J . Phys. Chem. 1984,88, 3048-3051
3048
Theory of Etching of Polymers by Far-Ultraviolet, High-Intensity Pulsed Laser and Long-Term Irradiation H. H. G . Jellinek* Department of Chemistry, Clarkson University, Potsdam. New York 13676
and R. Srinivasan IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598 (Received: November 9, 1983)
The empirical functional relation between final depth of a hole and intensity of a far-UV laser pulse (A = 193 nm; 7 = 14 ns) has been derived on the basis of polymer degradation kinetics for random scission, depolymerization, and mending of main chain links (cage effect). The respective degrees of degradation have also been given. The experimental results for poly(methy1 methacrylate) have been analyzed in detail. The theory is also valid for any hole formation by long-term irradiation (including soft X-rays) provided heat is not evolved and pure photolysis takes place.
Far-ultraviolet photolysis of polymers has not been studied to any great extent. High-intensity far-UV laser (excimer) photolysis is just beginning to attract attention. During pulsed laser photolysis of solid polymers, so far investigated in the far-UV region (A N 200 nm), Srinivasan and co-workers have shown’ that well-defined holes are directly generated which will be suitable for electronic devices and for lithographic purposes. A laser was used in this work emitting a pulse of 14-11s half-width at a wavelength X = 193 nm. Material is ejected spontaneously from the irradiated polymer. The final depth of a hole is a function of the incident intensity or fluence, respectively. Technique, experimental details, and results will be communicated in a forthcoming publication.2 The present paper deals with the derivation of the functional relationship between final hole depth and incident fluence (or intensity) on the basis of polymer degradation kinetic^.^ It is shown that the empirical relation between final depth and incident fluence results directly from such a derivation. This also holds good for long-term irradiation. Hole Formation by Pulsed Far-UV, High-Intensity Laser Radiation ( A = 193 nm; T = 14 ns) Solid poly(methy1 methacrylate) (PMMA), polycarbonate, poly(ethy1ene terephthalate) (Mylar), and polyimide (Kapton) were exposed to such pulses. All these polymers follow the empirical relation
m is the slope of the straight line of lf vs. In Fo;FTR is a threshold value for the fluence, at which hole formation just starts or stops, respectively; Fo is expressed in mJ/cm2 and 1, in micrometers. All values are normalized to a cross section A 1 cm2. The primary quantum yield, 4, for main chain link rupture is assumed to be unity. The polymer should actually be initially homogeneous (one chain length only), but operating with number-average values is a good approximation. Figure 1 shows the If vs. In Fo plots drawn through the experimental points. Random Rupture of Main Chain Links. The rate of rupturing of such links, n,, is proceeding completely statistically (Le., at r a n d ~ m ) .The ~ links at 7 = 0 are designated by n. The rate of breaking links at depth 1 is given by dn,/dt = klzT,/= k l ( F T , r / 7 links/(cm2 ) s)
(2)
(1) R. Srinivasan and V. Mayne-Banton, Appl. Phys. Lett., 41,576 (1982); R. Srinivasan, J . Vac.Sci. Technol. B, in press. (2) R. Srinivasan and B. Braren, J . Polym. Sci., in press. (3) H. H. G. Jellinek, “Encyclopedia of Polymer Science and Technology”, Vol. 4, Wiley, New York, 1966, pp 740-93; H. H. G. Jellinek, Aspects of Degradation and Stabilization of Polymers”, Elsevier, Amsterdam, 1978, Chapter 1, pp 2-38; H. H. G. Jellinek, J . Polym. Sci., 62, 281 (1962).
