Absorption saturation in germanium, silicon, and gallium arsenide at 10.6 μmA.F. Gibson, C.A. Rosito, C.A. Raffo, and M.F. Kimmitt Citation: Applied Physics Letters 21, 356 (1972); doi: 10.1063/1.1654410 View online: http://dx.doi.org/10.1063/1.1654410 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/21/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Nonlinear absorption due to shallow donors in germanium at 10.6 μm J. Appl. Phys. 52, 4748 (1981); 10.1063/1.329310 Enrichment of boron, carbon, and silicon isotopes by multiplephoton absorption of 10.6μm laser radiation J. Appl. Phys. 47, 595 (1976); 10.1063/1.322619 Silicondoped gallium arsenide antimonide electroluminescent diodes emitting to 1.06 μm J. Appl. Phys. 46, 3678 (1975); 10.1063/1.322099 The 10.6μm absorption of KCl Appl. Phys. Lett. 25, 109 (1974); 10.1063/1.1655399 10.6μm Laser Beam Absorption by a Particulate Cloud J. Appl. Phys. 43, 2446 (1972); 10.1063/1.1661520

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356 A. Y. CHO AND F. K. REINHART

masking arrangement in an ultrahigh -vacuum system. The masking is accomplished by a small-diameter wire in the beam path. The Al effusion cell is directed per­pendicular to the substrate so that the wire can form a sharp shadow with a width approximately the diameter of the wire where the GaAs effusion cell is situated at an angle with the substrate (Fig. 1). The reason for this arrangement is that it allows the GaAs beam to reach behind the masking wire where the Al beam is shadowed, thus resulting in a strip containing only GaAs.

The distance from the effusion cells to the substrate in this experiment is about 5 cm, while the masking wire is apprOximately 0.1 cm from the substrate. The GaAs substrate was kept at 560°C, and the effuSion cells of Al and GaAs were adjusted to give the AI-Ga ratio in the molecular beam for the predetermined AlAs mole fraction in the AlxGal_xAs. 4 The growth procedure can be stated in three steps: (i) growth of an AlxGal_xAs layer without the masking wire in place, (ii) growth of the second layer with the maSking wire in place, and (iii) growth of the third layer without the wire as in (i).

The change in the position of the wire was accomplished through an air-to-vacuum manipulator so that the crystal was not exposed to air between the growth of each layer. Figure 2 shows a photomicrograph of the guide cross section after angle lapping and staining with dilute HN03 •

In this demonstration, a 50-!lm tungsten wire was used as the maSking wire and the thickness of the guide was 2 !lm. Preliminary studies showed that these structures are indeed optical waveguides; that is, light has been confined in the plane perpendicular to the propagation direction. Further work on the studies of the guiding properties will be reported in a later paper.

IS.E. Miller, Bell System Tech. J. 48, 2059 (1959). 2D. T. F. Marple, J. Appl. Phys. 35.1241 (1964). 3R.E. Fern and A. Onton, J. Appl. Phys. 42, 3499 (1971). 4A. Y. Cho and S.E. Stokowski, Solid State Commun. 9, 565 (1971).

5A. Y. Cho, J. Vacuum Sci. Technol. 8, S31 (1971). 6F.K. ReinhartandB.I. Miller, Appl. Phys. Letters 20, 36 (1972).

IA. Y. Cho, J. Appl. Phys. 42, 2074 (1971); 41,2780 (1970).

Absorption saturation in germanium, silicon, and gallium arsenide at 10.6 J.lm

A.F. Gibson, C.A. Rosito,* C.A. Raffo,* and M.F. Kimmitt Department of Physics, University of Essex, Co/chester, Essex, Eng/and

(Received 6 July 1972)

The absorption of p-type Ge, Si, and GaAs at 10.6 /.1m decreases at high intensities. The saturation intensity of Ge, 10 MW cm-2 , is sufficiently low for it to be used for passive mode locking of a TEA laser.

Using a mode-locked COz laser in conjunction with an optical bridge, 1 we have studied absorption saturation in various semiconductors at 10.61-!lm wa .:length (the P22 line of COz).

The absorption coefficient, K, of a homogeneously broadened absorber varies with intensity I as

so that, if lin is the intensity incident on a sample of thickness L, the intensity of the radiation transmitted, lout, is given byZ

In(Iln/I "'t) + (lin - Iout)/Is == KoL, (2)

where Is is the saturation intensity and Ko is the small­signal absorption coefficient.

Figure 1 shows transmission data obtained with 1-0 cm p -type germanium, plotted in accordance with Eq. (2). Is is given by the slope of the resultant straight line, though it should be noted that the maximum intensity used was insufficient to unambigously confirm homoge­neous broadening. Z In the range 1-20 0 cm, the value of Is is found to be substantially independent of doping concentration and equal to 10± 3 MWcm-z at room tem­perature. Is decreases by a factor of about 2 on cooling to 100 K. For p-type GaAs at room temperature, the saturation intensity is 20 ± 5 MW cm-z. p -type silicon shows only a small degree of saturation below its

Appl. Phys. Lett., Vol. 21, No.8, 15 October 1972

damage threshold, and we estimate Is to be ~ 50 MW cm-z.

