J . Phys. Chem. 1990, 94, 1082-1087
1082
Photopumping of Quantum Well Heterostructures at High or Low 0 : Phonon-Assisted Laser Operation N. Holonyak, Jr.,* D. W. Nam,+ W. E. Plano, K. C. Hsieh, Electrical Engineering Research Laboratory, Center for Compound Semiconductor Microelectronics, and Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
and R. D. Dupuis’ A T & T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: April 28, 1989)
Data are presented showing the basic difference in the stimulated emission spectrum of a photopumped A1,Gal,As-GaAs or A1,Ga,,As-GaAs-InxGal,As quantum well heterostructure (QWH) heat sunk in a high-Q versus a low-Q cavity configuration. In the high-Q case a 1-2 pm thick narrow (25-50 wm) cleaved rectangle, with the (100) GaAs substrate removed, is heat sunk compressed in In under a sapphire, giving a high cavity photon lifetime because of metal reflectors folded up along the four samples edges. In the latter case (low Q) the (100) QWH rectangle is clamped under a sapphire into simple contact with Au, leaving the four cleaved {IIO)sample edges lossy and yielding, compared to carrier thermalization times, a short resonator photon lifetime across the sample. For photopumping (77 K, Ar+ laser, 5145 A) of a low-Q QWH sample, only lower energy recombination radiation is observed, including phonon-assisted laser operation (provided that the QWH is designed with good carrier, phonon, and photon confinement and with low alloy composition AlxGal+4s thermalization layers generating GaAs-like phonons near the QW). For photopumping of an otherwise similar QWH heat sunk in the high-Q configuration (long photon lifetime across the sample), recombination at higher energy can compete with carrier thermalization, and laser operation is observed on the confined-particle transitions, thus making unambiguous the identification of phonon sideband laser operation. Comparison of various QWHs heat sunk in the form of low-Q or high-Q resonators reveals the heterostructure layer configurations appropriate for phonon-assisted laser operation.
Introduction Ever since the transistor,’ interest in semiconductors and their optical properties has grown. Fundamental to a semiconductor is its energy gap, an electron-hole energy gap that ensures interesting optical properties. We mention that in the “beginning” it was not known whether Ge (the first transistor material) was direct gap or, as it happened to be, indirect gap,2 which, indeed, proved to be vital for the relatively long carrier lifetimes making possible the first bipolar transistors.I It is interesting to note that the distinction between a direct gap and an indirect energy gap was not lost on some of the earlier workers who considered using recombination radiation to achieve stimulated emission in a ~emiconductor.~*~ The importance of this for semiconductor lasers became quite apparent later.5-8 Immediately with the synthesis and discovery of the semiconductor behavior of 111-V compounds: direct-gap materials became available, and thus, if not initially that different in electrical properties than, say, Ge, they indeed proved to be different in optical properties. It is the direct-bandgap 111-V compounds that lie at the heart of optoelectronics and, because they support stimulated emission (stimulated recombination radiation), are of concern here. The difference between direct- and indirect-gap semiconductors is apparent in absorption measurements, and even more so in photoluminescence measurements, which, indeed, prove to be one of the simpler and more convenient methods of assessing semiconductor optical properties. This is particularly important for 111-V semiconductors because of their strong light-emitting properties,I0 not to mention the fact that they serve as the basis for heterojunctions and quantum well heterostructures. Photoluminescence, or at higher levels, photopumping, has the advantage that experimental samples may be homogeneous or of the form of sophisticated heterostructures or may be doped or undoped. The latter is important in fundamental studies where the complications of doping impurities are not desired. In addition, photopumping has the further advantage that, without the need of assembling complicated devices, device behavior can often be determined or at least approximated.
* To whom correspondence should be addressed. ‘Kodak doctoral fellow. 1 Work performed at Rockwell (Los Angeles).
