BOSE CONDENSATION AND THE ATHERMAL NATURE OF PULSED LASER ANNEALING

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BOSE CONDENSATION AND THE ATHERMAL NATURE OF PULSED LASER ANNEALING

J. van Vechten

To cite this version:

J. van Vechten. BOSE CONDENSATION AND THE ATHERMAL NATURE OF PULSED LASER ANNEALING. Journal de Physique Colloques, 1983, 44 (C5), pp.C5-11-C5-21.

�10.1051/jphyscol:1983502�. �jpa-00223082�

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Colloque C 5 , suppl6ment au nO1O, Tome 44, octobre 1983 page C5-11

BOSE CONDENSATION AND T H E ATHERMAL NATURE OF PULSED LASER A N N E A L I N G

J . A .

Van Vechten

IBM Thomas J . Watson Research Center, Yorktown Heights, ,New York, U.

Abstract - I review the athermal, cold plasma annealing model and recent supporting data, including optical second harmonic generation (with Td symmetry from irradiat- ed Si), optical transients and acoustic.

I - Introduction The fundamental mechanism of the remarkable phenomenon known as pulsed laser annealing has been intensely controversial. So as not to obscure the scientific issues of the controversy with semantic misunderstandings, I will define a few key words in the sense that 1 use them. The word "thermal" means "pertaining to a state of matter which depends upon its temperature alone". "Temperature", T, is defined by

T = ( d ~ / d ~ ) - ' , ( 1 )

where S is the entropy and E the internal energy of the system; T is thus well defined whenever (1) can be evaluated regardless of whether or not the system is thermal. The word "heat" means "that portion of the energy of a system which is chaotic, i.e., charac- terized by random motion or, equivalently, the thermal portion of the energy". The energies of an oscillator, a battery, a spring, a reactive chemical, a flywheel or of the linear motion relative to the observer, being organized and predictable, do not contribute to the heat, or the temperature, of the system. (Both heat and temperature are independent of the frame from which the system is viewed.) The word "anneal" means "to heat to a moderate and slowly diminished temperature o r other equivalent process". The word

"quench" means "to cool rapidly from a high temperature1' and is the antithesis of

"anneal". Thus, the expressions "rapid thermal annealing" and "thermal processes far from equilibrium" are contradictions in terms.

For purist, e.g, mathematicians, randomness, the essence of heat, is difficult to verify. For example, the number a = 3.14159 ... is not random because it may be generated by any of several simple algorithms, but it would pass many experimental tests for randomness (e.g., all digits appear with equal frequency). This serves to illustrate the importance of the consistency requirement. (A fundamental theorem shows that the admission of a single inconsistency into any logical system would allow any conclusion to b e derived from any premise and thus would result in total collapse.) However many tests an hypothesis may pass, any exception suffices to require it be rejected.

In contrast to mathematicians, most physicists are pragmatists. Although they should realize that the purely random, "thermal", system is an absolute which is really never reached, physicists are tempted to make an "engineering approximationt1 of many systems as thermal because of the simplifications allowed by use of well established results of the mathematical study of the statistics of truly random systems and by use of accurate measurements made on the materials in question under near thermal equilibrium condi- tions. A practical physical criterion to distinguish a (hot) random system from a (cold) non-random one is needed to determine when this "engineering approximation" should be introduced. I contend that this should be whether all the material parameters behave in a manner indistinguishable from those of a truly random system with the same components

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983502

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and total energy. (Ion sputtering might be likened to billiards and thought to have both thermal and athermal components; a skilled billiards player may predict the motion of the balls through four or more collisions while the unskilled player may as well regard the motion as random after the first collision. After how many collisions does Nature give up predicting the motion?) As in the case of .rr, a system that passes the randomness test by many experiments ought to be regarded as non-random if it fails any valid test within the field of the study; otherwise the logical structure of the treatment will collapse.

