KOH etching of high-index crystal planes in silicon

Sensors and Actuators A, 31 (1992) 283-287

283

KOH etching of high-index crystal planes in silicon E. Herr

and H. Baltes

Physical Electronics Laboratory, ETH Zurich. CH-8093 Zurich (Switzerland)

Abstract High-index silicon planes have been etched with KOH of concentrations ranging from 2 mol/l to 12 mol/l (lo-46 wt.%) at temperatures between 50 “C and 95 “C, using two kinds of samples. We have etched mechanically prepared {n 11) and {nnl) (n = 2, 3, 4) crystal planes which we obtained by bevelling silicon samples at accurately adjusted angles. Furthermore, we etched samples that were cut out of industrially fabricated (211) wafers. The results for the two kinds of (211) samples are found to agree for crystal planes that keep their orientation during etching. Non-reproducible etch rates are obtained, however, for those high-index etch fronts that disintegrate into facets of dissimilar crystal orientations.

1. Introduction

2. Experimental

Only few etch-rate data for etching high-index silicon planes (at least one Miller-index greater than one) are presently available. Some authors established polar diagrams for lateral etch rates by under-etching special mask patterns (e.g., polygonal, star-shaped, wagon-wheel-shaped). A straightforward derivation of high-index plane etch rates from these data presupposes that the etch front is composed of a single high-index plane only, and that its orientation can be identified. We determined etch rates [l] for the KOH etching of 6 high-index silicon planes ( {r~11} and {nn l}, n = 2, 3,4), which we prepared mechanically by bevelling (111) oriented silicon samples. A considerable deviation was observed [l] when comparing our results with under-etching results obtained by Linder et al. [2]. In our previous paper [l] we expected proximity effects to be the reason for this deviation, giving rise to different etch rates for different structure sizes. In order to investigate the validity of this assumption and in order to check the reliability of our etch-rate data, we have etched samples that were cut out of industrially fabricated (211) wafers. The wafers were masked with patterns that are composed of structures with sizes that range from several microns to several millimeters.

2.1. Bevelled

0924-4247/92/$5.00

details

samples

We prepared six high-index crystal planes by bevelling ( 111) oriented silicon at assorted angles. The samples are sawn out of a l-mm-thick n-type float-zone wafer with a resistivity of 100 R cm, at sizes of 7.5 mm x 10 mm. The bevel is ground with 12 pm alumina particles, and polishing is performed using a diamond paste with particle sizes of 2 pm and finally 0.25 pm. Masking is accomplished by growing a 5000 8, thermal oxide and manually laying on the photoresist, before two roughly OSmm-wide stripes of bare silicon are opened by oxide etching. KOH concentrations ranging from 2 mol/l to 10 mol/l and KOH temperatures between 70 “C and 95 “C are used for etching. 2.2. Wafer-cut

(21 I) samples

For the (211) crystal orientation, industrially fabricated wafers are at our disposal. They have been sawn out of a 4 inch (111) p-type Czochralski grown silicon ingot with a resistivity of 35 S2cm at an angle of 19.47” ( *0.03”), resulting in slightly elliptical wafers with thicknesses of 525 pm ( f 25 pm). After masking with a pattern of 5000 A thick SiO, the wafers are cut into samples with sizes of 7 mm x 11.7 mm. KOH concentrations ranging from 2 mol/l to 12 mol/l and etching temperatures between 50 “C and 90 “C are chosen. @ 1992 -

Elsevier Sequoia. All rights reserved

284

2.3. Etching and etch-depth

determination

After a lo-second HF-dip to remove the native oxide, the samples are etched for 10 minutes under stirring, resulting in etch depths between 5 pm and 40 pm. The density of the solution is controlled immediately before and after etching, and has been found to vary by less than 0.3%. The error in temperature has been found to be around +0.5 “C. The etch depths are measured by a surface profiler at different locations on the samples. To determine the etch rate, the mean value of these measurements is adopted. The errors given are derived from the standard deviation. Hence, systematical errors such as the effect of surface misorientations are not included.

3. Results

P

E3

n

2molwl

q H

6moM IOmolell

5 f2 5 5 1

n

v

~(122);211)(133)-(3111(411~(110~t144~ crvstal

orientation

Fig. 1. Dependence of etch rates on crystal temperatures of 90 “C.

orientation

for etch

plane in the crystal, that is given at the top of Fig. 1.