In this paper we show, in photopumping experiments on quantum well heterostructures (QWHs), the importance of the experimental sample edge condition, Le., whether it is naturally reflecting (-30%) or made almost fully reflecting and thus whether the Q W H sample is a low-Q or a high-Q active (photopumped) dielectric “slab”. In Figure 1 we show compressed into an In (or Au) heat sink” a cleaved (100) QWH rectangle (substrate removed) with all four ( I 10) cleaved edges imbedded and reflecting (high-Q sample). For photopumping at low Q we use a sapphire to clamp the QWH sample into simple contact with the heat sink. For a sample fully pumped across its width in the high-Q configuration (Figure l), laser operation with widely spaced modes is observed across the sample on confined-particle transitions ( h a i= E,,”). In contrast, laser operation along the partially pumped sample length (narrowly spaced modes) is observed with (1) Bardeen, J.; Brattain, W. H. Phys. Reu. 1948, 74, 230. ( 2 ) Bardeen, J . 0ptoelectron.-Deuices Technol. 1987, 2, 124, ( 3 ) Von Neumann, J. IEEE J . Quantum Electron. 1987, QE-23,659. See also the J. V. N. letter to E. Teller (p 671). ( 4 ) In 1962 J. Bardeen mentioned to one of us (N.H.) that several years earlier he had considered this same possibility for a student Ph.D. dissertation (Le., stimulated emission in a direct semiconductor) but was not familiar at the time with the most prospective direct-gap material to suggest for the study. See: Holonyak, Jr., N. IEEE J. Quantum Electron. 1987, QE-23, 684. ( 5 ) Hall, R. N.; Fenner, G. E.; Kingsley, J. D.; Soltys, T. J.; Carlson, R. 0. Phys. Rea. Lett. 1962, 9, 366. ( 6 ) Nathan, M. I.; Dumke, W. P.; Burns, G.; Dill, Jr., F. H.; Lasher, G. Appl. Phys. Lett. 1962, 1, 62. (7) Holonyak, Jr., N.; Bevacqua, S. F. Appl. Phys. Lett. 1962, 1, 82. ( 8 ) Quist, T. M.; Rediker, R. H.; Keyes, R. J.; Krag, W. E.; Lax, B.; McWhorter, A. L.; Zeiger, H. J. Appl. Phys. Lett. 1962, I , 91. ( 9 ) We refer the reader to the interview with Alferov: Alferov, Zh. I. Cradle of Soviet Physics. Priroda (Moscow) 1988 (Nov), 4-1 1. Alferov (p 5 ) points out that in 1950 N. A. Goryunova and A. R. Regel (Leningrad) synthesized one of the 111-V semiconductors and reported its properties at a meeting in Kiev. This report, and the fact that it revealed the 111-V semiconductors, precluded the issuance of an English patent at a later date to H. Welker. Alferov points out that the work of Goryunova and Regel is not often cited because the proceedings of the Kiev meeting issued 2 years late (in Inestia-Academy of Sciences, U S S R . ) , and at that time Soviet journals were not regularly translated or followed in the West. (IO) This is true of direct-gap crystals and at least to some extent of indirect-gap materials such as GaP or GaAs,,P, made quasi-direct by doping with an isoelectronic trap (N). ( 1 1 ) Holonyak, Jr., N.; Scifres, D. R. Rev. Sci. Instrum. 1971, 42, 1885.
0022-3654/90/2094-1082$02.50/0 0 1990 American Chemical Society
Photopumping of Quantum Well Heterostructures
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Figure 1. Diagram showing a cleaved rectangular quantum well heterostructure (QWH) sample compressed into an In (or Au) high-Q heat sink for photopumping. In the high-Q configuration shown, laser operation on confined-particle transitions ( h w E,) occurs across the width of the fully pumped sample (widely spaced modes). In contrast, in low-Q heat sinking with no metal reflectors on the sample edges, only narrowly spaced modes running along the partially pumped sample length (narrowly spaced modes) are observed one phonon below the lowest confined-particle transitions (hw Ell - hwLO),Le., below the fundamental absorption.
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sufficient pumping only for recombination processes below the fundamental absorption, e.g., recombination a phonon below the lowest confined-particle transition (Figure 1; ho = E l l- huLO). This type of laser operation occurs also for the case of low-Q heat sinking, if sufficient phonons are generated, because the Q along the sample (low absorption and low photon loss rate) is greater than across the sample (higher photon loss rate). We mention that the photon loss rate for a resonator of a given width w (or length I ) with no absorption is
I / & = (2C/?)W/2W) In (1/R,R2)1
(1)
where as usual c is the velocity of light, 9 is the semiconductor index of refraction (- 3.6), and R, and R2 are the semiconductor rectangle (Figure 1) edge reflection coefficients along or across 25 pm, which a rectangular sample. For a sample width w is of the order of the photopumping beam diameter, and with R I = R2 0.32 (lossy edges, low Q) t, 1.3 X s. For the same 0.9-0.99 (high Q) t, 1.4 X width sample and R I = R2 10-'L1.5 X IO-" s. We see from these estimates that in one case (low Q) the photon lifetime in the cavity (t,) is less than the carrier s) and in the other case (high Q) thermalization time (is equal or longer. Whether we heat sink a 111-V QWH in a low-Q or high-Q configuration for photopumping proves to be important in permitting recombination to compete with carrier thermalization. The result is that phonon-assisted laser operation can be identified unambiguously.I2 We return to this later.
