Modeling of information recording and selective etching processes in inorganic resists
Theoretical consideration and computer modeling of information pit recording and etching processes in chalcogenide vitreous semiconductors are proposed, namely we demonstrate how to record and develop information pits with the necessary shape and sizes in the inorganic resist using focused Gaussian...
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| Date: | 2005 |
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| Language: | English |
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Інститут проблем реєстрації інформації НАН України
2005
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| Cite this: | Modeling of information recording and selective etching processes in inorganic resists / A.N. Morozovska, S.A. Kostyukevych // Реєстрація, зберігання і оброб. даних. — 2005. — Т. 7, № 3. — С. 3-16. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860057297269555200 |
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| author | Morozovska, A.N. Kostyukevych, S.A. |
| author_facet | Morozovska, A.N. Kostyukevych, S.A. |
| citation_txt | Modeling of information recording and selective etching processes in inorganic resists / A.N. Morozovska, S.A. Kostyukevych // Реєстрація, зберігання і оброб. даних. — 2005. — Т. 7, № 3. — С. 3-16. — Бібліогр.: 13 назв. — англ. |
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| container_title | Реєстрація, зберігання і обробка даних |
| description | Theoretical consideration and computer modeling of information pit recording and etching processes in chalcogenide vitreous semiconductors are proposed, namely we demonstrate how to record and develop information pits with the necessary shape and sizes in the inorganic resist using focused Gaussian laser beam and selective etching. It has been shown that phototransformed region cross-section could be almost trapezoidal or parabolic depending on the resist material optical absorption, recording beam power, exposure, etchant selectivity and etching time. Namely, during the laser illumination and thermal heating caused by it, photosensitive material is the quasi-equilibrium microscopic mixture of the transformed and nontransformed phases with different optical absorption coefficients: temperature dependent near the absorption edge «transformed» coefficient бe and almost independent coefficient α0 . If αe ≤ α0 e after thermal heating, the photo-transformed region «bleaches» and the pit depth increases more rapidly under the following laser power increasing. If αe > α0 , the phototransformed region «darkens» and the pit depth increases sub-linearly or even saturates under the following laser power increasing. Thus, almost parabolic or flattened pits appear when αe ≥ α0, whereas the pits with elongated tops appear when αe << α0. After illumination, the spatial distribution of photo-transformed material fraction was calculated using the Kolmogorov-Awrami equation. Analyzing obtained results, we derived a rather simple approximate analytical expression for the dependence of the phototransformed region width and depth on the recording Gaussian beam power, radius and exposure time. Then the selective etching process was simulated numerically. The obtained results quantitatively describe the characteristics of pits recorded by the Gaussian laser beam in thin layers of As₄₀S₆₀ chalcogenide semiconductor. Our model open possibilities how to select the necessary recording procedure and etching conditions in order to obtain pits with the optimum shape and sizes.
Запропоновано теоретичний розгляд та комп’ютерне моделювання процесів запису інформації та селективного травлення в халькогенідних напівпровідниках. Змодульовано процес одержання інформаційних питів необхідної форми та розміру у неорганічному резисті, використовуючи сфокусований гаусівський лазерний пучок та селективне травлення. Показано, що переріз фототрансформованої області змінюється від майже трапецієвидного до параболічного в залежності від коефіцієнта оптичного поглинання, потужності лазерного пучка, експозиції, селективності травника та часу травлення. Просторовий розподіл долі фототрансформованого матеріалу розраховано з рівняння Колмогорова-Аврами. Проаналізовано одержані результати й виведено досить простий наближений аналітичний вираз для залежності ширини та висоти фототрансформованої області від потужності лазерного пучка, його радіусу, часу експонування та селективності травника. Одержані результати добре описують характеристики пітів, записаних у тонких шарах халькогеніду As₄₀S₆₀. Модель відкриває реальну можливість добору умов запису та травлення резисту, необхідних для одержання пітів з оптимальними розмірами.
Предложено теоретическое рассмотрение и компьютерное моделирование процессов записи информации и селективного травления в халькогенидных полупроводниках. Смоделирован процесс получения информационных питов необходимой формы и размеров в неорганическом резисте, используя сфокусированный гауссовский лазерный пучок и селективное травление. Показано, что сечение фототрансформированной области может изменяться от практически трапециевидного до параболического в зависимости от коэффициента оптического поглощения, мощности лазерного пучка, экспозиции, селективности травителя и времени травления. Пространственное распределение доли фототрансформированного материала рассчитано из уравнения Колмогорова-Аврами. Проанализированы полученные результаты и выведено достаточно простое приближенное аналитическое выражение для зависимости ширины и высоты фототрансформированной области от мощности лазерного пучка, его радиуса, времени экспонирования и селективности травителя. Полученные результаты хорошо описывают характеристики питов, записанных в тонких слоях халькогенида As₄₀S₆₀. Модель открывает реальную возможность выбора условий записи и травления резиста, необходимых для получения питов с оптимальными размерами.
