Diffractive lens and preparation method thereof

Method for the preparation of diffractive lens with one single etching step and using one single etching mask. While the widths and intervals of the masked areas of the photo masks are decided under a geometric relation, an etching mask can be prepared on the substrate of the lens where the widths and the intervals of the masked areas can be determined. As the included angle between the etching mask and the plan of the material of the lens is in a certain ratio to the etching efficiency of the etchant to the substrate of the lens, a one step etching process can be developed whereby multilevel diffractive lens with required number, widths and heights of the levels can be obtained. This invention also provides an oxidation-isotropic etching process on the diffractive lens so prepared.

FIELD OF THE INVENTION 
The present invention relates to a diffractive lens and a method for the 
preparation of the diffractive lens, especially to a method of preparing 
diffractive lens with one single mask under one single step. 
BACKGROUND OF THE INVENTION 
The diffractive lens is an important component in the 
micro-electromechanical systems and in the optical systems. The 
conventional diffractive lens has a so-called "terraced" diffractive 
structure which is prepared through etching or burning-off with laser 
beam, forming a multilevel structure on the substrate of the lens. Among 
the conventional approaches etching is frequently employed due to its low 
cost and convenience in operation. 
In the conventional art, the diffractive lens is prepared under a 
multi-step etching process, by using a plurality of masks. FIGS. 1a to 1c 
show the steps of the conventional preparation of the terraced diffractive 
lens. FIG. 1a illustrates the structure of the first mask and the 
structure of the substrate after the first etching step. As shown in the 
figure, on the substrate 4, the area corresponding to the transparent area 
of the first mask 1 is developed and etched to form a two-step terrace 
structure. FIG. 1b illustrates the structure of the second mask and the 
structure of the substrate after the second etching step. As shown in the 
figure, on the substrate 4, the area corresponding to the transparent area 
of the second mask 2 is developed and etched to form a four-step terrace 
structure. FIG. 1c illustrates the structure of the third mask and the 
structure of the substrate after the third etching step. As shown in the 
figure, on the substrate 4, the area corresponding to the transparent area 
of the third mask 3 is developed and etched to form a eight-step terrace 
structure. By using the etching process as described above, it is possible 
to form a 2.sup.n -step terrace structure on the substrate 4 with n masks. 
When the material of the substrate is silicon or germanium, the etched 
substrate 4 can function as a diffractive lens for infrared. 
In the conventional preparation of the diffractive lens, however, a 
plurality of masks and a series of etching (including developing) process 
are required. This does not only make the preparation of the diffractive 
lens time consuming and costly but that the problem of misalignment of the 
masks can not be avoided. For example, the distance between each stage of 
the terrace is approximately 2 .mu.m. When any two of the masks are not 
aligned, the lens so prepared would be defected. This misalignment problem 
has become the major obstacle in enhancing the yield rate of the 
diffractive lens. 
It is thus a need in the industry to have a diffractive lens that can be 
prepared under one-step etching process and with one single mask. It is 
also a need to provide a simplified method for the preparation of 
diffractive lens. 
OBJECTIVES OF THE INVENTION 
The purpose of the present invention is to provide a one-step preparation 
of diffractive lens that uses one single mask to prepare diffractive lens 
with multiple levels. 
Another purpose of this invention is to provide a simplified preparation 
method for the diffractive lens. 
SUMMARY OF THE INVENTION 
According to the present invention, while the widths and intervals of the 
masked areas of the mask are decided under a geometric relation, an 
etching mask can be formed on the substrate of the lens where the widths 
and the intervals of the masked areas can be determined. As the included 
angle between the etching mask and the surface of the substrate of the 
lens is in a certain relation to the etching efficiency of the etchant to 
the substrate of the lens, a one-step etching process can be developed 
whereby multilevel diffractive lens with required levels, widths and 
heights of the terraces can be obtained. 
This invention also provides an oxidation-isotropic etching process on the 
diffractive lens so prepared. 