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111-V Quantum Well Heterostructures The basic form of QWH of interest here is shown schematically in Figure 2. The active region is a GaAs quantum well (QW) of thickness L, 5 200 A. On either side are higher gap A1,Gal,As confining layers that are relatively thick (0.1-1 pm) and, when pumped with an Ar+ laser ( hop = 2.41 eV), serve as the absorbing IO4 cm-l) in which most of the electron-hole pairs layers (CY are generated and from which carriers are collected. If the GaAs quantum well is 200 8, thick or thicker, this rather elementary form of QWH captures sufficient photogenerated electron-hole pairs to permit laser operation (which is shown later).I3-l5
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(12) Holonyak, Jr., N.; Nam, D. W.; Plano, W. E.; Vesely, E. J.; Hsieh, K. C. Appl. Phys. Lett. 1989, 54, 1022. (13) Kolbas, R. M.; Holonyak, Jr., N.; Dupuis, R. D.; Dapkus, P. D. Pis'ma Zh. Tekh. Fir. 1978, 4, 69 [Sou. Tech. Phys. Lett. (Engl. Transl.) 1978, 4, 281. (14) Holonyak, Jr., N.; Kolbas, R. M.; Dupuis, R. D.; Dapkus, P. D. Appl. Phys. Lett. 1978, 33, 13. (15) Holonyak, Jr., N.; Kolbas, R. M.; Dupuis, R. D.; Dapkus, P. D. IEEE J. Quantum Electron. 1980, QE-16, 170.
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\
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Figure 2. Schematic diagram showing the basic structure of a simple single-well AI,Ga,-,As-GaAs quantum well heterostructure (QWH). High-energy electron-hole pairs generated by the pump signal hwp thermalize (via phonon generation, AE = hwL0)down to the band edges of the higher gap confining layers and are partially collected in the QW.
I
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1 hYL0
f
Eg (AlxGal .xAs)
Eg(GaAS)
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ihl
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Figure 3. Schematic diagram showing a single-well AI,Ga,,As-GaAs Q W H as in Figure 2 but with an additional thicker A1,Gal,As waveguide (WG) region that ensures carrier collection by confining electrons and holes (and phonons and photons) near the GaAs QW.
However, the QWH of Figure 2 is sufficiently limited at Q W sizes L, C 100 A, because carriers are not captured efficiently in the QW,l6 so that it must be modified to be useful in laser experiments. A simple improvement is to increase the number of wells, and thus the "size" of the active region that captures carriers, but then we lose t h e benefit of studying a simple single Q W system. This can be overcome with a QWH of the form shown in Figure 3, which basically is still a single GaAs Q W but located within a thin lower composition ( x Q 0.3) A1,Gal,As waveguide (WG) region ( L W ~ C 0.2 pm) that is further confined on either side with relatively thick (- 1 pm) higher gap A1,Gal,As ( x > 0.3) layers. The waveguide region is thick enough to ensure efficient capture of (16) Shichijo, H.; Kolbas, R. M.; Holonyak, Jr., N.; Dupuis, R. D.; D a p kus, P. D. Solid State Commun. 1978, 27, 1029.
1084 The Journal of Physical Chemistry, Vol. 94, No. 3, 1990
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Figure 5. Transmission electron microscope (TEM) image showing a simple AI,Ga,,As-GaAs QWH (as in Figure 2) grown ( 1 977) via metallorganic chemical vapor deposition (MOCVD). The inset shows the GaAs quantum well region at increased magnification. The relatively thick top (0.1 pm) and bottom (1 pm) AI,Ga,,As confining layers are indirect-gap crystal, x 0.6 > x, = 0.45, where x, = 0.45 is the "crossover" from direct-gap to indirect-gap crystal.
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Figure 4. Diagram showing downward scattering of photogenerated electrons in the step density of states of a QWH and, for comparison, in a bulk crystal (dashed lines). Note that hot carrier thermalization by phonon emission in a bulk crystal is limited by the decreasing density of states.
the photogenerated electron-hole pairs but is thin enough to ensure that the carriers scatter and reflect often enough in the vicinity of the QW to thermalize and be captured in the well before recombining. There is a further advantage of the QWH of Figure 3. Besides collecting and confining photogenerated carriers, the waveguide region and its relatively high index of refraction (compared to the thick confining layers) tend to confine the recombination radiation, which enhances even further the Q of a sample heat sunk as shown in Figure 1 (high Q). In addition, if most of the photogenerated carriers are collected and thermalize in the waveguide and QW region (AIxGal,As, x < 0.3), then a large phonon population can be generated and confined in the QW region. In addition, for alloy compositions x S 0.3 the thermalization phonon energies are not detuned all that much from the phonon energies of the GaAs quantum well (-36 meV),'* which is important for reasons of stimulated phonon emission.
