A polysilicon bridge-slider structure in which one end of the bridge is fixed and the other is connected to a plate sliding in two flanged guideways, is designed and fabricated to study the strain at fracture of LPCVD polysilicon. In the experiments, a mechanical probe is used to push against the plate end, compressing and forcing the bridge to buckle until it breaks. The distance that the plate needs to be pushed to break the bridge is recorded. Nonlinear beam theory is then used to interpret the results of these axially-loaded-bridge experiments. The measured average fracture strain of as-deposited LPCVD polysilicon is 1.72%. High-temperature annealing of the bridge-sliders at 1000°C for 1 h decreases the average fracture strain to 0.93%

Muller, R. S.

Tai, Y. C.

English

Caltech Authors - Main

FRACTURE STRAIN OF LPCVD POLYSILICON 
Y. C. Tai and R. S. Muller 
Berkeley Sensor and Actuator Center 
An NSF/Industry/University Cooperative Research Center 
Department of Electrical Engineering and Computer Sciences 
and the Electronics Research Laboratory 
University of California, Berkeley CA 94 720 
ABSTRACT 
A new polysilicon bridge-slider structure (Fig. 1), in which 
one end of the bridge is fixed and the other is connected to a 
plate sliding in two flanged guideways, is designed and fabri-
cated to study the strain at fracture of LPCVD polysilicon. In 
the experiments, a mechanical probe is used to push against the 
plate end, compressing and forcing the bridge to buckle until it 
breaks. The distance that the plate needs to be pushed to break 
the bridge is recorded. Nonlinear beam theory is then used to 
interpret the results of these axially-loaded-bridge experiments. 
The measured average fracture strain of as-deposited LPCVD 
polysilicon is 1.72%. High-temperature annealing of the bridge-
sliders at 1000 °C for one hour decreases the average fracture 
strain to 0.93%. 
INTRODUCTION 
Polysilicon has been demonstrated to have useful applica-
tions for sensors and actuators. Moreover, complex polysilicon 
micromechanisms have been shown to be feasible [1,2] using pin 
joints, gears, springs, and cranks. As a result, new devices like 
micro-motors and micro optical shutters are becoming possible. 
Proper design of these structures is hindered, however, by the 
lack of precise knowledge of the mechanical properties of 
polysilicon. Of these parameters, strain at fracture is particularly 
important. 
For single-crystal silicon, Eisner [3] reported a maximum 
fracture strain of 2.03% measured on whiskers about one 
micrometer in diameter under tension. Pearson, Read, and Feld-
mann [4] reported a maximum fracture strain of 2.6% for silicon 
whiskers both grown from vapor and cut from bulk silicon. 
Moreover, it is found that below 600 °C there is little or no plas-
tic flow in silicon whiskers about 20 Jlm in diameter before frac-
ture. 
It is expected that polysilicon will also behave linear-
elastically before fracture at room temperature because grain 
boundaries in polysilicon can greatly block dislocation motion 
[6] and make the polysilicon more like an ideal brittle material. 
Based on this assumption, Fan, Tai, and Muller [5] reported prel-
iminary experiments which determined an experimental fracture 
strain of polysilicon to be 1.7% using a spiral-spring-restrained 
pin-joint structure. However, such a spring-restrained pin-joint 
structure is not optimal for the fracture experiment. Moreover, it 
is generally accepted that a statistical method should be used to 
study the fracture strength in brittle materials [6]. 
We report here a systematic method to study the fracture 
strain of polysilicon. We introduce a new, easily implemented 
method using a bridge-slider structure to avoid the difficulties of 
handling small samples as reported in the silicon whisker experi-
ments [3,4]. The bridge-slider structure is specially designed and 
processed to improve experimental accuracy. 
BRIDGE-SLIDER STRUCTURE 