0022-3654/84/2088-3048$01.50/0
-
Here IT,/is the transmitted light intensity in mJ/(cm2 s) at depth T the pulse duration, kl is a rate constant in links/(mJ), and A = 1 cm2. If Beer-Lambert’s law holds, eq 2 becomes
1, FT,! in mJ/cm2 is the corresponding fluence,
dn,/dt = klI0e-@/= kl(Fo/T)e-p‘
(2a)
Here Io and Fo are the incident intensity and fluence, respectively, p = c’-[n]is the absorption coefficient for main chain links, n, in bum-’ at X = 193 nm, and e is the molar absorption coefficient if [n] is expressed in mol/L of links at 1 in a volume element dl (here I is in centimeters, i.e., e is in L/(mol cm)). Experimental facts of laser irradiation2 and consequences of its theory agree with the assumption that Beer-Lambert’s law is obeyed. The number of broken links at 1 [Le., n,(l) for the pulse time T] is obtained by integrating eq 2a with respect to n, and t
n,(l) = klZoe-@‘T= klFoe-Pc
(3)
n,(l) can be considered as the broken links in a volume element dl; IoTe-@/or Foe-@I,respectively, is then the intensity or fluence having entered this volume element per cm2 during 7 s. The intensity or fluence must be large enough to break all main chain links in the volume element producing monomer only, or alternatively it must break a large fraction of these links, generating fragments small enough to be ejected (Le., dimer, trimer, etc.). The kinetics of photodegradation of polymers is utilized in this c~ntext.~ The more links are ruptured, the more monomer or fragments will be ejected. Hence, the volume ejected is proportional to the number of main chain links ruptured ( A 1 cm2) n,(l) = k, d l (4) kv (crnw3)is a constant of proportionality. Combination of eq 4 and 3 gives k, dl = klIoTe-@’= k , Foe-@/
(5) In the following, all calculations will be carried out with fluences only. Equation 5 can be integrated between I = 0 and if
is the threshold value. This can be rearranged to
FTR
(7)
Multiplying the right side of eq 6 by FTR/FTR gives
e@‘(--1 = ( F T R ~ ~ P / ~ V ) ( F O /-F1) TR 0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol, 88, No. 14, 1984 3049
Theory of Etching of Polymers But
FTR
= FOe-arf;hence
.2
(earl - l)/(earf - 1) = 1 = F T R k l @ / k v Hence, eq 7 simplifies to the empirical eq 1, where m = l/p.
If = ( I / @ ) In (FO/FTR) pm
(8)
Equation 8 can also be expressed in decadic logs; then the absorption coefficient is p/2.303. It should be noted that the pressure of 0, has no effect on the results as the process is too fast for diffusion of this gas into the polymer. Random photolysis by long-term irradiation results also in eq 8; Fofor this case stands for the fluence of the whole irradiation time tR (or rotR= F,);this holds also for FTR. Detailed Analysis of the Pulse Photolysis. Results for PMMA The results were taken from the straight line through the experimental points. They are as follows: Fo(mJ/cm2), 100, 60, 40,20, 17.22; 1, (pm), 0.14,0.10,0.067,0.011,0; pk,./K, (cm2/mJ), 0.059, 0.058, 0.058, 0.052, average 0.057. Hence, 0 . 0 5 7 F ~=~ (0.057)( 17.22) = 0.99 1.O. This indicates the accuracy of the experimental data. The p k , / k , values were calculated by using eq 7. The energy of one photon (A = 193 nm) is given by
E = (1.980 X 10-1s)(103)/(1.930 X lo3 A)= 1.026 X
mJ/photon
Table I gives the respective numbers of photons absorbed (calculated from cfo(l - e-p');fo stands here for fluence in terms of number of incident photons/()ulse cm2) for a potential hole of depth If; also the respective numbers of broken and intact (Le., at t = 0) main chain links and corresponding degrees of degradation a are included; e.g., for FO= 60 mJ/cm2, a = fN/(DPdV); here f is the average number of links ruptured in one original chain molecule and N is the number of chains in volume 0 If. If DP, = 2 X lo3, for instance, then S = 1140 and the ejected chain is given by bP = DP,/(f + 1) = 1.75, Le., almost a dimer on the a ~ e r a g e .The ~ a values indicate that for FoC 200 mJ/cm2, dimer and trimer are ejected on the average. If, for instance, dimer is ejected, k , and k , are halved Le., k J k , = constant. Similar considerations hold for trimer, etc. Laser irradiation is expected to follow the kinetics of photodegradation. The data presented above for PMMA, for instance, can be accounted for by the theory proposed here. A few remarks have to be made about calculating the number of main links in a chain polymer. One unit mole of PMMA weighs 100 g. Its density is 1.19 g/cm3. Hence, 1 cm3 contains (1.19 g)( IO-, unit mol) equal to 1.19 x IO-, mol of links (a volume of 1-pm deplh has 1.19 X 10" unit mol of main chain links or (1.19 X (6 X loz3links)). The speed of ejection will be affected by the size of the fragments. However, this is not expressed in eq 8 and will not influence hole formation (except for a possible cage effect) as long as the fragments are small enough for ejection. Equation 8 can be written in a more general form
-
d r
= Wr, = ( P / @ In (Fo/FTR)
is the weight of the ejected material in grams for a depth of 1 pm, and W,, the weight loss due to a hole of depth If.
