# A comprehensive review on convex and concave corners in silicon bulk micromachining based on anisotropic wet chemical etching

- Prem Pal
^{1}Email author and - Kazuo Sato
^{2}

**3**:6

**DOI: **10.1186/s40486-015-0012-4

© Pal and Sato; licensee Springer. 2015

**Received: **23 June 2014

**Accepted: **10 January 2015

**Published: **27 May 2015

## Abstract

Wet anisotropic etching based silicon micromachining is an important technique to fabricate freestanding (e.g. cantilever) and fixed (e.g. cavity) structures on different orientation silicon wafers for various applications in microelectromechanical systems (MEMS). {111} planes are the slowest etch rate plane in all kinds of anisotropic etchants and therefore, a prolonged etching always leads to the appearance of {111} facets at the sidewalls of the fabricated structures. In wet anisotropic etching, undercutting occurs at the extruded corners and the curved edges of the mask patterns on the wafer surface. The rate of undercutting depends upon the type of etchant and the shape of mask edges and corners. Furthermore, the undercutting takes place at the straight edges if they do not contain {111} planes. {100} and {110} silicon wafers are most widely used in MEMS as well as microelectronics fabrication.

This paper reviews the fabrication techniques of convex corner on {100} and {110} silicon wafers using anisotropic wet chemical etching. Fabrication methods are classified mainly into two major categories: *corner compensation method* and *two-steps etching technique*. In corner compensation method, extra mask pattern is added at the corner. Due to extra geometry, etching is delayed at the convex corner and hence the technique relies on time delayed etching. The shape and size of the compensating design strongly depends on the type of etchant, etching depth and the orientation of wafer surface. In this paper, various kinds of compensating designs published so far are discussed. *Two-step etching method* is employed for the fabrication of perfect convex corners. Since the perfectly sharp convex corner is formed by the intersection of {111} planes, each step of etching defines one of the facets of convex corners. In this method, two different ways are employed to perform the etching process and therefore can be subdivided into two parts. In one case, lithography step is performed after the first step of etching, while in the second case, all lithography steps are carried out before the etching process, but local oxidation of silicon (LOCOS) process is done after the first step of etching. The pros and cons of all techniques are discussed.

### Keywords

MEMS Silicon anisotropic etching Micromachining Alkaline solution TMAH KOH Convex and concave corners Corner compensation## Introduction

*surface micromachining*and

*bulk micromachining*as presented in Figure 1 [9,10]. In surface micromachining, the micro/nanostructures are realized by the deposition and etching of thin structural and sacrificial layers on the top of the substrate, whereas bulk micromachining defines structures by selectively etching inside a substrate such as freestanding mechanical structures (e.g. beams and membranes) or three-dimensional features (e.g. cavities/grooves, through holes, and mesas). Silicon has excellent mechanical properties, which make it a promising candidate material for micromachining and microengineering [11,12]. Bulk micromachining is further divided into two major classes:

*wet bulk micromachining*and

*dry bulk micromachining*. Either method can be employed for isotropic or anisotropic etching. Dry etching involves the use of gas-phase etchants in plasma [13-18]. Due to the involvement of plasma in dry etching, it is often called plasma etching. Ion and laser beams based etchings also fall into the category of dry etching [19,20]. The dry etching process typically etches directionally and the etch rate is almost crystallographic orientation independent. On the other hand, wet etching is carried out in liquid-phase ("wet") etchants and can further be subdivided into

*isotropic etching*and

*anisotropic etching*as shown in Figure 1. In isotropic etching, the etch rate does not depend on the orientation of the substrate i.e. etching proceeds in all directions at equal rates. A mixture of hydrofluoric (HF), nitric (HNO

_{3}), and acetic (CH

_{3}COOH) acids (i.e. HNA) is most commonly used as silicon isotropic wet etchant [21,22]. In this composition, acetic acid can be replaced by water and the etch rate of silicon depends on the proportion of the acids in the mixture. In the case of wet anisotropic etching, the etch rate depends on the orientation of the crystallographic plane of the substrate. The anisotropic etchants etch materials much faster in one direction than in another, exposing the slowest etching crystal planes over time [1,2,4,10,23-27]. Several kinds of aqueous alkaline solutions such as potassium hydroxide solution (KOH) [23-26,28-35], tetramethylammonium hydroxide (TMAH) [27,36-45], ethylenediamine pyrocatechol water (EDP or EPW) [26,35,46,47], hydrazine [23,48,49], ammonium hydroxide [50], and cesium hydroxide (CsOH) [51] are employed for silicon wet anisotropic etching. Among these etchants, potassium hydroxide (KOH) and tetramethylammonium hydroxide (TMAH) are most frequently used. TMAH is a complementary metal oxide semiconductor (CMOS) compatible etchant as it does not contain alkali ions, unlike KOH. In all kinds of alkaline solutions, {111} are the slowest etching planes, while {110}, {100} and other high index planes are the fast etching planes. The etch rate and the etched surface morphology depend on several parameters of the etchant such as concentration, etching temperature, agitation during etching, additives, etc. However the selection of the type of etching process (dry or wet) mostly depends upon the requirement of the end product. Wet anisotropic etching has several advantages over dry etching including low cost, simple experimental setup, easy handling, batch processing, orientation dependent etch rate, unmatched capability to release mechanical structures, etc. Orientation dependent etch rate is employed to develop microstructures with vertical as well as slanted sidewalls. Wet anisotropic etching has been widely used in silicon based MEMS fabrication such as inkjet head [1,2], RF-MEMS components [52-55], mechanical sensors [56-61], thermal sensors [62-64], micro/nano calorimeters [65-67], microfluidic devices [68-71], and bio/chemical sensors [72-75], atomic force microscopy tips [76-78], etc.

