AlGaAs quantum wire lasers fabricated by cleaved edge overgrowth

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CRVSTAL GROWTH

Journal of Crystal Growth 150 (1995) 285-292

ELSEVIER

GaAs/AlGaAs W. Wegscheider

quantum wire lasers fabricated by cleaved edge overgrowth

a~1,*,L.N. Pfeiffer a, A. Pinczuk a, K.W. West a, M.M. Dignam a, R. Hull a, R.E. Leibenguth b a AT&T Bell Laboratories, Murray Hill, New Jersey 07974, USA b AT&T Bell Laboratories, SSTC, Breinigsuille, Pennsylvania 18031, USA

Abstract We have used the molecular beam growth technique which we call “cleaved edge overgrowth” to fabricate quantum wire lasers, in which 1D quantum confinement is entirely defined by the growth process. The active region of our lasers consists of atomically precise quantum wires that form at the T-shaped intersections of 7 nm wide GaAs quantum wells grown along the [OOl] crystal axis and after an in situ cleave along the [llO] crystal axis. The origin of the quantum mechanical bound state is the relaxation of quantum well confinement at this intersection. The high degree of structural perfection achievable in this way allows the observation of stimulated optical emission from the lowest exciton state in optically as well as in electrically pumped devices. The formation of a linear p-n junction in

which the quantum wires are embedded is achieved by doping with Be and Si in the two orthogonal growth directions. Efficient current injection into the wires is demonstrated by the almost complete suppression of optical emission K.

from the quantum

well states as well as by threshold

1. Introduction and operation of a semiconductor laser has been a challenge to the photonics field for more than a decade. Just as the quantum well (QW) lasers (2D) have replaced conventional double heterojunction devices (3D) due to their superior performance, Fabrication

quantum wire (QWR)

* Corresponding author. ’ Present address: Walter Schottky Institut, Technische Universitlt Miinchen, Am Coulombwall, D-85748 Garching, Germany. 0022-0248/95/$09.50 0 1995 Elsevier Science SSDI 0022-0248(94)00842-6

currents

as low as 0.4 mA for uncoated

devices at 1.7

further improvements in threshold current and modulation bandwidth as well as reduced sensitivity of threshold current and emission wavelength to ambient temperature are expected from QWR lasers (1D) [l-3]. The sharp peak in the density of states (DOS) at the band-edge of 1D systems as opposed to the square root and steplike DOS profile in 3D and 2D, respectively, should lead to a variety of interesting optical properties such as enhanced optical nonlinearities [4], narrower optical gain spectra and higher differential gain [2]. In addition, increased exciton binding [5,6], anomalously strong concentration of the oscillator strength at the lowest-energy

B.V. All rights reserved

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exciton state [71 and exciton condensation [8] are predicted as a result of Coulomb interaction in the electron-hole system confined to 1D. While several growth techniques are well suited to produce planar multilayer systems, the fabrication of structures in which charge carriers are quantum confined in more than one dimension is a very challenging task. Methods suggested and attempted include lithographic definition combined with etching and regrowth [9], growth on nonplanar [lo] and vicinal substrates [11,12], selective area deposition [13] and local interdiffusion [14,15]. The first lasers exhibiting signatures of carrier confinement to one dimension in the optical emission spectra have been prepared by organometallic chemical vapor deposition (OMCVD) on V-grooved substrates [lo]. However, the relatively large size of the crescentshaped QWRs fabricated by this technique (80100 by 10 nm> results in the occupation of many 1D subbands, and therefore in optical properties differing little from those of 2D systems. In order to observe characteristic 1D effects and the peculiar features associated with 1D excitons predicted by theory [7,8], the dimensions of the QWRs should be comparable to or smaller than the bulk exciton Bohr radius. Otherwise only the center-of-mass motion of the excitons shows 1D character while the electron-hole relative motion remains unaffected by the confining potential. It is, therefore, necessary to employ a fabrication technique which produces QWRs with uniform and precisely controlled dimensions of less than about 10 by 10 nm in the GaAs/AlGaAs system.

AlGaAs

Znd ME

step

1

Step

2

step

Growth

3

Fig. 1. The concept of quantum wire fabrication by MBE growth on the cleaved edge of a previously prepared multilayer structure.

situ cleave. After conventional growth of a QW structure on a [OOl] oriented substrate, a second growth takes place on the [llO] oriented sidewall which is exposed by the cleave. The post-cleave growth consists of another QW and a barrier layer. 1.2. Formation of ID states at T-shaped QW intersections Fig. 2a illustrates the physics of QWR formation at the T-shaped intersection of two QWs. The figure shows the cross-section of such an intersection together with contours of constant probability for electrons. The origin of the quantum mechanical bound state is the relaxation of QW confinement at the intersection. While a classical particle would be unbound for the given T-shaped potential, the expansion of the wavefunction into the larger available volume at the