Carrier Thermalization and Phonon Generation in QWHs An interesting and important feature of QWHs is apparent in Figure 4. Photogenerated or injected excess carriers scatter downward in energy (thermalize) to a lesser density of states by phonon emission (LO phonon, hwLo). In a bulk sample (L, 2 500 A), with a parabolic density of states as shown by the dashed lines of Figure 4, the phonon emission intensity I,, is proportional Similarly, to the final density of states or I,, 0: (E phonon absorption labsis proportional to (E + hi^^^)^/*, or clearly labs > le,. Thus, in a bulk sample, carrier thermalization by phonon emission has a tendency to be limited eventually by the decreasing density of states. On the other hand, within the constant density-of-states region of a quasi-two-dimensional quantum well system, no such limitation occurs (e.g., see the two-phonon "paths" in Figure 4). Figure 4 shows also that from the lowest (or last) conduction band step n = 1 in the density of states a virtual transition is possible which makes recombination and laser operation possible hwLo below the confined-particle energy gap E l l , Le., below the fundamental absorption. We illustrate this behavior later. This is the basis for the photopumped laser operation, at high excitation level, along the sample and thus the closely spaced modes X(EI, - hwLo) shown in Figure 1. ( 1 7) Burnham, R. D.; Streifer, W.; Scifres, D. R.; Holonyak, Jr., N.; Has, K.; Camras, M. D. J . Appl. Phys. 1983.54, 2618. (18) Parayanthal, P.; Pollak, F. H. Phys. Reu. Letf. 1984, 52, 1822.
Energy (eV) 1.4 I
1.5 1.6 Al&Gag.rlAs-GaAs QWH (Lp200 A) 300 K
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8.8
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(b) 2x105 W/c*/ d I
8.4 8.0 Wavelength (1 03 A)
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Figure 6. Photopumped continuous wave (CW) room-temperature (300 K) laser operation of the simple AI,Ga,,As-GaAs QWH of Figures 2 and 5 (same QWH used 10+ years ago to demonstrate first CW 300 K laser operation of a QWH). The (100) QWH rectangle (27 pm X 160 pm) is heat sunk in a high-Q configuration (Figure 1) compressed in Au under a diamond window. Continuous 300 K laser operation, curve a, occurs at an excitation level of 1.6 X lo4 W/cm2 or an equivalent current density Jq = 6.6 X lo3 A/cm2. Curve b shows laser operation on higher energy confined-particle transitions at a pulsed excitation of 2 X lo5 W/cm2.
Whether we observe unambiguously this type of laser operation is a matter of the form of the sample heat sinking, Le., whether the QWH sample is arranged in the form of a low- or high-Q resonator and, of course, whether the phonon generation in the QW region is adequate (with even the possibility of being stimulated). For example, the QWH configuration of Figure 3 is a better choice than that of Figure 2 for this purpose because carrier collection and thermalization occur in a compact region centered at the quantum well. Essentially the phonon generation is confined near the quantum well and not "wasted" beyond the well. Also, as already mentioned, an attempt is made to thermalize the carriers in low composition A1xGa,-xAsalloys ( x S 0.3) so that the phonon energies are not detuned from hwLo(GaAs) 36 meV.
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Photopumped QWH Laser Operation We illustrate these ideas by first showing the photopumped laser operation of a nonoptimum QWH of the form of Figure 2. A transmission electron microscope (TEM) image of the actual A1xGal-xAs-GaAsQWH is shown at two magnifications in Figure 5. A simple L, x 200 A GaAs QW is confined on top with a 0.1 pm AIxGal,As ( x 0.6) layer and a similar layer 1 pm thick on the bottom. Cleaved rectangles of the QWH (substrate re-
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Photopumping of Quantum Well Heterostructures Energy (eV) 1.5 1.6 1.7 Alo.gGao.4As-GaAsQWH (Lz=200 A)'
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7.8 7.4 Wavelength (1 03 A)
1.5
1.8 (a) 5 ~ 1 ' 0 ~ (b)5x104 (c) 2x105 Wicm2
77 K ( L )
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The Journal of Physical Chemistry, Vol. 94, No. 3, 1990 1085
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7.0
Figure 7. Low-temperature (77 K) photopumped laser operation of the AI,Gal-,As-GaAs Q W H of Figures 5 and 6 with high level pulsed excitation. The laser operation on the higher energy confined-particle transitions of spectral curves a and b was obtained IO+ years ago on cleaved (100) rectangles (26 and 31 pm wide) heat sunk in the high-Q configuration of Figure 1. In contrast, curve c shows recent data obtained on a (100) rectangular QWH sample (35 pm X 320 pm) heat sunk in the low-Q configuration clamped with a sapphire into contact with Au. Laser operation on only the lowest energy confined-particle transitions is observed ( h w = Ell,Le., the n = 1 e hh electron-to-heavyhole and n' = 1' e Ih electron-to-light-hole transitions).
