rates have been observed to depend on aspect ratio
~
depth/width
!
rather than the absolute feature size.
1
Several mechanisms have been invoked to explain the ‘‘rule’’ of aspect-ratio-dependent etching
~
ARDE
!
, but no general theory has emerged that captures the variety of seemingly conflicting experimental observations reported in the literature. 1,2
For example, while an ion-neutral synergy model with pure neutral flux shadowing appears to be con- sistent with a wealth of ARDE measurements in semiconductors, 2 it does not hold for the etching of insula- tors. Indeed, Doemling et al.
3
have reported inverse ARDE of trenches and holes in SiO
2
in a high-density CHF
3
plasma at 20 mTorr. Remarkably, they also reported aspect ratio independent etching
~
ARIE
!
when the pressure was lowered to 6.7 mTorr; for fixed etching time, the etch depth was the same for a variety of trench widths and hole diameters
~
as low as 0.25 m m, corresponding to an aspect ratio of 8.5:1
!
.
These authors convincingly argued that the strong influence of feature geometry on neutral flux of an etch inhibitor, pro- duced in the CHF
3
plasma, is responsible for the inverse
ARDE at the higher pressure. The low pressure results were explained by hypothesizing that the neutral density at the bottom of the trench or hole, while ‘‘too low to cause inverse
ARDE, it was still sufficient to suppress regular ARDE.’’
This hypothesis must be valid for all trenches and holes etched at the low pressure, which spanned the regime of aspect ratios between 2.1:1 and 8.5:1. Bailey and Gottscho
4
examined in detail the possibility of ARIE by exploiting the ability of etch inhibitors to slow down the etch rate in smaller aspect ratio trenches and concluded that this method
‘‘may be useful in minimizing ARDE but only over a limited range of aspect ratios and only with peculiar inhibitor fluxes.’’ Even in the best of cases, with an ad hoc exponen- tial dependence of inhibitor flux, they calculated that ARIE should break down at an aspect ratio of
'
5:1. Even if the
‘‘magic’’ value of the required inhibitor flux was acciden- tally chosen by Doemling et al.
,
3 their smallest trench
~
0.25 m m
!
should have been etched less deep than the larger trenches. Given the substantial reduction in inhibitor flux to the trench bottom at the low pressure, the latter argument is highly suggestive of a different mechanism responsible for
ARIE up to the
~
impressively
!
high value of 8.5:1.
Differential surface charging of insulating surfaces has been suggested
5–7
as a possible mechanism for ARDE during oxide etching, because local electric fields may significantly perturb ion transport in a trench, thus reducing the ion energy and flux arriving at the bottom surface. Two theoretical studies 6,7 addressed the localized charging in rectangular trenches with profound differences in the calculated potential distribution along the trench surfaces. Arnold and Sawin
6
found a precipitous drop in the potential at the trench middle and speculated that the trench bottom will evolve to be con- cavelike. In contrast, Shibkov et al.
7
calculated a potential distribution that peaks in the trench middle, suggestive of a convex trench bottom. Joubert et al.
8
showed that both shapes of the bottom contours are observed, albeit as a result of the specific etch-inhibiting chemistry employed rather than charging effects. The influence of sheath dynamics on the ion and electron energy and angular distributions arriving at the wafer was not considered in these simulations. Further, surface discharge currents were neglected, despite the con- jecture that these could decrease surface potentials and, thus, reduce ARDE as well. Interestingly, Shibkov et al. calcu- lated electric fields that were very close to the breakdown threshold for bulk oxide
~
1 MV/cm
!
and argued that some surface discharge mechanisms must exist to reduce the bot- tom potential ‘‘because otherwise local charging would make it impossible to etch reasonably deep trenches in insu- lators.’’ In this letter, we report results from Monte Carlo simu- lations of charging and ion dynamics in high aspect ratio trenches by considering the sheath oscillation effect, surface discharge currents, and validated methodology and proce- dures for calculating charging potentials
9
with proven predic- tive capabilities.
10
The simulation begins by calculating real- istic ion and electron energy and angular distributions at the wafer from sheath theory, based on a sinusoidally varying sheath electric field.
11
Then, charged particles, with transla- tional energy and angle of approach determined by randomly sampling the corresponding distributions, are generated at a small distance above the wafer
~
where surface potentials de- cay to zero
!
and followed as they impinge at various surface cells, 12 where they transfer their charge. Since the surface is insulating, charge deposition creates local electric fields which alter ion trajectories. The Laplace equation is solved iteratively in the simulation domain to account for the evo- lution of the electric fields as more charge accumulates.
When the surface electric field exceeds a discharge thresh- old, E
̃
s
, currents are allowed to flow along the surface, thereby reducing surface charging. Steady state is reached when the potential distribution at the bottom and sidewall surfaces no longer changes. At that point, a dynamic equilib-
458 Appl. Phys. Lett.
71
(4), 28 July 1997 0003-6951/97/71(4)/458/3/$10.00 © 1997 American Institute of Physics
Downloaded 30 Apr 2006 to 131.215.240.9. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp rium is established where the ion current arriving to each surface cell is balanced by electrons arriving from the plasma and neighboring cells.
The plasma conditions play a critical role in sidewall charging. Here, we employ a low-pressure
~
,
5 mTorr
!
plasma with a density of 1
3
10
11
cm
2
3
; to fix the ion mass a fully ionized chlorine plasma is assumed.