1.1. Cleaved edge overgrowth The QWRs reported in this paper which led to the first demonstration of stimulated optical emission using 1D exciton recombination [161 were realized by the cleaved edge overgrowth (CEO) method. This molecular beam epitaxy (MBE) technique is capable of producing intersecting QWs with atomic control of thicknesses in two orthogonal directions, as illustrated in Fig. 1 and described in detail elsewhere [17,18]. The conceptually simple and straightforward method consists of two growth steps separated by an in

Fig. 2. Contours of constant probability (1 I&I* = 0.1,0.2,. . .,0.9) for electrons confined at the T-intersection of two QWs (a) and binding energy with respect to the lowest QW state of electrons to the QWR as a function of QW width for equally thick wells (b).

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of Crystal Growth 150 (1995) 285-292

junction results in a smaller kinetic contribution to the total energy of electrons and holes. Consequently, motion of the 1D carriers is limited to the line defined by the intersecting planes of the two QWs. In contrast to other QWR fabrication techniques which rely on introducing additional confinement of the carriers in a previously prepared 2D system, e.g. by partial removal of a QW layer and subsequent overgrowth with barrier material, the QWR states in our structure are energetically located below the ground state QW transitions. The existence of such confinement relaxation QWR states was experimentally demonstrated for the first time by Goiii et al. [19]. The calculated binding energy for electrons to the QWR with respect to the lowest QW state is plotted in Fig. 2b as a function of the QW width. In order to obtain the electron and hole wavefunctions for the T-shaped confining potential, we have employed a two-dimensional transfer matrix technique using a one-band model for the hole with masses determined via the diagonal term in the Luttinger Hamiltonian with the angular momentum quantization axis parallel to the [llO] overgrowth direction 1201.In the absence of electron-hole Coulomb interaction the holes are, due their larger mass, only weakly bound to the T-intersection.

2. Experimental

results and discussion

All experiments reported here were carried out under continuous excitation conditions with the samples immersed in superfluid He (1.7 K). Emitted light was either dispersed in a 0.85 m double monochromator and detected with a charge-coupled-device camera or focused onto a Si photodiode detector. 2.1. Optical excitation A schematic cross-section of the QWR laser structure is shown in Fig. 3. The first MBE growth formed the layer structure to the right of the arrow marked “cleave”. It consists of a 1 pm Al,,Ga,,As cladding layer followed by a 22period GaAs/Al,,,,Ga,,,As multiple quantum

direction of overgrowth [llOI +

287

10011

1St growth T direction

GeAs QWs

Fig. 3. Cross-section through the QWR laser structure. The dashed line represents a contour plot of the optical mode at 10% of the maximum intensity.

well (MQW) structure with well and barrier thicknesses of 7 and 38 nm, respectively, as illustrated in the magnified area, followed by a 3 pm Al,,Ga,,As cladding layer. After growth of the layers to the left of the arrow marked “cleave”, 22 QWRs form at the T-intersections of the 7 nm wide QWs. The Al,,Ga,,As and Al,,Ga,,As layers surrounding the QWRs serve as a T-shaped dielectric waveguide. Their purpose is to confine an optical mode to the vicinity of the QWR array (see the dashed line in Fig. 3) as confirmed by waveguide calculations within the effective refractive index approximation. In this way a completely index guided structure with an effective refractive index step of dneff = 0.029 from the core of the T-shaped waveguide to the surrounding three-layer slab waveguides is obtained. The high degree of structural perfection of the QWRs attainable by the CEO method is manifested by the planarity and abruptness of the interfaces along both growth directions, as

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demonstrated in the transmission electron micrograph depicted in Fig. 4. The QWs appear in this image, taken with the electron beam aligned along the wire axis, as dark bands oriented parallel to the edges of the figure, while the AI,Ga,_,As layers show brighter contrast corresponding to their x-value. It should be noted at this point that we could not detect any defects in the overgrown structure originating from the (110) cleave which served as a starting plane for the second MBE growth step. In order to achieve lasing in the 1D structures, mirrors were cleaved perpendicular to the axis of the QWRs. The cleaved mirrors were left uncoated so that each mirror had a reflectivity R of only about 0.3. Optical excitation from either the (001) or the (110) surface of the samples was

Fig. 4. Cross-sectional bright-field transmission electron micrograph of the QWRs and the surrounding waveguide layers. The location of one T-shaped QW intersection is marked by an arrow.

