# Patent

## Title
Condition before TMAH improved device performance

## Abstract

The present disclosure relates to a method of forming a back-side illuminated CMOS image sensor (BSI CIS). In some embodiments, the method comprises forming a plurality of photodetectors within a front-side of a semiconductor substrate. An implant is performed on the back-side of the semiconductor substrate to form an implantation region having a doping concentration that is greater in the center than at the edges of the semiconductor substrate. The back-side of the workpiece is then exposed to an etchant, having an etch rate that is inversely proportional to the doping concentration, which thins the semiconductor substrate to a thickness that allows for light to pass through the back-side of the substrate to the plurality of photodetectors. By implanting the substrate prior to etching, the etching rate is made uniform over the back-side of the substrate improving total thickness variation between the photodetectors and the back-side of the substrate.

## Background
BACKGROUND
CMOS image sensors are widely used in many modern day electronic devices to convert an optical image to an electric signal. A CMOS image sensor can be fabricated as a back-side illuminated or as a front-side illuminated CMOS image sensor. Back-side illuminated CMOS image sensors, which receive light on a back-side of a workpiece, offer superior performance (e.g., high resolution) over front-side illuminated CMOS image sensors.
Light incident on a back-side of a thinned semiconductor substrate, travels through a thin layer of semiconductor material to a plurality of photodetectors located within a front-side of the semiconductor substrate. The incident light generates carriers within the photodetectors which are transferred to back-end metal wiring levels that provide the carriers as an electric signal to a signal processing unit.



BRIEF DESCRIPTION OF THE DRAWINGS
FIGS. 1a-1b illustrate cross-sectional views of the formation of a conventional back-side illuminated CMOS image sensor.
FIG. 1c is a graph showing a total thickness variation over the back-side of a conventional back-side illuminated CMOS image sensor.
FIG. 2 is a flow diagram illustrating some embodiments of an exemplary method for forming a disclosed back-side illuminated CMOS image sensor.
FIG. 3a is a graph showing some embodiments of an exemplary etching rate as a function of implantation parameters.
FIG. 3b is a flow diagram illustrating some alternative embodiments of an exemplary method for forming a disclosed back-side illuminated CMOS image sensor.
FIGS. 4-8 are cross-sectional views of some embodiments of an exemplary semiconductor substrate upon which a method of forming a back-side illuminated CMOS image sensor is performed.
FIG. 9 is a graph showing a total thickness variation over the back-side of a disclosed back-side illuminated CMOS image sensor.
FIG. 10 illustrates a cross-sectional view of some embodiments of a back-side illuminated CMOS image sensor, as disclosed herein.