3. I. Bevelled samples Stability of etch bottoms: Stable etch bottoms, where the prepared crystal orientation is kept during etching are only observed when etching: (211) planes with 6 m, 8 m and 10 m KOH (all temperatures); 9 (311) planes with 8 m and 10m KOH (all temperatures); (411) planes with 6m, 8 m and 10m KOH (all temperatures). In all other cases, the etching of high-index planes resulted in etch bottoms, where only on a macroscopic scale the original orientation is kept. Microscopically a disintegration into etch-bottom structures composed of facets with other crystal orientations occurs. Since the sizes of the microfacets are small compared to the overall etch depths, a so-called ‘macroscopic’ etch rate can still be determined, which represents an average etch-rate value for the manifesting crystal orientations. l

l

Etch rates: Etch-rate data for the bevelled samples at temperatures of 90 “C are plotted in the bar graph of Fig. 1. The ‘macroscopic’ etch rates for the disintegrating etch bottoms which are included here, fit fairly well into the etch-rate sequence for the stable etch fronts. The whole data set exhibits a correlation between etch rate for a certain plane and its minimum angle with the next (Ill]

Etch-bottom morphology: To identify the orientation of the facets that develop in disintegrating etch bottoms, laser reflection measurements have been performed. The plane orientations that can be identified are listed in Table 1. Distinct reflexes as well as smeared out intensity lobes are observed. In the case of distinct reflexes, unique planes causing the reflexes can be depicted. If the intensity is smeared out around a maximum, only a range of adjacent planes can be given, denoted by a range of rational numbers for the Miller indices in Table 1. Integer Miller indices can be adapted by multiplication with an appropriate factor. Since the formation of the micro-facets does not depend appreciably on temperature, Table 1, which is set up for an etching temperature of 80 “C, can be applied to all temperatures. Our observations can be summarized as follows: -fast etching planes around (1 lo} form together with slowly etching {nn l> planes, with n ranging from 1 to 3; -the (nn 1) planes (n = 2 . . .4) predominantly disintegrate into facets belonging to the same crystallographic zone as the ( 111) plane and the prepared (nnl) plane; -for (n 11) planes (n = 2 . . .4) the facets are found to belong to the two equivalent crystallo(ill)-(221)-. . -(llO) and graphic zones (11 l)-(212). . . -( 101).

285

TABLE

I. Crystal orientations

Plane orientations

of etch-bottom

Orientations

of micro-facets

6 mol/l

8 mol/l

10 mol/l

[1101,[1011

[PP 11. IP IPI pz1.8...2

Stable

Stable

Stable

[ IPPI pzl...2

[ IPPI pal...2

[ IPPI pcl...2

[PP 11% [P IPI PS2... 2.5 [Vll, [qW

Stable

Stable

[ IPPI pzl.3...2

1IPPI p z 1.3..

I1221

p % 1.9,

[ IPPI

[III1 .2.1

[ Ipql, [ lrlP1 pxl.5...2 q x 2. . .2.5

[1101,[~011

[~~Ol,[~O~l

‘P’Il$ p-

[PP

IPI 2

LO1 11 [ IPPI

p z 1.5..

[4111

of KOH concentration

4 mol/l

[PP 11. [P IPl p x 1.3.. 1.6

[I331

as a function

2 mol/l

12111

13111

facets

[lOOI [PP 11,[P IPI

p 2 1.5..

1.8

1.8

11% [P 1Pl

p=:l.9...2.1

[ Ipql, I 14Pl p z 2.2. . .3 q rz 3.. .3.5

[PP 11, [P IPI pzl1.8...2 [qrll, [qlrl qzl2...14 rzl...3

LOIII

10111

[ IPPI. U441 p % 1.4,. . 1.5 (I z 1.5.. 1.8

t IPPI, VPPI p 4 2.3.. .2.5

3.2. Wafer-cut (211) samples In order to investigate the conjectured [l] effect of structure size on etch rate and to check the reliability of our results for the bevelled samples, we have etched samples that are cut out of industrially fabricated (211) wafers. The mask used for the KOH etching is composed of different structure sizes, ranging from several microns to large open areas of several millimeters. The etch rates generally are found to be independent of the structure size. There are cases, however, in which two different etch depths have been found in the etch bottom. Deeper etching at lateral walls: As previously reported [l] a faster etching of regions along adjacent side-walls can be observed for certain crystal orientations and KOH concentrations.

qe4...4.3 r z 2.5

2.1

[ lPP1 p % 1.2..

2.5

[W>[W

[Iqrl,

[IUfl

Ilqrl.

1.5

[Irql

q%l.2...1.5 rz3...4

qe2...5

r-5.,.8

r-9.,.11

Stable

Stable

Stable

[ IPPI, Uqql pz3...5 q-l...2

1 lPP1. IT441 pzl...4 qz2...5

[Ill1

qe7...9

VW1

qz4...cc

This is confirmed by etching wafer-cut (211) samples at 6 m KOH. As we see in the SEM picture of Fig. 2, the occurrence of this effect’ depends on the composition of the side-walls. No deeper etching can be observed at the left-to-right side-wall on the picture, which is a (11 l} plane with an angle to the sample surface of 19.5”. Along the bottom-to-top side-wall, which is composed of facets with various crystal orientations, a deeper etching is observed. The etch depth for the open area in Fig. 2 is 28.8 pm, whereas the depth along the bottom-to-top side-wall equals 34.3 pm. The oxide mask for this sample originally extended to the middle of the deeper etched groove, but has broken off near the edge of the surface to the side-wall. The lateral under-etching at the sample surface for the bottdm-to-top side-wall is 32 pm.

286

depths can result, depending on how the groove is aligned. Morphology of etch bottom: As in the case of the bevelled (211) samples, the etch bottoms of the wafer-cut (211) samples remain stable when etching with KOH of concentrations 26 mol/l. For 2 m and 4 m KOH, facets with the same orientations as were seen with the bevelled samples form, but they are much less pronounced.

