InP V-groove quantum wires

Physica E 2 (1998) 969—973

First observation of symmetry breaking in strained In Ga As/InP V-groove quantum wires 0.7 0.3 Oliver Stier*, Volker Tu¨rck, Michael Kappelt, Dieter Bimberg Institut fu( r Festko( rperphysik, Technische Universita( t Berlin, Hardenbergstra}e 36, D-10623 Berlin, Germany

Abstract Quenching of ground-state luminescence is observed for strained InGaAs/InP V-groove quantum wires. This is the first experimental evidence for geometrical symmetry breaking of the lowest valence-band states due to pseudomorphic strain, which was previously predicted by us. There is good agreement between optical characterisation and theoretical modelling. ( 1998 Elsevier Science B.V. All rights reserved. Keywords: Semiconductor quantum wires; Band structure; Symmetry breaking; Piezoelectricity

1. Introduction The research on the fabrication and modelling of semiconductor quantum wires (QWs) during the past 15 years was stimulated by the prediction of promising electronic and optical properties [1] which enable the design of low-threshold current lasers [2,3]. Apart from their device relevant advantages QWs may also display novel basic physical phenomena. In particular, strained V-groove QWs have been predicted to exhibit size-dependent symmetry breaking (SB) in their valence band (VB) structure due to anisotropic strain distributions [4]. This unusual feature is observable under conditions which are almost contrary to those for good lasing operation, namely at very low carrier densit* Corresponding author. Fax: #49 30 31 42 25 69; e-mail: [email protected].

ies in the QW and, in consequence, at minimum light output. We recently observed optical properties of In Ga As/InP V-groove QWs which con0.7 0.3 currently point to the presence of SB in the onedimensional (1D) top VB. The key issue is that the luminescence from the ground-state interband transition is quenched due to the built-in piezoelectric field. Three years ago we predicted the occurrence of such SB in perfectly symmetrical, compressively strained V-groove QWs [4]: the shape-dependent spatial distribution of the pseudomorphic strain e(r) has a direct impact on the electronic band structure, which to first order can be visualised by an effective potential » (r) superposing the confine453!*/ ment by the bulk band discontinuities. Further, the piezoelectric charging of the structure contributes a static field F(r)"!+U(r). The sum » " 505 » #U was found to be attractive for electrons 453!*/

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O. Stier et al. / Physica E 2 (1998) 969—973

(e) in the groove center r , and repulsive for holes #%/ (h). Hence, the 1D VB has a bimodal ground-state (n"1) envelope function and degenerates as » (r )P!R. In this limiting case the degener505 #%/ ate n"1 eigenspace can be expanded into two particularly graphical basis functions, one of which is localised on the right of r while the other is on #%/ the left. Such a lateral splitting of formerly one state is the typical characteristic of geometrical SB. It mainly results in a spatial separation of e’s and h’s and the recombination becomes spatially indirect. In a not perfectly mirror symmetrical structure there is no exact degeneracy, so that the left and right holes will have slightly different energies. Now the former arbitrarily chosen basis vectors turn out to be the most physical ones, the signature of SB remains clear. A year ago we have shown that SB in the more generalised sense of near-degeneracy occurring in geometries with only single mirror symmetry is not restricted to the ground state [5]: it may affect an excited valence subband as well, while leaving the n"1 subband in its normal fashion. As the main consequence of the reduced e—h overlap we expect increased carrier lifetimes and a low luminescence intensity. The effect is the more pronounced the larger the QW is. For large QWs the piezoelectric potential U dominates over » so that we can neglect the latter. Besides, note 453!*/ that » is only a one-band-theory vehicle to 453!*/ support imagination but does not appear in our present calculation. The ground-state e’s and h’s are well separated only if their total number is not too large. For a strong population of the respective 1D subbands the Coulomb potentials of the carriers yield a screening of » so that the SB will disappear in 505 favour of a blue shift of all transitions involved (Stark shift). Since the 1D density of states (DOS) in QWs allows for 1D carrier densities of more than 108 cm~1 such screening usually will occur. Only if the excitation of the QW, i.e. both carrier generation by photoabsorption and carrier capture, is very inefficient we can expect to observe quenching of the ground-state luminescence according to our theory. Further, a high carrier temperature would be of advantage because it distributes the few carriers over possibly many 1D subbands. Thus, the

most separated and most strongly localised lowest states are possibly poorly populated while a larger amount of e’s and h’s is less localised. This will damp the screening effect significantly.

