EP1152977A1

EP1152977A1 - Method for producing three-dimensional structures by means of an etching process

Info

Publication number: EP1152977A1
Application number: EP00907450A
Authority: EP
Inventors: Nils Kummer; Roland Mueller-Fiedler; Klaus Breitschwerdt; Andre Mueller; Frauke Driewer; Andreas Kern
Original assignee: Robert Bosch GmbH
Current assignee: Robert Bosch GmbH
Priority date: 1999-01-28
Filing date: 2000-01-26
Publication date: 2001-11-14
Also published as: KR100702822B1; DE19904307A1; WO2000044667A1; JP4653316B2; KR20020018648A; DE19904307C2; US6663784B1; JP2002538972A

Abstract

The invention relates to a method for producing three-dimensional structures, especially microlenses, in a substrate by means of an etching process. First, at least one original form (11) with a known original surface form is located on a part of the substrate (10). The etching process has at least one first etching removal rate a1 and a second etching removal rate a2 which are dependent on the material and at least one of which can be temporally modified. The etching process transforms the original form (11) into a target form (12), the original surface form of the original form (11) and the target surface form of the target form (12) to be obtained being known before the start of the etching process. At least one of the etching rates a2 or a1 is regulated through a modification of at least one etching parameter, this modification being calculated as a function of the etching time before the start of the etching process, in order to obtain the target surface form.

Description

Process for the production of three-dimensional structures by means of an etching process

State of the art

The invention relates to a method for producing three-dimensional structures by means of an etching process.

Such methods and etching systems suitable for carrying them out are widely known and are used, for example, for etching silicon or for producing microlenses from a silicon substrate. For this purpose, reference is made to the method known from DE 42 41 045, in which an inductive coupled plasma source for deep silicon etching with very high etching rates is used, which uses inductive high-frequency excitation in order to generate fluorine radicals from a fluorine-supplying etching gas and from a teflon-forming monomer to produce passivating gas (CF ₂ ) _X - to release radicals. The plasma source generates a high-density plasma with a relatively high density of ions (10 ¹⁰ -10 ^{1: L} cm ^"3 ) lower

Energy, while etching and passivating gases for etching trenches in a masked silicon wafer are used alternately in an empirically determined time sequence.

Furthermore, it has already been proposed in the unpublished application DE 197 363 70.9 to temporally influence an aterial-dependent etching removal rate when etching a silicon wafer by means of so-called "parameter ramping" in this way to reduce profile deviations of etched structures in the silicon wafer.

However, the methods mentioned serve only to make an etching process which is isotropic per se locally anisotropic and thus, for example, to etch trenches of defined depth and good profile accuracy. However, they do not offer the possibility of converting a three-dimensional original shape on a substrate into a three-dimensional target shape with a defined surface shape.

In particular in the production of microlenses, where first an optical surface is created by melted polymers such as a photoresist due to their surface tension, and this optical surface is then transferred to an inorganic substrate material such as silicon for IR optics by a dry etching process Problem of transferring this surface shape of the melted polymer into the substrate during the etching process and at the same time specifically changing the surface shape of the starting polymer to a desired surface shape of the microlens in the substrate material.

When the polymers are melted, neglecting the gravitational forces, with correspondingly small lenses and with free adjustment of the contact angle, spherical surfaces are generally produced, as are also used for macroscopic lenses. However, if the influence of the gravitational forces can no longer be neglected in the case of lenses with a larger diameter, that is to say a few mm, it is known that aspherical surfaces of the melted polymer material are produced which, with a circular base surface, are trical and with a projection into the xz plane of the coordinate system by conical functions hu (x)

can be described with a radius of curvature R _x , a lens height E _λ and a conical constant Ki ≠ 0. After the etching process, these aspheric surfaces are then transferred to the substrate in the known etching processes, and, moreover, it often happens that the conical constant Ki in the melted polymer becomes an original form during etching and thus when the original form is molded into the substrate conical constants K ₂ changed.

This results in an aspherical microlens in the substrate with different optical properties than expected due to the shape of the melted polymer. A sufficient correction or avoidance of this aspheric surface of the microlenses is often not possible with known static etching processes, even if they have different etching removal rates for the substrate material and the polymer.