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Фізичні основи, принципи і методи
реєстрації даних
ISSN 1560-9189 Реєстрація, зберігання і обробка даних, 2005, Т. 7, № 3 3
UDC 621.315; 592:539.213
A. N. Morozovska, S. A. Kostyukevych
V. Lashkaryov Institute of Semiconductor Physics, NAS of Ukraine
41, pr. Nauki, 03028 Kiev, Ukraine
morozo@mail.i.com.ua; sekret@spie.org.ua
Modeling of information recording and selective
etching processes in inorganic resists
Theoretical consideration and computer modeling of information pit record-
ing and etching processes in chalcogenide vitreous semiconductors are pro-
posed, namely we demonstrate how to record and develop information pits
with the necessary shape and sizes in the inorganic resist using focused
Gaussian laser beam and selective etching. It has been shown that photo-
transformed region cross-section could be almost trapezoidal or parabolic
depending on the resist material optical absorption, recording beam power,
exposure, etchant selectivity and etching time. Namely, during the laser il-
lumination and thermal heating caused by it, photosensitive material is the
quasi-equilibrium microscopic mixture of the transformed and non-
transformed phases with different optical absorption coefficients: tempera-
ture dependent near the absorption edge «transformed» coefficient eб and
almost independent coefficient 0a . If 0aa £e after thermal heating, the
photo-transformed region «bleaches» and the pit depth increases more ra-
pidly under the following laser power increasing. If 0aa >e , the photo-
transformed region «darkens» and the pit depth increases sub-linearly or
even saturates under the following laser power increasing. Thus, almost pa-
rabolic or flattened pits appear when 0aa ³e , whereas the pits with elon-
gated tops appear when 0aa <<e . After illumination, the spatial distribution
of photo-transformed material fraction was calculated using the Kolmogo-
rov-Awrami equation. Analyzing obtained results, we derived a rather sim-
ple approximate analytical expression for the dependence of the photo-
transformed region width and depth on the recording Gaussian beam pow-
er, radius and exposure time. Then the selective etching process was simu-
lated numerically. The obtained results quantitatively describe the cha-
racteristics of pits recorded by the Gaussian laser beam in thin layers of
As40S60 chalcogenide semiconductor. Our model open possibilities how to
© A. N. Morozovska, S. A. Kostyukevych
mailto:morozo@mail.i.com.ua
mailto:sekret@spie.org.ua
A. N. Morozovska, S. A. Kostyukevych
4
select the necessary recording procedure and etching conditions in order to
obtain pits with the optimum shape and sizes.
Key words: information pits, optical disks, inorganic resist, selective etch-
ing.
Introduction
Laser recording of profiled microstructures are widely used in modern manufactur-
ing of optical compact disks (CD) and originals of diffraction elements, synthesized ho-
lograms, etc [1]. Numerous experimental and theoretical investigations [2–8] devoted to
the information recording and reading by optical methods has already been performed.
Despite numerous achievements, a great amount of different problems concerning rec-
orded information quality and its density increase still remains unsolved. It was shown
[8–12], that using the inorganic resists based on As40S60 chalcogenide glass allows to
obtain the profiled structures with sizes much smaller than the diameter of the recording
focused laser beam at the wavelengths nm. )532436( ¸=л
This paper is devoted to the theoretical consideration of the question how to record
pits with the necessary depth profile in photosensitive materials by varying their activa-
tion energy, optical absorption, recording Gaussian beam power and exposure as well as
the etchant selectivity and etching time. We used the following assumption: the change
of thin film structure and temperature caused by a laser beam is the main factor that de-
termines the photo-thermo-transformed material amount. We assume that in the course
of illumination photosensitive material is quasi-equilibrium microscopic mixture of the
transformed and non-transformed phases with relative fractions M and (1 – M) respec-
tively. These phases have different photo-chemical properties and the optical absorption
coefficients ea and 0a [6]. The approximate formula for the photo-thermo-transformed
region that determines the profile parameters (width and height) of the pit has been ob-
tained. It has been shown, that pit profile depending on photosensitive material parame-
ters, recording beam power, exposure and etching conditions could be flat with rounded
edges or parabolic (see Sch. 1).
