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Determination of the possible magnitude of the charging effect
in a SCALPEL mask membrane
M. M. Mkrtchyan,
a)
A. S. Gasparyan, K. A. Mkhoyan, J. A. Liddle, and A. E. Novembre
Bell Laboratories of Lucent Technologies, Murray Hill, New Jersey 07974
Received 3 June 1999; accepted 10 September 1999
Previously, we theoretically investigated the charging of free standing dielectric thin lms irradiated
by 100 keV electrons and formulated kinetic equations describing the dynamic process M.
Mkrtchyan et al., Microelectron. Eng. 46, 233 1999 . It was shown that in the currently used
SCALPEL
�
masks comprising a 1000-�-thick amorphous SiN
x
lm supported by a grillage of Si
struts, the membrane charging could be signicant and might have an adverse effect on the system
performance. The membrane charging, sensitive to both the conductivity and the geometry of
conductive path, can be regulated in a straightforward manner by tailoring both of them; for
instance, by applying a top surface conductive layer TSCL with an appropriate thickness and
doping level. Here we discuss the results obtained on the basis of our charging model modied to
be applicable to the case of a SiN
x
membrane with a TSCL e.g., a 10-nm-thick amorphous Si or
poly-Si lm doped by boron . The results presented demonstrate that this modication of the
membrane is sufcient to avoid the adverse effect of the mask-membrane charging. The required
structure can be generated simply by regulating the gas ows in the low-pressure chemical vapor
deposition process to produce a thin nal layer of a:Si or poly-Si which can be doped during or after
deposition. � 1999 American Vacuum Society. S0734-211X 99 12406-5
I. INTRODUCTION
Charging of SCALPEL mask membranes can have an ad-
verse effect on the system performance. It creates an electro-
static eld in the membrane that deects the incident elec-
trons while they travel through the mask membrane. The
current SCALPEL masks consist of a thin SiN
x
lm sup-
ported by a silicon grillage
1
Figs. 1 and 2 . The latter can be
grounded to provide a conductive path for the electrostatic
charge accumulated in the insulating lm during the electron
irradiation.
Our investigation has shown that SiN
x
mask-membrane
charging is mostly due to the limited conductivity of the
membrane dielectric material, the small cross section of the
conductive path dened by the membrane thickness nor-
mally 7501500 � , and the existence of a high density of
trapping centers for the charge carriers.
2
Because the trap-
ping centers are uniformly distributed throughout the mem-
brane, the charge accumulated in the membrane will be dis-
tributed uniformly as well, giving rise to a nonuniform
distribution of the electrostatic eld, E, inside the membrane
volume exposed by the electron beam; E will be zero in the
center and maximal at the edges of the subeld and at the
membrane surfaces. Depending on the exposure dose, the
electrostatic eld can cause either image placement errors
for low doses or illumination nonuniformities for high
doses on the wafer across the scan stripe Sec. III .
1
Recently we have investigated the charging and radiation
damage effects that occur when a free standing thin dielectric
lm is exposed to constant irradiation by energetic
electrons.
13
We have measured electron energy loss spectra
of 100 keV electrons transmitted through the SiN
x
lms
and have performed accelerated lifetime radiation testing
using a scanning transmission electron microscope STEM
equipped with a high-brightness cold eld-emission gun.
3
These results were used as a supplement to the theoretical
investigation of the processes responsible for the charging in
free standing dielectric thin lms. We have developed a
comprehensive model of the electrostatic charge accumula-
tion in free standing dielectric lms supported by a Si gril-
lage and have formulated kinetic equations describing the
dynamic process.
1,2
The lm charging effect is sensitive to many factors such
as the material electrical characteristics, its electronic struc-
ture, and the sample geometry; for instance, lm thickness
change might change not only the quantity but also the sign
of the accumulated charge and related surface potential.
4
In
this article we have extended our model
13
to analyze the
charging effect of the SCALPEL mask membranes with a
TSCL Fig. 1 . The simulation results presented here dem-
onstrate that a simple modication of the mask membrane
deposition process Sec. IV can dramatically suppress the
adverse effect of membrane charging on the image quality in
a SCALPEL system.
II. CHARGING OF SiN
x
MEMBRANES WITH TSCL
The variety of processes responsible for the charging of
free standing a:SiN
x
thin lms irradiated by 100 keV elec-
trons has been discussed elsewhere.
1,2
The mechanism for
the charging of free standing dielectric lms irradiated by the
fast electrons is shown in Fig. 2.