This is usually due to a very high conical constant of the original polymer form, a change in volume of the original form by the etching process or a time-dependent variation of the etching parameters during the etching process, for example by heating the substrate with magical cooling.

The ratio of the rate of etching removal of the substrate material to that of the master molding material is otherwise referred to as selectivity S. Known static etching processes therefore have constant selectivities. It is also already known that, in the case of photoresist lenses with a diameter of a few mm, conical constants K _x <-100 initially set. With a selectivity of S = 4 required for the surface quality of the lenses, only known microlenses with a conical constant K ₂ <-5 can be produced with known static etching processes in a silicon substrate. In particular, a desired setting of K ₂ = 0, ie a spherical lens, is not possible.

Advantages of the invention

The method according to the invention with the characterizing features of the main claim has the advantage over the prior art that it is suitable for the production of three-dimensional structures such as, in particular, spherical microlenses of largely any size, in a substrate such as silicon, in particular on the substrate initially in some areas is at least one archetype with a known surface shape. The fact that the etching removal rates for the substrate material and the primary molding material differ in a defined manner and, at the same time, that these can be set specifically as a function of time by setting apparatus etching parameters, so that the selectivity of the etching process changes in a defined time

Surface shape during the etching process can be converted into a desired and predetermined target surface shape. This is advantageously done by removing the original shape during the etching process and structuring a target shape out of the substrate in its place.

The calculation of the required change in the etching removal rates over time is carried out before the beginning of the etching, with the exception of some apparatus influences which are conditions must be determined exclusively via the known surface shape of the original shape and that of the target shape, so that constant control of the etching process and extensive empirical tests to achieve a desired target shape and continuous determination of the surface shape of the target shape already achieved as a function of the etching time are not necessary .

Further advantageous developments of the invention result from the measures mentioned in the subclaims.

In order to facilitate the calculation, it is very advantageous if the surface shape can be described at least approximately by an original function h _υ which is known in particular before the beginning of the etching process and the target surface shape can be described at least approximately by an objective function h _s which is particularly explicitly known before the beginning of the etching process.

The apparatus setting of at least one etching parameter as a function of time during the etching process takes place advantageously and in a known manner, for example by changing the flow of at least one of the etching gases used, the concentration and / or composition of the etching gas used, the process pressure in the piasmaatz chamber, the substrate voltage applied to the substrate, the substrate temperature or the coil voltage of an ICP plasma system. A computer-controlled and operated control is particularly suitable for setting the individual parameters. The advantageous property is used in particular that the etching removal rates are also material-dependent.

It is also very advantageous that the method according to the invention allows a desired target to be achieved in a simple manner. shape, starting from an original shape on the substrate, to be structured out of it.

It is thus possible in a simple and advantageous manner to use an aspherical lens with a circular base surface as the primary form, which consists, for example, of a melted polymer such as a photoresist, which is located on a silicon substrate or another semiconductor substrate, and the surface of which is described by a conical function can be converted into a spherical microlens structured out of the silicon substrate during the etching process.

With the aid of the method according to the invention, a significantly better optical quality of microlenses is thus achieved, and the development process is significantly shortened, particularly in the case of larger microlenses, since extensive tests and etching with empirical variation of the etching parameters are omitted.

However, the method according to the invention is advantageously not bound to special materials or compositions of the original shape or the target shape to be achieved, provided suitable etching processes known per se are available for this purpose.

The possible surface shapes of the original shape and the target shape for the method according to the invention advantageously include diverse geometric structures and are not only limited to shapes which, like aspherical microlenses, have so far been of particular importance in practice.

The method according to the invention is particularly advantageously suitable for producing three-dimensional structures with a circular base area and a surface shape which is cylindrical symmetry with the z-axis of the coordinate system, since in this case the substrate defined by the substrate At all levels, the etching takes place at the same etching removal rates or with the same selectivity, which only changes as a function of time.