The above and other objectives and advantages of this invention can be 
clearly understood from the detailed specification by referring to the 
following drawings. 
In the drawings, 
FIG. 1(a) to (c) show the process of a conventional preparation of a 
diffractive lens wherein FIG. 1(a) shows the relation between the first 
mask and the lens as etched using the mask, FIG. 1(b) shows the relation 
between the second mask and the lens as etched using the mask and FIG. 
1(c) shows the relation between the third mask and the lens as etched 
using the mask. 
FIG. 2 illustrates the relation between the included angle between the 
etching mask and the surface of the lens and the terrace structure. 
FIG. 3 shows the flow chart of the method for preparation of diffractive 
lens of this invention. 
FIG. 4 shows the progresses of etching of the lens under the methods for 
preparation of diffractive lens of this invention. 
FIG. 5 illustrates a mask suited in the method of this invention. 
FIG. 6 illustrates another mask suited in the method of this invention. 
FIG. 7 illustrates the parameters applied in the specification of this 
invention.

DETAILED DESCRIPTION OF THE INVENTION 
The followings are detailed description to the method for preparation of 
diffractive lens of the present invention. 
Although it is not intended to limit the scope of the present invention, it 
is found that the included angel between the etching mask and the surface 
of the lens material has certain influences on the terrace structure as 
etched. FIG. 2 shows the relation between the included angle of the 
etching mask and the surface of the lens material and the height of the 
terrace. Reference can be made to Mattias Vangbo and Yiva Backlund, 
"Terracing of (100)Si with One Mask and One Etching Step Using Misaligned 
V-Grooves", Journal of Micromechanics and Microengineering, Vol. 6, No. 1, 
March 1996, pp. 39. This finding can be of reference in this invention. 
FIG. 3 illustrates a flow chart of the method for preparation of the 
diffractive lens of this invention. FIG. 4 shows the progresses of etching 
of the lens under the method for preparation of diffractive lens of this 
invention. The following description will follow the sequence of FIG. 3 by 
referring to FIG. 4. 
As shown in FIG. 3, at 101 a dice containing a lens is prepared according 
to the conventional art. The material of the lens may be silicon, 
germanium or other suited material. At 102 a mask is prepared. The pattern 
of the mask is designed to decide the heights and widths of the levels of 
the diffractive lens. 
FIG. 5 illustrates a mask suited in the present invention. As shown in this 
figure, the mask has a multi-homecentric pattern of the masked areas. Also 
as shown in the figure, the widths and intervals of the masked areas 
varies from level to level. In the masked areas labeled as "step 1", the 
width of and the interval between the masked areas are b.sub.1 and a.sub.1 
respectively and the height of the lens so prepared in this step is 
h.sub.1. In the masked areas labeled as "step 2", the width of and the 
interval between the masked areas are b.sub.2 and a.sub.2 respectively and 
the height of the lens so prepared in this step is h.sub.2. And so on. The 
interval between the masked area of step 1 and that of step 2 is b.sub.2, 
and so on. The premise of the diffractive lens is h.sub.1 =h.sub.2 
=h.sub.3 =. . . =h. From this condition we known that array [a.sub.n ] and 
array [b.sub.n ] have an arithmetic progression relation. 
In the present invention, the intervals and widths of the masked areas in 
different steps formed arithmetic progressions: 
1. Intervals: a.sub.n =a.sub.1 +(n-1)A wherein a.sub.1, a.sub.2, . . . , 
a.sub.n represent the intervals between the masked areas; and 
2. Widths: b.sub.n =b.sub.1 -(n-1)B wherein b.sub.1, b.sub.2, b.sub.3 . . . 
, b.sub.n represent the widths of the masked areas and n represents 
numbers of levels, n=1, 2, 3, 4, . . . 
In the above equations, 
##EQU1## 
f.sub.100 represents the etching efficiency of the (100) surface, f.sub.1 
is the etching efficiency in the side direction which is relative to the 
included angle of the etching mask and the surface of the dice; and 
R.sub.n -R.sub.n-1 is the least width of the terrace. 