At wavelengths around 10 !lm, absorption in p -type Ge, Si, and GaAs is primarily due to the excitation of holes

0.5

:) --- o ..f

£; 0.3

o

0.20 L ---------11.0---------:2':-.0--­

Itn-Iout (MWcm- 2)

FIG. 1. Intensity incident upon (Iln) and emerging from (Iout) an approximately 2-mm-thick sample of 1-0 cm p-type germanium set at the Brewsters angle, plotted in accordance with Eq. (2). Upper trace, room temperature (I.=10 MWcm-2); lower trace, 115 K (Is"" 5 MW cm-2).

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ABSORPTION SATURATION IN Ge, Si, AND GaAs AT 10.6 Jlm 357

TABLE 1. Published values of hole absorption cross sections and deduced values of the rmalization time, T.

Material CT (xl0-16 cm2) T (xl0-12 sec)

Ge (300 K) Ge (100 K) GeAs (300 K) Si (300 K)

3 9 2

:;3

aW. Kaiser, R.J. Collins, and H.Y. Fan, Phys. Rev. 91, 1380 (1953).

bH. Y. Fan, Semiconductors and Semimetals (Academic, New York, 1967), Vol. 3, p. 406.

cH. Hara and Y. Nishi, J. Phys. Soc. Japan 21,1222 (1966).

from the heavy to the light hole band, 3 though in Si phonon absorption and transitions involving the split-off band are also important. Since a finite time, 'T, is re­quired for the hole distribution to return to equilibrium, saturation of the absorption occurs when the intenSity is sufficient to significantly deplete the hole population in the heavy hole band. Let I(x) be the intensity in an element dx a distance x into a sample of unit area and thickness L. If dI(x) is the net change in intensity (ab­sorption minus stimulated emission) in this element, the rate of filling of holes is dI(x)/hv, where hI! is the photon energy. Under steady -state conditions (t» 'T),

the denSity of holes in the element is then

P(x) = P _ 'T dI(x) , hvdx

where P is the hole density at zero incident intensity. By definition, the absorption coefficient at x, K(x), is given by

K(x) = _1_ dI(x) I(x) dx

and related to the local hole density by

K(x) = aP(x),

(3)

(4)

(5)

where a is the absorption cross section. Eliminating K(x) and P(x) among Eqs. (3)-(5), integrating with the boundary conditions I(x) =/10 at X= 0 and I(x) = lout at x=L, and writing aP=Ko gives Eq. (2), with

(6)

which is independent of P, in agreement with the experi­mental results.

Of the parameters in Eq. (6), 'T is known with the least confidence. It is therefore convenient to use the ob­served values of Is to deduce 'T for comparison with theoretical and other experimental estimates. The value of hI! is 1. 87x 10-20 J. Published values of a and the de­duced values of or are given in Table I.

To return to equilibrium, the excited holes must lose a substantial amount of energy, so it is not surprising that 'T is of the same magnitude as the energy relaxation time observed in high -electric -field experiments -e. g. , about 5X 10-12 sec in p-type germanium. 4 However, the only experimental estimate of 'T of which we are aware that is directly comparable with ours is that by Feldman and Hergenrother, 5 who observed photoconductivity in­duced by a CO2 laser in a sample of fairly heavily doped p-type germanium. They estimate that 'T lies between 5x 10-12 and 5x 10-11 sec, though the tolerances quoted for the data upon which these figures are based suggest that the uncertainty is somewhat greater than a factor of 10.

A rough theoretical estimate of 'T in germanium can be obtained by noting that the photon energy is nearly four times the optic phonon energy and that the relative coupling of holes to optic and acoustic phonons is about 4: 1. 6 Optic phonon emiSSion is the most effiCient energy loss process available to the holes, but even so a mini­mum of five collisions is required and a reasonable guess at the actual number would be ten. Hence, we would expect 'T to be an order of magnitude greater than the momentum relaxation time deduced from mobility data, as observed. The somewhat smaller value of 'T

observed for GaAs is presumably due to stronger coupl­ing to optic phonons in this partially ionic material and the increase in 'T on COOling germanium due to the de­crease in phonon density.

Materials showing nonlinear absorption at power densi­ties appreciably below their damage threshold have a number of applications, including passive mode locking. Though the mode-locked laser used in these experiments employed hot CO2 as the saturable absorber, 7 we have found that a TEA CO2 laser can be mode locked by simply inserting a suitable slice of germanium into the cavity. Since the saturation intenSity of heated CO2 in­creases as the square of the pressure (which must at least equal that in the amplifier) and reaches 10 MW cm-2 at about 700 Torr, germanium offers some ad­vantages at high pressures.

*On leave from Facultad de Ingenieria, Universidad Nacional de Buenos Aires, Argentina.

lA. F. Gibson, C.A. Rosito, C.A. Raffo, and M. F. Kimmitt, J. Phys. D (to be published).

2W. W. Rigrod, J. Appl. Phys. 34, 2602 (1963). 3A.H. Kahn, Phys. Rev. 97,1647 (1955). 4A.F. Gibson, J.W. Granville, andE.G.S. Paige, Proceed­ings of the International Conference on Semiconductor Physics (Czechoslovak Academy of Sciences, 1960), p. 112.

5J. M. Feldman and K. M. Hergenrother, Appl. Phys. Letters 9, 186 (1966).

6E. G. S. Paige, J. Phys. Soc. Japan Suppl. 21, 397 (1966). 7A. F. Gibson, M. F. Kimmitt, and C.A. Rosito, Appl. Phys. Letters 18, 546 (1971).

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