In principle, however, it is also possible with the etching method according to the invention to change at least one of the etching parameters or the selectivity as a function of the location on the substrate surface and / or as a function of time, so that, for example, the etching removal rates for the original form and target form are not just a function the time but also the location coordinates x and y. However, this continuation of the method according to the invention, which only requires a higher computing effort when calculating the changes to the etching parameters to be set, has not been of practical importance since corresponding etching systems are still lacking. The temperature of the substrate or the substrate voltage, for example, come into question as a function of the location coordinates and the etching time.

In particular, with the method according to the invention, it is advantageously possible, starting from an original shape with a circular base surface and a surface shape, which is described by a first conical function h _υ with radius of curvature R _x , conical constant Ki and Hohe Hi, using a one calculated before the etching process to convert temporal variation of at least one etching parameter into a target shape in a substrate, the surface shape of which is described by a second conical function h _s with radius of curvature R ₂ , conical constant K ₂ and height H ₂ . In the particularly relevant case K ₂ = 0, a spherical target shape is advantageously obtained in this way, while in the case Ki ≠ K ₂ the first conical function, which describes the surface shape of the original form, is deliberately converted into the second conical function, the the surface shape of the target shape writes, can convict. A particularly simple case of this procedure results advantageously in the case which is particularly important for practice in that the heights H _x and H ₂ and / or the radii of curvature R _τ and R _{2 are the} same. The method according to the invention thus very advantageously allows a spherical target shape to be produced from aspherical archetypes.

The method according to the invention is particularly simple if the etching removal rate of one material, such as the substrate material, is kept at least substantially constant during the etching process and only the etching removal rate of the other material, for example the master molding material, is changed over time via the etching parameters. This reduces the calculation effort before etching, increases the reliability and precision of the etching parameters set and the reproducibility of the etching result.

In order to be able to take account of deviations in the etching removal rates and selectivity that occur during the etching process and are not initially taken into account in the calculation, which lead to a deviation of the actual surface shape achieved from the desired surface shape of the target shape, which is included in the calculation First of all, a test statute is made, whereby the temporal change in the etching parameters resulting from the calculation taking into account the surface shape of the original shape (described by the function h _u ) and the desired surface shape of the target shape (described by the function h _s ) is used first becomes. Thereafter, a surface shape which differs slightly from the desired surface shape of the target shape is often established, which is determined by a function h _{s test} is described. In order to be able to compensate for this deviation at least in the first order, a previous calculation of the change in the etching parameters for converting the original form into the target form with a newly defined function h ⁿ S, new = 2'h ⁿ S - hS is then advantageous in all further etching processes , Teκt made, which takes the place of the previously used function h _s .

drawings

The invention is explained in more detail with reference to the drawing and the description below. FIG. 1 shows a schematic diagram of an original shape on a substrate material before the etching process, FIG. 2 shows a schematic diagram of a target shape made of a substrate material after the etching process, FIG. 3 shows the coating time Tι (x) [min] as a function of the location x [μm], 4 shows a representation of the paint removal rate a _x (t) [μm / min] as a function of the etching time t [min] and FIG. 5 shows a representation of the selectivity S (t) as a function of the etching time t [min].

embodiments

FIG. 1 shows a substrate 10 made of a silicon wafer, on which a melted photoresist as the primary mold 11 is located in regions. The surface of the substrate 10 lies within the plane defined by the coordinate axes x and y. The original shape 11 has the shape of an ellipsoid symmetrical to the z-axis or a conic section with a circular base area. The surface of the original form 11 is described by an original function h ₀ , the projection of which into the xz plane of the coordinate system is given by the conical function where Ηi is a height, Ri is a radius of curvature and Ki is a ko ^¬ African constant, which is not equal to 0 here and is in particular between 0 and -200. In the projection, the size h _u (x) denotes the respective distance between the surface of the original form 11 and the substrate 10 as a function of x according to FIG. 1. The origin of the x axis is located, as in all the other cases explained , in the center of the circular base surface of the original shape 11 or the target shape 12.