One may obtain a relatively non-controversial initiation into the present subject from experiments that track in semiconductors initially at cryogenic temperatures /1-4/ the transfer of energy from a laser pulse to excited electrons, e-'s, to athermal phonons (first LO and then zone boundary LA or TA) and finally to thermal phonon distributions. With pulses into GaAs much less intense than those used for PLA, von der Linde et al. showed /1/ the characteristic time for energetic e-'s to excite LO phonons was re-LO < 2 ps and the characteristic time for these to excite the zone boundary LA phonons was rLO-LA(zb)

= 7 ps at 77 K. However, even after 30 ps this energy had not been thermalized; this was evidenced from the fact that the frequency of the zone-center LO mode had not shifted from its initial value to that characteristic of the final temperature to which the system would eventually rise. Ulbrich et al. and Wolfe and coworkers found /2-4/ that for GaAs or Ge initially below T = 4 K, the time to thermalize the LA phonons rLA(zb)-T 2 2 11s.

Indeed, van Driel suggested /5/ that such "phonon bottle-neck" phenomena might account for the remarkable (athermal) aspects of PLA.

One should expect that the net time to thermalize the energy of the initial excitation, re-*, would vary with the intensity of the (laser) excitation and with the total fluence. One might also expect

to decrease with increasing initial lattice temperature, TL. I suggest

that the remarkable aspects of PLA result from pulses of duration

< ^rc 5 re-T and, further, that r, - 200 ns for pulse intensities characteristic of PLA and for initial TL = 300 K. To support this I first note that Rutherford backscattering experiments by Okigawa e t al. / 6 / (Fig. 1) show a qualitative difference between the effect of 15 ns and of 600 ns laser pulses (at 532 nm or 536 nm) into GaAs or G a p initially at TL = 300 K.

The 15 ns pulses produce some damage which is independent of fluence, involves no phase separation, and is characteristic of PLA in compounds. (I have suggested that PLA is not as successful in compounds as in Si because of the formation of large numbers of antisite defects in the highly ionized solid as it recrystallizes.) The 600 ns pulses produce phase separation of the compound into its constituent elements and damage which increases monotonically with fluence. Whereas there seems to be, as Okigawa e t al. claim, a major

0.~1

Fig. 1 -

Okigawa et al. /6/

Rutherford backscattering.

laser tluence

.

athermal contribution to the damage produced by the 600 ns pulse, the result is qualita- tively similar to that expected from severe heating and quenching. (The thermal diffusion depth ( D T ) " ~ - 1.7 ym for

= 600 ns and the specific heat is about 2 J / c r n 3 0 ~ , so an absorbed energy density of 0.4 J/cm2, or about 0.7 ~ / c m ~ incident, would suffice to raise the surface to the congruent melting point (151 1 K) if the energy were thermalized within the irradiated volume. Note t h a t this crude analysis underestimates by about 40 % the fluence at which massive damage begins; this probably indicates the degree t o which the thermal energy density (heating) was overestimated.) This damage introduction should be compared to that reported by Chantre /7/ for Si irradiated for similar periods with a scanning CW-laser, which was well fitted with a realistic non-equilibrium solid phase heating and quenching analysis. (Of course, Si does not separate into constituent elements as do Gap and GaAs when heated without confinement of the more volatile element.) If the 15 ns pulse had produced similar or more severe heating and quenching, qualitatively similar, but perhaps more severe, damage would be expected.

Since its discovery, many investigators, including this author, have found experimental grounds, such as Fig. 1, to conclude that the PLA effect is athermal /8-18/. The most fundamental ground was that the material effect was entirely unlike ordinary quenching but rather similar to gentle, thermal annealing, although it was obviously not a slow process. (Hence the term "laser annealing". /8/) T o account for this, there was (in addition to van Driel's "phonon bottle neck" hypothesis / 5 / ) first developed a "hot plamsa annealing", HPA, model /19,20/, which invoked the previously established mechanisms of optically induced dislocation glide / 2 1 / , ionization and recombination enhanced point defect migration /22/, and reduction of the sheer modulus of the covalent lattice by excitation of e-'s to antiboding states /23/ to the point that a "cool liquid"

phase distinctly different from the ordinary melt (Si at 1685 K) is formed /19,24,25/.

