Binary half tone photomasks and microscopic three-dimensional devices and method of fabricating the same

Description of equivalent WO 2004066358 A2

BINARY HALF TONE PHOTOMASKS AND MICROSCOPIC THREE-DIMENSIONAL DEVICES AND METHOD OF FABRICATING THE SAME

FIELD OF THE INVENTION

[ 0001] The present invention generally relates to binary half tone ("BHT")

photomasks and three-dimensional microscopic structures (e.g., micro-

electromechanical systems ("MEMS"), micro-optics, photonics, micro-structures, imprint lithography applications and other devices) and a method for designing and

fabricating the same.

BACKGROUND OF THE ΪNΨENΗON

[ 0002] Recent technological advances have made it possible to use three- dimensional MEMS, micro-optical devices and other micro-structures in a variety of fields, including photonics, communications, and integrated circuits. In the past, these tiny devices were fabricated using laser micro-macMning tools. However, this

method was time consuming and expensive, and thus, it was typically difficult for

manufacturers to meet production requirements in a cost efficient manner. In this regard, such techniques did not work well with commonly applied techniques for

manufacturing integrated circuits because each pixel of the design had to be rewritten

using a new algorithm. Since this was a laborious and time-consuming undertaking,

many have avoided the use of micro-machining tools.

[ 0003] In light of the desirability to use small scale, three-dimensional

structures, other manufacturing techniques have been developed in an attempt to

avoid the problems associated with laser micro-machining tools. In particular,

traditional optical lithography techniques used for fabricating integrated circuits have been adapted to manufacture tm-ee-dimensional microstructures. In traditional optical lithography, a fully resolved pattern is etched into a binary photomask and transferred to a wafer by exposing the wafer through an exposure tool (e.g., stepper). More particularly, binary photomasks are typically comprised of a substantially transparent substrate (e.g., quartz) and an opaque layer (e.g., chrome) in which the pattern to be transferred is etched. It is also Imown that other layers maybe included -orαJ-he- hQtomaslζj, mdudm ^ or-e3εam ie -a ^tir flec& ay^ - oxide). The photoresist in the substrate on the integrated circuit being processed is then developed and either the exposed or unexposed portions are removed. Thereafter, the material on the substrate is etched in the areas where the photoresist is removed. An example of the technology involved in manufacturing a traditional binary photomask (e.g., chrome-on-quartz) and its use to manufacture integrated circuits is disclosed in, for example, U.S. Patent No. 6,406,818. ■ [ 0004] These known processes for fabricating binary photomasks and semiconductor devices have been modified for the manufacture of riiree-dimensional, microscopic devices. In this regard, it is known to use a continuous tone pattern on

the photomask (e.g., chrome-on-glass) instead of a binary, fully resolved mask pattern to yield a continuous tone intensity through the photomask during image

formation. One type of continuous tone, variable transmission photomask is

commonly known as a binary half tone ("BHT") photomask. BHT photomasks use two levels of gray tones (e.g., 0% transmissive and 100% transmissive). Another type

of continuous tone, variable transmission photomask is known as gray scale photomasks, which use varying levels of transmission of light through the photomask (e.g., 0%, 50%, 100%, etc.). By using these types of variable transmission photomasks, a three-dimensional structure can be formed in the photoresist on a wafer through the use of a continuous tone pattern.

E 0005] BHT photomasks are typically designed to have sub-resolution features that partially transmit exposure source light intensity based on feature modulation in width-and pitch. Jn-this-regard,itis4αιown-inthe ar to design a BHT photomask layout for microscopic surfaces by dividing the patterned area of the photomask into pixels and sub-pixels (commonly referred to as "sub-pixelation") which define areas on the mask through which light is to be transmitted, as shown in Figs. 1 and 2. The sub-pixels defining the BHT photomask pattern are designed to be smaller than the resolution of the exposure tool being used so that a gray scale image can be created on the resulting wafer. The boundaries of the sub-pixel's size are typically defined by Rayleigh's equation (1) as follows: (1) R=kλ/NA where R is the miriimum resolvable half pitch feature of the wafer, λ is the exposure tool wavelength, NA is the numerical aperture of the optical system of the es osure tool being used and k (k factor) is a unitless constant whose value depends on

process capability (e.g., the smaller the k factor, the better low contrast aerial images

can be seen). Generally speaking, the sub-pixels that are required by gray scale designs need to be unresolved in the imaging system, and thus, the k factor should preferably be less than 0.5. As a practical matter, however, the k factor can be somewhat greater than 0.5 and still be unresolved by the total process for some

exposure tools. Photomask designers have used calibrated simulation tools, such as

the Prolith/2 manufactured by KLA-Tencor, to converge on the optimum unresolvable

feature size. Unfortunately, there are many other tools which do not meet the

requirements of equation (1), and thus, the design of the photomask is often limited

by the capabilities of the design tools available to the designer. Moreover, since phQt©ma8te-ar≤ ommαx 4lesig e :o-m^

dimensional, binary components such as integrated circuit patterns) in addition to a three-dimensional device (e.g., photonics application), this problem is even more complex than implied by the above equation. In such cases, certain BHT cell designs

may involve isolated spaces in chrome or chrome islands on the mask and the notion of half pitch is not defined.