FIG. 2 shows, as in FIG. 1, by means of an etching process known from DE 42 41 045, for example, in which an inductive coupled plasma source is used, the original mold 11 is converted into a target mold 12, which consists of the

Substrate 10 is structured out. The surface shape of the target shape 12 is described by a target function h _s , the projection of which into the xz plane of the coordinate system is given by the conical function

where H ₂ denotes a height, R ₂ denotes a radius of curvature and K ₂ denotes a conical constant. In this case, the size h _s (x) in the projection is again to be understood as the distance of the surface of the target shape from the substrate base area as a function of x according to FIG. 2.

In this exemplary embodiment, the conical constant is given by K ₂ = 0, that is, the target shape 12 has a spherical surface shape, so that, for example in the production of microlenses, an aspherical master shape 11 is converted into a spherical target shape 12. For the Krum radii applies Ri ≠ R ₂ . However, it should be emphasized that the method according to the invention can also be carried out with much more general original functions and target functions, which, however, have hitherto had little practical significance.

Typical dimensions for the original shape 11 and the target shape 12 are a diameter of the base area of approx. 1 to 10 mm, a height of 0.1 mm to 5 mm and a conical constant from 0 to -200. Since the conical functions describe conic sections (ellipses, parabolas, hyperbolas), positive conical constants are also conceivable. Overall, the target function h _s now takes the simpler form b ' _s i' (Vx ^Λ ) / = H " ₂₂ - R" ₂₂ + VR ^~ ? on. Furthermore, the etching process for the substrate material (silicon) has an etching removal rate a ₂ and in the master molding material (polymer or photoresist) an etching removal rate a _lr, both of which can be changed over time by apparatus etching parameters. In this exemplary embodiment, a change in the etching gas flow or the etching gas concentration changes the etching removal rate ai defined in the photoresist as a function of time, while the etching removal rate a _{2 is kept} at least substantially constant.

In static etching processes with temporally and locally constant etching removal rates ai and a ₂ and a selectivity S which is defined via

_{S (t) =} a ₂ «) ₌ a _{= s (4)} α, (a, the conical constant K ₂ from formula (1) changes depending on the selectivity S and a given conical constant Ki from formula ( 2) in this simple case according to tf ₂ = - - l (5)

In the dynamic etching process according to the invention with a change in the etching removal rate aι (t) in the photoresist and an etching time Tι (x), which indicates the time required for etching at a location x to reach the substrate, the following applies with formula (1): ? 1W

J a (t) dt = h _υ (x) = H, - * .- IR, ² - (l + ^) x ²

: β)

\ + K,

The same applies accordingly in the silicon substrate using

Formula (3) and in particular K ₂ = 0:

, (t) S (t) dt = h _s (x) = H ₂ - R ₂ + VR? -x ² (7)

T is the total etching time. The same applies with the stipulations

and

7 SA (t) = Yes, (t) S (t) dt {9)

1 where A (t) is the total etching depth achieved in the photoresist and SA (t) is the total etching depth achieved in the silicon substrate after the time t: h _υ (x) = A (T ₁ (x)) (10) and h _s ( x) = SA (T _] (x)) (11)

Differentiating by x using the chain rule then results in the following differential equations:

T; () α, (7, (X)) (12) T; (x) a _] (T (x)) S (a _l (T _] (x))) = h _s (x) =: i 3)

V ^

This determines the location-dependent selectivity at the point of transition from photoresist (primary form 11) to silicon substrate (target form 12), i.e. then at the edge of the remaining original form (11):

κ ₂ - x

The function S = S (aι) is known according to formula (14) for the particular etching system used or can be set as a function of time when the etching parameters change by varying the system parameters in the manner described.

The etching removal rate ajtt) at the respective location x of the transition from photoresist to silicon substrate, which changes over time in the course of the etching process, is obtained by using (14) by forming the inverse function:

In connection with formula (12), T _x ^λ (x) is initially calculated.

By integration, this function then provides the required etching time in the photoresist Tι (x) until the substrate is reached as a function of the respective location x.

From this, in turn, the function Tι ^_1 (t), which is only dependent on time, is obtained by forming the inverse function.

After all, you have the desired, only time-dependent etching removal rate in the photoresist with: ^α ₁ ( ^/ ) = α ₁ ⁽ r _I ⁽ τ; - ^{, (} 0) ⁾ < ¹⁶ > from which the time-dependent selectivity S is immediately calculated.

