HAL Id: jpa-00226790
https://hal.archives-ouvertes.fr/jpa-00226790
Submitted on 1 Jan 1987
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.
SPECTROSCOPIC INVESTIGATION OF THE SUBBAND EDGE RENORMALIZATION IN ELECTRON-HOLE PLASMAS IN GaAs/GaAlAs
QUANTUM WELLS
E. Lach, G. Tränkle, A. Forchel, G. Weimann
To cite this version:
E. Lach, G. Tränkle, A. Forchel, G. Weimann. SPECTROSCOPIC INVESTIGATION
OF THE SUBBAND EDGE RENORMALIZATION IN ELECTRON-HOLE PLASMAS IN
GaAs/GaAlAs QUANTUM WELLS. Journal de Physique Colloques, 1987, 48 (C5), pp.C5-403-C5-
406. �10.1051/jphyscol:1987586�. �jpa-00226790�
Colloque C5, supplBment au n0ll, Tome 48, novembre 1987
SPECTROSCOPIC INVESTIGATION OF THE SUBBAND EDGE RENORMALIZATION IN ELECTRON-HOLE PLASMAS I N GaAs/GaAlAs QUANTUM WELLS
E. LACH, G. TRANKLE, A. FORCHEL and G. WEIMANN*
4. Physik Institut, Universitat stuttgart, 0-7000 ~tuttgart-80, F.R.G.
*~orschungsinstitut der Deutschen Bundespost, 0-6100 Darmstadt, F.R.G.
Abstract:
In quasi-two-dimensional GaAs/GaAlAs multiple quantum well structures we have investigated the renormalization of the different subband edges due to many-body effects in electron-hole plasmas. We observe a rigid shift of all subbands to lower energy with increasing total carrier density independent of the density in a particular subband.
Correlation interactioris lift the independence of the subbands and trace the band renormalization to the total plasma density.
A high density electron-hole plasma (EHP) in semiconductors leads to a renormalization of the fundamental band gap due to many-body effects [I]. In two-dimensional (2D) semiconductor structures bandfilling effects lead to the occupation of the higher subbands. The carrier density in the higher subbands is smaller than in the lower ones depending on the density-of-states and on Fermi statistics. From theoretical considerations of the exchange and correlation interactions which depend strongly on the carrier density it is not clear whether the renormalization of the higher subbands edges is different for the different subbands or whether it is the same as that for the fundamental band gap.
To study the band renormalization of the higher subbands in 2D semiconductor structures we performed high excitation photoluminescence measurements at lattice temperatures between 2 K and 300 K in GaAs/GaAlAs MQW-structures grown by MBE with well widths LZ between 9.6 nm and 18 nm and Al-contents between 22 % and 43 %. We excited an EHP using a dye laser pumped by a N2-laser with excitation intensities up to 1 M W / C ~ ' . Compared to typical relaxation times in quasi 2D systems [2] the pulse width of the laser ( T = 10 ns) was large enough to provide quasistationary excitation conditions, permitting the description of the EHP in thermal equilibrium. To avoid the observation of stimulated emission backscattering geometry was used in all high excitation experiments. In order to obtain the energetic positions of the optical transitions between the different subband edges at zero carrier density and to determine experimentally the subband structures o f ' t h e samples we performed absorption measurements at low temperatures.
Figure 1 shows a series of photoluminescence measurements of a sample with a well width of 9.6 nm recorded at room temperature illustrating the general behaviour of the spontaneous luminescence of a 2D EHP. Due to band filling we observe a drastic broadening of the emission line (up to 400 meV). On the
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987586
C5-404 JOURNAL DE PHYSIQUE
I I I high energy side of the plasma spectra various new structures appear indicating the occupation of the higher subbands. The structures correspond to allowed (An = 0) and forbidden-but-parity-allowed (A n =
+
2) transitions between these subbands [3]. The flattening of the high energy sides of the spectka show the rising of the plasma temperature due to nonresonant excitation of the samples.The low energy edges of the spectra resulting from transitions between the first electron subband and the first heavy hole subband shift to smaller energies (dashed line) in contrast to the maxima of the lineshapes which are affected only at the highest intensities. The shift of the low
-
energy edges of the transitions between the higher subbands cannot be deduced from these plasma spectra3 directly, because these are a superposition of all possible 1.40 1.45 1.50 1.55 1.60 transitions which covers the individual features of the
Energy (eV)
higher ones.
Fie.