[ 0006] As understood by those skilled in the art, tolerable surface roughness effects the minimum feature size in the device under fabrication. For example, where

the k factor is 0.7 in equation (1) (i.e., the minimum feature size is resolvable by the

optical system), an attempt to construct a BHT photomask having a step-ramp layout

will result in a sub-ripple within each step of the ramp pattern, as shown in Fig. 3. In some applications where the specifications of the device permit, a ripple-effect may^¬

be acceptable, albeit undesirable. However, in many applications, a sub-ripple effect

is not acceptable since a smoother profile is needed for optimal performance of the

device being fabricated. Since the prior art BHT photomask design requires the use of a small k factor to achieve a smoother profile, the mask designer is limited to equipment meeting this requirement.

[ 0007] In addition to the k factor, the design of a BHT photomask layout is

governed by other specifications of the optical lithography equipment being used,

including, for example, its resolution, magnification, wavelength, etc. In this regard,

known gray scale applications, such as micro-optical surface generation, require data

to have a bJgh.er_resoluti.ori , ώan what is typical of most mask pattern generators. As a result, the mask designer is limited to only those write tools that have the ability to

match the gray level grid design associated therewith. For example, an electron beam write tool such as the MEBES 4500, with a write grid of 20 nm cannot properly replicate a BHT design whose sub-pixel variations is 10 nm. A laser beam write tool, by contrast, such as the ALTA 3500 having a write address of 5 nm is capable of replicating the same design.

[ 0008] Moreover, an imaging solution requiring custom materials at the mask

will often add cost and complexity in the overall manufacturing process due to the

difficulties typically associated with integrating new materials into a photomask. For

example, it is known in the art to use variable attenuating films ("VAF")_S rather than

a BHT photomask, to make three-dimensional devices. However, VAFs are typically

expensive and yield less than desirable results.

I 0009] Once the mask pattern design is completed, the design is transferred to

the photomask using optical lithography methods similar to those used to process a

conventional binary photomask, as shown in Fig. 4. More particularly, a binary photomask having photoresist 51, chrome 53 and quartz 55 layers is placed under a photomask pattern generator. The photoresist layer 51 is exposed to an optical, laser, electron beam or other write tool in accordance with the data file defining the BHT photomask. The exposed portions of the photoresist layer 51 are developed (i.e., removed) to expose the underlying chrome portions of the chrome layer 53. Next, the exposed chrome portions are etched away (e.g., by dry plasma or wet etching techniques). <img file="WO2004066358A2_D0001.tif" /> completed BHT photomask in accordance with the BHT photomask layout. [ 0010] The variable intensity gray tone pattern defined by the mask is next transferred to a wafer coated with photoresist using a wafer stepper or other optical lithography tools. More specifically, varying light intensities are exposed to portions of photoresist on the wafer as defined by the openings in the BHT photomask. The photoresist, in turn, exhibits changes in optical density and- a gray scale profile is created thereon. It is noted, however, that the photoresist process is often limited to the variable dose pattern generator being used. Next, the exposed photoresist is removed and the remaining photoresist forms a gray scale pattern which corresponds to the mask design. The photoresist and wafer are then etched to predetemiined

depths to conform to the gray scale pattern. The result is a three-dimensional micro- structure on the wafer.

[ 0011J In the known methods described above, the minimum feature size suiting the needed application (e.g., three-dimensional microscopic structure) is determined through known simulation techniques, by experimentation or other methods. Once the minimum feature size is determined, a pixel defining the mask dimensions is generated. Various methods have been applied to array a gray scale

design (e.g., squares, pixels or spots using variable pitch and variable sub-pixelation

methods). These methods, however, have their limitations. In this regard, it is

known that contact hole and spot features are more difficult to control than line and

space features. As a result, both corner rounding and linearity of the design are

<img file="WO2004066358A2_D0002.tif" /> different algorithm to be applied at each pixel position to carefully define the correct

opening in the BHT mask. When considering the dynamic range for the layout, the square pixel changes non-linearly since the size is varied over the contact area. This can limit the ability of a mask designer to make the fine changes required to correct

for process non-linearity. These methods add to the costs and processing time in preparation of the mask since they require a large number of adjustments to be made to the overall design.

[ 0012] One example of a known method for designing a BHT photomask is

described in U.S. Patent No. 5,310,623 ("the '623 Patent'). The ^{623 Patent teaches a

method for fabricating microlenses through the use of a single ejφosure mask with

precisely located and sized light transmitting openings to enable an image replica to

be produced in photoresist materials, and ultimately transferred to a substrate. As

disclosed, the design for the photomask is generated using three-dimensional

modeling software, wherein a single pixel defines the shape of the microlens. The

single pixel is sub-divided into "sub-pixels", which in turn are sub-divided into gray scale resolution elements. Each sub-pixel and gray scale resolution elements is

designed to be "equal [in] size" on each side. (Col. 6, line 30). In other words, each

sub-pixel and gray scale element is a perfect square.

[ 0013] U.S. Patent No. 6,335,151 discloses a method for fabricating a

microscopic, three-dimensional object by creating a mask having consisting of pixels

and "super-pixels" which define the contours of the object's surface, imaging the

mask's pattern onto a photoresist film, and trarisierriiig tih^titøee-dimensiπnal surfac

from the photoresist to a substrate.

[ 0014] Although useful, the conventional square pixel array methods used in the prior art have their shortcorriings. In this regard, the prior art discloses the use of square pixels having a size which is less than the minimum resolvable feature size of

an optical system. Each pixel is then divided into sub-pixels whose respective areas

are changed in both the x and y axes, as disclosed in the '151 and '623 Patents. As a result, the change in area of each sub-pixel is a square of the amplitude, thereby making the change in light intensity between each gray level non-linear and often

infinite. Thus, the transmission of light is limited by the square sub-pixel's size as

well as the mirdmum dimensions permitted by the mask pattern generator.