Thus, by specifying the two functions hu (x) and h _s (X), the time-dependent change of at least one etching parameter required to achieve a predefined surface form of the target form 12, as a function of time, is predefined, starting from the surface form of the original form 11.

This calculation, which is carried out with the aid of a computer program, is then followed by a known, time-dependent variation of an etching parameter, such as, for example, the etching gas concentration or the etching gas flow, which results in the required time-dependent change in selectivity or at least one of the two etching removal rates ai or a ₂ leads. In the example explained, only the etching removal rate a _{λ was} changed.

The temporal variation of the appended etching parameters determined from the calculation preferably also takes place via a computer control, which sets the values calculated in advance at the right time during the etching process. Thus, once a parameter set has been calculated, all further etchings of the same geometric shape of the original shape and the target shape can now be carried out.

In summary, a possible procedure in the example explained thus consists of the following steps:

1. First of all, K _lr R _x , H _x (archetype 11) as well as K ₂ , R ₂ and H ₂ (target form 12) are specified, with the following particularly valid: K ₂ = 0. 2. Furthermore, the function S (t) resulting as a function of the etching removal rate a _x based on system and process-specific properties is determined experimentally as a function of the etching time with externally constant etching parameters and this device-specific function is approached for easier handling, for example by a polynomial Order.

3. With these specifications, all the selectivities required in the subsequent etching process (as an interval, but not as a function of time from (14)) are immediately known. In particular, this also applies to their maximum and minimum, so that the boundary conditions or extremes already exist for the following calculation.

4. Now use formula (4) and (5) or (11) and (12) to calculate the function aχ (T (x)) and obtain the spectrum of the possible etching removal rates aχ (Tχ (x)).

5. Then one determines Tχ ^Λ (X) from formula (12).

6. Finally, one integrates, in particular numerically, the function Tχ ^Λ (_) with the boundary condition that the etching time at the edge of the original form 11, ie at the location of the transition to the substrate 10, is zero and thus obtains Tx (x).

7. Since the function aχ (Tχ (x)) and the function Tχ (x) are now known, the function Tχ ^_1 (x) then given as a function of t is formed, for example numerically, and finally set in formula (16 ) so that the result you get is a t (t).

FIG. 3 shows an explanation for an original form 11 made of a photoresist and a target form made of silicon in a silicon umsubstrat 10 a result of the calculation of the coating time Tχ (x) in minutes as a function of the location x in μm. FIG. 4 shows an associated representation of the paint removal rate aχ (t) calculated as a function of the etching time t [min] in μm / min. FIG. 5 finally shows the associated representation of the selectivity S (t) as a function of the etching time t [min]. It should be noted that both functions in Figures 4 and 5 are not straight lines.

In a second exemplary embodiment, the method described in the first exemplary embodiment is carried out somewhat modified.

First of all, the described method is carried out in a test statute as described in the first exemplary embodiment. If there is a surface shape of the target shape (12) that deviates from the desired function h _s (x) = H ₂ - R ₂ + τjR ₂ ² -x ² (7) from formula (7), What can be caused by deviations in the etching removal rates and selectivity that occur during the etching process and are not initially taken into account in the calculation, which lead to a conical constant K ₂ ≠ 0, is experimentally determined and the function of the surface shape of the target shape 12 is described the designation h _{S test} with the constants K ₃ and R ₃ determined experimentally according to the test statute

^h S eΛ ^X ) = ^H i [IT instead of the function to be expected based on the calculation

To compensate for this, after the test statute, initially slightly defective surface shape, a new function h _{S, e} Λx) = 2h _s ( _X ) -h _{s 7esl} (is then approximated in a first order using formulas (17) and (7). x (18) defines, which replaces the previously used function h _s (x).

With this function for describing the surface shape of the target shape 12, together with the original function hu (x) for describing the surface shape of the original shape 11, the calculation according to the first exemplary embodiment is then carried out again, the result of which is then finally in the form of a defined temporal change of aχ (t) is used for the further etchings via corresponding etching parameters. As a result, the above-mentioned deviations caused by the etching system can be compensated for, and with these further etchings a surface shape of the target shape 11 is obtained which at least comes very close to the desired surface shape described by the function h _s (x).