DETAILED DESCRIPTION
The description herein is made with reference to the drawings, wherein like reference numerals are generally utilized to refer to like elements throughout, and wherein the various structures are not necessarily drawn to scale. In the following description, for purposes of explanation, numerous specific details are set forth in order to facilitate understanding. It may be evident, however, to one of ordinary skill in the art, that one or more aspects described herein may be practiced with a lesser degree of these specific details. In other instances, known structures and devices are shown in block diagram form to facilitate understanding.
FIG. 1 a illustrates a cross-sectional view 100 of the formation of a conventional back-side illuminated CMOS image sensor (BSI CIS). During formation of the conventional BSI CIS, a back-side of a semiconductor substrate 102 is etched by an etchant 108 to reduce the original thickness t of the semiconductor substrate 102 by a thickness of d, resulting in a thinned semiconductor substrate 106 having a relatively small thickness. The thinned semiconductor substrate 106 comprises a plurality of photodetectors 104, which are positioned within a front-side of the thinned semiconductor substrate 106.
The thinned semiconductor substrate 106 has a thickness (t-d) that allows for light incident on the back-side of the thinned semiconductor substrate 106 to penetrate through the thinned semiconductor substrate 106 to the photodetectors 104. Therefore, the uniformity of substrate thinning achieved by etchant 108 must be extremely precise since excess silicon on the back-side of the thinned semiconductor substrate 106 acts as a barrier to light. FIG. 1b is a graph 110 showing a trend line 112 corresponding to the etchant depth as a function of position on the back-side of the semiconductor substrate 102. The etchant depth is greater in the center of the substrate 102 than at the edges, resulting in a total thickness variation TTV1 of approximately 0.1 μm over the back-side of the thinned semiconductor substrate 106.
After etching is performed to form the thinned semiconductor substrate 106, the back-side of the thinned semiconductor substrate 106 is subjected to an implant 116 that forms an implantation region 118 within the thinned semiconductor substrate 106, as shown in cross-sectional view 114 of FIG. 1c. However, the implant 116 cannot be tightly controlled and results in an implantation region 118 that comes into contact with the plurality of photodetectors 104, causing degradation of the performance of the plurality of photodetectors 104.
Accordingly, some aspects of the present disclosure provide for a method of forming a back-side illuminated CMOS image sensor (BCI CIS) with improved device performance and a small total thickness variation (TTV) between one or more photodetectors and a back-side of a thinned semiconductor substrate. In some embodiments, the method comprises forming a plurality of photodetectors within a front-side of a semiconductor substrate. An implant is performed on the back-side of the semiconductor substrate to form an implantation region having a non-uniform doping concentration. The back-side of the semiconductor substrate is then exposed to an etchant, having an etch rate that is inversely proportional to the doping concentration, which thins the semiconductor substrate to a thickness that allows for light to pass through the back-side of the semiconductor substrate to the plurality of photodetectors. By implanting the semiconductor substrate prior to etching, the uniformity of the etching rate can be improved over the back-side of the substrate, thereby improving TTV.
FIG. 2 is a flow diagram illustrating some embodiment of an exemplary method 200 for forming a disclosed a back-side illuminated CMOS image sensor (BSI CIS). The method 200 performs an implant on a back-side of a semiconductor substrate prior to performing an etch on the back-side, to reduce the thickness of (i.e., thin) the semiconductor substrate. Since the etch rate is a function of the doping concentration, the total thickness variation over the back-side of the semiconductor substrate can be reduced.
While the method 200 provided herein is illustrated and described below as a series of acts or events, it will be appreciated that the illustrated ordering of such acts or events are not to be interpreted in a limiting sense. For example, some acts may occur in different orders and/or concurrently with other acts or events apart from those illustrated and/or described herein. In addition, not all illustrated acts may be required to implement one or more aspects or embodiments of the description herein. Further, one or more of the acts depicted herein may be carried out in one or more separate acts and/or phases.
At step 202 a semiconductor substrate is provided. In some embodiments, the semiconductor substrate comprises a bulk substrate having a first dopant type (e.g., an n-type dopant).
At step 204 one or more photodetectors are formed within a front-side of the semiconductor substrate. The one or more photodetectors may comprise pinned diodes formed by masking the semiconductor substrate and then selectively implanting the semiconductor substrate with a first implant (e.g., a p-type implant) followed by a shallow, second implant (e.g., an n-type implant) aligned with the first implant.
At step 206 the front-side of the semiconductor substrate is affixed to a support substrate.
At step 208 an implant is performed on the back-side of the semiconductor substrate. The implant may comprise a second dopant type (e.g., a p-type dopant) such as boron, for example. The implant forms an implantation region. In some embodiments, the implantation region comprises a doping concentration profile that decreases as a function of the distance from a center of the semiconductor substrate. This provides for a higher doping concentration at the center of the semiconductor substrate than at edges of the semiconductor substrate (i.e., the doping concentration is proportional to the radial distance from the center of implantation region).