The HPA is a one-electron approximation model. However, the excited carrier density, N, induced by PLA pulses was estimated /20/ to be 4 x 1 0 ~ ~ cmu3 so the importance of many body effects should have been expected.

Indeed, several experimental observations compelled the formulation of a second, athermal plasma model /25-27/, the cold plasma annealing model, CPA, in which many body effects, in particular, a Bose condensation, play a leading role. (It should be noted that Nagy and Noga /28/ reached a similar conclusion from very different data and reasoning.) The Bose condensation hypothesis contains two parts - the formation of the

"Bogoliubons", the quasi-bosons that may condense, from the fermions of the one electron approximation and the condensation of these Bogoliubons. The Bogoliubon of the CPA is the metastable exciton /29-32/ produced by the very strong coulombic attraction between

Fig. 2

Aspnes and Studna /33/

Real and Imaginary

Dielectric functions

of Si.

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one electrons states separated by energies corresponding to the zero-crossing of and the corresponding spike in c2, known as the E2 peak of the interband absorption spectrum.

See Fig. 2, which is adopted from /33/. This metastable exciton has been called by several names over the last 21 years; recent authors /31,32/ call it a "Frenkel exciton". I use this name because of close similarities between the effect of this metastable exciton and the long studied effect of stable Frenkel excitons in alkali and silver halides /34/.

A consequence of the Bose condensation of the CPA model is that, due to the condensa- tion and binding energies, neither the exciton itself nor the e- and hf from which it is composed can be scattered out of the macroscopic state to which it condensed by interac- tion with the lattice phonons. Just as the supercurrent carried by a superconductor flows without dissipation t o the metal lattice, so the Bose condensed excitons would not dissipate their energy to the semiconductor lattice. This is offered as the best explanation to date for the absence of rapid heating of the lattice during PLA that is demonstrated by Raman scattering measurements / 17,18/.

Others have seen fit to assume /35-40/ that the laser energy is thermalized in a time short compared to all but the shortest laser pulses now available; i.e.,

<

lo-''

I will herein review data that is inconsistent with the thermal hypothesis and supportive of the cold plasma annealing model.

11 - Differences between Molten and CPA Phases

Let us begin by enumerating the differences between normal, thermal molten Si and the athermal liquid, CPA phase of Si. These differences are listed in Table 1. A few clarify- ing remarks about the table follow. Re density, the value shown for the CPA density is that of the CPA solid at the critical density, Nc = 4 x 1 0 ~ ' cm-3 for TL = 600 K /25/, for

TABLE 1

Differences Between Thermal and CPA Liquids (Si)

Thermal CPA

Temperature Density Coordination Symmetry Energy Density Phase Transition I m ~ u r i t y Segregation 3.35 pm Opt. Absorp.