In this article, we have reviewed the fabrication methods of convex corners on {100} and {110} silicon wafers using silicon bulk micromachining based on anisotropic wet chemical etching. This paper is intended to be an independent guide to understand the main reason behind undercutting, protection of convex corners, the advantages and disadvantages of undercutting in silicon-based MEMS fabrication, etc. We have discussed the issues of “where to use what kinds of structure and the points to be considered to select the type of etchant”.

## Difference between etch rate, underetching and undercutting

_{{hkl}}) can be expressed by following relation:

where *d*
_{{hkl}} and *t* are the etch depth measured perpendicular to the {hkl} plane and the etching time, respectively.

The *undercutting* and *underetching* are the lateral etching which occur under the masking layer. Mostly, the words “undercutting” and “underetching” are used interchangeably. In reference [1], underetching is specifically used to define the etching under the mask edges which do not contain extruded/convex corners. This kinds of underetching takes place due to the misalignment of mask edges or/and owing to finite etching of the {111} planes. If the mask patterns include convex corners, the underetching at convex corners is termed as undercutting. Hereafter, mainly undercutting word is used for the lateral etching at any type of mask edge and corner. In the case of {100} wafers, significant undercutting takes place at the edges aligned along non-<110> directions if an etchant is used without any additives (i.e. pure KOH or TMAH). In order to fabricate the square/rectangle cavity of controlled dimensions in {100} silicon wafers, the sides of square/rectangle mask opening are aligned along the <110> directions as the mask edges aligned with these directions exhibit minimum undercutting owing to the appearance of {111} planes. If the sides are slightly misaligned from the <110>direction, the undercutting starts at the edges resulting in a cavity of bigger dimensions than the requirement as shown in Figure 3.

*l*) to etch depth (

*d*) is defined as

*undercutting ratio*(U

_{ r }=

*l*/

*d*). This review article is primarily focused on the role of convex corners in silicon-based MEMS. Hence, the undercutting issue is addressed for sharp convex corners.

Alignment of mask edges along crystallographic directions on wafer surface plays a significant role in controlling the shape and size of etched profiles. In order to align the mask patterns with respect to the crystallographic directions on the wafer surface, primary flat is commonly employed as reference. In this case, any degree of misorientation in primary flat leads to the misalignment of mask patterns with respect to crystallographic directions. A small degree of misalignment of the mask edge with crystallographic direction results in oversized microstructure due to the undercutting at the misaligned mask edges. Therefore, in the fabrication of silicon-based MEMS structures using wet etching, a high precision alignment of mask pattern to crystal orientation is desirable in order to control the dimensions of fabricated structures. Several studies have been performed for the precise alignment of mask patterns with respect to crystallographic directions on {110} and {100} silicon wafers [155-160]. All these techniques are based on the development of mask patterns to create the pre-etched pattern for the identification of crystallographic directions, for instance, <110> direction on {100} oriented wafer surface.

## Advantages and disadvantages of corner undercutting

^{+}-Si, SiO

_{2}, Si

_{3}N

_{4,}etc., silicon beneath a structural component needs to be removed [1-5,10,70,161-163]. If the process is done only on one side of the wafer, the removal of underneath material is only possible by undercutting process [70,161,162]. In order to minimize the release time as fast as possible undercutting is desirable. Hence, a high undercutting rate is advantageous for the formation of suspended structures. Figure 9 illustrates the application of undercutting for the fabrication of suspended cantilever beam.

## Why does undercutting starts at convex corners?

*et al.*explained the undercutting mechanism on {110} surface by comparing the density of break bonds (i.e. dangling bonds) at convex corner and {111} surface [86]. The break bond density of silicon atoms at convex corner is higher than that of {111} planes. This fact results in undercutting at convex corner as the removal rate of the atoms belonging to convex corner is higher than that of the atoms pertaining to {111} planes. The silicon atoms at concave corners do not contain any break bond and therefore the shape of concave corner is not distorted.