At step 210 the back-side of the semiconductor substrate is etched. Etching the back-side of the semiconductor substrate reduces the thickness of the semiconductor substrate to form a thinned semiconductor substrate having a thickness that allows for light to pass through the back-side of the thinned semiconductor substrate to the plurality of photodetectors. The etch has an etch rate that is a function of the doping concentration of the implantation region, such that by performing the implant (step 208) prior to the etch (step 210) the doping concentration profile can be used to decrease total thickness variation over the back-side of the semiconductor substrate.
In some embodiments, the etch is performed using an etchant having an etch rate that is inversely proportional to the doping concentration of the implantation region. For example, in some embodiments the etchant comprises Tetramethylammonium hydroxide (TMAH). Since the etch rate is inversely proportional to the doping concentration, areas having a higher doping concentration will have an etch rate that is decreased by a greater amount than areas having a lower doping concentration. By doping the back-side of the semiconductor substrate to have a greater doping concentration at the center of the substrate than at the edge (e.g., a Gaussian doping concentration), the natural variation in etching rates (e.g., shown in FIG. 1b) is offset by changes in etch rate caused by the implant. This offset results in a lower TN variation over the back-side of the semiconductor substrate.
For example, FIG. 3a illustrates a graph 300 showing a trend line 302 corresponding to the etch rate of a silicon substrate for different implant doses and energies. As shown in FIG. 3a, the etch rate of the silicon substrate decreases as the implant dose (and doping concentration within the substrate) increases. For example, the average etching rate of silicon without an implantation region is approximately 0.09 pm/min. The etch rate decreases to approximately 0.06 μm/min for an implantation region formed with a 5 KeV implant having a dose of 2×1013 cm−2 and to 0.055 μm/min for an implantation region formed with a 10 KeV implant having a dose of 2×1014 cm−2. In other words, increasing the doping concentration decreases the etch rate.
It will be appreciated that the implant can be performed over a wide range of energy and dose. In some embodiments, the implant can be performed using a dose in a range from about 1×1013 cm−2 to about 1×1016 cm−2 and having an energy in a range from about 5 Kev to about 30 Kev, for example. In other embodiments, the energy and dose of the implant may be greater than or less than the above disclosed values.
In some embodiments, the implant can be varied to tune etching characteristics (e.g., etch rate, etch depth, etc.) of the substrate, since etch rate is a function of the doping concentration. For example, FIG. 3b is a flow diagram illustrating some embodiment of an exemplary method 304 for forming a disclosed a back-side illuminated CMOS image sensor (BSI CIS). Method 304 is similar to method 200, but further comprises steps of determining etch characteristics (step 306) and selecting implant parameters corresponding to the determined etch characteristics (step 308). The etch characteristics may comprise etch rate, etch depth, etc. The implant parameters may comprise implant dose, implant energy, implant species, etc.
For example, in some embodiments the depth of the implant can selectively controlled to control a distance between the photodetectors and the back-side of a semiconductor substrate. For example, using a higher implant energy drives dopants to a greater depth within the semiconductor substrate, causing the etch to proceed deeper into the substrate before it is slowed by the high doping concentrations. Similarly, the total thickness variation can be controlled by increasing or decreasing the dose of the implant to change the variation in etch rate between different locations on the back-side of the substrate.
Some embodiments of an exemplary semiconductor substrate, whereon a method for forming a CBS CIS (e.g., method 200 and/or 304) is implemented, are illustrated in cross-sectional views of FIGS. 4-8.
FIG. 4 illustrates a cross-sectional view 400 of a semiconductor substrate 402. The semiconductor substrate 402 has a front-side 404 and a back-side 406. The semiconductor substrate 402 may comprise any type of semiconductor body (e.g., silicon/CMOS bulk, SiGe, SOI, etc.) such as a semiconductor wafer or one or more die on a wafer, as well as any other type of semiconductor and/or epitaxial layers formed thereon and/or otherwise associated therewith. Furthermore, the additional and/or different processing steps may occur prior to operation of method 200 or 304.
FIG. 5 illustrates a cross-sectional view 500 of one or more photodetectors 502 formed within the semiconductor substrate 402. The one or more photodetectors 502 are formed within the front-side 404 of the semiconductor substrate 402. In some embodiments, the photodetectors 502 comprise pinned photodiodes, for example.
FIG. 6 illustrates a cross-sectional view 600 of the semiconductor substrate 402 affixed to a support substrate 602. The support substrate 602 may comprise a silicon substrate, for example. The semiconductor substrate 402 is placed face-down so that the front-side 404 of the semiconductor substrate 402 is affixed to the support substrate 602. In various embodiments, the semiconductor substrate 402 can be affixed to the support substrate by using a dilute adhesive or by molecular bonding, for example.