Particle Loss

xtal + 15 % xtal - 1 %

- ^{8 4}

None

7 . 1 x 1 0 3 ~ / c m 3 5 . 7 x 1 0 3 ~ / c m 3

Strictly First Order Weakly First or Second Order

BSP BSP - A Qausi-Ef

Evaporation Sputtering

thermionic e- photo + thermionic

L large E field

the phase transition to the "cold plasma liquid". Density is given relative t o the normal crystal at room temperature. This CPA density, which corresponds to the normal crystal density a t 1000 C , was calculated /41/ using Pauling's bond-order to bond-length relationship. (The Figielski-Gauster effect /42/ of carrier excitation upon bond length in semiconductors is well established.) At N = 4 x 1 0 ~ ~ cm-3 within the CPA liquid, the same formula would predict the CPA liquid to be 8 % less dense. (Thus, the CPA liquid density would be about the same as that of amorphous Si, a-Si, which is typically 10 % less dense than the crystal.) While the estimate for the solid might be accurate to + 30 ^%, the extrapolation to the liquid might error by more than a factor of 3. Re energy density, the CPA value, 80 % of that of thermal melting, follows from the observation that the kinetic energy of the atoms contribute only 20 % to the thermal value (none of the latent heat of melting and half the sensible heat t o raise TL to 1685 K), the major part being contributed by the electrons that must be excited out of bonding states (latent heat) or provide the potential energy part of the lattice vibration energy (sensible heat). The two liquids both have the bonds broken to a similar degree, so the difference is the kinetic energy of the atoms. Re the impurity segregation, a well accepted theory for the effect of crystal growth rate upon impurity incorporation was given /43/ by Burton, Prim, and Slichter (BPS); Hoonhout has shown /44/ that extrapolation of this theory t o PLA using thermal model does not predict observed dopant incorporation. It is also known that impurity incorporation is strongly affected by the ionization levels of the dopant and the position of the quasi-Fermi levels at the growth interface; it can be greatly increased by splitting the quasi-Fermi levels with ionizing radiation /44,45/. Thus, /19/ interpreted the greatly enhanced solubility of dopants in terms of the ionization of the recrystallizing material.

I11 - Measurements of Lattice Temperature

The lattice temperature, TL, is by definition the temperature which characterizes the excitation of lattice phonons. Provided that the phonons are thermalized, i.e., random, a measure of the phonon excitation level suffices to determine TL unambiguously. Also, if the phonons are thermalized, then it does not matted whether one measures their popula- tion at the zone center of the optic branch, as in ormal Raman scattering, or at the zone

P

boundary, as in second order Raman scattering, o anywhere else within their distribution.

If it should be determined that phonon population does vary in an athermal manner through the zone, as was found in /1-4/, then only a portion of the lattice excitation is heat and TL is & than would be inferred from the average phonon population.

As has been noted before, direct measurements of the zone center optic phonon population by Raman scattering find T - 600 K in agreement with the CPA prediction and contra- dicting the hypothesis that tke thermal approximation is applicable. While adherents to the thermal approximation have questioned the calibration of these measurements, those questions were decisively answered in Ref. /17/ and elsewhere; in addition t o the best calibration technique under the exact conditions of the measurement using the Principle of Time Reversal Invariance, calibration with furnace heated samples and with CW laser heated samples give similar results and all contradict the thermal model.

There has also recently arisen the speculation that the laser heating might be extremely

inhomogenous producing cool solid regions between regions of normal molten Si. Such an

hypothesis has been offered within the thermal model to explain surface ripples that are

observed after certain types of PLA. Adherents t o the thermal model suggest the Raman

determined TL characterizes only the cool bands between the severely heated and molten

bands. One reason to discount this hypothesis is a complete absence of surface ripples

from the samples of /17,18/. Another is that such inhomogenous heating would produce

lateral stresses that would introduce dislocations and other damage not found in the very

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strain-free and defect-free (well "annealed") final surface. A conclusive reason is that, when the experiment was done with samples that initially were amorphous /13/, the measured TL was similar (higher only by an amount corresponding to the energy of crystallization of a-Si) and was obtained from the first appearance of a crystalline Raman spectrum, which had to have come from the first material to have crystallized from the irradiated zone; there was no other crystalline surface present.

It has also been claimed that T could be inferred from transient x-ray scattering estimates of the lattice constant /47-49/L The assumption that lattice constant is uniquely correlat- ed with T is spurious, as demonstrated by the Figielski-Gauster effect /41,42/. Note that the ekctronic excitation of Si to moderate levels leads to a contraction that might reach 0.1 % /SO/. Thus, with purely electronic excitation, one would observe during PLA a slight contraction followed by the expansion indicated in 11. /51/ reports seeing this contraction at the onset of a 3 0 ns PLA pulse by means of acoustic measurements with a (very short) 10 ns response. /47,48/ do not report this contraction, but their data for a B doped surface layer has been interpreted /49/ in this way and were admitted to be inconsistent with the thermal model /47/. (The technique of /47,48/ suffers from the fact that it samples about 50 pm of the surface and is probably not as sensitive a measure of density changes as the acoustic techniques.)