In the case of concave corner, regardless of its shape, the concave ridge consists of atoms with no dangling bonds (or unsatisfied bonds) i.e. all the bonds of concave edge atoms are engaged with neighboring atoms. Owing to this fact, no undercutting is initiated at the concave corners and they remain intact and firmly defined by the intersection of {111} planes regardless of the etching time, etch depth, etchant concentration and the etching temperature, as schematically shown in Figure 13.

## Etched profile of undercut convex corners

The orientation of the facets appearing at the convex corners mainly depend on types of etchant, concentration and additives [79-87]. The etching time and temperature also affect the shape and orientation of beveled planes. In general, these facets in the case of {100} surface are typically {311}, {211}, {331}, {411}, {212}, {772}, etc. [80-85,90]. The orientation of the undercutting planes significantly affected by the additives in the etchant, for example, IPA in KOH (Figure 11) and the surfactant in TMAH (Figure 12). However the orientation of beveled planes at undercut corners depend on the choice of etchant and its concentration, different research groups have reported different indices for same etchant. For instance in KOH solution, the beveling planes at the convex corners reported by*,* Shikida *et al.*, Chang Chien *et al.* and Mayer *et al.* are {311}, {772} and {411}, respectively [83,84,92]. Hence, there is some disagreement in the literature about the exact orientation of planes that emerge at the convex corners during etching process. Shikida *et al.* explained that the fast etching planes emerging at convex corners are located at the saddle point in the etch rate diagram [83]. The location of the saddle point in the etch rate diagram depends on the etching parameters, for instance, it is located around {311} plane for 34 wt% KOH. In the case of {110} wafers, the etch front planes at the undercut convex corner of the mesas structures formed by <112> direction estimated by Kim and Cho for KOH are {311} and {771} planes for acute and obtuse corners, respectively [116]. The beveled angle (*α*) (Figure 15) vary from structure-to-structure on same sample [80]. Therefore the index of beveled facet will also change. Consequently, the index of the undercut plane for an etchant cannot be defined absolutely. In principle, the undercutting takes place due to the exposure of low coordination atoms with high removal rates, but the facets at the undercut corners are not the highest etch-rate planes. Instead, they are local maximum etch-rate planes, which lie in the vicinity of the saddle point in the etch-rate contour map [166]. In the surfactant-added TMAH and IPA-added KOH, the etch rates of {110} and its vicinal planes are suppressed to considerably low level. Due to this factor, the undercutting at extruded corners, curved and non-<110> edges on {100} surface is significantly reduced [136-146]. It may be emphasized here that the surfactant-added TMAH is not suitable for the fabrication of microstructures on {110} wafer as the etch rate of {110} orientation is very low as presented in Figure 12. As will be discussed in next section, knowledge of the beveled planes is not significantly important to fabricate protected convex corners. The undercutting ratio (*l/d*) and beveled angle (*α*), as illustrated in Figure 15, are primarily required to develop a method to realize well-shaped convex corners.

## Fabrication methods of convex corners

A significant amount of research has been devoted for the realization of convex corners on Si{100} surface as this orientation is most extensively used in MEMS fabrication [24,88-114,118-126]. However, much less is reported for Si{110} as it is employed only for specific applications [115-117,127,128]. In this article, the fabrication of convex corners are reviewed for both types of orientations (i.e. Si{100} and Si{110}). Several techniques have been developed for the formation of protected convex corners using wet anisotropic etching. Each fabrication technique has its own set of advantages and disadvantages in terms of process flexibility, time, cost and the quality of fabricated corner. These methods are described in following sections.

### Corner compensation technique

_{{100}}or R

_{{110}}); etch depth (

*d*); undercutting length (

*l*); beveled angle (

*α*) i.e. an angle between the direction of maximum lateral undercutting and mask edges; undercutting ratio: (U

_{r}=

*l/d*).

#### Corner compensation geometries for Si{100} wafer

The design methodology of corner compensation geometry is same for all types of anisotropic etchants. The dimensions and shapes are analyzed by relative etch rates of crystallographic planes. However different kinds of compensation geometries, as presented in Figure 20, are proposed, four types of designs, namely, triangle, square, <110> band and <100> oriented beam are the basic structures. Other shapes are the derivatives of these structures.