Sch. 1. The photo-thermo-transformed region shape, i.e. ),( zrM spatial distribution calculated
at sufficiently small (plot a) and high (plot b) beam exposures
X
Y
X
Y
b a
Modeling of information recording and selective etching processes in inorganic resists
ISSN 1560-9189 Реєстрація, зберігання і обробка даних, 2005, Т. 7, № 3 5
Fundamental equations
When the intensive focused laser beam illuminates the photosensitive layer, the
optical absorption in the layer l<< z0 is described by the Bouguer-Lambert-Beer law:
( ) ( )
.0,0
,,,,),,,(,,,
Httz
tzyxItzyx
z
tzyxI
££³
-=
¶
¶
a
(1а)
Here ),0,,( tyxI is the intensity of the laser beam focused onto the surface 0=z . In ac-
cordance with the adopted assumption [6], the light absorption coefficient a is as fol-
lows:
( ) ),,,(),,,(1),,,( 0 tzyxMtzyxMtzyx e ×+-= aaa . (1b)
It is obvious, that a depends on the exposing beam wavelength l , intensity, tempera-
ture and exposure time Ht owing to its dependence on M. The system (1) can be rewrit-
ten using the light transmission coefficient b, namely:
( ) ),,(),(,,, 0 tyxIzMtzyxI ×= b , (2a)
( ) ( )
ú
ú
û
ù
ê
ê
ë
é
×--×-= ò
z
dtyxMzztzyxM e
0
),,,(exp),,,,( 00 xxaaab . (2b)
Here ( ) ),0,,(,,0 tyxItyxI = is the incident laser beam intensity, 1),,,(0 << tzyxM and
eaa <0 . Let us consider the model situation when the axial-symmetrical Gaussian laser
beam moves along Y-axis at the distance d with the constant velocity J . The full expo-
sure ),,( zyxH could be calculated directly from (11) and (2), namely:
( ) ( )
ò ÷÷
ø
ö
çç
è
æ -+
-×=
Ht
m
tyxIztzyxMdtzyxH
0
2
0
22
exp),,,,(),,(
r
J
b . (3)
Here Im is the recording beam maximum intensity, b is the light transmission coefficient
(2b), 0r is the recording beam characteristic radius, Ht is the exposure time. The inte-
gration in (3) could be performed exactly when 1=b , i.e. at z = 0 [7]. If only
10 >>rd and 00 rr -<< dy , )0,,( yxH profile almost coincides with the intensity
profile in X-direction. Thus, one obtains that
÷÷
ø
ö
çç
è
æ
-» 2
0
2
0 exp)0,,(
rJ
rp xIyxH m . (4)
A. N. Morozovska, S. A. Kostyukevych
6
One can obtain from (4) that the exposure spatial distribution is Gaussian. We assume
that the distribution of the photoresist temperature ),,,( tzyxT is determined by the light
absorption [3, 9]. Dissipation of the thermal flux during the laser pulse time tH could be
neglected, if the characteristic penetration depth of the thermal flux HT t~c is higher
than the film thickness l . In this case, the stationary temperature distribution exists [7],
namely:
B
a
P k
E
I
tzyxItzyxTtzyxTTtzyxT ),,,(),,,(),,,,(),,,( 0 =DD+» . (5)
aE is the activation energy. The function PI formally introduced in (5) has the mean-
ing of some characteristic intensity, any increase above which can provide registration
of sizable amounts of photo-transformed material in our recording conditions.