p
Absorption Coefficient p (PMMA) p can be expressed in cm-' instead of pm-'. Chromophores in PMMA are methoxycarbonyl groups. The moles of main chain links equal the moles of chromophore groups. The concentration is 1.19 X 10' mol/L main chain links. Hence, the molar extinction coefficient E amounts to E =
12.43 X lo4 cm-' = 1.045 X lo4 L/(mol cm) 1.19 X 10' mol/L
for qglq= 0.45 X IO4 = c/2.303 L/(mol cm). This value is of a magnitude usually found for wavelengths near X = 200 nm. The
.1
'f P"
( m J/c
m 2)
Figure 1. I f (rm)vs. In Fo (Fo in mJ/cm2): (B) poly(methy1 methacrylate); (Q) polycarbonate, ( 0 )poly(ethy1ene terephthalate) (Mylar); (A)polyimide (Kapton).
percentage of incident radiation absorbed for If = 0.1 pm equals 71% and for 0.2 pm 97%. All the above named polymers exposed to the laser pulse obey eq 1 (see Figure 1). The relevant parameters are given in Table 11. Whether the variations in the threshold values are real or due to experimental variations cannot be decided at this juncture. If they were real it may be due to 4 # 1, cross-linking or the cage effect. It would not be useful discussing here the very scanty information available concerning far-UV photolysis of polymers. The same equations are valid for long-term irradiation of polymers. Instead of 7,the total radiation time t R has to be used. Etching of PMMA resists by radiation from a D,-discharge lamp in the region of X = 180-290 nm has been investigated by Ueno et aL4 (see Table 111). Material was ejected on irradiation generating a hole. Their results have been taken from the published curve through the experimental points. (The graph is rather small and the values are therefore not highly accurate.) The experiments were performed under vacuum at 25 "C as 0, affects the results. The total power of the source was ca. 7 mJ/(cm2 s) for X = 180->290 nm and the partial power for X = 180-290 nm was only 2 mJ/(cm2 s). The plot of If (pm) vs. In F, gives a good straight line: for total power, p = 10.9, FTR = 665 mJ/(cm2 s); for partial power, p = 16.7, F T R = 992 mJ/(cm2 s). The corresponding values for the laser are as follows: @ = 12.43, FTR = 17.22 mJ/(cm2 s); total power, 7.94 X lo9 mJ/(cmz s). Also cases can be dealt with by the theory where the exposed polymer has to be dissolved instead of being ejected as long as heat is not developed during irradiation. The theory deals with photolysis and not with the removal of the irradiated polymer. However, during long-term or high-power irradiation there is always the possibility of changes in the molecular extinction coefficient with exposure time. The absorption coefficient of PMMA at ca. 193 nm has been given by Mimura et al.,5who have also published the absorption spectrum of PMMA in the range of wavelengths X = 180-260 nm. The absorption has a maximum at 215 nm and a minimum at ca. 190 pm. The corresponding absorption coefficients are ca. 0.27-0.47 pm-' at the maximum and about 0.046 pm-] at the minimum. The absorption coefficient of the present theory at X = 193 nm is p/2.303 = 5.4 pm-'; Le., practically 100%of the radiation is absorbed by 1 pm of polymer (for 0.1 pm, 7 1% is absorbed). Fox and co-workers6 have shown that the absorption increases very appreciably during irradiation. (4) W. Ueno, S. Konishi, K. Tanimoto and K. Sugita, Jpn. J. Appl. Phys., 20, 709 (1981). ( 5 ) Y. Mimura, K. Ohkuba, T. Takeuchi, and K. Sekikawa, Jpn. J . Appl. Phys., 17, 541 (1978). See also B. H. Lin, J . Vac.Sci. Techno[., 12, 1317 (1975). (6) R.B. Fox, C. G. Isaacs, and S . Stokes, J . Polym. Sei., Part A, 1, 1079 (1963).