1.56

1.57

1.58

ENERGY (eV) Fig. 5. Photoluminescence (PL) spectra recorded below, at and above threshold for stimulated emission in the QWRs (Ptll _ 10 mW).

performed by focusing the output of a dye laser tuned to A = 775 nm to a stripe of about 700 pm in length and 5 pm in width oriented parallel to the QWRs. At this wavelength significant light absorption occurs only in the GaAs QW and QWR layers. However, because the QWR volume is so small, light absorption takes place mainIy in the QWs. Fig. 5 compares emission spectra of a 600 pm long QWR laser below and above threshold for stimulated emission. At low excitation power (0.25 mW> exciton recombination in the QWRs and QWs is observed at about 1.563 and 1.58 eV, respectively, indicating that the 1D state is about 17 meV deep with respect to the QW state. The doublet structure in the QW emission is beIieved to originate from slightly different confinement energies for the QWs grown along the [OOl] direction and the [llOl oriented QW formed during overgrowth. With increasing pump power the contrast in the Fabry-P&rot (FP) oscillations, which develop on the low energy side of the QWR peak, increases and at about 10 mW stimulated emission occurs. Further increase of the pump power leads to a significant narrowing of the QWR emission spectrum until at pump levels above about 30 mW laser operation predominantly in a single longitudinal mode takes place. The unusually strong contrast in the FP oscillations even at the lowest excitation level indicates

W. Wegscheider et al. /Journal

1.0

of Crystal Growth 150 (1995) 285-292

I

T = 1.7K E = 1.60 eV

0

o-

I 1.562

1.564

1.566

ENERGY (ev)

_

B

~+f(, 0

20 EXCITATION

(

,j.

30 40 50 POWER (mw)

Fig. 6. QWR laser output versus excitation power. High-resolution emission spectra recorded at 4, 10, 15, 30 and 50 mW excitation power are shown in the inset.

a high degree of transparency in the waveguide within this spectral region. This is due to the small fraction r of the optical intensity distribution, of about 3 x 10e3, that overlaps with the QWRs. For comparison, the corresponding value for the QWs in our structure is r N 0.15. The laser output as a function of pump power is shown in Fig. 6, together with high-resolution spectra of the QWR emission. In contrast to the QW peak intensity which increases linearly or sublinearily with excitation power, superlinear behavior is observed. In addition, the QW photoluminescence (PL) signal red-shifts by as much as 5 meV with increasing pump power (see Fig. 5). This is consistent with exciton ionization and photoexcitation of a free electron-hole plasma which is subject to band-gap renormalization effects. For 50 mW excitation (- 3 kW/cm’) we expect a sheet carrier density of N 101* e-h pairs/cm2, assuming an absorption length of 0.5

289

pm in GaAs and a recombination time of 1 ns [21]. The shrinkage of the free-particle band-gap for this density is about 15 meV [4] and exceeds the exciton binding energy in the QWs by about 5 meV. Strikingly, no appreciable shift in the QWR emission occurs for all pump powers used in this experiment. We interpret the implied absence of band-gap renormalization effects as the signature that electron-hole recombination in our QWRs is exclusively excitonic in character. To the best of our knowledge this represents the first observation of excitonic gain in a III/V semiconductor laser. It thus appears that the exciton gas phase in 1D is more stable against ionization compared to its 2D counterpart. Excitonic gain has recently been reported for ZnSe QW lasers 1221. The enhanced stability of the excitons in this case is attributed to the large exciton binding energies in II/VI materials. In order to estimate the binding energies of the 1D excitons in our structure, we compare the experimental data with the energetic difference in the free-carrier QW and QWR transitions predicted by theory (see Fig. 2b). For 7 nm wide QWs the theoretical value for the electron-heavy-hole transition is 10 meV. This is considerably less than the observed red-shift of 17 meV. Since both the QWR and the QW transition at this low excitation level (- 15 W/cm*) are undoubtly of excitonic nature, the energy difference of about 7 meV directly reflects the enhancement of the exciton binding energy due to the reduced dimensionality. Taking a 2D exciton binding energy of lo-11 meV [23,241 for the 7 nm wide QWs into account, we obtain a 1D enhancement of more than 50% to about 17 meV for the QWRs. This considerably exceeds the largest previously reported 1D enhancement of 15% observed in lithographically defined structures with a crosssection of about 70 by 14 nm [25]. 2.2. Current injection A schematic view of the QWR laser structure suitable for current injection is shown in Fig. 7. In this case the MQW region with well and barrier thickness of 7 and 58 nm, respectively (15 periods), is &doped using Be. Except for these