Figure 1 shows an SEM photograph of the newly designed 
bridge-slider structure. The right end of the free-standing bridge, 
shown in Fig. 1, is anchored to the silicon substrate, while the 
left end is connected to a sliding plate guided by two flanges. 
The outer edges of the slider flanges are sawtooth shaped with a 
tooth pitch of 4 Jlm to provide scales for locating the end of the 
slider. This sawtooth feature greatly simplifies our experiments. 
Figure 2 shows a cross section of the slider to demonstrate its 
translational freedom of motion. Clearly, the slider, made of 
second-layer polysilicon, is fully separated from the restraining 
elements that are made of first-layer polysilicon. The flanges 
one of which is circled in Fig. 2 allow the slider only to slide in 
and out of the plane of Fig. 2. 
Figure 1 A bridge-slider structure. The bridge-slider is made 
of second-layer polysilicon. Integrated sawtooth 
scales are defined at the outer side of flanges. The 
marker is 30 Jlm in length. 
TH0215-4/88/0000-0088 is) 1988 IEEE 
2nd polysilicon 
Figure 2 Cross section of the flanged plate slider. The plate 
can move freely in and out of the paper. 
This bridge-slider structure is fabricated using five masks in 
a sacrificial layer technique. Fabrication starts by coating the 
four-inch wafers with 1.5-jlm-thick low-pressure-chemical-
vapor-deposited (LPCVD) phosphosilicate glass (PSG). Mask 1 
is used to open anchor windows for the first-layer polysilicon. 
The first-layer LPCVD polysilicon is then deposited and pat-
terned using mask 2. Polysilicon is patterned in a CC14 plasma 
by reactive-ion-etching (RIE) to provide anisotropic etching. 
Mask 3 is used to open the flange windows with a time-
controlled PSG etch in 5:1 buffered hydrofloric acid (BHF). This 
step creates a 1.5 jlm-long undercut of the first-layer-polysilicon 
restraining element which forms the flanges. A LPCVD silicon-
nitride sacrificial layer is then deposited to coat all the exposed 
surfaces including the flange undercuts. This silicon-nitride layer 
is 200 nm thick and, therefore, determines the gap between the 
two polysilicon layers. Mask 4 opens the anchor windows for 
the bridges. The second-layer polysilicon is then deposited and 
patterned using mask 5. The last step .which frees the structures 
in concentrated HF (49%) takes several hours. For unannealed 
polysilicon structures, the highest temperature in the fabrication 
process is 650 oc which occurs during deposition of the 
phosphorus-doped polysilicon films. Annealed samples are 
treated at 1000 °C for one hour before the final etching. 
EXPERIMENTAL PROCEDURE 
Figure 3 demonstrates the fracture experiment. By pushing 
the slider with a mechanical probe, an initially straight bridge 
can be buckled until it fractures. Pushing is done under an opti-
cal microscope and the whole procedure is video-taped to pro-
vide a record. Since the edges of the flanges are shaped with 
sawtooth scales, the maximum distance t:,L that the slider can be 
pushed is easily measured. Figure 4 shows some pre-pushed and 
buckled bridge-sliders to demonstrate the experiment. The 
bridges retain their buckled shapes in Fig. 4 because they are 
jammed in the slider under such high strain. Figure 5 also 
shows a pre-buckled bridge to demonstrate the clamped boundary 
conditions used in our theory. Once t:,L is measured, a nonlinear 
beam-bending theory is used to interpret the strain in the beam. 
89 
B 
, .... L 
Figure 3 Side view of a buckled beam. The beam is straight 
before loading. Points A, B, and C have the max-
imum bending moment and therefore are the 
expected locations of fracture. 
Figure 4 SEM picture of strained bridge-sliders. When 
sufficiently strained, the bridges retain their buckled 
shapes. The lengths of the bridges are 4, 3, and 2 
mm, respectively, from top to bottom of the picture. 
Figure 5 SEM picture of a strained bridge-slider. The buck-
