diameter) which is larger than the area size (or the diameter) of the semiconductor relief. In concrete terms, the diameter of the current aperture is 20 μm.  
         [0005]     The document “Increased-area oxidized single-fundamental mode VCSEL with self-aligned shallow etched surface relief” (H. J. Unold, M. Grabherr, F. Eberhard, F. Mederer, R. Jager, M. Riedl, K. J. Ebeling; Electronics Letters, 5th Aug. 1999, Vol. 35, No. 16) furthermore discloses a method for producing a laser, in which the semiconductor relief and the current aperture are produced in a self-aligning manner. This means that the current aperture is arranged in a concentrically aligned manner relative to the semiconductor relief. The self-alignment is achieved by virtue of the fact that both the position of the semiconductor relief and the position of a mesa structure of the VCSEL laser are defined in the same mask step. The mesa structure is produced in subsequent etching steps, the semiconductor relief inevitably remaining arranged centrally in the mesa structure. The area size of the current aperture is defined in the context of an oxidation step during which the sidewalls of the etched mesa structure are oxidized. This oxidation step effects lateral “oxidation into” the current aperture layer contained in the mesa structure. The semiconductor relief is separated from the current aperture by an upper mirror layer.  
       SUMMARY OF THE INVENTION  
       [0006]     Accordingly, the invention provides a laser production method in which a current aperture and a semiconductor relief are produced; the area size of the semiconductor relief and the area size of the current aperture are defined in the same production step.  
         [0007]     An essential advantage of the method according to the invention is that it is always ensured that the area size of the semiconductor relief and the area size of the current aperture are in a fixed relationship with respect to one another, since both the semiconductor relief and the current aperture are defined in the same production step. By way of example, if production tolerances occur on account of fluctuations in the production conditions (e.g. production temperature, moisture fluctuations), then the area size of the semiconductor relief will change under certain circumstances; however, since the semiconductor relief and the current aperture are defined in the same production step, the area size of the current aperture will also simultaneously be affected by the fluctuations in the production conditions, so that its size changes as well. As a result, the area size of the semiconductor relief and the area size of the current aperture will consequently change relatively “similarly”, so that they will nevertheless have a size ratio with respect to one another that corresponds to the actually desired size ratio without production tolerances. The area size of the semiconductor relief and the area size of the current aperture thus comply with a predetermined size ratio “in a self-scaling manner”; a “self-scaling” does not occur in the case of the previously known method described in the introduction, because the definition of the semiconductor relief and the definition of the current aperture are effected in separate production steps.  
         [0008]     A further essential advantage of the common production process for the semiconductor relief and the current aperture is that the yield in the production of the lasers is increased: it is because generally each current aperture diameter is matched only by a specific semiconductor relief diameter in order to obtain a single-mode radiation with a maximum optical output power at the output of the laser. The fixed scaling of the semiconductor relief and of the current aperture considerably increases the production yield and the process stability.  
         [0009]     The area size of the semiconductor relief and the area size of the current aperture may be defined for example in an oxidation step; this procedure is advantageous in particular because current apertures are usually produced in an oxidation step. Consequently, in this refinement of the method, the size of the semiconductor relief is defined during the oxidation of the current aperture.  
         [0010]     During the production of the VCSEL laser, an oxidizable auxiliary layer for the definition of the area size of the semiconductor relief and an oxidizable current aperture layer for the definition of the current aperture are preferably subjected to the common oxidation step. In this case, the ratio between the oxidation rate of the oxidizable auxiliary layer and the oxidation rate of the current aperture layer defines the size ratio between the area size of the resulting semiconductor relief and the area size of the resulting current aperture. The oxidizable auxiliary layer and the current aperture layer may be for example layers made of AlGaAs material, the proportion of aluminum determining the oxidation rate: the higher the proportion of aluminum, the greater the oxidation rate.  
         [0011]     During the production of the VCSEL laser, a mesa structure is preferably produced, which mesa structure encompasses or includes the oxidizable auxiliary layer and also the current aperture layer. The sidewalls of the mesa structure are subsequently oxidized, thereby also effecting oxidation “into” the oxidizable auxiliary layer and the current aperture layer within the mesa structure. The size ratio between the area size of the semiconductor relief and the area size of the current aperture is defined in this case.  
         [0012]     In order to produce the VCSEL laser, it is possible, by way of example, firstly to arrange at least one semiconductor intermediate layer on the oxidizable current aperture layer of the VCSEL laser. The oxidizable auxiliary layer is subsequently arranged on the semiconductor intermediate layer. A covering layer is applied to the oxidizable auxiliary layer, for example by being grown epitaxially. The mesa structure is subsequently etched into the resulting layer stack, and the sidewalls of the mesa structure are subjected to the oxidation step. The oxidizable current aperture layer and the oxidizable auxiliary layer are laterally oxidized simultaneously during this oxidation step.  
         [0013]     The VCSEL laser is completed particularly simply and thus advantageously by subsequently removing the oxidizable auxiliary layer in its oxidized regions, a region of the semiconductor intermediate layer being uncovered. The semiconductor intermediate layer is subsequently etched in the uncovered region down to a depth corresponding to the depth of the semiconductor relief to be produced. In addition, the covering layer and the non-oxidized regions of the oxidizable auxiliary layer are completely removed, thereby uncovering the semiconductor relief in the semiconductor intermediate layer. This then concludes the formation of the semiconductor relief.  
         [0014]     Afterward, a mirror layer or a mirror layer stack comprising a plurality of mirror layers, which forms the upper mirror layer of the laser, is preferably deposited on the semiconductor relief. The semiconductor relief is thus arranged between the mirror layer of the VCSEL laser and the current aperture of the VCSEL laser.  
         [0015]     In contrast to the previously known methods mentioned in the introduction, the area size of the semiconductor relief is preferably made to be larger than the area size of the current aperture in order to achieve an optimum radiation behavior.  
         [0016]     The upper mirror layer (or the upper mirror layers) deposited on the semiconductor relief may be for example layer stacks or layer pairs made of dielectric materials, preferably made of aluminum oxide and titanium oxide.  
         [0017]     Furthermore, it is regarded as advantageous if an upper electrical contact of the VCSEL laser is arranged in a self-aligned manner relative to the current aperture and relative to the semiconductor relief, as a result of which a homogeneous current injection is achieved.  
         [0018]     The upper electrical contact is preferably an intra-cavity contact, that is to say a contact which makes contact with a semiconductor layer of the VCSEL laser that is arranged below the upper mirror layer of the VCSEL laser.  
         [0019]     The intra-cavity contact may be formed for example on the semiconductor intermediate layer already mentioned above.  
         [0020]     The invention furthermore relates to a vertically emitting laser, in particular a VCSEL laser, with an as far as possible optimum radiation behavior.  
         [0021]     The invention provides a laser, in particular a VCSEL laser, with a semiconductor relief for radiating undesirable modes, in which the semiconductor relief is arranged between an upper mirror layer of the laser and a current aperture of the laser.  
         [0022]     Disturbing higher modes of the laser can be suppressed particularly simply and thus advantageously if the area size of the semiconductor relief is chosen to be larger than the area size of the current aperture. One advantage of the area ratio chosen in this way between the semiconductor relief and the current aperture consists in avoiding incomplete depletion of charge carriers below the semiconductor relief and—caused by a slow diffusion process—impairment of the modulation behavior of the laser.  
         [0023]     The mirror layer of the VCSEL laser preferably comprises layer stacks or layer pairs made of dielectric materials, preferably made of aluminum oxide and titanium oxide.  
         [0024]     As already mentioned in the introduction the VCSEL laser may have an intra-cavity contact as the upper electrical contact; as an alternative or in addition, the second or “lower” electrical contact of the laser may also be an intra-cavity contact. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0025]     For elucidating the invention,  
         [0026]      FIGS. 1-8  show a first exemplary embodiment of the method according to the invention and a laser according to the invention on the basis of diagrammatic illustrations,  
         [0027]      FIGS. 9-16  show a second exemplary embodiment of the method according to the invention and a laser according to the invention on the basis of diagrammatic illustrations, and  
         [0028]      FIGS. 17-23  show a third exemplary embodiment of the method according to the invention and a laser according to the invention. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0029]     In FIGS.  1  to  23 , the same reference symbols are used for identical or comparable components.  
         [0030]     Firstly, a first exemplary embodiment of the invention is explained in connection with FIGS.  1  to  8 .  FIG. 1  shows a semiconductor layer stack  10  comprising a lower mirror layer stack  20  having a plurality of lower mirror layers, a lower weakly doped laser layer  30 , an active (photon-generating) laser layer (laser zone)  40 , a weakly doped upper laser layer  50 , a current aperture layer  60 , a semiconductor intermediate layer  70 , an oxidizable auxiliary layer  75  and a covering layer  80 . The semiconductor layer stack  10  is arranged on a substrate  85 .  
         [0031]     A mask layer  100  is applied on the covering layer  80  of the semiconductor layer stack  10 , which mask layer is patterned and will subsequently define a mesa structure. The mask layer  100  may be formed by a hard mask or a photoresist mask; a hard mask made of an oxide or made of a nitride, for example, is preferably involved.  