**(i) Triangle:**The triangular shape geometry, as shown in Figure 22, is a simplest compensating design in terms of determining its shape and dimensions [90,91,120]. In order to calculate the dimensions of the compensating triangle, the undercutting length along the <110> direction (OP, or OC, or

*l*in Figure 22) and the beveled angle α = ∠OPB = ∠OCB = ∠APO = ∠ACO are needed. The lines PB and CB are representing the intersection of the beveling planes with the wafer surface if no compensating pattern is used. The sides of the triangle AP and AC are chosen to coincide with the <

*lm*0> family of lines corresponding to PB and CB. In other words, the sides of the triangle are the highest lateral etch rate directions on {100} surface as illustrated using a red color diagram of lateral etch rates whose center is matched with the convex corner. The length of the sides of the compensating triangle (i.e. AP or AC ) can be determined using the law of sines (or sine rule) as follows:

It is clear from this formula that the length of the sides of the compensating triangle depends on the undercutting length *l* and the beveled angle *α*. The angle *α* and the undercutting ratio (*U*
_{r} = *l*/*d*) depend on the type of etchant. Thus, in order to determine the dimensions of compensating triangle to fabricate a protected convex corner for etch depth *d*, the length *l* and an angle *α* for an etchant must be known. The successive consumption of compensating design during etching is shown by dotted lines.

**(ii) Square:**The triangular shape geometry require more space to its long sides. In this scheme, square shape design is proposed to reduce the spatial requirement to fit in lesser space at the target corner in comparison to triangular shape as shown in Figure 25. In this case, a square whose center coincides with the apex of the convex corner is used for the time delayed etching to protect the convex corner [24,88,89,91,120,122,125]. It can be noticed from Figure 25 that the square shape compensation design contains three convex corner (m, n and T) and therefore this structure is consumed by the undercutting that starts from these corners. In order to determine the side length of the compensation geometry (

*a*) for etch depth

*d*, a simple formula can be derived using geometrical relations. The calculation is based on the time required for beveled edge \( \left[\overline{l}m0\right] \) (or <

*lm*0>) to evolve from point m to point O as illustrated in Figure 25.

*r*from a point m(−

*a*/2,

*a*/2) to a line OS which is parallel to \( \left[\overline{l}m0\right] \) (or <

*lm*0>) and passing through ‘O’ (

*i.e. y = tan α.x*)

The relation between *r* and *l* is \( l=\frac{r}{ \sin \alpha } \)

*a, r*and undercutting ratio (U

_{r}=

*l/d*)

**(iii) <110> oriented beam:**The main objective behind the design of compensation structure is to reduce the spatial requirement and to achieve well-shaped convex corner. In this case, a simple <110> oriented beam (or rectangle) as illustrated in Figures 20(d) and 28 or the combination of <110> oriented beams and squares as shown in Figure 20(e)-(h), is added at the convex corner, [89,94-99,110,120,126]. The progressive etched profiles of simple and asymmetric <110> beams are shown by dotted lines in Figure 28. The consumption of <110> compensation beam takes place by the initiation of undercutting at its convex corners which is illustrated using the lateral etch rates diagrams shown by red color lines. It can be observed from the etched front indicated by dotted lines, <110> beam type compensation design exhibits significant beveling, depending on the beam’s width. In order to reduce the beveling, the width of the beam should be as small as possible. The beveling can also be minimized using asymmetric shape beam, as shown in Figure 28(b). Let

*W*and

*L*

_{<110>}are the width and length of the compensation beam, respectively. A mathematical relation between these dimensions and the etch depth

*d*can be determined using simple geometrical formulae as employed for the square compensation geometry in previous section. In this case, the perpendicular distance

*r*is calculated from point B to a line OG which passes through ‘O’ (

*i.e. y = cota.x*). The following relations are obtained for two differently shaped beams (i.e. symmetric and asymmetric):

- (a)
Simple beam (Figure 28(a))

- (b)
Asymmetric beam (Figure 28(b))

**(iv) Simple <100> oriented beam:**None of the compensation structures discussed so far (i.e. triangle, square, <110> −beam) provides sharp edge convex corner. In continuation of the efforts to fabricate sharp convex corner, a simple <100> oriented beam is proposed as presented in Figure 30 [92,100,103,105,108,109,120,122,125]. As shown by dotted lines, the beam is consumed by undercutting initiated from the free end and the lateral undercutting that starts at the long edges of the beam.

*ij*0} as illustrated in Figures 31 and 32. To predict the etched profile of <100> beam, different conditions based on the etch rate ratio of {

*ij*0} and {100} (i.e. R

_{{ij0}}/R

_{{100}}) can be defined using Figure 31 as follows:

- (a)
If \( \frac{R_{\left\{ij0\right\}}}{R_{\left\{100\right\}}}\le sin\theta \), only {

*ij*0} planes will be developed at <100> edges - (b)
If \( sin\theta <\frac{R_{\left\{ij0\right\}}}{R_{\left\{100\right\}}}<\frac{1}{cos\theta} \), both (100) and {

*ij*0} will expose - (c)
If \( \frac{R_{\left\{ij0\right\}}}{R_{\left\{100\right\}}}\ge \frac{1}{cos\theta} \) , only vertical (100) planes emerge

The etched shapes corresponding to the conditions (a), (b) and (c) are illustrated in Figure 32(a)-(c), respectively. It can be easily observed in Figure 32 that the <100> compensating geometry provides sharp convex corners only if the condition \( \frac{R_{\left\{ij0\right\}}}{R_{\left\{100\right\}}}\ge \frac{1}{cos\theta} \) is satisfied i.e. the sidewalls possess only vertical {100} planes during etching as demonstrated by the SEM picture and the schematic drawing in Figure 32(c).