13
The sheath volt- age is
V
sh
5
0.5
V
rf
~
1
1
sin v t
!
1
V
dc
, where
V
rf
5
50Visthe rf bias,
V
dc
5
67 V is the dc sheath voltage, and v 5
1 MHz is the rf bias frequency. The electron and ion temperatures are taken to be 4.0 and 0.5 eV, respectively. These conditions result in bimodal ion energy distribution at the platen, similar to that expected for oxide etching.
14
The geometry consid- ered ~
Fig. 1
!
consists of equally spaced trenches
~
aspect ratio of 3:1
!
, formed in a uniform dielectric. We assume that the insulator can sustain surface potential gradients of
E
̃ s 5
1
MV/cm, a value close to the breakdown of good quality bulk oxide ~
A
mode
15
!
.
The calculated potential distributions along the trench surfaces ~
Fig. 2
!
are different for various trench widths, de- spite the constant aspect ratio—an indication that ARDE will not hold. The distribution for the 0.5 m m trench
~
identical to that for a 1.0 m m trench
!
shows some undulations at the bottom surface, with dips near the sidewalls
@
Fig. 2
~
a
!#
. The sidewall potential does not vary smoothly with distance be- cause larger absolute potentials can be sustained over longer distances ~
AB
5
1.5
m m ! along the surface without exceeding
E
̃ s . When the trench width and depth are decreased to 0.3 and 0.9 m m, respectively, a smoother distribution is observed along the sidewalls
@
Fig. 2
~
b
!#
. The distribution at the trench bottom does not change discernibly, except for a small de- crease in the average potential. The trench width must de- crease to 0.15 m m
@
Fig. 2
~
c
!#
before significant changes oc- cur. Indeed, since the trench depth is now only 0.45 m m, surface currents flow more readily, thus decreasing the bot- tom potential. Upon further decrease in the trench width and depth to 0.09 and 0.27 m m, respectively, the reduction in the potential becomes more dramatic. Note the similarities be- tween the potential distribution and the topography along the trench bottom, seen experimentally:
3
they are both triangular.
The decrease in the potential at the trench bottom results in large gains in the energy of ions arriving at that surface, as illustrated in Fig. 3. The initial bimodal ion energy distribu- tion undergoes a significant change, which clearly depends on the absolute trench depth since the aspect ratio is fixed.
The distributions for the 1.0 and 0.5 m m trenches are superimposable—the ARDE-rule holds. A large number of ions are lost to the sidewalls and the average energy de- creases considerably. Upon decreasing the trench width to
0.3
m m, the ion energy distribution begins to shift t
1
MV/cm, a value close to the breakdown of good quality bulk oxide ~
A
mode
15
!
.
The calculated potential distributions along the trench surfaces ~
Fig. 2
!
are different for various trench widths, de- spite the constant aspect ratio—an indication that ARDE will not hold. The distribution for the 0.5 m m trench
~
identical to that for a 1.0 m m trench
!
shows some undulations at the bottom surface, with dips near the sidewalls
@
Fig. 2
~
a
!#
. The sidewall potential does not vary smoothly with distance be- cause larger absolute potentials can be sustained over longer distances ~
AB
5
1.5
m m ! along the surface without exceeding
E
̃ s . When the trench width and depth are decreased to 0.3 and 0.9 m m, respectively, a smoother distribution is observed along the sidewalls
@
Fig. 2
~
b
!#
. The distribution at the trench bottom does not change discernibly, except for a small de- crease in the average potential. The trench width must de- crease to 0.15 m m
@
Fig. 2
~
c
!#
before significant changes oc- cur. Indeed, since the trench depth is now only 0.45 m m, surface currents flow more readily, thus decreasing the bot- tom potential. Upon further decrease in the trench width and depth to 0.09 and 0.27 m m, respectively, the reduction in the potential becomes more dramatic. Note the similarities be- tween the potential distribution and the topography along the trench bottom, seen experimentally:
3
they are both triangular.
The decrease in the potential at the trench bottom results in large gains in the energy of ions arriving at that surface, as illustrated in Fig. 3. The initial bimodal ion energy distribu- tion undergoes a significant change, which clearly depends on the absolute trench depth since the aspect ratio is fixed.
The distributions for the 1.0 and 0.5 m m trenches are superimposable—the ARDE-rule holds. A large number of ions are lost to the sidewalls and the average energy de- creases considerably. Upon decreasing the trench width to
0.3
m m, the ion energy distribution begins to shift towards larger energies—the ARDE rule begins to break down. Fi-
FIG. 1. Schematic of the simulation domain.
FIG. 2. Charging potential distributions along the trench surfaces as a func- tion of the trench width
~
W
!
at constant aspect ratio
~
3:1
!
and with a surface discharge threshold of 1 MV/cm. Four cases are shown with
W
:
~
a
!
0.5,
~
b
!
0.3,
~
c
!
0.15, and
~
d
!
0.09 m m. The length scales have been normalized by the corresponding width or length of a particular segment
~
bottom, wall, top !
, to facilitate comparisons. For notation, see Fig. 1.
FIG. 3. The energy distribution of ions arriving at the trench bottom as a function of the trench width at constant aspect ratio
~
3:1
!
and with a surface discharge threshold of 1 MV/cm.
459
Appl. Phys. Lett., Vol. 71, No. 4, 28 July 1997 G. S. Hwang and K. P. Giapis
Downloaded 30 Apr 2006 to 131.215.240.9. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp