DENSE-PLASMA DYNAMICS DURING PULSED LASER ANNEALING

(1)

HAL Id: jpa-00219917

https://hal.archives-ouvertes.fr/jpa-00219917

Submitted on 1 Jan 1980

HAL

is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire

HAL, est

destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

DENSE-PLASMA DYNAMICS DURING PULSED LASER ANNEALING

Ellen Yoffa

To cite this version:

Ellen Yoffa. DENSE-PLASMA DYNAMICS DURING PULSED LASER ANNEALING. Journal de

Physique Colloques, 1980, 41 (C4), pp.C4-7-C4-13. �10.1051/jphyscol:1980402�. �jpa-00219917�

(2)

JOURNAL DE PHYSIQUE Cdoque C4, supplc3ment au n o 5 , Tome 41, mai 1980, page C4-7

Ellen J. Yoffa

IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, U.S.A.

Abstract.- The flow of energy from the laser to the lattice during pulsed laser annealing of Si is examined, with particular attention paid to the influence of the dense'plasma of hot, photoexcited carriers on-the manner in which this energy transfer occurs. Consideration of carrier thermalization and recombination at high carrier densities suggests that under certain conditions carrier diffusion may increase the spatial extent to which the lattice is heated and consequently decrease the rate of temperature rise near the surface.

Because it has recently been argued that simple-melting or strictly-thermal mo- dels for pulsed laser annealing of ion- implanted and amorphous Si cannot provide consistent explanations for a large body of experimental evidence, /1-3/ an important subject to be addressed is the manner in which the energy is transferred from the laser to the semiconductor lattice. Considera- ble theoretical and experimental investiga- tion of hot carrier relaxation on picosecond to nanosecond time scales in Ge / 4 , 5 / and GaAs /6-10/ has indicated that as carrier densities increase, the effects of carrier- carrier interactions grow in importance. In this paper, the influence of the dense plasma of photoexcited carriers on the laser-to- lattice energy tranfer will be examined.

previous calculations have been performed which assume that the laser energy is depo-

sited in the lattice in the same region in which it is initially absorbed /11-15/.

However, consideration of carrier thermalization and recombination at high carrier densities suggests that under certain conditions, carrier diffusion may increase the spatial extent to which the lattice is heated and consequently decrease the rate of temperature rise near the surface.

Most of the laser energy is ultimately deposited into the semiconductor Aattice in the form of heat. However, the laser energy does not couple directly to the lattice but is instead initially absorbed by the

carriers, where it resides for a short time interval. During this intermediate step,

h his

work was supported in part by the Air Force Office of Scientific Research under

several mechanisms redistribute the carriers both energetically and spatially, thereby altering the original, absorbed distribution of energy before its final delivery to the lattice. The photoexcited carriers then thermalize and recombine by means of rapid Coulomb collisions. At the same time, they diffuse from the surface as a result of the large carrier gradients generated by the laser. An important point which shall be demonstrated is that these processes take place primarily within the system of carriers, thereby conserving the total carrier energy. It is then only through phonon emission by the carriers within the plasma that a significant amount of energy can be transf erred. The spatial distribution of this plasma consequently directly influences the spatial distribution of lattice heating.

Carrier redistribution in both space and energy occurs as the plasma responds to the driving forces set up by the laser- induced generation of carriers. The characteristic absorption profile causes large carrier density gradients resulting in diffusion of the carriers--and the energy they contain--inward from the surface. At the same time, because the carriers are origi- nally excited into nonequilibrium energy distributions, collisions among them lead to rapid thermalization and establishment of individual electron and hole distributions characterized by a common,temperature which is much higher than the lattice temperature. In addition, the high density of

Contract No: F 49620-77-C-0005.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980402

(3)

C4-8 ^JOURNAL^DE^PHYSIQUE

excess electron-hole pairs leads to recombination, which occurs primarily by Auger processes for high laser excitation rates. An electron and hole can recombine, giving their energy to a third carrier. The driving force for this recombination is the concentration of carriers in excess of equilibrium (at the carrier temperature) which results from the optically-induced splitting of the electron and hole quasi-fermi levels. Finally, owing to the large difference between the carrier and lattice temperatures, the plasma energy can leave the carriers altogether by emission of phonons. In general, therefore, it is necessary to examine the rates at which the several intercarrier processes occur in order to determine the spatial and energetic distributions of these excited carriers when they interact with the lattice.