The fraction of photo-transformed material M could be calculated using the Kol-
mogorov-Awrami equation [1, 3, 7]. Allowing for (2) and (5) ),,,( tzyxI and
),,,( tzyxT depend on M(x, y, z, t), and so the fraction should be determined from the
Kolmogorov-Awrami equation in a self-consistent manner, namely:
( )
( ) ÷÷
÷
÷
÷
ø
ö
çç
ç
ç
ç
è
æ
÷
÷
÷
÷
ø
ö
ç
ç
ç
ç
è
æ
+
-×--
-»
ò
H
Pa
BPm
t
zM
I
yxI
E
Tk
zM
I
yxId
tzyxM
0 ),(
),,(
1exp),(
),,(
exp
1),,,(
00
0
tb
t
tb
t
t
t . (6)
The characteristic time mt depends not only on properties of recording medium but also
on the recording light wavelength l . One immediately obtains from (4) and (6) that the
total fraction ),,,(),(0 HtzyxMzxM º of photo-thermo-transformed region cross-
section could be estimated by the iteration method starting from the point z = 0:
.)0,(1))0,((,exp)0,(
,
))0,((
exp)0,(exp1),0,(
02
0
2
0
0
÷÷
ø
ö
çç
è
æ
+=÷÷
ø
ö
çç
è
æ
-=
÷
÷
ø
ö
ç
ç
è
æ
÷÷
ø
ö
çç
è
æ
---»=
T
m
B
a
m
H
xHTxHTxHxH
xHTk
E
H
xHHzxM
r
(7)
Here the characteristic exposures PmIH t=0 , ( ) HpaBT tIETkH 0= and the maximum
exposure ( ) Hmm tIH Jrp 0» are introduced. Characteristic exposure TH is inversely
proportional to the activation energy. It is noteworthy, that at 0HH T << significant
thermal heating occurs even at small exposures 0HH m < , and as a result visible struc-
tural transformations ( 5,0~0M ) inside the exposed region start at 0HH m < (see the
Modeling of information recording and selective etching processes in inorganic resists
ISSN 1560-9189 Реєстрація, зберігання і обробка даних, 2005, Т. 7, № 3 7
light-blue curve in Fig. 1). In contrast to this, at 0HH T >> no thermal heating occurs at
exposures Tm HH < and visible structural transformations inside the exposed region
starts only at 0HH m >> (see the violet curve in Fig. 1). The intermediate case is rea-
lized at 0~ HH T , when at small exposures pm HH < only weak photo-structural trans-
formations take place, then at pm HH ³ thermal heating occurs (see the dark-blue curve
at Pm HHH >0 in Fig. 1).
Fig. 1. Fraction ),0,0(0 mHM from (7) vs. the exposure 0HH m , at 50 =TkE Ba
and different 0HH T ratios: 0.1 (light-blue), 1 (dark-blue), 5 (violet)
Thus, for the majority of photosensitive materials the conditions Tm HH < and
0HH T > determine the cases of photo-transformations with a weak sub-linear or linear
dependence of mm HHM ~),0,0(0 . This case is realized in laser lithography with wide
homogeneous beams and holographic grating recording. Whereas the conditions
Tm HH ³ and 0HH T < determine the cases of photo-thermo-transformations realized
in CD recording by a focused laser beam.
Using (7) as a starting point, one obtains from (2b), (6) and (7) the expression for
0M in the first approximation over the parameter ( ) 00 aaa -e :
( )( ) )0,,()0,,(exp),,( 00000 yxMzyxMzzyxM e ×××--×-» aaa . (8)
As it follows from (8), if 0aa £e after the thermal heating, the exposed region
«bleaches», and the pit depth increases more rapidly under the following laser power
0 2 4 6 8
0
0,2
0,4
0,6
0,8
1
HT/H0 = 0,1
HT/H0 = 1
HT/H0 = 5 Fr
ac
tio
n
M
0(0
,0
,H
m
)
HP
Exposure Hm/H0, rel. units
A. N. Morozovska, S. A. Kostyukevych
8
increasing. If 0aa >e , the exposed region «darkens» and the pit depth increases sub-
linearly or even saturates under the following laser power increasing. Thus, almost pa-
rabolic or flattened exposed region could appear when 0aa ³e , whereas the pits with
elongated tops appear when 0aa <<e .