2
This mechanism still ap-
plies when a TSCL is used on top of the basic dielectric
membrane because the thickness of the boron doped silicon
TSCL is expected to be much smaller than the mean free
path for the dominant charge carrier generation process,
.
a
Electronic mail: masis@lucent.com
2888
2888
J. Vac. Sci. Technol. B 17 6 , Nov/Dec 1999
0734-211X/99/17 6 /2888/5/$15.00
�1999 American Vacuum Society This process originates from the decay of plasmons gener-
ated by the incident electrons
1,2
which have a
p
of
about 110 nm in the case of SiN
x
membrane irradiated by
100 keV electrons.
2
The kinetic equations describing the dynamics of the
charging effect need to be modied to account for the exis-
tence of a TSCL with a conductivity much higher than the
conductivity of the basic membrane supported by Si struts.
According to the charging mechanism presented in Fig. 2,
the dielectric membrane will be positively charged generat-
ing an electrostatic eld that is symmetric to the center of the
exposure eld.
2
The electrostatic eld will force mobile
holes out of the membrane exposed area. The cross section
of the exposed region of the membrane stack (SiN
x
TSCL) supported by Si struts is schematically shown in
Fig. 1 b . Accordingly, one needs to consider three uxes of
mobile holes; i the ux from SiN
x
into the top conductive
layer, I
1
, driven by the E
z
component of the electrostatic
eld, ii the ux driven by E
y
in the TSCL, I
2
, parallel to
the membrane surface, and iii the ux through the edge of
the membrane, I
3
, again due to E
y
Fig. 1 b .
The hole current in different regions, I
i
, is proportional to
the electrostatic eld strength, E
i
, the effective cross section
of the hole conductive path, A
i
, in the particular region, and
the conductivity of the material,
i
e
i
Ni, in that region
dened by the hole mobility,
i
, and density, Ni,
I
i
i
E
i
A
i
.
2.1
Here E
i
is the electrostatic eld supporting the hole ux in
the i</i>th region averaged over the effective cross section of the
corresponding conductive path; E
1
E
z
SiN
x
, E
2
E
y
Si
,
and E
3
E
y
SiN
x
.
In Table I, the expressions and values of all parameters
involved are summarized. The strength of the electrostatic
eld, E
i
, is presented in units of E
Q
Q/(2
0
A
1
) where Q
is the total charge accumulated in the membrane volume, V
A
1
t
m
, exposed by the electron beam and
0
is the permit-
tivity of the free space. In the expressions presented in Table
I, p is the density of mobile holes, N
d
is the hole density in
B-doped poly-Si, N
t</i>2
is the density of hole shallow trap lev-
els in SiN
x
, N
t</i>2
is the fraction of trapped holes thermally
released into the valence band
1,2
contributing to the hopping
conductivity
5
see below . Finally, F
z
(t
m
) and F
y
(t
m
) are
weak functions of the membrane thickness
7 and
20,
respectively obtained from the numerical calculation of in-
tegrals representing E
y
and E
z
see Eqs. 5.2 and 5.3 in
Ref. 2 .
It is assumed that the accumulated electrostatic charge is
distributed uniformly throughout the SiN
x
membrane in ac-
cordance with the uniform distribution of the hole trap
levels.
1,2
Previously, we have calculated the electrostatic
eld of a uniformly charged SiN
x
dielectric membrane.
2
In
the case considered here, a thin conductive surface layer is
added on top of SiN
x
. Thus, the electrostatic eld will be
dened by the solution of the Poisson equation for the
multilayer stack shown in Fig. 1 b with boundary conditions
at the three interfaces. The problem can be simplied by
taking into account the fact that the relative dielectric con-
stants of Si and SiN
x
are close 10 and 7 correspondingly
6,7
and, in the rst approximation, one can use our previous
results obtained for SiN
x
lms Ref. 2, Eqs. 5.1 and 5.2
correcting them to account for the small jump of the normal
component of the eld, E
z
, at the Si/SiN
x
boundary;
Si
E
z
Si
SiN
x
E
z
SiN
x
.
The total charge escaping from the exposed area of the
F
IG
. 1. Structure and charge transport schematics for a SCALPEL SiN
x
mask membrane supported by the Si struts when a TSCL is applied on top
of the membrane; a general view, b cross section of the exposed region
of the membrane stack and hole uxes responsible for the charge transport.
Vertical scale is exaggerated to make demonstration of details possible.
F
IG
. 2. Schematic view of a SCALPEL mask blank irradiated by the ux of
fast electrons and the mask-membrane charging mechanism see Ref. 2 .
T
ABLE
I. Charge carrier density, N
i
, drift mobility,
i
, conductive path cross section, A
i
, and the average
electrostatic eld, E
i
, in the different regions with hole uxes shown in Fig. 1 a .
i
Region
A
i
N
i
E
i
i
m
2
/V s
i
e
i
N
i
1
SiN
x
4<i>a
2
( p
N
t</i>2
)
E
Q
F
z
/ (1
SiN
x
)
SiN
x
5.0
10
6