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moved) are imbedded in Au under a diamond window as shown in Figure 1." In spite of the simple form of this QWH, Le., its relatively poor efficiency for carrier collection and phonon generation, it is quite capable of continuous wave (CW) room-temperature (300 K) photopumped (Ar' laser, 5145 A, 2.41 eV) laser operation as shown by curve a of Figure 6 . This laser operation, with the high-Q heat sinking of Figure 1, clearly occurs on the confined-particle transitions, Le., without phonon sidebands. The laser operation of Figure 6 is particularly notable because we have used in this experiment the exact same A1,Gal,As4aAs QWH (grown by metallorganic chemical vapor deposition, MOCVD)19 that was used over 10 years ago to demonstrate the first CW 300 K laser operation of QWHs.I4 This laser operation is possible (and proved a point very early, 1978)14because of the very effective heat sinking and the influence of a high-Q resonator. In some respects the photopumped laser operation of this particular Q W H (Figures 2 and 5) is more interesting at 77 K. Curves a and b of Figure 7 show the high-energy laser operation (E; 1.5 eV < hu < 1.8 eV E:) on confined-particle transitions that was first obtained in the high-Q heat sinking configuration (full pumping across the sample, Figure 1) and reported over 10 years ago.13 In contrast, curve c shows recent data obtained on a cleaved rectangle (same QWH) that is heat sunk in the low-Q configuration, Le., with no reflective metal on the sample edges and consequently a much larger resonator photon loss rate. Carrier thermalization occurs all the way down to the lowest confined-particle transitions, but not lower because of the rather inefficient carrier collection and relatively weak phonon generation. However, laser operation can occur across the sample because of no appreciable absorption and just enough gain to accommodate the photon loss rate (if all the collected carriers are available to recombine in a narrow spectral range). In the case of curve c of Figure 7 carrier recombination on the higher confined-particle transitions cannot compete with the rate of carrier thermalization. Since the sample of curve c of Figure 7 is clamped into contact with the heat sink, it is possible to take one set of data (Figure 7) and then later compress the sample further into the heat sink," folding soft metal up along the sample edges and making them highly reflecting (in the process shifting the Q W H from low Q to high Q ) . This is the basis for the high-Q spectral curve b shown in Figure 8. Spectral curve a is for the same Q W H sample (low Q) shown in Figure 7 as curve c. Note that for the high-Q case
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Energy (eV) 1.6 1.7 A10,6Ga0.4As-GaAsQWH (Lz=200 A) 2xi05W/cm2(fi) 77 K
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(19) Dupuis, R. D.; Moudy, L. A.; Dapkus, P. D. In Proceedings of the 7th Iniernaiional Symposium on GaAs and Relaied Compounds; Wolfe, C . M., Ed.; Institute of Physics: London, 1979; pp 1-9. See also: Ludowise, M.J. J . Appl. Phys. 1985, 58. R3.
Wavelength (103 A)
Figure 8. Pulsed (2 X los W/cm2) photopumped laser operation (77 K) of the cleaved sample c of Figure 7 (35 pm X 320 pm) "switched" from (a) low Q to (b) high Q by compressing the sample deeper into Au and folding metal (Au) up along the initially free edges. For (a), low Q, laser operation on only the lowest energy confined-particle transitions (hw = E , , or n = 1 e hh, n'= 1' e Ih) is observed. The surne rectangular sample switched to high Q, curve b, moves up in laser operation to the higher energy confined-particle transitions (carrier recombination competing with scattering).
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Energy (eV) AI,Gal.,As-GaAs QWH (75 A) 35 pm x 240 pn
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Wavelength (1 03 A) Figure 9. Photopumped laser operation (77 K) of an AIxGal,As~aAs 0.2 waveguide confining layer (see Figure 3) that Q W H with an x improves carrier collection and that helps confine carriers, phonons, and photons near the QW. The cleaved (100) Q W H rectangle is heat sunk under sapphire in In as in Figure 1 (high Q). Curve a shows the spontaneous emission at a continuous wave (CW) excitation of 90 W/cm2. Phonon-assisted laser operation (narrowly spaced modes) located AE = huLobelow the lowest confined-particle transitions (n = 1 e hh, n' = 1' e lh; widely spaced laser modes) occurs (b) at a photopumping At the threshold of 9 X IO3 W/cm2 (CW) or Jog = 3.7 X lo3 A/". higher pulsed excitation level of 2 X los W/cm2, curve e, phonon-assisted laser operation persists, and even higher energy laser operation on the n = 2 e hh confined-particle transitions is evident (small modes on the right).
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b of Figure 8 laser operation has been "turned on" (with increased sample Q) on the higher confined-particle transitions, where now the photon lifetime across the sample ( t , lo-" s) is longer than s). That is, for (b) of the carrier thermalization time (Figure 8 recombination can compete with scattering and thermalization, and, as a consequence, laser operation can be observed on the higher energy confined-particle transitions.