The experimental possibilities of photoresist etching in definite selective etchant
are characterized by the etching rates: nJ of non-exposed regions with 0®M and eJ
for the exposed ones with 1®M . Similarly to the model (1b) used for absorption coef-
ficient a, the etching rate ( )zx,J in the point with the relative fraction ),,(0 zHxM m has
the form:
( ) ),,(),,(1),,( 00 memnm HzxMHzxMzHx ×+-= JJJ . (9)
After selective etching with time tE, the exposed layer depth profile ),,( Etyxz can be
determined using (9) as:
( )( )
{ } .0,0,1,0,0)0,(,0)0,,(
),,(),,(),,(1
),,,(
0
00
E
memn
m
ttlzrnyxz
trnHzxMHzxM
td
tzHxrd
££££==
××+-=
vr
vr
v
JJ
(10)
Here 0l is the initial thickness of the photoresist layer, ),,( zyxnr is the etched region
external normal. The approximate analytical expression for residual layer height profile
can be obtained from (7)–(10) in the case of mainly normal-directed etching at
12
0
2 <rx , when the equation (10) transforms into the scalar differential equation
( ) ( )( )( )
.0)0,,(
,),(),0,(exp),0,(),(
0000
=
××-+--+»
yxz
txzHxMHxM
td
txzd
memnen aaaJJJ
(11)
The equation (11) has the following analytical solution for the etched relief height pro-
file:
( )( )
( )
( ) ).,0,(),(
,
),(exp
1),(exp),0,(1
ln
),(
1),(
000
0
mem
nm
nmm
n
e
m
HxMHx
tHx
tHxHxM
Hx
txz
×-+=
÷
÷
÷
ø
ö
ç
ç
ç
è
æ
+
+-÷÷
ø
ö
çç
è
æ
-
=
aaaa
Ja
Ja
J
J
a
(12)
In the important for applications case of a highly selective positive etchant with
1>>ne JJ and for the exposed region with 1),( £tHx nm Ja , 0aa »e , the expression
(12) describing the relief height profile can be approximated as:
Modeling of information recording and selective etching processes in inorganic resists
ISSN 1560-9189 Реєстрація, зберігання і обробка даних, 2005, Т. 7, № 3 9
( ) ),0,(),( 0 mnen HxMtttxz ×-+» JJJ . (13)
The expression for ),0,(0 mHxM is given by (7). First, let us consider the region of
photo-thermo-transformations with ( ) Tm HH 10~10 ££ , which is used for CD holo-
graphic recording and further development in a highly-selective positive etchant with
1>>ne JJ . In this case, the approximation (13) is valid. The dependence of the resi-
dual layer thickness on the exposure Hm at the fixed etching time tE is presented in Fig.
2 for different 0HH T ratios. It is clear from the figure that the smaller is 0HH T ra-
tio, the more significant is the contribution of thermal transformations and so residual
layer thickness decreases more rapidly with the exposure increase.
Fig. 2. Residual layer thickness (13) in z0a units vs. the exposure 0HHm after positive selective
etching ( nEt Ja 05,0= ) at 50 =TkE Ba , 0aa =e and different
0HHT ratios: 0.1 (light-blue), 1 (dark-blue), 5 (violet)
There, let us consider the region of photo-thermo-transformations with 0HH T << .
It is easy to obtain that at fixed exposure Hm the residual layer thickness decreases with
the etching time increase (see Fig. 3).
The residual layer thickness dependence over the exposure Hm at fixed etching time
tE is shown in Fig. 4. Various cases can be realized for positive and negative etching,
respectively.
Photo-thermo-transformed region shapes at fixed exposure 0HH m and increasing
selective etching times Et are presented in Fig. 5. It is seen that the modulation depth
increases with the etching time at the initial stage, then the etched profile «falls down»
as a whole.
0 2 4 6 8
-0,5
-0,4
-0,3
-0,2
-0,1
0
HT/H0 = 0,1
HT/H0 = 1
HT/H0 = 5
La
ye
r t
hi
ck
ne
ss
, a
0z
Exposure Hm/H0, rel. units
unexposed region x®¥ Positive etching Je/Jn= 10
A. N. Morozovska, S. A. Kostyukevych
10
Photo-thermo-transformed region shapes at the fixed selective etching time Et and
different exposures 0HH m are presented in Fig. 6. It is seen that the modulation depth
increases with the exposure, while the profile becomes more trapezoidal. Thus, almost
parabolic or flattened pits could appear when 0aa ³e , whereas the pits with elongated
tops appear when 0aa <<e .
0 2 4 6
-5
-4
-3
-2
-1
0
Etching time tE, a.u.
Positive etching Je/Jn = 10
unexposed
region x®¥
exposed
region x®0
La
ye
r t
hi
ck
ne
ss
, a
0z
0 2 4 6 8
-5
-4
-3
-2
-1
0
Etching time tE, a.u.