FIG. 7a illustrates a cross-sectional view 700 of the semiconductor substrate being subjected to an implant 702 that forms an implantation region 704. The implantation region 704 is formed by implanting dopants into the back-side 406 of the semiconductor substrate 402. The dopants comprise boron dopants in some embodiments. In some embodiments, the resulting implantation region 704 is separated from the photodetectors 502 by a spacing S.
FIG. 7b is a graph 712 showing a trend line 714 corresponding to a lateral doping concentration profile (cross-section 706 in FIG. 7a) of the semiconductor substrate 402 as a function of position. The doping concentration profile comprises a Gaussian distribution, such that the doping concentration is higher in the center of the substrate compared to the edges of the substrate. For example, at a first lateral location Ip1, the doping concentration profile has a first doping concentration C1, while at a second lateral location Ip2 the doping profile has a second doping concentration C2 that is lower than the first doping concentration C1. In some embodiments, the mean and variance of the doping concentration profile can be varied by changing implant parameters to change the rate at which different regions on the back-side 406 of the semiconductor substrate 402 are etched.
In some embodiments, the doping concentration profile may also be controlled in the vertical direction to control the resulting etching depth and device performance parameters. FIG. 7c is a graph 716 showing a trend line 718 corresponding to a vertical doping concentration profile (cross-section 710 in FIG. 7a) of the semiconductor substrate 402 as a function of position. As shown in graph 716, the vertical doping concentration varies between the back-side 406 of the semiconductor substrate 402 and the photodetectors 502. For example, at a first vertical location vp1, the doping concentration profile has a third doping concentration C3, while at a second vertical location vp2 the doping profile has a fourth doping concentration C4 that is lower than the third doping concentration C3.
In some embodiments, the implant energy can be chosen to form an implantation region 704 configured to extend within the semiconductor substrate 402 to a depth that spatially separates the implantation region 704 and the photodetectors 502 from one another. By separating the implantation region from the photodetectors 502, the performance of the photodetectors is improved.
In additional embodiments, the location of a peak in the vertical doping concentration can be controlled by changing the implant energy. By changing the location of the peak of the vertical doping concentration, the location of an effective etch stop layer defined by the peak can be changed within the semiconductor substrate 402. For example, as shown in graph 716 a peak of the vertical doping concentration is located at the first vertical location vp1. Since the etch rate at the peak is the lowest, the etch can be effectively stopped at a vertical position corresponding to the peak (e.g., at location vp1).
FIG. 8 illustrates a cross-sectional view 800 of a semiconductor substrate exposed to an etchant 802. The etchant 802 is configured to remove silicon from a back-side 808 of the semiconductor substrate (e.g., semiconductor substrate 402 of FIG. 7a) to form a thinned semiconductor substrate 804, having a thickness that is sufficiently thin to allow light to pass through the back-side 808 of the thinned semiconductor substrate 804 to the plurality of photodetectors 502 within a front-side 806 of the thinned semiconductor substrate 804. In some embodiments, the etchant 802 is configured to reduce the thickness of the semiconductor substrate by a distance d of approximately 0.7 μm, from a thickness t of approximately 3 μm to a thickness t−d of approximately 2.3 μm.
FIG. 9 is a graph 900 showing a trend line 902 corresponding to a total thickness variation of the back-side of a disclosed back-side illuminated CMOS image sensor. The implantation region has a doping concentration that reduces the etchant depth in the center of the substrate (e.g., compared to the graph 110 of FIG. 1b), resulting in a total thickness variation TTV2 that is reduced due to the inverse relationship between the etching rate and the doping concentration. For example, a Gaussian distribution in the doping concentration provides for a higher doping concentration at the center of the semiconductor substrate than at the edge of the semiconductor substrate. Since the etch rate is inversely proportional to the doping concentration the etch rate at the center of the substrate is reduced, reducing the total thickness variation over the back-side of the substrate. In some embodiments, the total thickness variation can be reduced over conventional methods by up to 50% (e.g., from a value of TTV1=0.1 μm to a value of TTV2=0.05 μm).
FIG. 10 illustrates a cross-sectional view of an embodiment of a back-side illuminated CMOS image sensor (BSI CSI) 1000, as disclosed herein.
The disclosed BSI CIS 1000 comprises a thinned semiconductor substrate 804 having a front-side 806 and a back-side 808. The front-side 806 of the thinned semiconductor substrate 804 comprises a plurality of photodetectors 502 and abuts a support substrate 602. The support substrate 602 is configured to provide mechanical support to the thinned semiconductor substrate 804. The back-side 808 of the thinned semiconductor substrate 804 is exposed to an external environment. In some embodiments, the thinned semiconductor substrate 804 is a bulk silicon substrate comprising a semiconductor material such as silicon, for example.