led shape is a result of clamped boundary conditions. 
y 
' • I 
I 
I ~--1--· ·~F 
Figure 6 Side view of an axially loaded cantilever. 
THEORY 
Because the bridge bending is symmetric (Fig. 3), only one 
quarter of the structure needs to be analyzed. Figure 6 shows the 
bending of a cantilever beam due to a horizontal force. The 
analysis starts with the bending equation [7] 
_1 __ M(x,y) 
r(x,y) - Eyi (1) 
where the r(x ,y) is the curvature, M (x ,y) is the bending 
moment, E y is Young's modulus, and I is the moment of iner-
. . wt3 
tra. In the case of a rectangular cross sectron, I = U. Here, w 
is the beam width and t is the beam thickness. Eq. (1) can be 
rewritten as 
y" - F[y(l)-y] 
(1 +y'2)3t2 - E y I (2) 
where l is the projection length of the beam on the x -axis and 
y (l) is the beam-end deflection (which will be solved for later). 
The boundary conditions on Eq. (2) are y' (0)=0 and y" (l )=0. 
The solution for y (1), obtained by solving Eq. (2), is [8] 
y(l) = zit) (3) 
and intermediate solutions for for l and F are 
l = L-l'lL =.!::_ [2E(p) _ 1 ] 
4 4 K(p) 
(4) 
F = 16£ I .!5!:JEl y L2 (5) 
where L is the total length of the bridge and p = Y ~) W 
is defined to simplify the derivation. The quantities K (p) and 
E (p) are complete elliptic integrals of the first and second kind, 
respectively. These two functions are defined by 
1tl2 lh 
K(p)=J
0 
(1-p 2sin<)>)- d<l> (6) 
1tl2 lh 
E(p)=J
0 
(1-p2sin<l>) d<l> (7) 
90 
For a given value of p , both K (p ) and E (p ) can be obtained 
from mathematical tables. The parameter p can be obtained 
using Eq. (4) since I'lL is measured and p is the only unknown 
in Eq. (4). Knowing p, one can calculate the force F from Eq . 
(5) andy (I) from Eq. (3). 
Once F and y(l) have been calculated, the maximum strain 
can also be determined. The maximum strain (which occurs at 
the clamped end) is [7] 
E:1max = ± M (O,O)t _ _ F_ 
2Eyi wtEy 
= ±4pK(p)..!....- j_K2(p)(..!....)2 
L 3 L 
(8) 
where the + sign stands for tension and the - sign for compres-
sion. Since we have used one-dimensional beam theory, strain is 
independent of beam width w. As shown in Fig. 6, the lower 
half of the polysilicon beam is in tension and the upper part is in 
compression. In fact, the difference in magnitude between 
compressive and tensile strains is twice the last term in Eq. (8). 
This term represents compressive strain caused by horizontal 
force. It is relatively small compared to the bending strain due to 
its ( ± i dependence. Moreover, in brittle materials, tensile 
stress is usually regarded as the most significant cause of fracture 
[6]. Therefore, we consider only the maximum tensile strain 
which is 
t 4 2 t 2 
E+max = 4pK(p )- - -K (p )(-) 
L 3 L 
(9) 
Figure 7 shows the results of theoretical calculations of E+max 
using Eq. (9) for bridge lengths L = 100, 200, 300, and 400 11m 
and thickness 1.27 11m. Using Fig. 7, one can convert the exper-
imental I'lL into fracture strain. For example, one finds !:!.L to be 
41 llffi for a bridge that is 200 11m long. This value of I'lL can 
be used with Fig. 7 to find the corresponding fracture strain 
which is 1.88%. 
0.03 
O.~~~rrTIIIrT,irTTIIII., 
0. !50 100 1!50 200 
M.., (Jlm) 
Figure 7 Theoretical calculations of E+max(!:!.L) from Eqs. (4) 
and (' 1. Thickness of the bridges is 1.27 11m. 
Since the cantilever beam is only one quarter of the full 
bridge, the maximum strain occurs at the center and the two ends 
of the bridge as pointed out in Fig. 3. Therefore, the theory 
predicts that fracture should happen at those three points, as is 
observed experimentally. 
RESULTS 
In brittle materials, fracture occurs when a crack can pro-
pagate in the material. Cracks can originate from defects in 
solids such as impurity inclusions and segregations, and grain 
boundaries. The probability that these defects will cause fracture 
depends heavily on their spatial extent, shape, and orientation, 
which are statistically distributed. Therefore, the study of 