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Phonon-Assisted Laser Operation As already noted, a QWH of the form of Figures 2 and 5 is not particularly well designed in respect to either GaAs-like phonon generation, nor for phonon confinement near the QW; in fact, no phonon sidebands are evident in the data shown so far (Figures 6-8). The QWH of Figure 3 is much better in both respects, both for phonon confinement and for phonon generation at hwLo 36 meV. Even better perhaps is the QWH shown in the inset of Figure 9, which is grown in an Emcore GS 3000 DFM MOCVD reactor. Except for the thin x 0.8 AI,Ga,,As confining layers
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1086 The Journal of Physical Chemistry, Vol. 94, No. 3, 1990
on the top and bottom of the crystal (left and right in Figure 9), which eliminate surface losses, all of the layers in the central region of I-pm thickness are in the composition range x 5 0.3. This is a deliberate design choice for the QWH to ensure that all the phonon generation per pump photon, n 2 (2.41 - 1.88)/0.036 15, will be tuned relatively close to GaAs-like phonon energies hwLo(GaAs) = 36 meV.18 Actually, the AI,Ga,,As waveguide region (LWGi= 0.15 pm) of composition x 0.2 improves the carrier collection, carrier confinement, phonon tuning, phonon confinement, and phonon yield ( n (2.41 - 1.76)/0.036 18), not to mention photon confinement and hence resonator Q. Thus, for the Q W H of Figure 9, which is a 35 pm X 240 pm platelet heat sunk in the high-Q configuration of Figure 1, we do, in fact, observe photopumped laser operation on phonon sidebands (cf. Figure 4). This is evident in Figure 9, curves b and c, from the closely spaced longitudinal modes at h 7930 A, which “turn on” at a CW pump level of 9 x IO3 W/cm2 (or equivalent current 3.7 X lo3A/“). These modes are located hwLo density of Jq below the calculated position of the n = 1 electron-to-heavy-hole hh) confined-particle recombination transitions of the L, (e i= 75 8, GaAs QW. More important, in the high-Q heat sinking configuration, widely spaced modes across the sample “turn on” more or less simultaneously (Figure 9b) on confined-particle transitions. These serve as an experimental reference for the position of the confined-particle transitions. These modes can be turned on or off depending upon whether we choose to employ low-Q or high-Q heat sinking for the long narrow rectangular QWH samples. We can test these ideas by another form of QWH, which is a modification of the A1,Gal,As-GaAs Q W H of Figure 3. We enlarge the GaAs quantum well into a bulk layer of thickness 700 A and “insert” (grow) into its center a pseudomorphic In,Gal-,As (x 0.1 5) layer of thickness L, = 150 A. We show a TEM cross section of this A1yGal-,.As-GaAs-In,Gal,As QWH elsewhere.20 In Figure 10 we show the photopumped laser operation of two cleaved rectangular samples of this QWH, the first (a) heat sunk (55 pm X 290 pm) clamped against Au with the edges remaining free and thus low Q and the other (b) imbedded (55 pm X 310 pm) into In with metal reflecting edges (Figure 1) and thus high Q. Both Q W H samples are photopumped (77 K) pulsed at the very high level of lo5 W/cm2 (JW 4.1 X lo4 A/“) to ensure a large (a confined) phonon population. Note also that the laser operation on the close spaced modes along the sample, for either the low-Q sample (a) or the high-Q sample (b), occurs at h 9025 A or hw 1.374 eV. Therefore, we expect a maximum phonon generation per pump photon of n (2.41 - 1.37)/0.036 28. In other words, the phonon generation rate at a photopumping level of IO5 W/cm2 is extremely high, and it is only a matter of the sample Q, (a) low Q or (b) high Q, whether laser operation occurs (a) only at low energy (A 9025 A) along the sample ( h w i= E l l - huLo 1.37 eV) or also (b) on widely spaced modes on the confined-particle transitions (A 8795 A, 1.41 eV). The phonon sideband laser operation of Figure 10 occurs along the partially pumped sample (Figure 1) beneath the absorption. The laser operation across the sample, which is distinctly different, occurs only for high-Q heat sinking, when the photon loss rate across the sample is reduced. Absorption is not an issue across the sample, and the gain is sufficient for laser operation if the photon loss rate is low enough. In this case, recombination at higher energies in a QW can compete with carrier thermalization. We note that from the Q W H sample sizes used in this work (25-50-pm widths) and the photon lifetimes estimated for low-Q and high-Q heat sinking (and laser operation), we can bracket the carrier thermalization time and put it at 1Vi2s, which agrees with generally known values.
Energy (eV) 1.44
AlyGal.yAs - GaAS - In,Gai.,As
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Discussion and Conclusions Although the QWH shown schematically in Figure 2, and in experimental form in Figure 5, is not a particularly good choice (20) Nam, D.W.; Holonyak, Jr., N.; Hsieh, K. C.; Gavrilovic, P.; Meehan, K.; Stutius, W.; Williams, J. E. J . Appl. Phys. 1989, 66, 1347.