Accordingly, three-dimensional objects made by the prior art methods tend to have

jagged surfaces, especially where the objects are sloped. Since these methods

produce marginal results, many have migrated away from the use of BHT photomasks

for making three-dimensional microscopic devices. [ 0015] Thus, there is a long felt need for new design rules and layout choices

for making BHT photomasks to overcome these shortcoming associated with the prior

art.

[ 0016] While the prior art is of interest, the known methods and apparatus of the prior art present several limitations which the present invention seeks to

overcome.

0.0.17] In<img file="WO2004066358A2_D0003.tif" /> a method for designing a BHT photomask layout having a smooth profile. [ 0018] It is a further object of the present invention to provide a method for designing a BHT photomask layout which meets the specifications of a wide range of optical systems.

[ 0019] It is another object of the present invention to design a BHT photomask wherein the change in light intensity between each gray level is both linear and finite. [ 0020] It is another object of the present invention to solve the shortcomings of

the prior art.

[ 0021] Other objects will become apparent from the foregoing description.

SU MAR OF TEE ilM MTEOW

[ §022] It has now been found that the above and related objects of the present

invention are obtained in the form of a BHT photomask and microscopic three-

dimensional structure and method for designing and fabricating the same. The

method for designing the layout of BHT or gray scale photomasks is governed by

specific design rules calculated within an electronic database. [ 0023] More particularly, the present invention is directed to a binary half tone

photomask comprising a substantially transparent substrate and an opaque layer

having a pattern formed therein. The pattern is defined by at least one pixel, wherein

each pixel is divided into sub-pixels having a variable length in a first axis and fixed

length in a second axis. In one embodiment of the present invention, the pixel is a square and the sub-pixels have a height and a length, wherein th height of each of the

<img file="WO2004066358A2_D0004.tif" /> pixel is linearly varied in opposite directions along one axis only. In another embodiment, the pixel is circular and the sub-pixels have a radius and an arc length, wherein the radius of each of the sub-pixels is approximately one half of the pixel's pitch and the arc length of each sub-pixel being linearly varied in opposite directions along one axis only.

C 0024] The present invention is also directed to a method for designing a layout of a binary halftone photomask pattern to be used to fabricate a three-

dimensional structure. This method comprises the steps of generating at least two

pixels, dividing each of the pixels into sub-pixels having a variable length in a first

aids and fixed length in a second axis, and arraying the pixels to form a pattern for

transmitting light through the pixels so as to form a continuous tone, aerial light

image. In a preferred embodiment, the sub-pixel's area is smaller than the minimum

resolution of an optical system of an exposure tool with which the binary half tone

photomask is intended to be used. [ 0025] Additionally, the present invention is directed to a method for making a

binary half tone photomask. This method comprises the step of providing a binary

photomask comprising a photoresist layer, an opaque layer and a substantially transparent layer in a lithography tool. Additionally, the photoresist layer is exposed

to the lithography tool in accordance with a binary half tone photomask pattern on

the photomask, wherein the pattern is defined by at least one pixel. Each pixel is

<img file="WO2004066358A2_D0005.tif" /> second axis. Next, undesired portions of the photoresist and portions of the opaque layer underlying the removed photoresist portions are etched. Thereafter, the

remaining portions of the photoresist layer are removed. Here again, each sub-pixel's area is preferably smaller than the minimum resolution of an optical system of an

exposure tool with which the binary half tone photomask is intended to be used. [ 0026] The present invention is also directed a microscopic three-dimensional

structure made in accordance with the methods described above. In this regard, the

three-dimensional structure comprises a wafer having a continuous tone,

substantially linear and smooth surface, wherein the surface of the wafer corresponds

to the shape of a light aerial image generated from a binary half tone photomask.

The binary half tone photomask comprises a pattern formed therein which is defined

by at least one pixel, wherein each pixel is divided into sub-pixels having a variable

length in a first axis and fixed length in a second axis. Here again, each sub-pixel

preferably has an area that is smaller than the minimum resolution of an optical system of an exposure tool with which the binary halftone photomask is intended to

be used.

[ 0027] The present invention is also directed to a method for fabricating a

three-dimensional microscopic structure in accordance with the methods described

above. In this regard, the method for fabricating a three dimensional structure

comprises the step of providing a binary half tone photomask between an exposure

tool -and-a- wafer coated- ith a-photor-esistr layer. T4ιe-bmary ιalf-tøne-phøtΘfflasfe comprises a substantially transparent substrate and an opaque layer having a pattern formed therein. The pattern is defined by at least one pixel, wherein each pixel is

divided into sub-pixels having a variable length in a first axis and fixed length in a second axis. The sub-pixels' area is preferably smaller than the minimum resolution of an optical system of an exposure tool with which the binary half tone photomask is intended to be used. Next, the photoresist layer of the wafer is exposed to the exposure tool in accordance with pattern on the binary half tone photomask.

Thereafter, undesired photoresist is removed to form a three-dimensional profile in

the photoresist which has not been removed. Next, the wafer is etched to a

predetermined depth to correspond in shape to the three dimensional profile formed

in the remaining photoresist. Thereafter, the remaining photoresist is removed.