The following is a description to factors A and B: 
1. From (7) of FIG. 4 we have: 
##EQU2## 
and represents the time required in etching the substrate counting from 
when the b1 mask is uncovered to when the substrate becomes a plan and 
f.sub.100 is the etching efficiency of the (100) surface; and 
##EQU3## 
is the mean etching efficiency from the under-cut to when the substrate 
becomes a plan, as shown in (5)-(7) in FIG. 4, and f.sub.111 is the 
etching efficiency of the (111) surface. 
We thus have: 
##EQU4## 
2. Also from (7) in FIG. 4 we have: 
##EQU5## 
wherein 
##EQU6## 
and represents the time required to etch the substrate under mask b.sub.2 
until it becomes a plan; wherein 
t.sub.p2 represents the time counting from when the substrate becomes a 
plan in step 2 to when it becomes a plain in step 1 and t.sub.p2 can be 
seen as the time difference between the etching of b.sub.1 and the uncover 
of b.sub.2. So that: 
##EQU7## 
In addition, f.sub.1 is the etching efficiency in the side direction and is 
relative to the included angle of the mask and the surface of the dice. 
We thus have: 
##EQU8## 
3. From (6) of FIG. 4 we have: h.sub.2 =H.sub.3 -H.sub.2 wherein 
##EQU9## 
We then have: 
##EQU10## 
and is the distance between the surface of the dice and the surface of the 
first level after etching; 
##EQU11## 
for n=1, 2, 3 . . . 
Because the heights of the level are the same in the Fresnel lens, so that 
##EQU12## 
This phenomenon can be used as the basis in designing the lens, as 
follows: 
.lambda. is the wave length of the infrared; 
L is the total number of levels of the Fresnel lens; 
.mu. is the fraction index of Si for infrared; 
##EQU13## 
EQU a.sub.n -a.sub.n-1 =a.sub.n-1 -a.sub.n-2 =A&gt;0 or a.sub.n =a.sub.1 +(n-1)A; 
and 
EQU b.sub.n -b.sub.n-1 =b.sub.n-1 -b.sub.n-2 =B&lt;0 or b.sub.n =b.sub.1 -(n-1)B. 
In consideration of the manufacture process, the factors shall be limited 
to a certain scopes: 
(1) a.sub.1 : The least difference between the masked areas. In deciding he 
value of a.sub.1, the limitation in the lithography process and the 
resolution in the etching process shall be taken for consideration. 
(2) a.sub.n : The largest difference between the masked areas. Its 
limitation is the condition that at the surface of the narrowest level 
where the width is R.sub.n -R.sub.n-1), the width shall be at least 
2*b.sub.n, as shown in FIG. 7. That is, 
##EQU14## 
k=1, 2, 3, . . . and is the largest number of masks that can be contained 
in the surface of the narrowest level. 
Because: 
##EQU15## 
if b.sub.n =b.sub.1 +(n-1)B is substituted into the above equation, we 
have: 
##EQU16## 
The result is used to the resolution of the simultaneous equations with 
##EQU17## 
and we have: 
##EQU18## 
and 
##EQU19## 
wherein 
##EQU20## 
(3) K is the number of the masked areas in the narrowest level so that: 
##EQU21## 
At 103 photoresist and material of the etching mask is applied to the 
substrate. Here the material of the etching mask may be SiO.sub.2 or 
Si.sub.3 N.sub.4 or other suitable material. The masks prepared in the 
preceding process are used to have the etching mask exposed and the 
patterns in the masks are transformed to the etching mask so prepared, 
using any suitable technology. At 104 the photoresist is removed and an 
etching mask is obtained. The substrate is then etched in an etchant at 
105. 