         [0032]     The semiconductor layer stack  10  illustrated in  FIG. 1  is subjected to an etching step, thereby forming the mesa structure  110  illustrated in  FIG. 2 . It can be seen that the mask layer  100  is slightly undercut.  
         [0033]     The sidewalls  115  of the mesa structure  110  are subsequently subjected to an oxidation step. Particularly the current aperture layer  60  and also the oxidizable auxiliary layer  75  oxidize in this case, since these two layers are particularly disposed to oxidation. If the semiconductor layer stack  10  is a III/V semiconductor material system based on GaAs, then the oxidizable auxiliary layer  75  and the current aperture layer  60  have a correspondingly high aluminum content, for example, since the proportion of aluminum critically determines the oxidation rate in gallium arsenide layers.  
         [0034]     The oxidized region of the oxidizable auxiliary layer  75  and the oxidized region of the current aperture layer  60  are indicated by hatching in  FIG. 2 . It can be seen that oxidation is effected significantly “deeper” into the oxidizable auxiliary layer  75  and into the oxidized region of the current aperture layer  60  than into the remaining layers  50 ,  70  and  80  of the mesa structure  110 .  
         [0035]     A current aperture  60 ′ of the laser forms in the current aperture layer  60  as a result of the oxidation; the position of a semiconductor relief of the laser is defined in the oxidizable auxiliary layer  75  as a result of the oxidation—as will become clear below. An automatic “self-scaling” thus takes place with regard to the position of the current aperture  60 ′ and the position of the semiconductor relief, since the current aperture  60 ′ and the semiconductor relief are defined during the same production step.  
         [0036]     In a subsequent step, a further (second) mask layer  120 —preferably a photoresist mask—is applied to the oxidized mesa structure  110  and also to the (first) mask layer  100  and patterned. The resulting structure is shown in  FIG. 3 .  
         [0037]     The resulting structure is subsequently subjected to an etching step which cuts through both the first mask layer  100  and through the covering layer  80 . The etching step is ended on the oxidizable auxiliary layer  75 . The etching step is preferably carried out as a “selective” etching step, so that the etching of the covering layer  80  is ended automatically.  
         [0038]     Afterward, the oxidized region—that is to say the hatched region in  FIG. 3 —of the oxidizable auxiliary layer  75  is removed selectively. The structure illustrated in  FIG. 4  is formed, in the case of which the semiconductor intermediate layer  70  has been uncovered at those locations at which the oxidizable auxiliary layer  75  had previously been oxidized.  
         [0039]     Etching is subsequently effected into the semiconductor intermediate layer  70 , so that a raised region, called semiconductor relief  130  hereinafter, is formed in the semiconductor intermediate layer  70 . The resulting structure is shown in  FIG. 5 .  
         [0040]     The step of etching into the semiconductor intermediate layer  70  may be carried out wet-chemically, for example. In order to achieve an automatic etching stop in the semiconductor intermediate layer  70 , a highly doped contact layer, for example, may be integrated therein, the etching step stopping automatically on said contact layer. The highly doped contact layer is indicated by dashed lines in  FIG. 5  and provided with the reference symbol  150 .  
         [0041]     The etching depth in the course of etching the semiconductor intermediate layer  70  is chosen in such a way as to produce a semiconductor relief in the case of which higher modes of the VCSEL laser to be formed are suppressed to a sufficient extent.  
         [0042]     Afterward, a metal contact layer  155  is deposited, for example by vapor deposition, on the mesa structure  110  using the second mask layer  120 . The resulting structure is shown in  FIG. 6 .  
         [0043]     Afterward, the further mask layer  120  and also the non-oxidized region of the oxidizable auxiliary layer  75  are removed selectively, as a result of which the covering layer  80  that remains on the auxiliary layer  75  and also the metallization present on the further mask layer  120  are lifted off. The semiconductor structure illustrated in  FIG. 7  with a semiconductor relief  130  in the semiconductor intermediate layer  70  is formed.  
         [0044]     An annular metal contact  160  is formed by the residual metal contact layer  155  on the semiconductor intermediate layer  70 .  
         [0045]     A mirror layer or a mirror layer stack  200  is subsequently applied to the mesa structure in accordance with  FIG. 7 . This may be effected in the context of a “lift-off” method or in the context of a patterning method. The resulting VCSEL laser is shown in  FIG. 8 .  
         [0046]     Since the annular metal contact  160  makes contact with a semiconductor layer below the mirror layer or the mirror layer stack  200  and is thus situated in the “cavity region” of the laser, the annular metal contact  160  forms a so-called “intra-cavity contact”.  