I 00 8] In another embodiment of the present invention, a method for making

step and flash templates is provided. This method comprises the step of providing a

binary photomask having a photoresist layer, an opaque layer and substantially

transparent in a lithography tool. The photoresist layer is exposed to a lithography tool in accordance with a binary half tone photomask pattern defined by at least one

pixel, wherein each pixel is divided into sub-pixels having a variable length in a first

axis and fixed length in a second axis. The sub-pixels' area is preferably smaller than

the minimum resolution of an optical system of an exposure tool with which the

binary half tone photomask is intended to be used. Next, undesired portions of the

photoresist is removed from the photomask and portions of the chrome layer - underlying he- moved-photoresist-portions -are etched away. Thereafter,_xemaining portions of the photoresist layer are removed and the pattern in the binary half tone

photomask is transferred to a second substrate to produce a continuous tone pattern defined by the photomask thereon. The second substrate is preferably made from a

rigid material, including, but not limited to, fused silica, glass, metals, crystalline structures, plastics or other similar materials. The second substrate may then be used as an imprinting or stamping plate for fabricating imprint lithography applications.

E 0029] Another embodiment of the present invention is directed to a gray scale

photomask made in accordance with the methods described herein. The gray scale

photomask comprises a substantially transparent substrate and an opaque layer

having a pattern formed therein. The pattern is defined by at least one pixel, wherein

each pixel is divided into sub-pixels having a variable length in a first axis and fixed

length in a second axis. The sub-pixels' area is preferably smaller than the minimum

resolution of an optical system of an exposure tool with which the binary half tone

photomask is intended to be used. BRIEF DESCRIPTION OF THE DRAWINGS

[ 0030] The above and related objects, features and advantages of the present

invention will be more fully understood by reference to the following, detailed

description of the preferred, albeit illustrative, embodiment of the present invention

when taken in conjunction with the accompanying figures, wherein:

Figs. 1 and 2 illustrate examples of BHT photomask patterns known in the

-prior-art -

Fig. 3 illustrates the ripple effect that results from a step-ramp layout designed in accordance with prior art sub-pixelation methods, such as those shown in Figs. 1

and 2;

Fig. 4 illustrates the process of making BHT photomask pattern using

conventional lithography techniques;

Figs. 5a and 5b show a square pixel divided into half-pitch sub-pixels whose

area is varied along one axis only in accordance with the method of the present

invention;

Figs. 6a and 6b show a circular pixel divided into half-pitch sub-pixels whose

area is varied along one aids only in accordance with the method of the present

invention;

Fig. 7 shows the surface roughness of a three-dimensional device as it relates

to photoresist thickness and the critical dimensions of the device;

Fig. 8 shows the dynamic range of BHT gray levels pixel sizes as a function of

photoresist contrast; Fig. 9 shows a linear ramp design for a BHT photomask made in accordance with the method of the present invention as shown in Figs. 5a and 5b;

Fig. 10 is an SEM cross section of a printed BHT design on a wafer;

Fig. 11 shows an AFM profile of the photoresist slope of the ramp design

shown in Figs. 9 and 10;

Fig. 12 shows a simulated photoresist profile from the design of Figs. 9 and 13;

Fig. <img file="WO2004066358A2_D0006.tif" /> made in accordance

with the method of the present invention as shown in Figs. 6a and 6b;

Fig. 14 is an AFM image of a lens array that was printed in accordance with the ramp design shown in Fig. 13;

Fig. 15 shows a side view of one of the conical sections shown in Fig. 14; and

Fig. 16 is a pixel having multiple sub-pixels arrayed therein.

DETAILED DESCRIPTION OF THE INVENTION

[ 0031] The present invention generally relates to improved BHT photomasks

and microscopic three-dimensional structures made from such photomasks. The

present invention is also directed toward a method for designing and fabricating BHT

photomasks to be used in creating such microscopic three-dimensional structures

(e.g., MEMS, micro-optics, photonics, micro-structures and other three-dimensional,

microscopic devices). More particularly, the present provides a method for designing

a BHT photomask layout, transferring the layout to a BHT photomask and fabricating

three-dimensional microscopic structures using the BHT photomask designed by the

method of the present invention. As will be seen below, the method of the present invention enables a photomask designer to design a BHT photomask to have continuous gray levels such that the change in light intensity between each gray level is both finite and linear. As a result, when this BHT photomask is used to make a three-dimensional microscopic structure, it is possible to produce a smoother and

more linear profile on the object being made. Likewise, it has been found that BHT photomasks designed in accordance with the method of the present invention meet

<img file="WO2004066358A2_D0007.tif" /> oi most, jf ioralL optical took. -Eac aspect of the present invention is now described.

[ 0032] The first aspect of the present invention is .directed to the method by which the design for a BHT photomask is generated. More particularly, the method of the present invention implements specific design rules calculated within an electronic database to generate a photomask pattern which achieves substantially linear changes in variable light intensity when transmitted through the photomask. [ 0033] More particularly, the BHT photomask design method of the present invention uses a series of pixels, preferably either square or circular, whose area is varied in a manner so as to avoid the limitations of the resolution of the mask pattern generator being used. (While square or circular pixels are preferred_^ the present

invention is not so limited, and may apply to other shaped pixels, such as oval shaped, rectangular, etc.). In a preferred embodiment, a pixel 19 is generated such

that its area is larger than the minimum resolution of the mask pattern generator being used. Thereafter, each pixel 19 is divided into two half-pixels, such as sub-

pixels 21a and 21b, as shown in Figs. 5a-b and 6a-b. Each sub-pixel 21a and 21b has a height h (in the case of a square pixel, see Figs. 5a-b) or radius r (in the case of a