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984
3050
Jellinek and Srinivasan
TABLE I: Parameters for PMMAa
F,,mJ/cm2
4, fim
FTR?mJ/cm2
100 60 40 20
0.143 0.10 0.0673 0.01 1
17.00 17.34 17.32 17.44 17.22 (av)
FabsrC mJ/cm2 82.8 42.8 22.8 2.8
1 0 - ~ ~ ( n 0of. broken links)d 0.81 0.42 0.22 0.027
1 0 - ~ ~ ( n 0of. links at t = O ) e 1.03 0.717 0.482 0.079
"0 = 12.43 @rn-', 7 = 14 ns, X = 193 nm. b=Foe-@'f.'=FO(l - e-@'f)= Fo - FTR.d=no. of photons absorbed in 0 of broken links)/(no. of links at f = 0).
cr'
I/" 1.27 1.74 2.17 2.9
0.79 0.57 0.40 0.34
-
If (6 = 1). e I n 0
-+
I,. f(No.
TABLE II: Parameters for Pulse Photolvsis of ExDosed Polymers PET"
12.43
polycarbonate 18.49
13.31
Polyimideb 15.71
17.22 1.19 100 1
37.34 1.2 258 1
45.60 1.38 177 2
54.0 1.42 354 4
1.05
3.62
3.41
14.6
PMMA
PP m i ' ; io4@,cm-' FTR, mJ/cm2 400C,10 g/cm3 MI of repeat unit no. of chromophores per repeat unit, i.e. >C=O groups lo+€, L/(mol cm)
"Mylar. bKapton. 'Reciprocal slopes of straight lines in Figure 1.
TABLE 111: Analysis of Results of Long-Term Irradiation of PMMA' exposure time, s 6000 4800 2400 924
4:
w-n
0.2 0.19 0.146 0.1
0' 0
fluence, mJ/(cm2 s) total partial power power 42 000 33 600 16 800 6 468
Figure 2.
0.00
a vs. 1 (or L ) for F,
0.12 0 16 I (pm)
0.20
0.24
= 100, 60,40,20 mJ/cm2 trimer produced
at IF
12 600 10080 5 040 1 640
Figure 2 shows CY (for Fo = 100 and 40 mJ/cm2) plotted vs. 1 or L, respectively. Trimer is the average product ejected near lf. It has a molecular weight of 300 and its rate of vaporization will be extremely slow at 25 OC (ca. 6 X g/(cm2 s)).* Also
Depth of hole.
This will also be the case during the very high power irradiation by the laser pulse. This radiation will, to a large extent, pass through exposed PMMA, which by then will have an absorption much higher than that of the original spectrum at X = 193 nm. X-rays having energies of a few keV also follow Beer's law. Feder, Spiller, and Topalian,' for instance, have investigated PMMA exposed to X-rays of X = 8.3 A. The results can also be represented by eq 1. Degree of Degradation a Breaking links does not cease at If, but the fragments become too large to be e j e ~ t e d .The ~ rate of breaking links at L (here Lo = 0 corresponds to If and L > Lo) is given by
n,(L) = fTRe-OL (9) is the transmitted fluence at Lo = 0 (Le., lE)equal to the threshold value in numbers of photons/cm-2 during pulse time r. The degree of degradation a is obtained by dividing eq 9 by the total number of main chain links at t = 0 in the volume element dL at L ( A = 1 cm2)
fTR
aL = fTRe-PLdL/(no dL) = ake-PL
I
004
(10)
More accurately, eq 10 should be expressed by the fluence entering a volume element minus that leaving it fTR[e-OL- e-O(L+dL)] fTRe-BL(1 - e - W ) aL = (loa) no dL no dL As long as a volume element dL is involved, eq 1Oa is equivalent to eq 10. However, for numerical evaluation of C Y , a volume AL is taken and then the following equation has to be used: aL = fTRe-PL(1 - e-@AL) /(noAL) (7) R. Feder, E. Spiller,and J. Topalian,Polym. Eng. Sci., 17, 385 (1977).
cy,
= a,,,e+
(lob)
In eq 10, no is the number of main chain links in a volume unit at t = 0 and ah is the degree of degradation at L = 0 (Le., at If), which is the largest of all L values. Equation 10 can be integrated
Also
Long-term irradiation gives the same equations. Depolymerization There is another important, fundamental degradation process for long-chain polymer molecules, the so-called depolymeri~ation.~ In this case, one or both chain ends must consist of strong chromophores; Le., they must be photolyzed very much faster than main chain links. As soon as one chain end has absorbed a photon (&rimary l), the chromophore is activated or a chain end radical is produced and the whole chain unzips at once to monomers. Hence, for one photon absorbed, DP, - 1 N DP, main chain links are broken in each chain molecule. The rate of activating chain ends or producing radical chain ends, n,, in the system, is given by dn,,/dt = 2klF'T,,/r (12)
The factor 2 is here due to the possibility of one photon being absorbed by one of the two chromophores in a chain. (8) L. A. Wall, NBS Spec. Publ. ( U S . ) , No. 357, 47 (1972).