It isimportant to recognize thatthe magnitude of the photon absorption rate, g, plays a crucial role in determining the physics of

the ensuing interactions For g

2

l ~ ~ ~ c m - ~ s - ~ , carrier densities N (N = 2Ne) attained du-

ring the laser pulse /16/ will in general exceed 10'~cm-~. As an example, a typical /17/ 10 nsr0.53pm laser annealing pulse of 1 ~ / c m ~ (i.e. 108w/cm2), corresponds to a surface absorption rate of g ~ 1 ~ 3 1 c m - 3 s - 1 , and therefore leads to ~ > 1 0 ' ~ c m - ~ . Because higher generation rates result in higher carrier densities, a number of important differences exist between the cases of low and high excitation. For high carrier densities (~>10'

,

/18/ the carrier-phonon scattering rate, which is proportional to N, is dominated by the rate of intercarrier collis~ons, which is proportional to iV2 and is found to exceed 1014 collisions/s. Addi- tionally, a hot carrier may lose a considerable fraction of its energy (-lev) due to collisions with other carriers, whereas only a small fraction of an eV is lost by phonon emission. /19/ Therefore, carriers thermalize among themselves long before they thermalize with the lattice. Also at high carrier concentrations, recombination is comprised primarily of nonradiative Auger processes /20/ (with rates proportional to N ~ ) as op- posed to the radiative recombination (with

rates proportional to lower powers of N) that occurs at lower generation rates. Fi- nally, higher values of g result in larger excited carrier gradients, thereby increasing the extent of carrier diffusion.

Because typical pulsed laser annealing ex- periments involve generation rates inexcess of 10~~cm-'s-', this paper will focus on the high excitation regime.

Thelaser energy is absorbedby thecar- riers via both electron-hole pairexcitation and free-carrier absorption. At the startof the laser pulse, the former process domina- tes, but as the free carrier density rises, its contribution to the absorption grows.

Because both mechanisms have characteristic N -dependent absorption lengths, the degree of excitation determines the details of the generated carrier profile. Both processes are phonon-assisted, but the amount of energy lost through phonon emission during absorption is negligible compared to the total energy absorbed per photon. The primary consequence of absorption, then, is the creation of a non-equilibrium distribution of very hot carriers which initially contains nearly all of the original laser energy.

Theelectrons' and holes will thenrapi- dly begin to relax to thermal distributions characterized by distinct quasi-fermilevels but a common temperature Te = Th which greatly exceeds the lattice temperature.

plasmons are emitted during this carrier thermalization process, /18,21/ most of which rapidly decay. Because plasmon energies exceed available phonon energies, the plasmons decay primarily by carrier re- excitation rather than by phonon emission.

(During a short period near the start of the laser pulse,theplasmafrequency passes through resonance with the phonons, but only a small amount of energy will be transferred in this manner /1'6/). In addition, it will be shown that some of the excess carrier energy is used to thermally popula- te plasmon modes. The entire carrier thermalization process, as a consequence of

the rapid carrier-carrier collisions at high carrier densities, occurs within

(4)

-

10-l4 s of excitation and does not involve appreciable transfer of energy from the carriers to the lattice.

At these high densities, Auger processes will dominate the carrier recombination /20/. Except at extremely large N, the recombination time falls as /22/ 1/iV2. Auger reduces the laser generation-induced separa- tion between the electron and hole quasi- fermi levels. However, the most important aspect of these processes is that the pair recombination energy is given to a third carrier, which then rapidly thermalizes with the remaining carriers through the means discussed above. As was the case for the phonon-assisted absorption processes, energy transferred to the lattice by any phonon emission accompanying the recombination is a negligible fraction of the total energy gained by the hot carrier. Consequently, althhugh the carrier number density changes, the carrier energy density does not. Because essentially all, of the energy is retained in the carrier system during absorption, carrier thermalization, and recombination, an interdependence is established between that energy and the carrier temperature and number density. The rela,tive amounts of pair creation and free carrier absorption, for example, are therefore unimportant, as are the details of the thermalization and recombination processes. The crucial aspect of these events is that they respond to the driving forces which tend to restore quasi- equilibrium by redistributing the absorbed laser energy within the carrier system.

The carrier energy is partitioned into three primary reservoirs : energy of excitation across the gap, kinetic energy, and thermally-excited collective carrier oscillations. Assuming dispersionless plasmons, the third contribution is given by

with E the bulk dielectric constant /24/and m* the appropriate reduced effective mass. r /25/ The importance of this term is clear from figure 1, where the carrier temperature is plotted as a function of the average energy per carrier in excess of the gap excitation energy. The temperature falls below that value calculated by neglecting the plasmons. This reflects the fact that some of the carrier energy is tied up in the form of plasma oscillations rather than in kinetic energy. In other words, the heat capacity of the carrier system is increased as a consequence of the partitioning of energy into the additional degrees of free- dom provided by the plasmons, so that an energy increment is less effective in rai- sing the carrier temperature.

where kc is the plasmon cutoff wavevector /18,23/ (roughly equal to the Debye wavevector) and w is the plasma frequency

P

Fig. 1 : k~ as a function o f ( E -7%' E )/A'. Ed2--- tot e G

i s the con&ibution t o the average energy per car- r i e r from e x c i t a t i o n across the gap.

(5)

C 4 - 1 0 JOURNAL DE PHYSIQUE

This result is shown in figure 2, which depicts the fraction of the total carrier energy contained in the plasmons. For semiconductors under normal conditions the plasma frequency is sufficiently small that although many plasmons are thermally excited, their contribution to the total energy is negligible. For metals, on the other hand, the energy of the plasmons is so large that few are thermally excited and the fraction of the total energy that they contain is si- milarly small. However, for just those values of carrier temperature and density

(km ~ 0 . l — 1 eV and tf~io19 — 1 02 1c m- 3) rele- e

vant to the pulsed laser generation rates referred to earlier, this fraction may be as large as 10 per cent.

„ 0 3 r - 1

>•

a tr

UJ

z

UJ in IS) UJ

£ 0 2 "

<

\-o

H \ >-

O

<r

% o i -

UJ / —.

z / ^ \ .

" o I ^^—| |

001 01 10 10 kTe(eV)

Fig. 2 : Fraction of excess carrier energy contained in the plasmons as a function of carrier temperature kl .

e

Nevertheless, the carrier temperature will be very much higher than that of the lattice, so that the likelihood of phonon emission is many orders of magnitude greater than phonon absorption, and the rate of energy transfer from the carriers to the lattice will be largely independent of lattice temperature /26/. For moderate carrier temperatures and densities in crystalline Si, the frequency of phonon emission /27,28/

I / T Z I O1 3 s- 1. The manner in which the presence of a dense plasma of hot carriers influences this rate has been calculated /16/

and is shown in figure 3. Dense-carrier effects do not become important until N

exceeds a critical value N ~2 - 4xl02 1cm~3, at which point the scattering frequency be- gins to deviate from its constant value and then falls rapidly as 1/N2. However, because the steady-state carrier density is not likely to become so large, the scattering frequency is, to a good approximation, independent of N. In addition, due to the extent to which the Si lattice is amorphi- zed and selection rules relaxed, the phonon emission rate may be considerably increased /29/. In any event, the rate at which energy will be transferred to the lattice in a given volume within the semiconductor depends not only on the manner in which the carrier interactions discussed above redistribute the laser energy among the carriers but also on the details of the spatial distribution of the plasma at the time inter- action with the lattice occurs.

I

' | ^ \^ w ' ~ \

— \

^ \ ooi 01 io~ IO

^ • ^ ( N / NC)E

6 6~5 To T~5 2 0 2 5 ( N / Nc)2

Fig. 3 : Phonon emission frequency 1/ras a function of (N/N ) z . The insert shows log 1/ras a function of log (N/N f.

The ability of a dense plasma to rapidly thermalize leads to considerable ana- lytical simplification when the energy distribution of the phonon-emitting carriers is considered. Any change in the carrier energy density caused by photon absorption or phonon emission is rapidly followed by rearrangement of the carriers so that they are again adequately described by fermi distributions at the new carrier temperature. In contrast, this is not necessarily possible at lower excitation rates for which carrier collisions are less rapid.

The laser creates a gradient in

(6)

carrier density which drives a net carrier diffusion current inward from the surface and leads to local changes in carrier density given by

where D~ is the ambipolar diffusion coeffi-

yc

*

cient /30,31/, Da = 2 k T e ~ e ~ h / ( m e ~ h + mhTe), with T the carrier-phonon scattering ti-

e , h

mes. Due to the high carrier densities, Da may be quite large /16/ (-10~cm~/s). Because gradients in carrier density (TVN) are so much larger than those in carrier temperature (UVT), the former constitute the primary driving force for the diffusion, as indicated in equation (2)

.

It is important to emphasize that because carrier number is not a conserved quantity, this is not a simple diffusion process. As carriers diffuse from a given volume, they take their energy with them, thereby reducing both the carrier density and energy left behind. Additional recombination then occurs in order to reestablish equilibrium at the lowered carrier temperature. The total energy, on the other hand, must be conserved, so that the rate of change of total carrier energy, Etot, is given by

The first term reflects the rate at which energy is delivered to the carriers, which have an effective absorption length 6 at laser photon energy hwL. The second term re- presents the rate at which the carrier energy density in a given region varies as a result of energy diffusion by means of carrier diffusion. The rate at which energy leaves the carriers by phonon emission is indicated by the last term, where hw is a typical optical phonon energy andvris an effective carrier-phonon mattering time.

Note that in the steady state

-- -

aE _at= 0

--

the carrier distribution does not change with time. However, the presence of the non-

zero phonon emission term means that the lattice temperature is increasing. Steady

state therefore refers to the carrier system only.

Of course, all of the laser energy will in steady state be delivered to some region of the lattice, leading to the energy conservation condition

Solving equation (3) for the steady-state carrier density, we find

1 /2

where a% ( D a 7

<Eta

t>/fiw)

,

with <Etot> the average energy per carrier, Etot/N. Having obtained an expression for N e , s s , it is of course first necessary to verify that the inherent assumptions of high carrier density (e-g., rapid carrier thermalization, Auger recombination dominant, etc.) are valid. In fact, for the typical laser pulse described earlier, the steady-state value of Ne near the surface is /16/ -lo2 ~ m - ~ , which ,is indeed in the high-density regime.

The effective diffusion length a has the form of a,conventional diffusion length

(Dt) '/2, where here t is the time during : I

which a hot carrier can diffuse before it has given up most of its excess energy by phonon emisssion. Such a process requires

< E ~ ~ ~ > / R w collisions, so that t = (<Etot >/

h w ) ~

.

The fact that this result has such a simple physical interpretation suggests that it may be applicable in general provided an appropriate diffusion coefficient can be found.

The energy transfer rate can be exa- . ^L

mined in two limiting cases using the carrier-density equation. when diffusion is not important, so that a<<&,

In this case, the laser energy is transferred to the lattice at the same rate and

(7)

c4-

12 JOURNAL DE PHYSIQUE

with the same spatial distribution (characteristic depth 6) with which it is absorbed.

In contrast, when diffusion plays an important role, a>>6, and

The laser energy is now given to the lattice over a region of depth a, determined by the diffusion. (The factor 6/a necessarily ap- pears to ensure total energy conservation.)

At the semiconductor surface,

&here N O = N e , s s (x = 0)

.

This energy e , s s

transfer rate is plotted in figure 4 as a function of incident laser power density.

For the case shown, hwL = 2.3eV1 so that 6-10-~cm. At a typical generation rate g..1031cm-3s-1, a is comparable to 6 and carrier diffusion has a considerable effect on the rate at which energy is transferred to the lattice. The rate of surface heating and, consequently, the ultimate temperature rise, is significantly reduced.

Fig. 4 : Energy transfer rate at the surface,

- - h / r , as a function of the rate of laser ener-

an effective depth 6' which depends on both 6 and a, as shown in figure 5.a, which is a function of the total carrier energy, in- creases monotonically with laser generation rate. It is clear from the figure that es- pecially at high generation rates, 6' may deviate markedly from 6, due to the influem ce of carrier diffusion. At a given absorption length 6, increasing g eventuallyleads to lattice heating over a larger region.

Thus, a higher laser pulse energy is requi- red to attain the same lattice temperature rise near the surface as was necessary for smaller g. In addition, reducing 6 (e.g., by increasing the laser frequency) will not necessarily reduce the extent of the region heated, since for sufficiently small 6, carrier diffusion will ultimately limit the minimum depth of this region.

Fig.5.Effectiveabsorption depth 6 ' as a function of aborption depth 6, for several laser generation ra- tes, with g9>g2>g1. a is the effective diffusion length.

Acknowledgements.- It is a pleasure to thank J.A. Van Vechten, R. C. Frye, W. P. Durnke, P. J. Price, F. Stern, R. Tsu and R. T. Hodgson for helpful discussions and important suggestions at many stages of this work.

References

4, ss

gy input, g h L , for hL = 2.3eV. The dashed line /1/ Khaibullin,I.B., Shtyrkov, E.I., was derived by neglecting carrier diffusion. Zaripov, M.M., Bayazitov, R.M., and

Galjautdinov, M.F., Radiat. Effects The laser energy enters the lattice in - 1 36 ' (1978) 225.

(8)

/2/ Rornanov, S.I., Kachurin, G.A., Smirov, /26/ Conwell, E.M., Solid State Phys., L.S., Khaibullin, I.B., Shtyrkov, E.1, Suppl.

-

9 (1967).

and Bayazitov, R.M., International

Conference on Ion Beam Modification of /27/ Folland, N.O., Phys. Rev. BL, (1970)

l r n o

Materials, Paper C12, Budapest, 4-8 I O S O .

Sept 1978. /28/ For a review, see Jacoboni, C., Canali, /3/ Van Vechten, J.A., Tsu, R., Saris, F - C., Ottaviani, G., and Alberigi

W. and Hoonhout, D., Phys. Lett.

z,

Quaranta, A., Solid State Electron.2

1 1 9 7 9 ) 417. (1977) 77.

, - - . - ,

/4/ Elci, A., Scully, M.O., Smirl, A.L.,

and Matter, J.C., Phys. Rev. B g , /29/ Dumke, W.P., to be published.

(1977) 191. /30/ Price, P.J., Phil. Mag.

46

(1955) 1252.

Elci, A., Smirl, A.L., Leung, C.Y. and /31/ Shanks, H.R., Maycock, P.D., Sidles, Scully, M.O., Solid State Electron. P.H., and Danielson, G.C., Phys. m v . 21 (1978) 151.

- -

130 (1963) 1743.

Shah, J., and Leite, R.C.C., Phys. Rev.

Lett,

22

(1969) 1304, Shah, J., Phys.

Rev. B g (1974) 3697, Shah, J., Solid State Electron.

21

(1978) 43.

Ulbrich, R., Phys. Rev. BE, (1973) 5719, Ulbrich, R.G., Solid State Elec- tron.

21

(1978) 51.

Auston, D.H., McAfee, S., Shank, C.V., Ippen, E.P., and Teschke, O., Solid State Electron.

21

(1978) 147.

Shank, C.V., Fork, R.L., Leheny R.F., and Shah, J., Phys. Rev. Lett. 42,

(1979) 112.

Von der Linde, D., and Lambrich, R., Phys. Rev. Lett. 42, (1979) 1090.

Ghez, R.A., and Laff, R.A., J. Appl.

Phys.

46,

(1975) 2103.

Wang, J.C., Wood, R.F., and Pronko, P.P., Appl. Phys. Lett.

33,

(1978) 455.

Lax, M., Appl. Phys. Lett.

33

⁽¹⁹⁷⁸⁾

786.

Schultz, J.C., and Collins, R.J., Appl.

Phys. Lett.

34

(1979) 84.

Lietoila, A. and Gibbons, J.F., Appl.

Phys. Lett.

2

(1979) 335.

Yoffa, E. J., Phys. Rev.BGr(1980) ,in press Tsu, R

.,

Baglin, J.E., Tan, T.Y., Tsai, M.Y., Park, K.C., and Hodgson, R., Laser-Solid Interactions and Laser Processing--1978, Materials Research Society, Boston, AIP Conference Pro- ceedings No. 50 (AIP, New York, 1979), p. 344.

Pines D. and Bohm, D., Phys. Rev.

85

(1952) 338.

Hearn, C.J., Proc. Phys. SOC.

86,

(1965) 881.

Beattie A.R., and Landsberg, P.T., Proc. Roy. Soc. =A, (1959) 16.

Quinn, J.J. Phys. Rev.

126,

(1962) 1453.

Haug, A., Solid State Electron.

21

(1978) 1281.

Bohnm D., and Pines, D., Phys. Rev.

82 (1951) 625.

-1

Walter J.P., and Cohen, M.L., Phys.

Rev. Bz (1972) 3101.

Kardontchik, J.E., and Cohen, E., Phys Rev. Lett.

42

(1979) 669.