circular pixel, see, Figs. 6a-b), wherein the height h or radius r for each sub-pixel 21a

and 21b is a fixed length. In one embodiment, the height h or radius r of each sub-

pixel 21a and 21b, as the case may be, is equal to approximately one-half of the pitch

p of pixel 19. It is noted, however, that the height h or radius r (as the case ma be) of the sub-pixels 21a and 21b can be divided into other fixed lengths, including, but

notlirmted tø^thefoHomng-arrang≤m the pitch of the pixel 19 and sub-pixel 21b is two-thirds of the pitch of pixel 19, or

vice versa; height h or sub-pixel 21a is one-fourth of the pitch of the pixel 19 and sub- pixel 21b is three-fourths of the pitch of pixel 19, or vice versa; etc. In this regard, the height h or radius r of each sub-pixel 21a and 21b should be divided in a manner such that their total pitch, when added together, is equal to the pitch of the pixel 19

from which they were divided. Next, the length 1 (in the case of a square pixel) or arc θ (in the case of a circular pixel) of each sub-pixel is varied in opposite directions

along one axis only, in a staggered arrangement to either increase or decrease the

total area of the full pixel, depending upon the particular pattern design being

generated, as shown in Figs. 5a-b and 6a-b, respectively. In this regard, the area of

each sub-pixel 21a and 21b should be linearly varied to an amount that is equal to or

less than the minimum resolvable pitch of the optical system of , the exposure tool

being used. Additionally, where only a small number of sub-pixels are arrayed to

form the BHT photomask design, it is preferable that the pixels 19 are sized to meet

the minimum resolution of the exposure tool being used to ensure that the sub-pixels 21a and 21b will not be resolved during the image writing process, and thus, avoid

the sub-ripple effects exhibited by the prior art. Each modified pixel 19 is hereinafter

referred to as a Half-Pitch Expansion Cell ("HPEC"). This process is repeated, with a

series of HPECs being arrayed in a manner to reflect the design of the three-

dimensional device to be fabricated. By arraying the HPECs in this manner,

continuous gray levels are created such that the change in light intensity between

each-gra 4evel-(Le._y amplitude)4s both-linfiar-and-finite, I -this^regard, -since the-

number of possible gray levels in the patterned array is increased by this method, the BHT mask design achieves a substantially continuous, variable pixel size from the maximum opening to the smallest opening to yield 100% to 0% transmission through the mask. As a result, smoother surfaces are created on the three-dimensional object being formed with the BHT photomask.

[ 0034] The arrayed design is created as a hierarchical, two-dimensional image

written within a Computer Aided Design ("CAD") system. Any CAD tool having all-

angle polygon"capability can be used to write the pixels 19 for the purposes of the present invention. One example of an appropriate a mask pattern generator to write

a pixel is the L-Edit CAD tool by Tanner EA.

I &gt;OS5] The hierarchical design created with the method of the present

invention incorporates a layer for each gray level and allows each HPEC to be arrayed

uniquely from other gray levels. This hierarchical design is used to compile a mask

pattern generator file for writing the BHT pattern on a photomask, with the hierarchy

being maintained in such file. By using this method, the mask pattern generator file size remains very small compared to one that has been flattened where all gray level

pixels are within a single layer, as is the case using prior art methods. As a result, it

is possible to achieve a quicker write time, thereby reducing the cost to manufacture

the photomask. Furthermore, it has been found that BHT layouts designed by the

method of the present invention are more easily arrayed with a repeating symmetry

that lends well to polar and orthogonal arrays without interference from one sub-

.pixeLto .another, ϊnthis-regardj uniike-thβ prior art,- hich required a -pattern tobe

rewritten each time it was transferred to a wafer, the method of the present invention allows a pattern to be transferred in a serial manner once it is arrayed. This too

results in faster processing time to manufacture the resulting devices, and thus, greater throughput.

[ 0036] Furthermore, by forming the HPECs in accordance with the method of the present invention, the sub-pixels 21a and 21b should be below the minimum resolution of most optical systems of exposure tools. Thus, unlike the prior art, the

BHT design made in accordance with the present invention is Kmited only by the CAD

tool design grid that is chosen to array the mask pattern (which is typically 1 nm, but

may be other sizes if desired) and the CAD tool being used. Moreover, as should be

understood from the foregoing, the sub-pixels 21a and 21b are created as a single cell

within a design having a width which can be modulated for each gray level, while at

the same time maintaining a constant pitch for that gray level. Thus, when each sub-

pixel 21a and 21b is arrayed with a layer and each gray level has an assigned layer, the single cell open area can be easily changed for the photoresist process when

correction for process non-linearity are required.

[ 0037] In the second, related aspect of the present invention, the mask pattern

generator file is transferred to a photomask. In this regard, a blank photomask is

made using a standard binary (e.g., chrome-on-quartz) photomask and conventional

lithography techniques, as shown in Fig. 4. Preferably, the blank binary photomask is

<img file="WO2004066358A2_D0008.tif" /> It is noted however, that the photomask may have other layers (e.g., an anti-reflective layer such as CrO) if needed or desired. To process the photomask, designated portions of the photosensitive material on the photomask are exposed to the mask

pattern generator in accordance with the BHT photomask design stored in the mask pattern generator file and the exposed portions of the photoresist are removed such that the chrome portions 53 are no longer covered by the photoresist 51. Next, the

uncovered chrome portions 53 are etched away using standard techniques (e.g., wet

or dry etching), thereby exposing the quartz portions 55 underlying the areas of

removed chrome 53. Thereafter, the remaining photoresist (i.e., the unexposed

photoresist) is removed. The result is a BHT photomask having the BHT design

etched thereon. The opaque portions 53 of the BHT photomask attenuates the

passage of light energy through the mask such that the transmitted light will have

varying intensity as governed by the photomask design.