The Journal of Physical Chemistry, Vol. 88, No. 14, 1984 3051
Theory of Etching of Polymers However, for each “ruptured” chain end, DP, main chain links are broken
= dn,/dt = 2klDPOFT/7= 2klDPoFoe-f’[n*]//~ (13) Here ne,, = n,/DPo; 6’ is the molar absorption coefficient of the chromophores and ne is the concentration in mol/L of chain ends (chromophores) in the volume element dl at I ; further €’[ne] = d(DP,n,,)/dt
p’.
If k2 >> k3 (this the usual case), then As before, eq 19 leads finally to
The corresponding degrees of degradation a’, and d Lare
Equation 13 results finally, as was shown before, in
If = - In p’
(
2DPo)R: :
p’ is the absorption coefficient for chromophores in Km-l. It can again be shown that (klp/kv)F’TR= 1. There is an important variation of this process. The primary act (Le., rupture) consists in random splitting of one main chain link (dprimary = 1); as soon as this happens, the two fragments completely unzip to monomer. Here the photon has a choice of splitting one of the DPo links. The rate of primary ruptures, np,r, is given by dn,,/dt = DPok1F$,,/7
Hence “’I _ ---
“I
k3
k2 + k3
(1 or
oll)dI
Further
(15)
Each primary rupture produces DP, scissions
Ffm = Fgp‘f. If the concentration of all the links ( t = 0) is taken, then E [ ~ , ] D P=~3( as in eq 8. Rupture and Mending (Recombination) of Links (Cage Effect) For relatively slow ejection, there may be a chance of mending links. The radical fragments produced by random rupture are first confined to a medium cage. There, many collisions of the radical ends take place and the possibility of mending the ruptured link is great. This is the so-called cage effecte9 If, however, appreciable excess energy is available, recombination cannot occur. Under normal conditions, mending of the geminate pair is much more frequent than escape, leading to permanent scission. The cage effect can be exemplified by
Effect of Wavelength lf of the finished hole will not change as long as the wavelengths remain in the far-UV region and the number of incident photons per cm2 and per second are equal for the wavelengths. But the excess energy as well as the speed of ejection will be functions of A.
The rate of permanently breaking main chain links is given by
Excess Energy” Any excess energy may appear as kinetic energy. Heat is likely to be produced during irradiation. The extreme rapidity of the process excludes transfer of heat beyond the dimensions of the potential hole. A paper concerning this topic from the standpoint of physics is in press.* Ejection can be visualized to be similar to exhausting gases from a rocket. Ejection starts very soon after the pulse has been absorbed. The excess energy appears as kinetic energy. Thus, in the potential hole, there is momentarily a highly compressed gas (or superheated liquid) at a “high temperature” ejecting so quickly that there is no time for heat transfer. Also the larger specific volume of the monomer compared to that of the polymer will play Some (&onomer = 0.94 g/cm3, dpolymer,PMMA,solid = l.19 g/cm3 at 20 O c ) . l o Molecules of average mass, m , will escape with a velocity u
dn,/dt = k3(cage)
c = [2(excess energy)/rn]’I2 cm/s
P + hv polymer chain
hT1l
G (R1”*R2) k2 cage; potential break
k3
RI + R2 permanent break (17)
The number of cages is obtained by the steady-state method
The direction of the ejected molecules will first be in line with the long axis of the hole, but soon the molecules will spread in air in all directions.
(cage)steady state = klFT,//(k2 + k3)
(18)
dnr/dt = k3klFT,//(k2 + k3)
(19)
Registry No. PMMA (homopolymer), 901 1-14-7; PET (SRU), 25038-59-9; Kapton, 25036-53-7; Kapton MON, 25038-81-7.
(9) H. H. G. Jellinek and J. J. Lichorat, Polym. J., 12, 347 (1980). (10) J. Brandrup and E. H. Immergut, “Polymer Handbook”, 2nd ed., Wiley, New York, 1975.
(11) B. Garrison and R. Srinivasan, J . Chem. Phys., submitted for publication.