Negative etching Jn/Je = 10
La
ye
r t
hi
ck
ne
ss
, a
0z
unexposed
region x®¥
exposed
region x®0
Fig. 3. Residual layer thickness (12) in z0a units vs. selective etching time measured in units nJa 0
at fixed exposure 50 =HHm , 0HH T << and 05,0 aa =e (light-blue),
0aa =e (dark-blue), 02aa =e (violet)
Modeling of information recording and selective etching processes in inorganic resists
ISSN 1560-9189 Реєстрація, зберігання і обробка даних, 2005, Т. 7, № 3 11
0 2 4 6 8
-2
-1.5
-1
-0.5
Positive etching Je/Jn=10
exposed
region x®0
unexposed region x®¥
Exposure Hm/H0, rel. units
La
ye
r t
hi
ck
ne
ss
, a
0z
0 2 4 6 8
-0.5
-0.4
-0.3
-0.2
-0.1
0
Negative etching Jn/Je=10
unexposed region x®¥
exposed
region x®0
Exposure Hm/H0, rel. units
La
ye
r t
hi
ck
ne
ss
, a
0z
Fig. 4. Residual layer thickness (12) in z0a units vs. the exposure 0HH m at fixed selective etching
time 5,0=Et measured in units nJa 0 and 0aa =e , 0HHT << (cf. Fig. 2)
A. N. Morozovska, S. A. Kostyukevych
12
Fig. 5. Photo-thermo-transformed region shape (12) at the fixed exposure 0HHm and increasing
selective etching times Et measured in units nJa 0 , 0aa =e , 0HHT <<
Fig. 6. Photo-thermo-transformed region shape (12) at the fixed selective etching time Et measured
in units nб J0 and different exposures 0HH m , 0aa =e , 0HH T <<
The characteristics of recorded pits
Finally, let us discuss the situation of information recording associated with the la-
ser recording on a master disc having a thin chalcogenide layer of As40S60 composition
[9–12]. In our recent experiments, the exposure of these thin layers was performed us-
ing focused laser light with the wavelength nm,)488...436(=л optical absorption
-4 -2 0 2 4
-2
-1.5
-1
-0.5
0
Negative etching Jn/Je=10, Hm/H0 = 2,5
Th
ic
kn
es
s,
a 0
z
tE = 0,1
tE = 0,5
tE = 1
tE = 2
x/r0, rel. units
-4 -2 0 2 4
-4
-3
-2
-1
0
Positive etching Je/Jn=10, Hm/H0 = 2,5
x/r0, rel. units
Th
ic
kn
es
s,
a 0
z
tE = 2
tE = 1
tE = 0,5
tE = 0,1
-4 -2 0 2 4
-2
-1,5
-1
-0,5
Th
ic
kn
es
s,
a 0
z
Positive etching Je/Jn = 10
unexposed
region x®¥
Hm/H0 = 0,1
Hm/H0 = 0,5
Hm/H0 = 2,5
Hm/H0 = 10
tE = 0,5
x/r0, rel. units
Modeling of information recording and selective etching processes in inorganic resists
ISSN 1560-9189 Реєстрація, зберігання і обробка даних, 2005, Т. 7, № 3 13
coefficient varied within the range 135
0 cm)103...103( -××»a [4], [13]), beam diame-
ter was close to мm8,0 and laser beam power varied from 0,2 to 1 mW. Then the de-
velopment of resist in positive selective etchant has been carried out. Under the positive
etching, the exposed regions were completely removed, while the unexposed ones re-
mained on the substrate. The etching rate of the exposed region is much smaller than
that of the unexposed one. So, the profile of the photo-thermo-transformed region after
positive selective etching could be determined from (12), (13) in the first approxima-
tion. Below, we have presented results for As40S60 thin layers (see Fig. 7, 8, 9).
The pit depth zp and halfwidth ap increase with the laser beam power P (see Fig. 8).
Starting from a definite laser power PP HP ~ (see Fig. 1), thermal transformations play
an important role in the structural transformations inside the exposed spot. We obtained
that for the examined As40S60 layer mW 1,0»PP , mW 7,0»TP ( tPH TT » , PtH m » ).
As it follows from both our theoretical calculations (13) and experiments, the pit height
zp increases linearly with P in the region Tp PPP << , then saturates under further P
growth. The pit halfwidth ap gradually increases with the laser beam power P.
Fig. 7. Dependence of the exposed pit bottom (triangles, nm) and unexposed disk surface (squares, nm)
vs. the etching time tE for As40S60 layer (l = 457 nm, h0 = 305 nm, positive etching, laser power
P = 0,46 mW). Solid lines are our fitting (12) at s/nm 85,1 ,s/nm 18 =J=J ne , 50 =HH m
and 15
0 cm10 -»б , 02ббe »
Using atomic force microscopy (AFM), we examined the obtained microstructures.