[ 0038] in the third, related aspect of the present invention, the design for the

i±iree-dimensional microscopic structure is transferred from the BHT photomask to a wafer to form the desired three-dimensional structure. In this regard, the BHT

photomask designed in accordance with the method of the present invention is placed between a wafer exposure tool (e.g., stepper) or other lithographic camera and a

wafer having photoresist (e.g. AZ 4400) deposited thereon. Light is then transmitted

from the wafer exposure tool through the openings in the BHT photomask in a

uniform, substantially linear manner to produce a three-dimensional light aerial image. <img file="WO2004066358A2_D0009.tif" /> aerial light image and developed to remove the exposed photoresist. As a result, a three-dimensional surface corresponding to the aerial image is formed in the

photoresist. Next, the wafer is etched to a predetermined depth to correspond in shape to the developed photoresist. As a result, a three-cliinensional image, defined by the BHT photomask, is formed on the wafer.

[ 0039] To achieve optimal linear results in designing a BHT photomask in

accordance with the present invention, there are several design and processing

considerations which a photomask designer should consider when designing a BHT photomask layout. In particular, the designer should consider the Umitations of the

CAD tool and write tool being used as well as the limitations of the wafer device

being used to fabricate the three-dimensional device. Each of these considerations

are discussed below. However, it is noted that there may be other design

considerations (e.g., active device tolerances and system resolution needed to

accurately reproduce the active device) depending upon the BHT process being used

and the device being made which a photomask designer may consider. [ 0040] As noted herein, a variety of different CAD tools may be used, provided

that such CAD tools have all-angle capability. Thus, depending upon the CAD tool

being used, the size of design grid may vary. Likewise, depending upon the mask

pattern generator being used, the size of the write grid may also vary. For example,

at the present time, conventional mask write grid values are typically even multiples of the design grid, both of which generally range between 5 nm and 200 nm. It

shouk±be noted, however,-that-the-desig4i-and write- grid-value-can-also-be-other

values (e.g., 0.1 nm, 1.5 nm, etc), including for example, non-integers, fractions, etc. In such cases, the design grid and gray level pixel size variation would need to be adjusted to fit the write tool grid in order to minimize the snap-to-grid that occurs when the design data is converted into the write tool grid format. Thus, the present

invention is not limited to the write tools and write grids described herein, as these

tools are merely described for exemplary purposes. In a preferred embodiment, when a BHT photomask design is patterned onto a photomask substrate, the design should

be adjusted to fit the mask pattern generator write grid. In this regard, it is preferred

that the size of the write grid is equal to the size of the design grid. The number of

gray levels that are possible in the design is governed by the equation (2) as follows:

(2) # Gray Levels for BHT photomask design = D_y/W_g

where W_g is the writer grid value and D_y is the sub-pixel size. Referring to Table 1

below, the difference in area change for a write tool address, the possible number of

gray levels for a design and the pixels' critical dimensions size at the minimum energy

threshold E₀ 10% of area is shown for both the HPECs designed in accordance with the method of the present invention as well as a conventional square pixel layout of the prior art. In this example, the pixel's size in each case is 2.5 microns.

TABLE 1

<img file="WO2004066358A2_D0010.tif" />

As can be seen, when the HPEC is changed in only one axis, the change in area is a linear function in multiples of the address unit. When the square pixel is changed in both axes, the change in area is an exponential function, with the address unit being the exponent. As a result, there is a non-linear change using the square pixel method. Moreover, when the area of the HPEC is varied as described herein, the number of possible gray levels doubles for a given dynamic range as compared with the square pixel method. Additionally, the light intensity is sufficiently low at the minimum energy threshold E₀ such that the photoresist will be unresolvable when exposed. [ 0041] In addition to considering the number of gray levels that are possible in

a design, the mask designer should also consider whether it is possible to actually

transfer these gray levels to the wafer device for which the BHT design is being designed. In this regard, the mask designer should determine the dynamic range (e.g., total number of gray levels of the image) that can actually be printed to the ^■ wafer device, which is governed by the equation (3) as follows: (3) # Gray Levels to be printed on wafer = X/G_w where x is the length of device and G_w is the width of an individual gray scale region. Since the design and write grid for CAD and write tools are measured in nanometers, the sub-pixel to sub-pixel variation and the number of gray levels possible is limited only by the wafer device length X and not by the grid size W_g. For example, if a micro-mirror is required to be X microns in length and the height is also X microns, J_he esιiltmg.mirrαr. a led designed BHT photomask in accordance with the present invention. [ 0042] A photomask designer should also consider the specifications for the surfaces of the micro-optical device being made. In this regard, surface roughness is a critical element in the optical efficiency of an optical component. Thus, if the number of gray levels in a photomask design is insufficient across the area of the design, the light intensity image will exhibit discrete steps that may be intolerable for the application. This problem is particularly prevalent in applications where thick photoresist is used and the device design includes rapid changes within short areas, as illustrated in Fig. 7. Thus, the photomask designer should consider the type of photoresist being used on the wafer in formulating a BHT design. In this regard, each type of photoresist process exhibits a unique response to the aerial image of an