Typical plasma spectra of highlyexcited G a A s / G a M s . The dashed line The first possibility to investigate the shift of the higher displays the shift of the fundamental band subbands is the comparison of the emission spectra with edge with increasing plasma density absorption measurements, which show the subband edges at zero density. In figure 2 we compare two high excitation spectra measured at low temperature
and at room temperature with a low temperature absorption spectrum of a sample with a well width LZ of 11.5 nm and an Al-content of 35 %. The luminescence lines are displaced relative to the absorption spectrum to account for the many-body renormalization at high densities and for the temperature induced gap shrinkage (room temperature spectrum) of corresponding transitions. Each structure of the EHP spectrum at low temperatures has a counterpart at the same energetic position in the plasma spectrum at room temperature (The deviation at the structure belonging to the transitions between the lowest subbands is a
consequence of the very strong luminescence 1.6 1.7 1.8
background of a GaAs buffer layer at low Energy (eV)
As indicated the dashed lines
&J
Comparison of experimental high excitation every structure in the absorption spectrum spectra (top trace: 300 K, middle trace: 2 K), (mainly due to excitonic transitions) has aabsorption spectra (bottom trace) and calculations counterpart in a low energy edge of a structure
transitions indicated in figure 2 using a rectangular potential well with finite barriers, a band discontinuity distribution of 60:40 and neglecting any exciton binding energies. If compared to the low energy shoulders of the high excitation spectra, both the experimentally observed structures in the absorption spectra as well as the calculated transition energies indicate that the relative subband spacing of the quantum wells is not altered under high excitation conditions.
The second possibility to study the relative shift of the subband edges is a lineshape analysis of the plasma spectra in a well-established model [4] for the band-band recombination between the different subbands. The model assumes momentum conservation and constant matrix elements for all allowed transitions as well as for the forbidden-but-parity-allowed transitions. The carriers are distributed in the different subbands assuming common quasi-fermi levels for the electrons and holes, respectively, and a common temperature for all carriers. We use a parabolic dispersion relation in the electronic subbands. To account for the strong nonparabolicity of the valence subbands we use a numerical dispersion relation calculated in the k.p Luttinger-Kohn formalism [5]. Furthermore a Landsberg type broadening [6] is included to account for the low energy edges of the different transitions.
I I I
Lineshape analysis of a plasma spectrum of a sample with LZ = 9.6 nm. The upper part shows a fit using shifts of the various subband edges according to the different carrier densities. The lower part depicts the fit using a rigid shift of the complete subband structure according to the total carrier density.
1.40 1.45 1.50 1.55 1.60
Energy (eV)
Assuming a rigid renormalization independent of the particular subband this lineshape analysis is based entirely on the subband level spacing determined from the absorption measurements. In figure 3 we show the results of the analysis of a plasma spectrum obtained in a sample with well width LZ of 9.6 nm. In the lowet. part we compare the experiment with the calculation of a plasma lineshape assuming a rigid shift of all subbands corresponding to the total plasma density. In the upper part on the contrary we depict the calculation assuming different shifts of the different subbands given by the carrier density in each subband only [7]. In this case the shifts of the higher subbands become very small (compare the components of the calculated lineshape). If we assume a rigid shift of the subbands the agreement between the experimentally
C5-406 JOURNAL DE PHYSIQUE
observed and calculated positions of all spectral features is rather good. Especially the low energy edges of the transitions between higher subbands occur exactly at the energies of the experiment. In the other case the experiment is not reproduced at all by the calculation. The components of the lineshape belonging to transitions between higher subbands (e.g. 13h- or 2hh- transitions) are shifted compared to the experiment by more than 20 meV. This gives strong evidence that the renormalization of the subband ladder occurs independent of the partial density in a particular subband.
The band renormalization is a consequence of correlation and exchange interactions between electrons and holes in EHP. The correlation interaction depends on the total carrier density in contrast to the exchange interaction which depends only on the partial density in the respective subband. Our results indicat that under the chosen experimental conditions the contribution of the exchange interaction must be small compared to the contribution of the correlation interaction.
In summary in our high excitation photoluminescence measurements we observed a rigid shift of all subband edges in quasi-2D quantum well structures. The correlation interaction between electrons and holes in a high density EHP lifts the independence of the various subbands and relates the band renormalization to the total plasma density.
We thank C. Ell, G. Mahler and M. Pilkuhn for valuable discussions. The work has been supported by the Deutsche Forschungsgemeinschaft under Contract No. Pi-71/20 and by the Stiftung Volkswagenwerk.
References
[I] Proceedings of the 3rd Trieste International Centre for Theoretical Physics - IUPAP Semiconductor Symposium, edited by M.H. Pilkuhn, J.Lumin. 30 (1985) [2] J. Shah, IEEE QE-22 (1986) 1728
[3] G. Trankle, H. Leier, A. Forchel and G. Weimann, Surf. Science 174 (1986) 211 [4] G. Trankle, A. Forchel, E. Lach, F. Scholz, M. H. Pilkuhn, G. Weimann, H.Kroemer,
S.Subbanna, G. Griffiths, M. Razeghi; Inst. Phys. Conf. Ser. No. 83, The Institute of Physics, Bristol and London 1987, p. 221
[5] D. A. Broido and T. L. Reinecke, private communication [6] P.T. Landsberg, phys. status solidi 15 (1966) 623
[7] For the density dependence of the band renormalizaton see e.g.
G. Trankle, H. Leier, A. Forchel, H. Haug, C. Ell, G. Weimann, Phys. Rev.Lett. 58 (1986) 419