At the chosen beam power region and exposure time, the cross-section of the photo-
thermo-transformed region is close to parabolic at small beam powers mW5,0£P (see
Fig. 9), whereas it flattens at higher laser powers [10–12]. The small discrepancy be-
tween the pit cross-section obtained using AFM (black curve) and the calculated one
0 30 60 90 120 150
50
100
150
200
250
300
Etching time tE , s.
unexposed layer, nm –
Pit bottom bP, nm –
R
es
id
ua
l t
hi
ck
ne
ss
, n
m
A. N. Morozovska, S. A. Kostyukevych
14
(blue curve) could be caused by the radial etching components neglected in our model
(12). It is clear, that the proposed model describes adequately the available experimental
data [8].
0 0,2 0,4 0 ,6 0 ,8
100
400
500
600
etching tim e 3 0s — ,
etch ing tim e 45s —
Laser po w er P , m W
FW
H
M
a
p,
nm
0,2 0,4 0,6 0,8
50
150
200
etching time 30s –
etching time 45s –
Laser power P , mW
PP 0
D
ep
th
z p
, n
m
Fig. 8. Pit depth and halfwidth FWHM vs. the Gaussian beam power for As40S60 layer ( nm 457=л ,
nm 3050 =h , etching time 30s (black triangles and squares) and 45s (grey triangles and squares)).
Solid curves are our fitting (13) and (10) at 9,10 =TkE Ba , mW 7,0=TP ,
s/nm 85,1,s/nm 18 =J=J ne (other parameters are the same as in Fig. 7)
Modeling of information recording and selective etching processes in inorganic resists
ISSN 1560-9189 Реєстрація, зберігання і обробка даних, 2005, Т. 7, № 3 15
ap = 249 nm, zp = 98 nm
ap
zp
Fig. 9. Cross-section of the cavity developed using positive etching of As40S60 layer ( nm 457=л ,
etching time 45 s, beam power 0,46 mW). The blue line is our fitting calculated in accordance
with expression (12) at 10 =HH m , 0ббe = , 10 =HHT
Conclusion
The rather simple analytical expressions (12), (13) for the pit height profile have
been derived. In the most important for CD recording case of photo-thermo-
transformations pits halfwidth and height are determined by the beam power, exposure,
radius 0r , optical absorption coefficients 0,ea , etching time and rate known for the re-
cording material. The proposed model quantitatively describes the characteristics of pits
recorded by a Gaussian laser beam in the thin chalcogenide layers of As40S60 composi-
tion [7, 8].
Evolved approach allows to select the necessary recording conditions in order to
obtain the pits with the optimum shape after positive selective etching of the chalcoge-
nide resist, which is useful for applications.
Acknowledgements
Authors are grateful to Dr A.V. Stronsky, PhD P.E. Shepeliavyi and PhD A.A. Ku-
dryavtsev for useful discussions of our model.
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Received 22.07.2005
Modeling of information recording and selective
etching processes in inorganic resists
Introduction
Fundamental equations
The characteristics of recorded pits
Conclusion
|
| id | nasplib_isofts_kiev_ua-123456789-50773 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-9189 |
| language | English |
| last_indexed | 2025-12-07T17:01:55Z |
| publishDate | 2005 |
| publisher | Інститут проблем реєстрації інформації НАН України |
| record_format | dspace |
| spelling | Morozovska, A.N. Kostyukevych, S.A. 2013-11-02T22:39:59Z 2013-11-02T22:39:59Z 2005 Modeling of information recording and selective etching processes in inorganic resists / A.N. Morozovska, S.A. Kostyukevych // Реєстрація, зберігання і оброб. даних. — 2005. — Т. 7, № 3. — С. 3-16. — Бібліогр.: 13 назв. — англ. 1560-9189 https://nasplib.isofts.kiev.ua/handle/123456789/50773 621.315; 592:539.213 Theoretical consideration and computer modeling of information pit recording and etching processes in chalcogenide vitreous semiconductors are proposed, namely we demonstrate how to record and develop information pits with the necessary shape and sizes in the inorganic resist using focused Gaussian laser beam and selective etching. It has been shown that phototransformed region cross-section could be almost trapezoidal or parabolic depending on the resist material optical absorption, recording beam power, exposure, etchant selectivity and etching time. Namely, during the laser illumination and thermal heating caused by it, photosensitive material is the quasi-equilibrium microscopic mixture of the transformed and nontransformed phases with different optical absorption coefficients: temperature dependent near the absorption edge «transformed» coefficient бe and almost independent coefficient α0 . If αe ≤ α0 e after thermal heating, the photo-transformed region «bleaches» and the pit depth increases more rapidly under the following laser power increasing. If αe > α0 , the phototransformed region «darkens» and the pit depth increases sub-linearly or even saturates under the following laser power increasing. Thus, almost parabolic or flattened pits appear when αe ≥ α0, whereas the pits with elongated tops appear when αe << α0. After illumination, the spatial