2. Sample structure Single QWs were fabricated by metal-organic chemical vapor deposition of nominally undoped InGaAs on a V-grooved InP : S (0 0 1) substrate and overgrown with 50 nm of InP [6,7]. The grooves are oriented along [11 11 0] having 5 lm distance. After growth the quantum wells formed on the ridges between the grooves were removed by wet chemical etching. Fig. 1a shows a cross section

Fig. 1. (a) Cross section TEM image of the QW; envelope functions of the CB ground state (b), the VB ground state (c), and the first excited VB state (d). The outermost isolines indicate 99% probability.

O. Stier et al. / Physica E 2 (1998) 969—973

transmission electron microscopy (TEM) image of a single QW. The QW width is 180 nm, the thickness is varying between 8.2 nm at r and 3 nm at #%/ the ends. The Ga content in the QW is yet unknown although expected less than 47% from the growth conditions. It can, however, well be estimated from the QW photoluminescence (PL) by comparison with calculated spectra for different Ga contents. We found that the wire must be under compressive strain and that 31$2% Ga fits best by far. Hence, the lattice mismatch is !1.1% and the critical InGaAs thickness is 21 nm. Our QW is much thinner than that.

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Fig. 2. Squared dipole matrix elements of the lowest transitions. The ground state transition is too weak to be displayed.

3. Theoretical properties We have calculated the strain distribution e(r), piezoelectric charging U(r) and the 1D band structure for a Ga content of 31% as outlined in detail in Ref. [8], assuming a sample temperature of 6.5 K. The cross section TEM was digitised with 0.7 nm spatial resolution, and from this e was calculated by finite elements, U by solving the Poisson equation including image charges, and the band structure by using the 8-band k ) p model and finite differences. All material parameters were taken from the newest available literature, and except to the Ga content none of them is adjustable. From the conduction band (CB) and VB eigenstates dipole matrix elements DSe De ) pDh TD2 were calculated to estimate osi j cillator strengths. The population of the 1D subbands was simulated using the calculated DOS, an estimated total number of carriers, and a carrier temperature derived from PL measurements. Fig. 1b shows the CB ground state, and Fig. 1c and d show the two top VB states which have emerged from the “unstrained case” ground state under the influence of SB. The effective masses in QW direction are m "0.048 and m "0.064, so % ) the 1D e is heavier than the bulk e (0.038) while the 1D h is much lighter than the bulk HH (0.446). The ground-state e and h have a spatial distance of 75 nm, and the difference of U between their positions is 29 meV. Thus, the piezoelectric field in this QW region has an average strength of DFD"3.9 kV cm~1. Fig. 2 shows the calculated recombination spectrum involving only states n , CB

n )5 for carrier wave numbers k "0. The VB ,QW quantum numbers n refer to both spin orientations without distinguishing them. Due to the near-zero overlap the ground-state transition Se De ) pDh T is 1 1 too weak to be displayed. Considering the states n , n )20 at a certain population (outlined beCB VB low), we find that the luminescence lines gather in three main groups: one is centred at 780 meV with FWHM"3 meV and a relative integral intensity of 1, the second at 810 meV with FWHM" 23 meV and intensity 457, and the third at 857 meV with FWHM"58 meV and intensity 417. The first group stems mainly from transitions from the CB ground state while the second and third are dominated by n "2,2, 8 and n *9, respectively. CB CB Further, we have calculated the charge distribution in the QW assuming it to contain 5]105 cm~1 e—h pairs with an effective carrier temperature of 550 K. The temperature was estimated from the PL spectrum at 50 W cm~2 excitation by an Ar` ion laser, see Fig. 3a. We emphasise that this carrier temperature is only used to model the energetic distribution of e’s and h’s. In fact, we cannot yet provide an explanation for this high value. The above excitation will generate 4]104 cm~1 e—h pairs by pure photoabsorption in the QW if the average carrier lifetime is 1 ns. From photoluminescence excitation spectroscopy (PLE) and cathodoluminescence (CL), we found that carrier capture from the InP barrier is very inefficient and not supposed to yield much more e—h pairs in the QW than direct photoabsorption. Therefore, we