In order to get a relation to determine the length of <100> beam (i.e. *L*
_{<100>}), the successive etched profile, as shown by black color dotted lines in Figure 30, should be analyzed. The lateral etch rate diagram is used to illustrate the directions of undercutting at the free end and the <100> mask edges. The progressive etched profile in Figure 30 is presented for the condition \( \frac{R_{\left\{ij0\right\}}}{R_{\left\{100\right\}}}\ge \frac{1}{cos\theta} \) as it provides sharp edge convex corner. The undercutting at the free end is caused by fast etching high index planes, while lateral undercutting at <100> edges occurs mainly due to the etching of {100} planes. This design aims to realize the convex corner by the lateral undercutting of {100} planes which appear at <100> edges. For the same reason, the width of the beam should be twice the required etch depth and the beam should be sufficiently long so that the final shape of the convex corner is formed by only the lateral undercutting of {100} planes. In order to determine the beam length (i.e. *L*
_{<100>}) to realize a microstructure with well-protected convex corner upto etch depth *d* (i.e. \( \frac{1}{2}W \)), a relation between *L*
_{<110>} and *d* can be developed by formulating the equation of various lines.

*lm0*>, a fast etching front line) passing through the fixed point \( \mathrm{B}\left(\frac{1}{\sqrt{2}}{L}_{<100>}-\sqrt{2}d,\frac{1}{\sqrt{2}}{L}_{<100>}\right) \) and having slope tan α with <110> edge is

*lm*0 > direction)

*d*(i.e. etch depth). In order to achieve a sharp edge convex corner the beam should be consumed by lateral etching of {100} planes at <100> edges and therefore following condition must be satisfied:

where *R*
_{<100>} and *R*
_{<lm0>} are the etch rates along the directions perpendicular to them.

*d*

_{1}from equation (8) into the equation (10) and re-arranging the terms, we get

**(v) Superimposed squares:**The major part of the research in corner compensation method has been focused to reduce the spatial requirement without compromising on the quality of convex corner. The spatial requirement for a particular etchant is primarily determined by two factors: the shape of the compensating pattern and the amount of corner undercutting in that etchant. However, <100> −oriented beam compensation design provides very sharp corner, high spatial requirement along its length is a serious concern. In order to reduce the spatial requirement, superimposed square shape design is proposed [107]. In this geometry, one square of side

*a*and two of side

*a*/2 are superimposed at the apex of the convex corner, as illustrated in Figure 34. The shape of compensating structure at different steps during etching is designated by dotted lines. In this case, the structure is first consumed by the fast etching planes appearing at its convex corners (i.e. B, D, E, F and H). After a finite interval of time, depending on the dimensions and etching parameters, the etch front is transformed into a <100> oriented beam whose free end is formed by the <

*lm*0> etch front lines as shown in Figure 34(b). After this stage, etching proceeds by both lateral undercutting of the {100} sides and fast propagation of the planes at the free end. Similar to <100> beam, the shape of the convex corner should be taken by the lateral etching of vertical {100} planes as shown in Figure 34(c). In order to get the sharp edge convex corners (i.e. criterion to get the convex corner by lateral etching of vertical {100} planes), the following condition must be satisfied [107]:

*a*and the etch depth d gives [107]:

As mentioned, this design relies on the transformation of the etch profile into a <100> beam and the <100> beam is not suitable for the fabrication of convex corners using surfactant-added TMAH. Therefore the compensation geometry formed by superimposed squares is not appropriate to achieve sharp corners in surfactant-added TMAH. Based on the above discussion, it can be stated that none of the compensating designs provides any improvement over the already nearly sharp convex corners obtained in surfactant-added 25% TMAH without compensation as presented in Figure 12(d) [120].

**(vi) Corner compensation design for bent V-grooves:**The basic problem associated with corner compensation design is the large spatial requirement around the convex corner. In several kinds of microstructures, for instance, the mesa structure surrounded by bent V-grooves and the crossed V-grooves for chip isolation as presented in Figure 36, the space available around the convex corner is less than that is required for the incorporation of compensating structure. In these cases, simple compensation structures (e.g. square, triangle, <100> and <110> beams) cannot be employed as they cannot be fitted in the existing space around the corner. As mentioned earlier, the spatial requirement for a particular etchant is primarily determined by two factors: the shape of the compensating pattern and the amount of corner undercutting in that etchant. Various designs have been reported to fabricate the bent V-grooves.