Furthermore, /49/ pointed out that the thermal interpretation of the x-ray scattering data of /47/ violates a boundary condition, Conservation of Energy, and a condition on the second derivative of the TL profile, d 2 ~ /dz2. In their third rendering of these data, the authors of /48/ claim t o have resolved tkese discrepancies. However, thier revised T,(z) curve still fails to agree with the simple thermal approximation in that the gradient in the near surface region (e.g., after recrystallization) is too steep to be given by thermal diffusion with the known diffusivity of Si; the region where dTL/dz - 0 should have a width

x 1 pm for

= 5 0 ns after the end of the liquid phase whereas the newly reported width is about 0.3 pm. Note that because the two hypothesises predict about the same degree of expansion, measurement of the maximal lattice constant does not serve to distinguish between them. This author proposed that the best criterion to distinguish between these models with this x-ray data would be through the magnitude of the gradient of the lattice constant near its greatest value. (This gradient is much steeper in the CPA than in the thermal model because of the self-confinement of the dense plasma and rapid variation of bond length with N near Nc.) As already noted /49/, by this criterion these data also strongly favor the CPA hypothesis.

It should also be noted that acoustic measurements have not detected the violent contrac- tion, AV/V = 25 % from a-Si, that would occur if the molten phase formed /10,27/

except for fluences above the annealing regime and into the damage regime.

1V - Symmetry

According to the CPA theory /25-27/, the electrostatic dipolar interaction between the

Frenkel excitons causes them to align with the same Td symmetry as, e.g., Gap. (Recall

that the localized holes are concentrated in the bond sttes and the highly localized elec-

trons are at the corresponding antibonding site on the other side of one of the two atoms

of that bond; thus, a translation by half the bond length along that (1 11) axis would place

a + charge on one Si atom and a - o n the other, as if they had been transmutated into a

111-V pair.) Provided that the atoms of the sample are not violently displaced by the

irradiation but retain their coordination and basic structure, i.e., behave as a "liquid

crystal" through the irradiation, the sample should the display diffraction and optic

properties of a Td lattice. On the other hand, if the sample is amorphized t o the normal

4-fold coordinated amorphous state, then those properties depending on long range order

should be lost. Of course, if the sample were to transform to the normal molten state, both long and short range order and their concomitant effects would be lost.

Optical second harmonic generation, SHG, is forbidden by inversion symmetry in the bulk of crystal Si. Due to a lack of long range order, SHG would be very weak and isotropic in a-Si or in molten Si. Surfaces can produce SHG; such contributions are easily distin- guished from bulk contributions by their lack of directionality and would be isotropic in the absence of long range order. The allowed third order optical susceptibility of Si combined with a strong static field gradient could produce SHG of definite symmetry in the crystal but would be isotropic in the absence of long range order. Thus, observation of bulk SHG is a definitive indication of long range order and test for symmetry.

Indeed, Guidotti et al. /52,53/ have found (Fig. 3) SHG from irradiated Si (about 1 0 % the magnitude of Gap) and verified that it; i) is a bulk rather than surface effect; ii) that the data is understood in terms of a second order susceptibility of Td symmetry; iii) that a second 10 ps pulse delayed by 8 ns from the first shows the same symmetry and magnitude SHG as the first 10 ps pulse, which was sufficient to leave the surface in the liquid (liquid crystal) phase for much longer times ; and iv) SHG is unaltered in symmetry or strength if a thin surface layer is amorphized by a previous pulse, but is drastically reduced if the surface is damaged (pitted). Thus, also with respect to symmetry (and thus coordination number), data are consistent with the implications of the CPA and contradict the thermal approximation.