The thinned semiconductor substrate 804 comprises a thin layer of semiconductor material that separates the back-side 808 of the thinned semiconductor substrate 804 from the plurality of photodetectors 502. The thin layer of semiconductor material has a thickness that allows for visible light 1002 to penetrate through the back-side 808 of the thinned semiconductor substrate 804 to the plurality of photodetectors 502. The thin layer of semiconductor material has a relatively small total thickness variation (TTV) (i.e., a relatively small thickness difference between the maximum and minimum values of thickness) between the back-side 808 of the thinned semiconductor substrate 804 and the plurality of photodetectors 502. For example, the TN may be approximately 0.05 μm.
The thinned semiconductor substrate 804 comprises an implantation region 704 located within the thin layer of semiconductor material that separates the back-side 808 of the thinned semiconductor substrate 804 and the plurality of photodetectors 502. The implantation region 704 is configured to reduce surface damage of the etch to improve performance of the plurality of photodetectors 502, for example by reducing recombination within the thinned semiconductor substrate 804 since etching the back-side 808 may increase concentration of generation-recombination centers that annihilate carriers generated within the thinned semiconductor substrate 804. In some embodiments, the thinned semiconductor substrate 804 comprises a first doping type (e.g., an n-type dopant) and the implantation region 704 comprises a second doping type (e.g., a p-type dopant type), having a doping concentration greater than that of the thinned semiconductor substrate 804.
Laterally, the doping concentration of the implantation region 704 is higher at the center of the thinned semiconductor substrate 804 than at the edges (i.e., the doping concentration is proportional to the radial distance from the center of implantation region). For example, the implantation region 704 may have a doping concentration with a Gaussian distribution. In some embodiments, the doping concentration vertically decreases from a peak doping concentration at the back-side 808 of the thinned semiconductor substrate 804 to a substantially zero doping concentration of the implantation region 704 at the photodetectors 502. In some embodiments, the implantation region 704 is separated from the photodetectors 502 by a distance S.
It will be appreciated that equivalent alterations and/or modifications may occur to one of ordinary skill in the art based upon a reading and/or understanding of the specification and annexed drawings. The disclosure herein includes all such modifications and alterations and is generally not intended to be limited thereby. In addition, while a particular feature or aspect may have been disclosed with respect to only one of several implementations, such feature or aspect may be combined with one or more other features and/or aspects of other implementations as may be desired. Furthermore, to the extent that the terms “includes”, “having”, “has”, “with”, and/or variants thereof are used herein, such terms are intended to be inclusive in meaning—like “comprising.” Also, “exemplary” is merely meant to mean an example, rather than the best. It is also to be appreciated that features, layers and/or elements depicted herein are illustrated with particular dimensions and/or orientations relative to one another for purposes of simplicity and ease of understanding, and that the actual dimensions and/or orientations may differ substantially from that illustrated herein.
Therefore, the present disclosure relates to a two-phase cleaning element that enhances polishing pad cleaning so as to prevent wafer scratches and contamination in chemical mechanical polishing (CMP) processes.
In some embodiments, the present disclosure relates to a method of forming a back-side illuminated CMOS image sensor (BSI CSI). The method comprises providing a semiconductor substrate having a front-side and a back-side and forming a plurality of photodetectors within the front-side of the semiconductor substrate. The method further comprises implanting the back-side of the semiconductor substrate to form an implantation region having a non-uniform doping concentration. The method further comprises etching the back-side of the semiconductor substrate to reduce the thickness of the semiconductor substrate between the photodetectors and the back-side of the semiconductor substrate, after forming the implantation region, using an etchant that has an etching rate that is a function of doping concentration.
In some other embodiments, the present disclosure relates to a method of forming a back-side illuminated CMOS image sensor (BSI CSI), comprising providing a semiconductor substrate having a front-side and a back-side and forming a plurality of photodetectors within the front-side of the semiconductor substrate. The method further comprises implanting the back-side of the semiconductor substrate to form an implantation region that has a doping concentration that decreases as a function of radial distance from a center of the implantation region. The method further comprises etching the back-side of the semiconductor substrate to reduce the thickness of the semiconductor substrate between the photodetectors and the back-side of the semiconductor substrate, after forming the implantation region, using an etchant that has an etching rate that is inversely proportional to the doping concentration.
In some other embodiments, the present disclosure relates to a back-side illuminated CMOS image sensor (BSI CSI). The BSI CSI comprises a semiconductor substrate, with a first doping type, having a front-side and a back-side. A plurality of photodetectors are comprised within the back-side of the semiconductor substrate. An implantation region having a second doping type is located within the semiconductor substrate, wherein the implantation region has a higher doping concentration at a center of the semiconductor substrate than at edges of the semiconductor substrate and is spatially separated from the plurality of photodetectors.