*et al.*proposed a design in which <100> oriented beam is fanned out into narrow <110> strips at both sides and its free end is connected to the external mask (or frame) by a narrow beam just to eliminate the convex corners as presented in Figure 37 [92]. In this case, the etching of compensation structure starts only from the convex corners at the free end of the <110> narrow beams. As soon as the undercutting from the free end of <110> strips reaches to the main <100> beam, it proceeds by the lateral etching at both sides of the beam. The dimensions of the compensating pattern can easily be calculated using schematic drawing shown in Figure 37(b). The consumption of main <100> beam through lateral undercutting by vertical {100} planes gives \( \frac{W_{<100>}}{2} \) etch depth, where

*W*

_{<100>}is the width of <100> beam. The length of <110> oriented narrow strips (i.e.

*L*

_{<110>}) for etch depth

*d*can be calculated as follows:

where \( V\left(=\frac{R_{< lm0>}}{R_{<100>}}\right) \) is the etch rate ratio between <*lm*0> (or the undercut direction at convex corner) and <100> directions.

It is obvious from relation that the length of <110> strips is independent from its width. It depends on the etch depth *d*, width of the main <100> beam (i.e. \( \frac{W_{<100>}}{2} \)) and the beveled angle *α* at convex corner. Hence the width of the <110> strips can be chosen according to convenience. This type of compensating structure can provide the sharp edge convex corner only if the compensation geometry at the end is consumed by only the lateral etching of vertical {100} planes. However, practically the undercut profile of vertical etched profile is distorted by <110> strips that results in the appearance of protruded mass at the bottom of convex corner as can be observed in the SEM images of Figure 37. If the etching is continued to remove this extra mass at the bottom, severe undercutting starts at main convex corners which degrades the shape of the mesa as can be seen in Figure 37(d). Moreover, this method requires more space along the length of the V-grooves and therefore suitable only if the grooves are long enough.

*et al.*proposed a design composed of superimposed rectangle and square patterns as shown in Figure 39 [118]. The evolution of the etched profile, initiating from corners B and H, is shown by dotted lines. In this design, the protection time mainly depends on the distance of beveled direction <

*lm*0> at point B (or H) from point O as indicated by

*r*in Figure 39(b). This can be formulated in terms of beveled angle (

*α*) and the dimensions of the rectangular strip (i.e. length

*l*

_{1}and width (

*g*

_{1}-

*g*

_{2})) as done for square and <110> compensation geometries. Furthermore, the distance

*r*can be correlated with etch depth

*d*and the etch rates of <

*lm*0> and <100> (i.e. R

_{<lm0>}and R

_{<100>}) as follows:

This equation is valid only if the length *l*
_{1} is greater than the width (*g*
_{1}-*g*
_{2}). This is the same case as considered for <110> compensation geometry. Furthermore, the size of square DEFX (or width *g*
_{2}) should be as small as possible to ensure that it is consumed before the beveling directions <*lm*0> from point B and H reach the main convex corner O. Figure 39(c) and (d) present the shape of bent V-grooves fabricated in 40 wt% KOH at 55°C using the compensation design shown in Figure 39(b). It can be noticed that the perfect compensation is not possible using this design as the deformation of convex corner and some residues of the compensation structure at the bottom of the corner is clearly visible. Moreover this design can be used only if the length of the groove is sufficient for compensation design to fit in the pattern.

*et al.*proposed superimposed <110> oriented beams, as shown in Figure 40, for the formation of crossed V-grooves for chip isolation [98]. As can be noted from the SEM picture of crossed V-grooves in Figure 40(b), the corners are damaged and some residual mass remains at the bottom surface.