         [0047]     The second electrical contact required for the VCSEL laser may be arranged—provided that the lower mirror layer stack  20  is conductive—for example on the rear side of the substrate  85 ; as an alternative, the second electrical contact may be provided as an alloying “intra-cavity contact” on the lower weakly doped laser layer  30 .  
         [0048]     As can be gathered from the explanations above, the area size or the diameter Ds of the current aperture  60 ′ in the current aperture layer  60  and also the area size or the diameter Dh of the semiconductor relief  130  in the semiconductor intermediate layer  70  are determined by the oxidation step to which the sidewalls  115  of the mesa structure  110  are subjected in accordance with  FIG. 2 . If production fluctuations or production tolerances then occur during the oxidation step, the area size or the diameter Ds of the current aperture and also the area size or the diameter Dh of the semiconductor relief  130  will fluctuate. However, since the current aperture  60 ′ and also the semiconductor relief  130  are produced during the same oxidation step, a virtually fixedly predetermined ratio between the area size of the current aperture and the area size of the semiconductor relief  130  will be formed. The ratio Ds/Dh will thus remain largely constant even in the event of production fluctuations. An effect of “self-scaling” thus occurs.  
         [0049]     In addition, a “self-alignment” between the current aperture  60 ′ and the semiconductor relief  130  also results, since the position of the current aperture  60 ′ and the position of the semiconductor relief  130  are defined by the same mask step.  
         [0050]     FIGS.  9  to  16  show a second exemplary embodiment of the invention. The semiconductor layer stack  10  arranged on the substrate  85  can be seen.  
         [0051]     A first mask  300 —preferably a hard mask—is applied to the semiconductor layer stack  10 , the outer edge  310  of which mask will define the mesa structure of the VCSEL laser (cf.  FIG. 9 ). There is an annular cutout present in the inner region of the mask  300 —which cutout is identified by the reference symbol  320  and will subsequently define the annular metal contact  160  in accordance with  FIG. 7 .  
         [0052]     In a second masking step, the annular cutout  320  is covered with a second mask  330 —preferably a photoresist mask—thereby producing the structure illustrated in  FIG. 10 .  
         [0053]     A mesa structure  110  is subsequently etched into the semiconductor layer stack  10 . The diameter of the mesa structure  110  is defined by the outer edge  310  of the first mask  300 .  
         [0054]     Afterward, the sidewalls  115  of the mesa structure  110  are oxidized. The structure shown in  FIG. 11  is formed, corresponding to the structure in accordance with  FIG. 2  apart from the configuration of the upper masks  300  and  330 .  
         [0055]     The second mask  330  is subsequently removed to form the structure in accordance with  FIG. 12 .  
         [0056]      FIG. 13  shows the resulting layer stack after a third mask  340 —preferably a photoresist mask—has been applied. The third mask serves for covering or protecting the sidewalls  115  of the mesa structure  110 .  
         [0057]     The resulting structure is subsequently subjected to an etching step which cuts through the covering layer  80 . The etching step is ended on the oxidizable auxiliary layer  75 . The oxidized region, that is to say the hatched region in  FIG. 13 , of the oxidizable auxiliary layer  75  is subsequently removed selectively. The structure illustrated in  FIG. 14  is formed, in the case of which the semiconductor intermediate layer  70  has been uncovered at those locations at which the oxidizable auxiliary layer  75  had previously been oxidized.  
         [0058]     Etching is subsequently effected into the semiconductor intermediate layer  70 , so that the semiconductor relief  130  is formed in the semiconductor intermediate layer  70 . The resulting structure is shown in  FIG. 15 .  
         [0059]     The step of etching into the semiconductor intermediate layer  70  may be carried out wet-chemically, for example. In order to achieve an automatic etching stop in the semiconductor intermediate layer  70 , a highly doped contact layer  150 , for example, may be integrated therein, the etching step stopping automatically on said contact layer. A metal contact layer  155  is subsequently deposited, for example by vapor deposition, on the mesa structure  110  using the third mask  340 . The resulting structure is shown in  FIG. 16 .  
         [0060]     The first and third masks  300  and  340  and also the non-oxidized region of the oxidizable auxiliary layer  75  are subsequently removed selectively, as a result of which the covering layer  80  that remains on the auxiliary layer  75  and also the metallization present on the third mask  340  are lifted off. The semiconductor structure already illustrated in  FIG. 7  with a semiconductor relief  130  in the semiconductor intermediate layer  70  is formed. An annular metal contact  160  is formed by the residual metallization  155  on the highly doped contact layer  150  of the semiconductor intermediate layer  70 .  