## Claims

1. A method of forming a back-side illuminated CMOS image sensor (BSI CSI), comprising:
providing a semiconductor substrate having a front-side and a back-side;
forming a plurality of photodetectors within the front-side of the semiconductor substrate; and
implanting the back-side of the semiconductor substrate to form an implantation region separated from the plurality of photodetectors, which continually extends below the plurality of photodetectors along a lateral plane parallel to the back-side of the semiconductor substrate, wherein the implantation region has a non-uniform doping concentration along the lateral plane and along a vertical plane perpendicular to the lateral plane; and
etching the back-side of the semiconductor substrate after forming the implantation region to reduce the thickness of the semiconductor substrate between the plurality of photodetectors and the back-side of the semiconductor substrate using an etchant that has an etching rate that is a function of doping concentration.

2. The method of claim 1, wherein the non-uniform doping concentration has a Gaussian distribution, such that a center of the semiconductor substrate has a higher doping concentration than edges of the semiconductor substrate.

3. The method of claim 2, further comprising:
selectively controlling implant dose and implant energy to control a mean and a variance of the Gaussian distribution to change the rate at which different regions on the back-side of the semiconductor substrate are etched.

4. The method of claim 1, wherein the etching rate is inversely proportional to the doping concentration.

5. The method of claim 4, wherein the etchant comprises Tetramethylammonium hydroxide (TMAH).

6. The method of claim 1, wherein a total thickness variation between the plurality of photodetectors and the back-side of the semiconductor substrate is approximately 0.05 μm.

7. The method of claim 1, further comprising:
determining one or more etch characteristics; and
selecting one or more of implant dose and implant energy to achieve the one or more etch characteristics.

8. The method of claim 7, further comprising:
selecting the implant energy to form the implantation region at a location that spatially separates the implantation region from the plurality of photodetectors.

9. The method of claim 1, wherein the semiconductor substrate comprises a first doping type and wherein the implantation region comprises a second doping type.

10. The method of claim 1, wherein the semiconductor substrate comprises a bulk substrate.

11. A method of forming a back-side illuminated CMOS image sensor (BSI CSI), comprising:
providing a semiconductor substrate having a front-side and a back-side;
forming a plurality of photodetectors within the front-side of the semiconductor substrate; and
implanting the back-side of the semiconductor substrate to form an implantation region that continually extends below the plurality of photodetectors along a lateral plane parallel to the back-side of the semiconductor substrate at a position that is separated from the plurality of photodetectors, and which is between the plurality of photodetectors and the back-side of the semiconductor substrate, wherein the implantation region has a doping concentration that decreases as a function of radial distance from a center of the implantation region along the lateral plane and along a vertical plane perpendicular to the lateral plane; and
etching the back-side of the semiconductor substrate after forming the implantation region to reduce the thickness of the semiconductor substrate between the plurality of photodetectors and the back-side of the semiconductor substrate using an etchant that has an etching rate that is inversely proportional to the doping concentration.

12. The method of claim 11, wherein the etchant reduces the thickness of semiconductor material between the photodetectors and the back-side of the semiconductor substrate to a total thickness variation of approximately 0.05 μm.

13. The method of claim 11, wherein the etchant comprises Tetramethylammonium hydroxide (TMAH).

14. The method of claim 11, further comprising:
selectively controlling an implant dose and an implant energy to control a location of a peak doping concentration in a vertical direction between photodetectors and the back-side of the semiconductor substrate.

15. The method of claim 11,
selectively controlling an implant energy to form the implantation region at a location that spatially separates the implantation region from the plurality of

16. The method of claim 1, wherein the implantation region has the non-uniform doping concentration between the plurality of photodetectors and the back-side of the semiconductor substrate.

17. The method of claim 16, wherein etching the back-side of the semiconductor substrate after forming the implantation region comprises removing a portion of the implantation region positioned between the plurality of photodetectors and the back-side of the semiconductor substrate.

18. The method of claim 1,
wherein the etchant has a first etching rate at a first lateral position located at a center of the semiconductor substrate and a second etching rate at a second lateral position between the first lateral position and the an outer edge of the semiconductor substrate, and
wherein the first etching rate is greater than the second etching rate.

19. The method of claim 11,
wherein etching the back-side of the semiconductor substrate after forming the implantation region comprises removing a portion of the implantation region positioned between the plurality of photodetectors and the back-side of the semiconductor substrate.

20. The method of claim 11,
wherein the etchant has a first etching rate at a first lateral position located at a center of the semiconductor substrate and a second etching rate at a second lateral position between the first lateral position and the an outer edge of the semiconductor substrate, and
wherein the first etching rate is greater than the second etching rate.