optical exposure tool. For example, various changes in the photoresist's thickness,

bake conditions, dyes and absorption coefficients can change the photoresist contrast or the slope of the contour of the BHT photomask. [ 0043] Accordingly, under a preferred embodiment of the present invention,

the mask designer should determine the dynamic range of the photoresist process being used. The dynamic range of the photoresist process is the range of the size of

sub-pixels 21a and 21b. The dynamic range of the photoresist process should

preferably vary from the minimum sub-pixel opening required to achieve the

rninimum energy threshold E₀ in the photoresist to the largest sub-opening required

to achiievje-the-masdmum-energy tlιreshold-E_f Le»- ose-to-cl@ar) n-A@ hotoresist. It is within the dynamic range E₀-E_f that the gray scale variations should be applied. [ 0044] In many cases, these responses with the dynamic range E₀-E_f will not be reahzed until after the BHT photomask is used and a caUbrated response is observed

with a particular design. Thus, it may be necessary, depending upon the BHT photomask design and the experience of the photomask designer, to fabricate a test BHT photomask and measure its response. Thereafter, a control design can be used

to normahze the photoresist to a linear response, where the pixel size variation is

calculated to be an equal change in transmitted light intensity throughout the gray

levels. This process may require one or more iterations, depending upon the initial

linearity achieved through the design. It should be noted, however, that as the mask

designer becomes more experienced with this method and learns how certain

photoresist materials react in response to certain designs, it may not be necessary to

normahze the control design as more accurate results can be achieved from the initial

design. Where measured and caUbrated responses are required to fine tune the BHT

photomask design, the mask designer should consider that the ampUtude of transmitted light through a sub-resolution opening (e.g., sub-pixels 21a and 21b) is proportional to the area of the opening. Accordingly; since the Ught intensity transmitted through the opening is proportional to the magnitude squared of the ampUtude (i.e., I « | A|²), then a linear change in wafer plane intensity is calculated by equation (4) as follows: (4) |A| «* I¹'² where A is the amplitude-of theJight at-the mask -plane and I4s the-intensity of the light at the wafer plane. Thus, when the sub-pixel is changed in one axis, there wiU be a linear change in intensity. It is noted that further calibration may be needed in cases where it is necessary to aUgn three-dimensional features with two dimensional features in the same photomask. After photoresist caUbratJon is completed, the variance from an expected response is measured. These values are then used to change the BHT photomask design, where each sub-pixel's size in each of the gray levels of the design is either enlarged or reduced in area in one axis only, in accordance with the disclosed method, to create the desired resist profile. As shown in Fig. 8, as the photoresist contrast decreases, the dynamic range of the photoresist process becomes wider. That is, the dynamic range E„-E_f of the photoresist process

changes with changes in the photoresist contrast C as weU as changes in the

minimum resolution of the optical system being used. Thus, the wider the dynamic range, the greater the number of gray levels possible within a BHT design.

[ 0045] Additionally, the photomask maker should consider the type of optical system in the exposure tool that will be used to make the three-dimensional device. In this regard, it is preferable to use an optical system that has a high reduction ratio

so as to enable the mask maker to print sub-pixels throughout the dynamic range and

within the latitude of the photomask making process. AdditionaUy, as the pixel size

of the design decreases, write tools and processes having higher resolutions maybe

required, which can drive up the cost of the process. Thus, to avoid this problem, it is

preferable to use a photoresist process having as large a dynamic range as possible, a relatively low contrast-photβresist e_^g., AZ-44ΘΘ"phøtøresist-ean-be-u§ed-to produce mirrors and lenses in single mode clad/core/clad polymer waveguides) and an optical

system having a relatively low numerical aperture and high magnification. If, by contrast, the wafer has requirements to pattern very small structures, then a higher NA and/or lower process resolution variation Kl should be used, and the BHT photomask design should be modified to perform under these conditions. Additionally, if necessary, the wafer designer can use multiple mask levels and double

exposure techniques at different NAs to achieve the optimum results.

[ 0046] AZ-4400 photoresist has been shown to exhibit desirable transparency, and photosensitivity at 365 nm. Referring to Table 2, typical flow for a process using the AZ-4400 resist is shown:

TABLE 2

<img file="WO2004066358A2_D0011.tif" />

It is noted that care should be exercised in developing a photoresist coating process so as to avoid a sunburst striation pattern, which typically occurs in thick photoresist coatings. Further, the smaU thickness variations present in photoresist striations wiU be reproduced in the three-dimensional structures. Furthermore, the process contrast can be reduced by under-baking the photoresist. It was found that a post-ei osure bake worked well to diffuse the photoresist development inhibiter, minimising the

patterning of the binary halftone step transitions .