#### Corner compensation geometries for Si{110} wafer

- (i)
**Triangular**: As discussed in the case of {100} wafer, undercut shape of the corner (i.e. beveled angles) and the amount of undercutting (i.e. undercutting length*l*) versus etch depth (*d*) depend on the etching conditions and vary from etchant-to-etchant. Therefore these parameters must be known to investigate the design of compensating geometry. The concept behind the design of this structure is the same as used for {100} wafer. However the compensation structure cannot be identical for all corners as the included angles at convex corners are not same as can be seen in Figure 44. In this design, the directions of the sides of the triangle at obtuse corners are the same as the directions of undercutting lines at acute corners and vice versa, as shown in Figure 44(a). In the absence of compensation pattern, the beveled shape (or undercut shape) at obtuse and acute angles are shown by red and yellow color lines, respectively. The successive etched profile of compensating pattern during etching is represented by dotted lines. The sides JP’ and KP’ of the compensating triangle at acute corners are chosen to coincide with <*uuv*> family of lines corresponding to the directions of the undercutting at obtuse corners as indicated by red color lines. Similarly at obtuse corners the sides of the triangle MO’ and LO’ should coincide with <*llm*> directions which are the directions of undercutting at acute corners as shown by yellow color. In order to calculate the dimensions of the triangle using the sine rule, the beveled angles and the lengths of undercutting along <112> directions at obtuse (i.e.*α*_{o}and*l*_{ o }) and acute (i.e.*α*_{ a }and*l*_{ a }) angles must be known. The SEM photographs of acute and obtuse convex corners fabricated using triangular compensation patterns in 42.5 wt% KOH at 80°C are shown in Figure 45(a) and (b), respectively [116]. It can be easily noticed that none of the corners is well-shaped, elongated residues of different lengths are left at both types of corners. - (ii)
**Rhombus (or Square):**This design is a shortened version of triangular shape pattern discussed in previous section. The original idea of this kind of shape is the same as the one reported by Puers*et al*. for the design of square shape compensation pattern for the formation of convex corners on Si{100} [91]. The sides of compensating rhombus aligned along <112> direction. The center of the rhombus coincides with the apex of the convex corners and it is of maximum size which can be inscribed in the triangle as illustrated in Figure 44(b). In the etching process, the compensating rhombus is totally consumed by the undercutting that starts from the three convex corners (A, B and C at acute corners, E, F and G at obtuse corners) as illustrated by the dotted lines in Figure 44(b). The dimensions of the rhombic pattern can simply be calculated using the sine rule as done earlier for other structures. The SEM images of the convex corners fabricated in pure and IPA-added 40 wt% KOH are shown in Figures 46(i) and (ii), respectively [115]. In all cases except acute corner in IPA-added KOH (Figure 46(c)-ii), irregular shape residue can easily be observed. - (iii)
**Parallelogramic beam (or Beam):**In this method, a <112> oriented beam (or parallelogramic beam) is fitted at the convex corner. In order to calculate the length of the beam to protect the corner for etch depth*d*, the undercutting versus etch depth data should be available. As illustrated in Figure 44(c), the length of the compensating beam corresponding to undercutting length*l*_{ o }(i.e. QX) for etch depth*d*should be QY. In this design, the beam width does not play any role and it should be as small as possible, but it should not be consumed by the lateral undercutting of {111} planes which appear at its edges. The great feature of this structure is that the same size beams are added at the acute and obtuse corners. The SEM pictures of convex corners fabricated in 42.5 wt% KOH using beam shape compensating geometry are presented in Figure 47(a) and (b), respectively. An SEM image of a cantilever beam with vertical sidewalls in {110} wafer realized in 25 wt% TMAH using this design is shown in Figure 48.

### Perfect convex corners using two-step etching techniques

- (i)The process steps of the first technique, which is proposed by Kwon
*et al.*, are described in Figure 49 [69]. The fabrication of convex corner is done using two masks. After defining a pattern using mask # 1, anisotropic etching is employed to form a cavity of desired depth (Figure 49(b)). Thereafter masking layer is deposited on exposed silicon. The masking layer can be thermal oxide or CVD nitride. If the oxide is used as mask, KOH is not a suitable etchant as it exhibits finite oxide etch rate. In that case, TMAH should be used as an etchant. Subsequent to the deposition of masking layer, second step of lithography is performed using mask # 2 to pattern the masking layer on the sidewalls as well as top surface. Due to uneven surface topography, it is very hard to coat the photoresist of a uniform thickness using spin coating technique [167-169]. The use of standard liquid photoresist deposited by a spin-coating process results in non-uniform thickness, especially on sloping sidewalls and convex edges/corners. At the convex edges, the film may be even discontinuous, as the photoresist reflows from these edges due to surface tension. Very thin or discontinuous photoresist coating at the convex edges fails to protect the masking layer at the sharp edges during the etching process. This, in turn, leads to etching of silicon during anisotropic etching. Moreover, due to reflow of spin coated photoresist, excessive amount of photoresist is accumulated on the bottom of the cavities/trenches. In order to coat the constant thickness photoresist, spray coating method is employed. The thickness, uniformity and surface roughness of spray-coated photoresist depend on several parameters such as viscosity of the photoresist, orifice of the spray nozzle and the air pressure applied to the nozzle [169-171]. After the patterning of masking layer using second step of lithography (Figure 49(c)), the next step of anisotropic etching is carried out (Figure 49(d)). At last, mask layer can be removed globally if required. An SEM picture of a microstructure fabricated using this method is shown in Figure 49(f) [69]. It can be noticed that the convex corners are well-protected.