         [0061]     A mirror layer or a mirror layer stack  200  is subsequently applied to the mesa structure in accordance with  FIG. 7 , as has already been explained in connection with  FIG. 8 . The VCSL laser is thus completed.  
         [0062]     The second exemplary embodiment of the invention—in the same way as the first exemplary embodiment—affords self-alignment and self-scaling between the current aperture  60 ′ and the semiconductor relief  130  since the position and the size of the current aperture  60 ′ and the position and the size of the semiconductor relief  130  are defined by the same mask step and the same oxidation step. Moreover, in contrast to the first exemplary embodiment of the invention, the position of the annular metal contact  160  is additionally self-aligned relative to the current aperture  60 ′ and to the semiconductor relief  130  since the position of the annular metal contact  160  is determined by the first mask  300 , which also simultaneously defines the position of the mesa structure. Three components, namely the metal contact  160 , the current aperture  60 ′ and the semiconductor relief  130  are thus self-aligned.  
         [0063]     A third exemplary embodiment of the invention is explained below in connection with FIGS.  17  to  23 .  
         [0064]     First of all, an annular metal contact  160  is vapor-deposited onto a semiconductor layer stack  450 , for example by means of a lift-off method. The semiconductor layer stack  450  corresponds—apart from the missing oxidizable auxiliary layer  75  and the missing covering layer  80 —to the semiconductor layer stack  10  in accordance with  FIG. 1  (cf.  FIG. 17 ).  
         [0065]     A first mask  500 —preferably a hard mask made of oxide or made of nitride, for example—is subsequently applied. The first mask  500  has an annular cutout  505 , the inner region of which will define a semiconductor relief  130  (cf.  FIG. 18 ).  
         [0066]     An etching step is subsequently carried out, which forms the semiconductor relief  130  below the central region of the mask  500  (cf.  FIG. 19 ).  
         [0067]     A second mask  510 —preferably a photoresist mask—is subsequently applied in such a way that the annular cutout  505  of the first mask  500  is covered. The mesa structure  110  of the laser is then produced by means of an etching step (cf.  FIG. 20 ).  
         [0068]     Afterward, the second mask  510  is removed and the mesa structure is oxidized. The semiconductor relief  130  is thus completed in a self-aligned manner with respect to the current aperture  60 ′ (cf.  FIG. 21 ).  
         [0069]     The first mask  500  is also removed in the further course of the process, thereby producing the structure shown in  FIG. 22 .  
         [0070]     Afterward, on the semiconductor relief  130 , an upper mirror layer stack  200  is either applied over the whole area and patterned or produced by means of a lift-off method. The VCSEL laser is thus completed.  
         [0071]     The third exemplary embodiment affords the self-alignment—already explained in connection with the first exemplary embodiment—between the current aperture  60 ′ and the semiconductor relief  130  since both the position of the mesa structure  110  and thus the position of the current aperture  60 ′ and the position of the semiconductor relief  130  are defined by the same mask. By contrast, a self-alignment with regard to the annular metal contact  160  does not occur.  
         [0072]     In the case of the above three exemplary embodiments of the invention, the semiconductor relief  130  is arranged by way of example between the upper mirror layer stack  200  and the current aperture  60 ′. The area ratio Ds/Dh is by way of example less than 1; this means that the area size (Dh) of the semiconductor relief is chosen to be larger than the area size (Ds) of the current aperture.  
       Reference Symbols  
       [0000]    
       
           10  Semiconductor layer stack  
           20  Lower mirror layer stack  
           30  Lower weakly doped laser layer  
           40  Active laser layer  
           50  Upper weakly doped laser layer  
           60  Current aperture layer  
           60 ′ Current aperture  
           70  Semiconductor intermediate layer  
           75  Oxidizable auxiliary layer  
           80  Covering layer  
           85  Substrate  
           100  Mask layer  
           110  Mesa structure  
           115  Sidewalls  
           120  Second mask layer  
           130  Semiconductor relief  
           150  Highly doped contact layer  
           155  Metal contact layer  
           160  Annular metal contact  
           200  Mirror layer stack  
           300  First mask  
           310  Outer edge  310   
           320  Annular cutout  
           330  Second mask  
           340  Third mask  
           450  Semiconductor layer stack  
           500  First mask  
           505  Annular cutout  
           510  Second mask
The invention is directed to a vertically emitting laser and a method of manufacturing such a laser having a current aperture and a semiconductor relief. The semiconductor relief and the current aperture are defined in the same processing operation, thereby causing the semiconductor relief and the current aperture to be substantially self-aligned with respect to one another. In addition, such processing results in an area ratio of the semiconductor relief and the current aperture to be substantially self-scaling with respect to processing variations.