I S i : ( I l l ) FACE

T

Fib. 3 -

Driscoll and Guidotti /53/ Optical Second Harmonic Generation variation With Azimuthal Angle

V - Order of the Phase

An increase in surface reflectivity, which adherents to both models ascribe to the phase transition to their respective liquids, is usually, but not always, concomitant with the PLA process. Thus, a surface reflectivity transient is assumed to give information about the kinetics of the transition.

First order phase transitions must be nucleated and will propagate at a rate that depends on the difference in free energy of the two phases. For example, the normal melting or freezing of Si propagates at 6 0 cm/s per degree of superheating or supercooling /54/.

Melting usually nucleates at edges or steps on the sample surface and can be very sluggish

if the surface is covered by an amorphous oxide, as is normally the case in PLA experi-

ments. For example, crystals so covered have been superheated more than 100 OC for

more than 1 0 minutes without nucleating the melt /55/. Thus, a strictly first order,

normal melting phase transition is expected to be sluggish on a scale of ns. Second order

phase transitions, as they do not involve a discontinuous change of any extensive parame-

ter, can occur simultaneously throughout large volumes and need not be nucleated at

special sites. Thus, a second order phase transition might be as rapid as the stimulus that

causes it. Weakly first order phase transitions are expected to be intermediately sluggish.

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While the original HPA hypothesis proposed a weakly first order phase transition, the CPA hypothesis implies the phase transition, a Bose condensation, could be either second order or (weakly) first order depending upon the ratio of the correlation length to the penetra- tion depth. That ratio is not yet clear. However, since the normal melting of Si is strictly first order, there is a clear distinction between the models. Thermal melting must be sluggish on a scale of ns and should require sufficient superheating ( > I 0 0

C) to have noticeable effect on the reflectivity of the molten phase /56/. Provided that the laser pulse is sufficiently short, the CPA implies a transition that is rapid on a scale of ns and relatively mild transients of TL and density.

On this point also the data /57,58/ decisively favor the CPA over the thermal model.

With 30 ps pulses von der Linde and Fabricius find the reflectivity attains its new value (Fig. 4) in 50 ps and then holds steady for the duration of the liquid (crystal) phase, about 100 ns /57/. There is no evidence of a reflectivity transient that would be consistent with the change in density or the superheating and subsequent cooling back to the melting point that the thermal hypothesis would require. (This point is treated in detail in / 2 7 / . ) With 90 fs pulses, Shank et al. observe /58/ even faster reflectivity transients, which are quite inconsistent with the normal melting, first order phase transition.

VI - Conclusions

Among the other distinctions between the two models of PLA listed in Table 1, some, namely the energy density required to induce the new phase and its infrared absorption, are so similar that most measurements would not be able t o distinguish. Observation of particle loss also decisively favors the CPA over the thermal model /15,27,34,59,60/, but space does not permit a review of that subject.

At least in this author's opinion, the evidence is conclusive that there is no logical integrity to descriptions of the PLA process within the thermal approximation. Questions remain as to the nature of the true process, e.g., whether it should be described as a superfluid or a persistent charge density wave and whether the quasi-Bosons are in fact the Frenkel excitons described in /31,32/ or some type of small polaron. I hope that the subject will remain sufficiently interesting that these somewhat academic questions will be resolved.

Of course, this does not mean that an "engineering approximation" cannot be introduced which uses some of the structure of normal thermal treatments and "empirically adjusts"

the thermal constants as needed to force a fit to the data at hand. Indeed, Gunn effect and other electron transfer devices made of GaAs were in fact engineered and brought to the market place with an entirely false assumption about the order of the conduction band valleys critically involved /61/. Scientists must accept that it is not really necessary to understand processes to use them. look

Fig. 4 -

1.06 pm Optical Transients for 30 ps 532 nm PLA (175 % of threshold) from /57/.

DELAY

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