- (ii)The second method for the fabrication of perfect convex corner also involve two steps of etching and requires two masks [70,112,128,175]. However it does not need any lithography after the first step of etching. Both steps of lithography using photomasks #1 and #2 are employed before the first step of etching. Figure 50 shows the SEM micrographs of the multiple reservoirs connected with each other through V-shaped channels. The convex corners formed by the intersection of the sidewalls are completely protected. The sequence of process steps are illustrated in Figure 51. The fabrication start with the pattering of nitride layer using mask # 1. Afterward, thermal oxidation is performed to grow the oxide layer. This step of oxidation is called local oxidation of silicon (LOCOS) as only exposed silicon is oxidized and remaining part is protected by nitride layer [176]. Now the oxide is patterned for the first step of anisotropic etching (Figure 51(c)). Thereafter, the etching is performed to a required depth (Figure 51(d)). In these structures, it can be noticed that grooves aligned along <110> can be formed in pure TMAH, while those that are aligned with <100> are possible only in surfactant-added TMAH (or IPA added KOH) as the inclusion of surfactant in TMAH (or IPA in KOH) reduces the undercutting at <100> edges. Now, the thermal oxidation is carried out to deposit an oxide layer on exposed silicon (second LOCOS). Again, nitride layer is selectively removed either by dry etching or wet etching in hot phosphoric acid (H
_{3}PO_{4}). If the nitride is etched out in hot phosphoric acid, sample should be immersed in buffered hydrofluoric acid (BHF) for a short time (about 20 sec) in order to remove any oxide layer formed over the nitride during the LOCOS process [177]. This step is attempted because the oxide etch rate in phosphoric acid is negligible in comparison to nitride etch rate. Subsequently, the buffered oxide is etched out in BHF. Now, the second step of silicon etching is employed. This step of silicon etching should be performed in TMAH as the oxide layer is being used as masking layer. The sidewalls of the currently etched cavities and of the grooves previously formed intersect each other in the shape of the convex corners, which are not etched back as they are passivated by the etch mask. Finally oxide layer is removed in BHF. As shown in SEM picture in Figure 50, the structure fabricated using this method comprise perfect convex corners. However, the process is illustrated for the fabrication of microfluidic channels with multiple reservoirs in Si{100} wafer, it can be utilized for other types of structures which contain convex corners such as proof mass for accelerometer [111]. Moreover this technique can be employed for Si{110} to form the microstructure with perfect convex corner as presented in Figure 52 [128]. Hence this is a generic process. In this method, the overlapped area between two mask is calculated using simple trigonometric relations. Accordingly the dimensions of masks are determined. It may me emphasize here that the dimensions of the mask for the fabrication of microstructure using wet anisotropic etching is determined considering the lateral undercutting and angles of etched sidewalls.

## Conclusions

This topical review is focused on the fabrication methods of convex corners in {100} and {110} oriented silicon wafers using anisotropic wet chemical etching based silicon bulk micromachining. In the corner compensation method, various kinds of compensating geometries used for the formation of protected corners are reviewed and discussed. In this technique, spatial requirement and the resultant shape of etched convex corner are the major concerns. In the case of {100} wafer, <100> oriented compensating design provides sharp edge corner under certain conditions, but its high spatial requirement is a main drawback, especially when the bent grooves are required to be realized. In order to reduce the spatial requirement and to get the sharp convex corner, a compensating geometry designed by superimposed squares is used provided the etchant characteristics fulfill certain requirements. Square shape design needs less space to fit at the corner, but it is not suitable to achieve sharp corners. In the surfactant added TMAH solution, triangular shape design is a best choice. In this etchant, formation of bent V-grooves with sharp convex corners is easily achievable. In the corner compensation method, it is concluded that <100> beam is appropriate choice for the formation of sharp convex corner in high concentration TMAH (e.g. 20–25 wt%) and KOH provided space around the convex corner is not a restriction. In the case of spatial restriction, such as bent V-grooves, surfactant added high concentration TMAH with triangular shape compensation geometry is a right choice. In order to protect the convex corner on Si{110} surface, <112> oriented beam (or parallelogramic beam) is an optimal compensating geometry owing to its simple design and the same size beams are used at the acute and obtuse corners.

Apart from corner compensation methods, two different techniques are also discussed. These methods are very useful when the convex corners with perfectly sharp edges are desired to be fabricated. Unlike the corner compensation method, the formation of sharp convex corner in these methods does not require any time controlled etching. However these techniques provide perfect convex corners, they require two-mask lithography and two-step etching. The extra mask and processing steps make them more expensive and complex.

## Declarations

### Acknowledgments

This work was supported by research grant from the Department of Science and Technology (Project No. SR/S3/MERC/072/2011), New Delhi, India and the Japan Society for the Promotion of Science (JSPS). Sincere thanks to Ms. Michiko Shindo (Secretory to Prof. K. Sato) for her assistance in obtaining permissions to reproduce some figures from published papers and Mr. Sajal Sagar Singh for his suggestions.

## Authors’ Affiliations

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