distribution of photo-transformed material fraction was calculated using the Kolmogorov-Awrami equation. Analyzing obtained results, we derived a rather simple approximate analytical expression for the dependence of the phototransformed region width and depth on the recording Gaussian beam power, radius and exposure time. Then the selective etching process was simulated numerically. The obtained results quantitatively describe the characteristics of pits recorded by the Gaussian laser beam in thin layers of As₄₀S₆₀ chalcogenide semiconductor. Our model open possibilities how to select the necessary recording procedure and etching conditions in order to obtain pits with the optimum shape and sizes. Запропоновано теоретичний розгляд та комп’ютерне моделювання процесів запису інформації та селективного травлення в халькогенідних напівпровідниках. Змодульовано процес одержання інформаційних питів необхідної форми та розміру у неорганічному резисті, використовуючи сфокусований гаусівський лазерний пучок та селективне травлення. Показано, що переріз фототрансформованої області змінюється від майже трапецієвидного до параболічного в залежності від коефіцієнта оптичного поглинання, потужності лазерного пучка, експозиції, селективності травника та часу травлення. Просторовий розподіл долі фототрансформованого матеріалу розраховано з рівняння Колмогорова-Аврами. Проаналізовано одержані результати й виведено досить простий наближений аналітичний вираз для залежності ширини та висоти фототрансформованої області від потужності лазерного пучка, його радіусу, часу експонування та селективності травника. Одержані результати добре описують характеристики пітів, записаних у тонких шарах халькогеніду As₄₀S₆₀. Модель відкриває реальну можливість добору умов запису та травлення резисту, необхідних для одержання пітів з оптимальними розмірами. Предложено теоретическое рассмотрение и компьютерное моделирование процессов записи информации и селективного травления в халькогенидных полупроводниках. Смоделирован процесс получения информационных питов необходимой формы и размеров в неорганическом резисте, используя сфокусированный гауссовский лазерный пучок и селективное травление. Показано, что сечение фототрансформированной области может изменяться от практически трапециевидного до параболического в зависимости от коэффициента оптического поглощения, мощности лазерного пучка, экспозиции, селективности травителя и времени травления. Пространственное распределение доли фототрансформированного материала рассчитано из уравнения Колмогорова-Аврами. Проанализированы полученные результаты и выведено достаточно простое приближенное аналитическое выражение для зависимости ширины и высоты фототрансформированной области от мощности лазерного пучка, его радиуса, времени экспонирования и селективности травителя. Полученные результаты хорошо описывают характеристики питов, записанных в тонких слоях халькогенида As₄₀S₆₀. Модель открывает реальную возможность выбора условий записи и травления резиста, необходимых для получения питов с оптимальными размерами. Authors are grateful to Dr A.V. Stronsky, PhD P.E. Shepeliavyi and PhD A.A. Kudryavtsev for useful discussions of our model. en Інститут проблем реєстрації інформації НАН України Реєстрація, зберігання і обробка даних Фізичні основи, принципи та методи реєстрації даних Modeling of information recording and selective etching processes in inorganic resists Моделювання процесів запису інформації та селективного травлення в неорганічних резистах Моделювання процесів запису інформації та селективного травлення в неорганічних резистах Article published earlier |
| spellingShingle | Modeling of information recording and selective etching processes in inorganic resists Morozovska, A.N. Kostyukevych, S.A. Фізичні основи, принципи та методи реєстрації даних |
| title | Modeling of information recording and selective etching processes in inorganic resists |
| title_alt | Моделювання процесів запису інформації та селективного травлення в неорганічних резистах Моделювання процесів запису інформації та селективного травлення в неорганічних резистах |
| title_full | Modeling of information recording and selective etching processes in inorganic resists |
| title_fullStr | Modeling of information recording and selective etching processes in inorganic resists |
| title_full_unstemmed | Modeling of information recording and selective etching processes in inorganic resists |
| title_short | Modeling of information recording and selective etching processes in inorganic resists |
| title_sort | modeling of information recording and selective etching processes in inorganic resists |
| topic | Фізичні основи, принципи та методи реєстрації даних |
| topic_facet | Фізичні основи, принципи та методи реєстрації даних |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/50773 |
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