polysilicon fracture should be done statistically. To facilitate 
this, we present statistical results obtained from our experiments. 
Table 1 lists U and E+max deduced from the theory 
presented for both the unannealed and annealed bridge sliders. 
The highest processing temperature for the unannealed polysili-
con is 650 °C. Annealing is carried out at 1000 °C. 
For the unannealed bridge-sliders, the average fracture strain 
is 1.72% with a 95% confidence interval bounded by 1.63% and 
1.81%. The variance is 0.217%. For the annealed bridge-sliders, 
the average fracture strain is 0.93% and the 95% confidence 
interval is (0.89%, 0.97%) with a variance of 0.1 %. 
Two important results emerge from this study. One is that 
the annealed bridge-sliders have a much smaller average fracture 
strain than do the unannealed samples ( 0.93% versus 1.72%). 
The second result is that unannealed bridges show larger scatter 
of the fracture strain in terms of both confidence interval and 
variance. Our experiments have shown that high-temperature 
annealing has, therefore, decreasect both the magnitude and distri-
bution of the fracture strain of polysilicon. 
REFERENCE 
[1] L. S. Fan, Y. C. Tai and R. S. Muller, "Pin joints, gears, 
springs, cranks, and other novel micromechanical struc-
tures," Transducers' 87, 4th Inti. Con f. on Solid-State Sen-
sors and Actuators, Tokyo, Japan (June 3-5, 1987), pp. 
849-852. 
[2] K. J. Gabriel, W. S. N. Trimmer, and M. Mehregany, 
"Micro gears and turbines etched from silicon," Transduc-
ers' 87, 4th Inti. Conf. on Solid-State Sensors and Actuators, 
Tokyo, Japan (June 3-5, 1987), pp. 853-856. 
[3] R. L. Eisner, "Tensile tests on silicon whiskers," Acta 
Metallurgica, Vol. 3, 1955, pp.414-415. 
[4] G. L. Pearson, W. T. Read Jr, and W. L. Feldmann, "Defor-
mation and fracture of small silicon crystals," Acta Metal-
lurgica, Vol. 5, April, 1955, pp.181-191. 
[5] L. S. Fan, Y. C. Tai, and R. S. Muller, "Integrated movable 
micromechanical structures for sensors and actuators," IEEE 
Trans. ED, (to appear June, 1988). 
[6] A. de S. Jayati1aka, "Fracture of engineering brittle materi-
als," London, Applied Science Publishers LTD, 1979. 
[7] S. Timoshenko and D. H. Young, "Elements of strength of 
materials," Princeton, N.J., D. Van Nostrand Co., 1968. 
[8] R. Frisch-Fay, "Flexible bars," Washington, Butterworth 
Inc., 1962. 
Table 1 Experimental fracture strain of polysilicon 
Size Unannealed Annealed 
L/wlt /!,L (Jlm) E+max(%) /!,L (Jlm) E+max(%) 
100/2/1.27 5,7 1.80,2.14 X X 
100/6/1.27 8 2.29 X X 
100/10/1.27 X X X X 
100/20/1.27 X X X X 
200/2/1.27 41 1.88 10,16 0.90,1.14 
200/6/1.27 36,40 1.75,1.86 11,15 0.94,1.11 
200/10/1.27 27,29,33,37 1.51 ,1.56,1.67 ,1.78 10,11 0.90,0.94 
200/20/1.27 29,31,35,37,41 1.56, 1.62,1.73, 1.78, 1.88 9,10 0.85,0.90 
300/2/1.27 124 1.87 35,36 0.93,0.94 
300/6/1.27 75,100 1.40,1.65 30,45 0.86,1.06 
300/10/1.27 77,95,97 1.42,1.60,1.62 38,38 0.97,0.97 
300/20/1.27 85 1.50 23,27 0.75,0.81 
400/2/1.27 X X 90,94 0.99,1.01 
400/6/1.27 X X 74,84 0.89,0.95 
400/10/1.27 X X 79,84 0.92,0.95 
400/20/1.27 X X 53,60 0.75,0.80 
91 


Fracture strain of LPCVD polysilicon

Defor mation and fracture of small silicon crystals,&quot;

Deformation and fracture of small silicon crystals,&quot;

Elements of strength of materials,&quot;

Flexible bars,&quot;

Fracture of engineering brittle materi als,&quot;

Fracture of engineering brittle materials,&quot;

Integrated movable micromechanical structures for sensors and actuators,&quot;

Micro gears and turbines etched from silicon,&quot;

Pin joints, gears, springs, cranks, and other novel micromechanical struc tures,&quot;

Pin joints, gears, springs, cranks, and other novel micromechanical structures,&quot;

Tensile tests on silicon whiskers,&quot;

http://authors.library.caltech.edu/31843/1/TAIsssaw88.pdf

Fracture strain of LPCVD polysilicon

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main