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Be-doping spikes (2 X 10” Be cm-2) in each AlO,,,Ga,,&!.s barrier located after 34 nm below or 24 nm above each QW (see magnified portion of Fig. 71, the whole layer sequence as well as the substrate is again undoped. Note that we have slightly off-centered the &dopant layers in order to compensate for expected Be surface segregation along the growth direction [26]. The postcleave growth sequence consists of a 7 nm GaAs QW (undoped) followed by a 7 nm Al,,,,Ga,,,,As barrier (undoped), a 43 nm undoped Al,,Ga,,As setback, a 124 nm doped Al,,Ga,,As layer (2 X 10” Si cmp3), a 1 pm wide Al,,Ga,,As cladding layer (2 x 1018 Si cmd3> and a 10 nm GaAs cap (2 X 101* Si cmp3>. This doping scheme leads to the formation of a linear p-n junction, i.e. a junction where holes and electrons meet along a line instead of a plane, in the vicinity of the QWRs. Fig. 8 compares the light versus current (L/I) characteristic of two QWR lasers with cavity lengths of 400 and 800 km and uncoated mirrors. The 800 pm long device shows clear superlinear behavior for currents in excess of about 0.5 mA, indicating a threshold current of less than 0.6

unner claddina

loo11 t direction

of

Be-dope

Fig. 7. Schematic representation to scale).

of the QWR laser diode (not

0.0

0.5

CURRENT

1.0

1.5

(mA)

Fig. 8. Light versus current characteristics of two QWR lasers with cavity lengths of 400 and 800 pm. Inset: Current versus voltage characteristics of the 400 Frn long device.

mA. The L/I curve of the shorter laser (400 pm> deviates much more weakly from a strictly linear relationship. This weak superlinear behavior suggests gain saturation in the QWRs, whereby the higher gain required to overcome the internal and mirror losses of the shorter cavity is just exceeded. Extrapolation of the superlinear branch of the L/I curve to zero output power leads to a threshold current of about 0.4 mA for the 400 pm long device. The current versus voltage characteristic of the 400 pm long QWR laser sample is depicted in the inset of Fig. 8. It exhibits a typical diode curve with a turn-on voltage of about 1.55 V, a leakage current below this voltage of less than 100 nA and a differential resistance in forward bias of a few hundred ohms. The breakdown voltage under reverse bias condition is larger than 10 V. The spontaneous emission spectra of the 400 pm long QWR laser sample operated at a current of 0.2 mA is shown in Fig. 9. The photoluminescence (PL) response of the QWR laser structure before overgrowth, i.e. of the MQW layer only, has also been included in this figure as a dashed line for comparison. The QWR laser diode emission is characterized by a single peak which exhibits a shoulder on the high-energy side. By comparison with the MQW reference spectrum,

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of Crystal Growth 150 (1995) 285-292

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criterion given above is 0.55 mA for the 800 pm long QWR laser cavity.

3. Conclusions

0 1.56

1.57

1.56

1.59

1.60

ENERGY (ev) Fig. 9. Spontaneous emission spectrum of the 400 pm long QWR laser structure recorded - 50% below threshold ) and photoluminescence response of the MQW (-structure before overgrowth (- - -I.

the latter can be unambiguously identified as the luminescence originating from the MQWs formed during the first growth step. The luminescence energy of the single QW formed during overgrowth is expected to be close to that of the MQWs, due to nominally identical well widths. The strong peak in the QWR laser emission centered at around 1.577 eV can, thus, only be attributed to radiative recombination from 1D states in the QWRs. The fact that the emission from our laser at injection levels considerably below threshold is almost completely dominated by optical transitions in the QWRs emphasizes the highly efficient way charge carriers are injected using this approach. Similarly to the results on optical excited QWR laser structures, closely spaced FP oscillations corresponding to different longitudinal modes within the optical cavity are superimposed onto the QWR response. At an injection current of 0.4 mA, the contrast ratio in these oscillations already exceeds the theoretically expected ratio for an empty cavity, (1 + R)*/(l - R)* = 3.45, using a mirror reflectivity R = 0.3. Thus the QWR laser already develops net gain at this injection current. Higher injection levels of 0.8 and 1.5 mA result in progressive narrowing of the laser emission envelopes as well as of the individual FP peaks. The corresponding threshold current to meet the FP contrast ratio

and prospects

We have used CEO to fabricate nearly perfect QWRs with a cross-section of only 7 by 7 nm. Stimulated excitonic emission in the 1D quantum limit, i.e. from the ground state exciton, was demonstrated at low excitation levels, where the QWs adjacent to the QWRs do not lase. Single mode laser operation with no appreciable shift of the emission at all pump powers indicates an enhanced stability of the exciton gas phase in 1D. As an extension of this work, we point out that the intersection of three QWs results in the formation of a zero-dimensional COD)bound state. A future implementation of the CEO method which involves two separate cleave and overgrowth steps should be well suited for the fabrication of a linear array of these OD structures.

Acknowledgments

We appreciate valuable discussions with S.L. McCall, H.L. Stiirmer, N.K. Dutta, M.S. Hybertsen, A. F. J. Levi, R.E. Slusher, N. A. Olsen and W.-K. Wang, focused ion beam sample preparation by F. Stevie and technical assistance from B.S. Dennis, B. Kane and D. Bahnck. One of us (W.W.) gratefully acknowledges financial support by the Deutsche Forschungsgemeinschaft during the initial stages of this project.

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