[ 0047] Having described the overaU method for designing and fabricating a BHT photomask and design considerations regarding the same, specific examples of the appncation of the method of the present invention are now described. [ 0048] Referring to Fig. 9, one embodiment of a BHT photomask design made in accordance with the method of the present invention is shown. More particularly, the gray levels in the design of Fig. 9 provide a ramp layout for a 45 degree rnicro-mirror, arrayed waveguide. When using the BHT photomask design of Fig. 9 and HPEC design method shown in Figs. 5a and 5b with a 365 nm optical tool having an NA of 0.4 and a sigma of 0.7, the BHT photomask transmitted Ught through its itL jiimtin α s, linear fashion. Acci_a:dingly ϊhαtor£sist on the wafer, when exposed, resulted in a substantially smooth and linear profile, as shown in the SEM of Fig. 10. The wafer was then etched to a predetermined depth to correspond to this resist profile. As shown in Fig. 11, a ramp of 45 degree ±2 degrees (the actual measure angle was approximately 46.5 degrees) was printed on the wafer for this particular photonics application. Additionally, the resulting surface on the wafer was sufficiently smooth for this particular photonic appUcations, as the surface roughness was less than 20 nm, as shown in Fig. 11. Furthermore, in this embodiment, the mean slope (46 degrees) curvature and notching were accurately predicted through simulations of the BHT photomask design, as shown in Fig. 12. More particularly, as shown in Fig. 12, the simulations for this embodiment predicted

the following: an angle of 89.74 degrees for the profile of this design between lines 71 and 73a where the horizontal and vertical changes in the profile were 166 nm and

7.214A, respectively; an angle of 46.5 degrees for the profile of this design between lines 73a and 73b where the horizontal and vertical changes were 3.689_/ m and 3.501/xm, respectively; and an angle of 88.52 degrees for the profile of this design between lines 75a and 75b where the horizontal and vertical changes were 196 nm

and 5.050 nm, respectively.

[ 0049] Fig. 13 shows another embodiment of a BHT mask design made from

the polar coordinate array made in accordance with the method of the present

invention. This mask design could be used, for example, to fabricate micro-optical

components, such as a micro-lens or a conical section. In this embodiment, a lens

was- rinted-u^mg-thejcimulaiiBHXphQtQmask design.of l±ig..13. anάthellEEC design

methods of the present invention as shown in Figs. 6a and 6b. This particular BHT photomask was used with a 365 nm optical tool having an NA of 0.4 and a sigma of 0.7. A substantially smooth and linear photoresist profile was formed using this design, as shown in the AFM images of Figs. 14 and 15. As can be seen, conical section objects were produced and exhibited no sub-ripple effect in the device. [ 0050] In another embodiment, the HPEC method of the present invention was used to print a specific sloped structure for a photonic application. In this

embodiment, an Applied Materials ALTA 3500 laser writer was used on a 5 nm write

grid. The ALTA 3500 laser writer was the best choice for this embodiment because it

had a p jεel-to-pixel critical dimension linearity at the wafer dimension which was

similar to the write tool grid size. It is noted, however, that in other appUcations,

more advanced e-beam and laser mask pattern generators (e.g., a CORE 2564,

MEBES 4500 E-beam tool, etc.) having smaUer grid sizes (e.g., 1.5nm-2.5nm) may

also be used provided that the BHT photomask design can be fitted to the write tool

grid and the desired gray levels can be achieved. Additionally, in this embodiment, a dry plasma chrome etch was used to process the BHT photomask. It is noted, however, wet etch techniques may be alternatively used. In such cases, response fidelity and gray scale performance wiU be limited by the write tool grid, and compromised by the mask bias. Irrespective of which etching technique and mask write tool is used, the linearity in the critical dimensions of the design must be maintained. Thus, to the extent the design exhibits non-Unearity_s such design should he Qrrected_after.the cahbration-of .the-waf er_prαcessJ ompleted- and compensated for in the BHT design. By using this type of process, mask dimensions can be controUed in a Unear fashion for smaU sub-pixel sizes ranging from 0.4 μ-m to the fuU pixel size of 2.5 m when the ALTA 3500 write tool is used. [ 0051] In another embodiment, the HPEC method of the present invention is used to develop step and flash templates. In this regard, a BHT photomask is made in accordance with the HPEC design method of the present invention. Thereafter, the three-dimensional image defined by the photomask is transferred in a reduction lithography system to a second substrate to produce a second photomask with continuous tone (i.e., gra scale) patterns. This second mask serves as an imprinting or stamping template for imprint lithography appUcations. The second photomask

should preferably be made from a rigid material capable of operating as a stamp. For

example, the second photomask may be made from a variety of different rigid

materials, including, but not limited to, fused siUca, glass, metals, αystaUine structures, plastics and any other rigid material now known or hereinafter developed.

In this embodiment, the second photomask is used to stamp or mold a three- dimensional structure. This may be done using an imprint stepper such as a Molecular Imprints stepper or other known or hereinafter developed tools. [ 0052] Now that the preferred embodiments of the present invention have been shown and described in detail, various modifications and improvements thereon will become readily apparent to those skiUed in the art. For example, in addition to designing BHT photomasks, the HPEC method of the present invention could be ιnojdtfi£d.tQ <img file="WO2004066358A2_D0012.tif" /> 10084,-etc. transmiss ty) to be used to make three-dimensional microscopic structures. Additionally, it is noted that each pixel can be divided into thirds, quarters, fifths, etc. to form three, four, five, etc. sub-pixels, respectively. In such cases, the area of each sub-pixel should be varied along one axis only in accordance with the methods described herein. For example, as shown in Fig. 16, a pixel 19 can be sub-divided in 4 sub-pixels 21a, 21b, 21c and 21d. In this example, each sub-pixel 21a-d is sub-divided to be one half of the pitch of the pixel 19 in a first axis with the width of each sub-pixel 21a-d being varied along a second axis. Moreover, it is noted that the HPECs designed in accordance with the method of the present invention could be combined on a photomask with other device designs (e.g., two dimensional binary structures such as an integrated circuit). The present embodiments are therefor to be considered in aU respects as illustrative and not restrictive, the scope of the invention being indicated

by the appended claims, and all changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.