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Wavelength (103 A) Figure 10. Pulsed (lo5W/cm2) photopumped laser operation (77 K) of (100) cleaved AI,Ga,_~sGaAs-In,Ga,,As QWH rectangular samples with the sample ( 5 5 pn X 290 pm) of (a) heat sunk low Q (on Au) and the sample ( 5 5 pm X 310 gm) of (b) heat sunk high Q (in In). The QWH is of the form of Figure 3 but with an InxGa,,As QW grown into the center of a 700-A GaAs layer. For the sample in the low-Q configuration, curve a, only phonon-assisted laser operation (A = 9000 A) is observed AE = huLo below the lowest confined-particletransitions (n = 1 e hh). In contrast, for (b) the sample in the high-Q configuration (as in Figure 1) laser operation is observed “turned on” at higher energy across the sample on the n = 1 e hh confined-particle transitions, with also phonon-sideband laser operation still occurring on narrowly spaced modes along the sample AE = haLolower in energy.
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to reveal phonon-sideband laser operation, it is basically simple and thus useful in shedding light on other related issues. Because this simple single-well QWH (Figure 5) is indirect-gap crystal everywhere except for the GaAs Q W itself, there is no question that the unusually large stimulated emission range shown in Figure 6 ( A h w 300 meV) is all owing to recombination in the QW. That is, the thick indirect-gap Al,Ga,-,As (x 0.6) barriers are not the source of the luminescence in spite of the fact that they constitute almost all of the crystal (98+%). For this Q W H not only is the carrier collection and the confinement of phonons and photons relatively weak (but sufficient for laser operation), any carrier thermalization outside of the quantum well favors AIAs-like phonon generation and not phonon-assisted laser operation involving GaAs-like phonons. These factors make it unlikely for this QWH to exhibit phonon-assisted laser operation unless unusually large pumping levels are employed. In spite of the fact that a Q W H of the form of Figures 2 and 5 is not, as mentioned, a good choice for phonon-assisted laser operation, laser operation on the lowest confined-particle transitions ( n = 1 e hh or n’ = 1’ e lh) is nevertheless easy to achieve by employing low-Q heat sinking (Le., free sample edges). In contrast to low-Q heat sinking (free sample edges), laser operation on confined-particle transitions can be achieved over a remarkably large energy range employing high-Q heat sinking (which tends to “trap” photons). Indeed, the fact that the elementary form of QWH of Figure 5 will operate as a CW 300 K photopumped laser demonstrates the unusual effectiveness of high-Q heat sinking. High-Q heat sinking, and thus reduced photon escape, permits recombination to compete with carrier scattering and thermalization and as a consequence to reveal recombination on confined-particle transitions. High-Q heat sinking permits viewing of the entire recombination radiation spectrum. This provides a sure reference to identify phonon-assisted recombination, which is relatively easy to achieve in a properly designed QWH crystal, specifically, in an AI,Ga,,As-GaAs QWH in which electron-hole thermalization takes place in GaAs or in low composition AI,Ga,-,As and a region is provided (Figures 3, 9, and 10) to confine carriers, phonons, and photons near the QW. Finally, because of the nature of this occasion-Harry G. Drickamer’s 70th anniversary and all the many years and many contributions he has made to high-pressure science-we wish to mention that the experiments we have described here are obvious candidates to be repeated under high-pressure conditions. For
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J . Phys. Chem. 1990, 94, 1087-1090 example, we have not determined yet whether in the process of observing phonon-assisted laser operation macroscopic occupation of a phonon mode occurs and whether we are operating a phonon oscillator. High-pressure measurements, among others, may help resolve these questions. In previous high-pressure measurements on QWHs we (N.H.) with H. Drickamer and our students have been able to probe, because of easily resolved confined-particle exciton states, the “inside” of an energy band and not just the band edges.21 High-Q heat sinking of a QWH and photopumping present an opportunity to observe confined-particle transitions (recombination radiation) and phonon sidebands (not just bulk(21) Kirchoefer, S. W.; Holonyak, Jr., N.; Hess, K.; Gulino, D. A.; Drickamer, H. G.; Coleman, J. J.; Dapkus, P. D. Appl. Phys. Lett 1982, 40, 821.
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crystal band-edge processes) and see how they “tune” with pressure. These are experiments worth pursuing. We wish many more vigorous years for Harry Drickamer and the opportunity to do more high-pressure studies with him, including high-pressure versions of the experiments described here.
Acknowledgment. We are grateful to John Bardeen for helpful discussions (N.H.) on macroscopic phonon occupation in photopumped QWHs. For technical assistance we thank B. L. Marshall, R. T. Gladin, and B. L. Payne. This work has been supported by the Army Research Office, Contract DAAL-03-89-K-0008, and by the National Science Foundation, Grants DMR 86-12860 and CDR 85-22666. Registry No. GaAs, 1303-00-0; AIGaAs, 37382- 15-3; Alo,6Gao,4As, 106804-30-2; In, 7440-74-6; sapphire, 1317-82-4.