AHII

CRIB

Fig. 2. Etch-depth side-wall.

EH

28.0S9.f3

dependence

JO),

-

on the morphology

*

of the adjacent

This suggests that the observed effect may only happen if the lateral under-etching takes place faster than the vertical etching. The deeper etched groove extends to both sides under the original edge of the mask. That means that for narrow structures or for long etching times, the deeper etching may occur for the whole width of the structure. This is demonstrated in Fig. 3, which shows another section of the same sample. Incidentally a small portion of the original oxide mask did not break off (see arrow). Apart from a few remaining facets in the middle of the groove, the whole structure is etched to a depth of 34.3 pm. Therefore, for narrow grooves two different etch

Etch rates: When the etch bottoms remain stable (KOH concentrations B 6 mol/l), the etch rates for the wafer-cut samples compare fairly well to the etch rates for the bevelled samples (see Fig. 4). For etching temperatures of 70 “C and 80 “C the data agree within 10%. For 90 “C the deviation is slightly higher, ranging from 10% to 20%. For disintegrating etch bottoms, occurring with KOH concentrations below 6 mol/l, the ‘macroscopic’ etch rates are found to be considerably higher for the wafer-cut samples. This is related to the lesser developed facets in the etch bottom. Thus, the formation of the etch-bottom facets and the corresponding etch rate for disintegrating planes depend critically on surface preparation and slight surface misorientations. The observation made for the bevelled samples, that 6m KOH always provides the highest etch rates, is not confirmed by these measurements. The ‘macroscopic’ etch-rate values for temperatures of 70 “C and 80 “C exceed the 6 m etch rate. According to the empirical relationship between etch rate and KOH concentration R = k0[HZ0]4[KOH]1’4 exp( --E,/kT)

Fig. 3. Increased etch depth for a narrow groove due to the side-wall eflect.

Fig. 4. Comparison samples.

of (211)

etch rates for wafer-cut

and bevelled

281

TABLE 2. Comparison of the fitting parameters R,, and E. obtained for (21 I> planes KOH cont.

E, (ev) 6 mol/l

8 mol/l 10 mol/l 12 mol/l

Bevelled samples

Wafer-cut samples

0.641 0.610 0.596 0.659

k + + +

0.006 0.017 0.01 0.009

R0 ( lo9 pm/min)

E, (eV)

& ( lo9 pm/min)

2.46 f 0.02 0.85 * 0.01 0.430 + 0.005 2.32 + 0.03

0.648 + 0.007 0.621 f 0.017 0.607 + 0.018

2.9 + 0.7 1.12*0.02 0.541 f 0.008

established by Seidel ef al. [3] for the crystal planes {110) and { 1001, the maximum etch rate can be expected for a concentration near 4 mol/l. Activation energies: The temperature dependence of the etch rates for the wafer-cut samples is examined by least-square fits according to the Arrhenius relation R = R, exp( - EJkT) The pre-exponential factor R,, and the activation energy E, are the independent fitting parameters. As observed for the bevelled samples [ 11good data fits with acceptable reduced chi-squares are only obtained for stable etch fronts. Within the measurement accuracy, the activation energies for the wafer-cut samples agree with the values obtained for the bevelled samples, as can be seen from Table 2.

4. Conclusions In the case of stable etch fronts (KOH concentration > 6 mol/l), our results for the etching of (211) oriented silicon with samples cut out of a (211) wafer confirm our results obtained by etching bevelled (211) samples. This applies to etch rates, activation energies, and plane-stability criteria. For 2-m KOH and 4-m KOH the wafer-cut samples exhibit considerably higher etch rates, but the orientation of the facets in the disintegrating etch bottoms are the same as with the bevelled samples.

The sometimes-observed faster etching near adjacent side-walls demonstrates that the lateral etch rate of the side-walls affects the vertical etching when small structures are etched (structure width comparable to the etch depth). Greater etch depths than expected from the etch-rate value for the crystal plane that is vertically etched may result. The previously [ 11observed disagreement of our high-index plane etch rates with the lower values obtained by Linder et al. [2] cannot be explained by this effect, but may still be related to it.

Acknowledgements

This work was performed in cooperation with ABB Corporate Research and funded by KWF (Kommission zur Forderung der wissenschaftlichen Forschung). The authors would like to thank Dr P. Roggwiller and J. Voboril, ABB, for their support.

References E. Herr and H. Baltes, KOH etch rates of high-index planes for mechanically prepared silicon crystals, Proc. 6fh Inr. Conf. SolidState Sensors and Actuators (Transducers ‘91), San Francisco, CA, USA, 1991, pp. 807-810. S. Linder and H. Bakes, High index plane etch rates and micromachining of power devices, Proc. Micromechanics Europe 1990, Berlin, FRG, pp. 25-30. H. Seidel, L. Csepregi, A. Heuberger and H. BaumgPrtel, Anisotropic etching of crystalline silicon in alkaline solutions, J. Elecrrochem.

Sot.,

137 (1990)

3612-3626.