It is obvious that the exemplary embodiments explained are neither restricted to the respective substrate and primary shape materials nor to the special surface shapes of primary shape 11 and target shape 12, but can be generalized in a simple manner.

Claims

claims

1. A method for producing three-dimensional structures, in particular microlenses, in a substrate (10) by means of an etching process, with at least one original shape (11) with a known surface shape being located in regions on the substrate (10), the etching process being at least one first etching removal rate a _: and a second etching removal rate a ₂ , at least one of which can be changed at least over time, and wherein the etching process converts the original shape (11) into a target shape (12) with a predetermined target surface shape that differs from the surface shape, characterized in that, in order to achieve the target surface shape during the etching process, at least one of the etching rates a ₂ or a _{x is set} via a change of at least one etching parameter calculated from the surface shape and the target surface shape at least as a function of the etching time before the beginning of the etching process.

2. The method according to claim 1, characterized in that the surface shape is at least approximately described by an original function known before the beginning of the etching process _υ and the target surface shape is at least approximately described by a target function h _s known before the beginning of the etching process.

3. The method according to claim 1, characterized in that the etching removal rates a ₂ and a ₂ via an apparatus setting etching parameters can be set as a function of time and are in particular material-dependent.

4. The method according to claim 1, characterized in that the target shape (12) from the substrate (10) is structured.

5. The method according to claim 1, characterized in that the etching process for the primary molding material has the etching removal rate ax and for the substrate material has the etching removal rate a ₂ .

6. The method according to claim 3, characterized in that the etching parameters are the flow of one or more of the etching gases used, the concentration and / or composition of the etching gas used, the process pressure, the substrate voltage applied to the substrate, the substrate temperature and the coil voltage.

7. The method according to claim 1, characterized in that the etching removal rate of the substrate material a _{2 is kept} at least substantially constant and only the etching removal rate a _{1 of} the original form is changed over time via the etching parameters.

8. The method according to claim 1, characterized in that the original shape (11) and / or the target shape (12) have an at least approximately circular base area.

9. The method according to claim 8, characterized in that the master form (11) and / or the target form (12) are cylinder-symmetrical to the z-axis of the coordinate system.

10. The method according to claim 1 or 3, characterized in that the surface shape is described by a cylinder-symmetrical original function hu, the projection of which in the xz plane of the coordinate system at least approximately by a conical function

is described with a conical constant K _x , a radius of curvature Rx and a height H _x , and that the target surface shape is described by a cylindrically symmetrical target function h _s , its projection into the xz plane of the coordinate system at least approximately by a conical function

R ₂ - ^ R ₂ ² - (l + K ₂ ) x ² h _s (x) H ₂ - l + K ₂ with a conical constant K ₂ , a radius of curvature R ₂ and a height H _{2 is} described.

11. The method according to claim 10, characterized in that the heights Hx and H ₂ and / or the radii of curvature R _x and R _{2 are the} same and / or that the conical constant K ₂ is 0.

12. The method according to claim 10, characterized in that the heights Hx and H ₂ and / or the radii of curvature Rx and R _{2 are the} same and the conical constant K _{2 is} not equal to the conical constant Kx.

13. The method according to at least one of the preceding claims, characterized in that a test statute is carried out for correcting deviations caused by the etching system with the change, calculated initially as a function of time, of at least one etching removal rate, according to which the surface shape of the target shape (12 ) descriptive function h _s, _T e _St , and that afterwards a new target function h _s , is _newly specified by with which, together with the original function h _u, the calculation of the change over time of at least one etching parameter for achieving the target surface shape of the target shape (12) is carried out again for further etching.

14. The method according to claim 13, characterized in that after the test statute a surface shape of the target shape (12) is set, the projection of which is given in the xz plane of the coordinate system by

15. The method according to claim 1, characterized in that the master mold (11) consists of a polymer, in particular a mask material or a photoresist.

16. The method according to claim 1, characterized in that the substrate material consists of a semiconductor, in particular silicon, or contains this.

17. Use of the method according to at least one of the preceding claims for the production of microlenses.