X-ray Absorption Fine Structure Study of Amorphous Germanium under High Pressure J. Freund,* R. Ingalls, Department of Physics, University of Washington, Seattle, Washington 98195
and E. D. Crozier Physics Department, Simon Fraser University, Burnaby, B.C., Canada V5A 1S6 (Received: May 5, 1989) The X-ray absorption fine structure (XAFS) of amorphous germanium under pressures ranging from 0.0 to 8.9 GPa is investigated. Contrary to some reports from the literature we cannot find a transition to crystalline germanium at about 6 GPa. Analysis of the XAFS phases of amorphous germanium and copper, which is used as a pressure marker, allows calculation of the bulk modulus at zero pressure, Bo. of the bonds (as opposed to the bulk modulus of the bulk material, containing voids) and its pressure derivative, B,,’. They are 97 f 8 GPa and 6 f 2, respectively. Bo is 30% larger than in crystalline germanium. Fair agreement is obtained with the two- and three-body potential energy formalism of Stillinger and Weber (1985).
Introduction The high-pressure behavior of amorphous germanium (a-Ge) has been of considerable interest since the 1970s. In a series of papers the group of Minomura, Shimomura, Tamura, and collaboratorsI4 observed that a-Ge, which is semiconducting at zero pressure, becomes metallic at 6 GPa but probably remains amorphous. At 10 GPa the resistivity drops further and the structure probably changes to a white& (SSn) structure. Some years later, Minomuras-* reported that at 6-7 GPa a-Ge becomes metallic and transforms to a (distorted) white& structure or remains semiconducting with a phase change to a body-centered cubic (BC-8) or diamond (FC-2) structure (over an amorphous background). Above 10 GPa it becomes metallic and assumes the white& structure. In this paper we present strong evidence that our a-Ge sample remains completely amorphous up to 8.9 GPa. Our evidence includes both the Fourier transform of the extended X-ray absorption fine structure (EXAFS) and the shape of the X-ray absorption near-edge structure (XANES) and its first-energy derivative. Pressures higher than about 9 GPa cannot yet be ( I ) Minomura, S., et al. Tetrahedrally Bonded Amorphous Semiconductors; AIP Conf. Roc. No. 20; American Institute of Physics: New York, 1974; p 234. (2) Shimomura, O., et al. Philos. Mag. 1974, 29, 547. (3) Tamura, K., et al. The Properties of Liquid Metals, Taylor and Francis: London, 1973; p 295. (4) Tamura, K.; Fukushima, J.; Endo, H.; Asaumi, K. J. Phys. Soc. Jpn. 1914, 36, 5 5 8 . (5) Minomura, S., et al. Proceedings of the 7th International Conference on Amorphous and Liquid Semiconductors; University of Edinburgh: Edinburgh, 1977; p 53. ( 6 ) Minomura, S . High-pressure and Low-Temperature Physics; Plenum: New York, 1978; p 483. (7) Minomura, S. J . Phys. Colloq. 1981, 42, C4, Suppl. 10, 181. (8) Minomura, S.Amorphous Semiconductor Technologies and Devices, 1982; North Holland: Amsterdam, 1981; p 245.
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routinely obtained with our pressure cell due to the difficulties with X-ray absorption spectroscopy, as described in our paper on copper under high p r e s ~ u r e . ~ In ref 9 we have shown that copper is an excellent pressure marker in XAFS experiments with errors of not more than 0.5 GPa. When the nearest-neighbor distance of a-Ge is extracted from the phase of the EXAFS and plotted versus pressure one is in a position to calculate the bulk modulus at zero pressure, Bo, and its first pressure derivative, B,,’, with any two-parameter isothermal equation of state. The bulk modulus we refer to here is the bulk modulus of the single Ge-Ge bonds, not the bulk modulus of the bulk material. Whereas in most materials both bulk moduli are the same, they are vastly different in amorphous materials with their variable amounts of voids. The voids in a-Ge, for example, collapse rapidly below 2 GPa, as was shown by Wu and Luo.Io Therefore, the two bulk moduli are very different in the low-pressure region. The bulk modulus of the bulk material can be calculated from measurements of the film thickness. The bond bulk modulus, on the other hand, can only be calculated from a knowledge of the compression on an atomic scale. Since EXAFS probes the short-range order it is particularly useful for this purpose. We find a bond bulk modulus that is about 30% larger than for crystalline germanium (c-Ge); i.e., a-Ge is harder than its crystalline counterpart once the voids have been expelled. Atomic potential models can be used to calculate the bond bulk modulus since it is proportional to the second spatial derivative of the potential. With the two- and three-body potential formalism of Stillinger and Weber” and the numerical values for Ge calculated by Ding and Andersen12 we find indeed that a-Ge must have a ~
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(9) Freund, J.; Ingalls, R. Phys. Rev. B 1989, 39, 12537. (10) Wu, C. T.; Luo,H. L. J . Non-Cryst. Solids 1975, 18, 21. (11) Stillinger, F. H.; Weber, T. A. Phys. Rev. B 1985, 31, 5262.
0 1990 American Chemical Society