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O. Stier et al. / Physica E 2 (1998) 969—973 Table 1 Groups of transition lines identified in the QW luminescence at 5/50/500 W cm~2

Fig. 3. (a) PL spectra at 8 K for four different excitation densities. (b) Line shape fit of the QW luminescence at 50 W cm~2.

No.

Center (meV)

FWHM (meV)

Rel. intg. intens.

1 2 3

765$4 808$4 851$3

11—16 49—56 82—115

—/1/7.4 57/437/777 26/403/5000

profiles, with no residual background. Only at 880—920 meV H O absorption had to be con2 sidered, see Fig. 3b. 0.5 W cm~2 gave too little signal for our analysis. For 5/50/500 W cm~2 we found the same three constituents each, which are listed in Table 1, except that d1 was not observable at 5 W cm~2. The relative integral intensities in Table 1 refer to the three excitations. They show how the population of the 1D subbands is varying with the excitation density. So there is an appreciable congruence with the theory. A similar group structure was found in the CL spectrum of a single QW. The carrier capture from the InP barrier is very weak.

consider 5]105 cm~1 a reliable upper boundary for the carrier density in the QW at 50 W cm~2 excitation. Then we find a weakening of U by the carrier potentials to DFD"2.6 kV cm~1 which will reduce the e—h distance by 2 nm only. Hence, the piezofield is not screened at excitations )100 W cm~2, and SB is observable.

5. Conclusion

4. Experimental results

Acknowledgements

Fig. 3a displays four PL spectra measured at 8 K and different excitation densities, each averaging ca. 40 QWs. The luminescence at 750—950 meV was unambiguously assigned to the QWs by spatially resolved CL. It surprises that at whatsoever low excitation luminescence from a spectral range of ca. 0.2 eV is obtained. The emission at 1.1 eV stems from quantum wells formed at the groove sidewalls. The spectra were each subjected to a rigorous lineshape analysis in which the QW luminescence was completely decomposed into Gaussian and Voigt

We thank Ju¨rgen Christen for valuable discussions. This work was funded by Deutsche Forschungsgemeinschaft in the frame of SFB 296.

We have observed the quenching of ground-state luminescence caused by geometrical symmetry breaking in pseudomorphic InGaAs/InP QWs. The computational modelling is in ample accordance with CL, PL, and PLE measurements.

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O. Stier et al. / Physica E 2 (1998) 969—973 [4] M. Grundmann, O. Stier, D. Bimberg, Phys. Rev. B 50 (1994) 14187. [5] O. Stier, M. Grundmann, D. Bimberg, in: M. Scheffler, R. Zimmermann (Eds.), Proc. 23rd Int. Conf. Phys. Semicond., World Scientific, Singapore, 1996, p. 1177. [6] M. Kappelt, V. Tu¨rck, O. Stier, D. Bimberg, H. Cerva, D. Stenkamp, P. Veit, T. Hempel, J. Christen, Extended

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Abstracts of European Workshop on MOVPE VII, at TU Berlin, Germany, 1997, p. E5. [7] M. Kappelt, V. Tu¨rck, O. Stier, D. Bimberg, Extended Abstracts of Indium Phoshpide and Related Materials ’97, Hyannis, MA, 1997. [8] O. Stier, D. Bimberg, Phys. Rev. B 52 (1997) 7726.