FIG. 4 shows the progresses of etching of the lens under the method for 
preparation of diffractive lens of this invention. In this figure, the 
mask is labeled as 0 and is used to show the relations between the pattern 
of the mask and the pattern of the etching mask. In same figure, 1 denotes 
the initial structure of the substrate. The substrate is etched gradually 
and in the stage labeled as 7, a three-leveled structure of the substrate 
is obtained. The relation between the heights of the levels and the 
applicable infrared is: 
##EQU22## 
is the height of each level; 
##EQU23## 
is the radium of the first level in the m.sup.th wave band under an 
L-leveled structure; and 
##EQU24## 
is the number of the wave bands; 
wherein .lambda. is the wave length of the infrared, .mu.is the fraction 
index of Si for infrared and is 3.4, L is the total number of levels of 
the Fresnel lens which is relative to the first-order efficiency of the 
lens. 
In the present invention, if KOH is used as the effective ingredient of the 
etchant, a KOH:water=50 g; 100 ml solution may be applied. The etching 
temperature may be 50-80.degree. C. The relation between the etching depth 
and the width of the masked area of the mask in each step can be expressed 
as: 
##EQU25## 
and is the time consumed in the etching counting from when mask b.sub.1 is 
uncovered to when the substrate beneath the mask becomes a plan wherein 
f.sub.100 is the etching efficiency of the (100) surface; and 
##EQU26## 
and is the average etching efficiency from the under-cut to when the 
substrate becomes a plan, as shown in (5)-(7) in FIG. 3, and wherein 
f.sub.111 is the etching efficiency of the (111) surface. 
After the etching process, a diffractive lens with high quality is 
obtained. In order to reduce the light scattering at the convex regions 
and to enhance the light condense effects, an oxidation-isotropic etching 
cycle may be optionally employed. 
At 106 the whole surface of the lens is grown a heat oxidation layer. The 
thickness of the heat oxidation layer may be, for example, 500 .ANG.. At 
107 the oxidation level is removed with HF gas. Steps 106 and 107 may 
repeated for 2 to 3 times if necessary. A smooth curve surface may be 
formed on the lens. 
The pattern of the mask as used in this invention may be a rectangular, 
multi-homecentric pattern, as shown in FIG. 5. If the corner-compensation 
effect is considered, the pattern shown in FIG. 6 can be used to prepare 
round-shaped lens. 
EMBODIMENT 
A diffractive lens is prepared according to the present invention where 
f=500 and D=200 (F number=2.5). The parameters of this embodiment are 
shown in the following Table. 
__________________________________________________________________________ 
L efficiency 
m h f.sub.100 /f.sub.1 
a.sub.1 
b.sub.1 
R.sub.n - R.sub.n-1 
k A B 
__________________________________________________________________________ 
3 0.68 2 1.389 
50 1 4 12.32191 
3 0.184462 
-0.04773 
__________________________________________________________________________ 
The following factors are determined according to the above equations, as 
follows: 
##EQU27## 
______________________________________ 
a.sub.n = a.sub.1 + (n - 1)A 
b.sub.n = b.sub.1 - (n - 1)B 
______________________________________ 
a1 = 1 b1 = 4 
a2 = 1.18 b2 = 3.95 
a3 = 1.37 b3 = 3.9 
a4 = 1.55 b4 = 3.86 
a5 = 1.74 b5 = 3.81 
a6 = 1.92 b6 = 3.76 
______________________________________ 
The masks are prepared accordingly. The patterns of the masks are 
transformed to the etching mask. The substrate (lens) is etched in a 
KOH:water=50 g; 100 ml solution for approximately 8-10 minutes. The 
structure of the lens is so obtained. 
EFFECTS OF THE INVENTION 
As shown in the above, the method for the preparation of diffractive lens 
inherent great advantages over the prior art. The diffractive lens may be 
prepared under one single etching step using one single etching mask. 
Under the present invention, not only preparation time is saved but also 
the problem of misalignment may be avoided. 
The present invention may be used to prepare single infrared microlens, 
infrared microlens array, micro condenser array for infrared image sensors 
and other diffractive lens with microstructures. 
As the present invention has been shown and described with reference to a 
preferred embodiment thereof, those skilled in the art will recognize that 
the above and other changes may be made therein without departing from the 
spirit and scope of the invention.