Inelastic-light-scattering measurements show that exchange Coulomb interactions in the twodimensional electron gas of GaAs microstructures are more important than previously anticipated. Small-wave-vector spectra from modulation-doped quantum wells exhibit unexpected single-particle intersubband transitions in addition to collective spin-density and charge-density modes. From the measured spectral energies the direct and exchange intersubband Coulomb interactions are determined and found to be of comparable strengths. PACS numbers: 71.45.Gm, 73.20.Dx, 73.20.Mf, 78.30.Fs Free electrons in semiconductor microstructures reveal new behaviors that arise from fundamental electronelectron interactions and the reduced dimensionality. 1 Strong correlations in the electron gas, as in the fractional quantum Hall effect, are revealed in magnetotransport 2 and also in magneto-optics. 3,4 More generally, Coulomb interactions and reduced dimensionality have strong manifestations in the elementary excitation spectrum of the free electrons. The energies and character of these excitations are directly studied in optical experiments, such as infrared absorption 5 and inelastic light scattering. 6The light-scattering method is especially powerful because both spin-density and charge-density excitations can be measured. 6 ' 7 At small wave vectors the energies of spin-density modes are shifted from single-particle transition energies by the exchange Coulomb interaction. 1 ' 8 Charge-density modes have energy shifts due to direct as well as exchange terms. 16 " 9 However, since exchange interactions were expected to be small in GaAs, 8 spin-density excitations were previously interpreted as the energy spacings of the quantum-well states and referred to as single-particle excitations. 7,10 " 12 Similarly, the shift of charge-density excitations from singleparticle transition energies was considered in terms of direct Coulomb interactions and coupling to polar optical phonons. 6 ' 7,10 This Letter presents new results showing that such widely used interpretations of inelastic-light-scattering experiments require important revisions. In spectra of small-wave-vector intersubband excitations we find unexpected single-particle transitions in addition to the peaks of collective spin-density and charge-density modes. The significant shifts of the spin-density excitations from intersubband transition energies reveal large exchange interactions. With increasing wave vector, the collective spin-density and charge-density modes display enhanced broadening when their energies overlap the continua of single-particle transition (Landau damping). Analysis of the energies of the three excitations yields quantitative determinations of Coulomb interactions in

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In optical experiments with laterally patterned GaAs quantum wells we observe confinement of free carriers to motion in one dimension. Optical recombination of band-gap transitions shows that free electrons and holes are confined in spatially indirect type-II multiple quantum wires. Resonant-inelasticlight-scattering spectra show intersubband excitations of the one-dimensional electron gas. From the optical measurements we obtain the Fermi energy as well as subband spacings and determine the linear free-electron density. PACS numbers: 78.55.Cr, 73.20.Dx, 78.30.Fs Advances in epitaxial growth and in nanometer-scale lithography have made it possible to fabricate semiconductor structures which exhibit one-and zero-dimensional properties. Semiconductor quantum wires and boxes have been found to exhibit new structure 1 " 4 or energy shifts 5 ' 6 in their photoluminescence (PL) spectra which have been ascribed to excitonic confinement effects. Transport properties of modulation-doped quasi-one-dimensional structures such as electron waveguiding, 7 quantization of resistance, 8 and quenching of the Hall effect 9 have also been observed. Reed et al. 10 observed resonant tunneling into quantum boxes. Less work has been done on the optical properties of one-and zero-dimensional modulation-doped structures. Hansen et al. 11 and, more recently, Heitman et al} 2 have observed intersubband resonances in a quasi-one-dimensional electron gas by means of infrared absorption.This Letter reports the observation of optical properties of a semiconductor one-dimensional (ID) electron gas that are markedly different from closely related two-dimensional (2D) systems. Band-gap optical absorption and emission in GaAs-(AlGa)As multiplequantum-wire structures reveal properties of conductionand valence-band states that are not obtainable from transport or infrared absorption measurements. Resonant inelastic light scattering is used to measure the energy spacings between the electron-gas states confined to one dimension. In these experiments we have determined that the lower states of electrons in conduction subbands and of holes in valence subbands show ID confinement in adjacent, spatially separated quantum wires. We describe this behavior as a type-II multiplequantum-wire heterostructure. 13 ' 14 Multiple quantum wires are fabricated from modulation-doped GaAs/AlGaAs single-quantum-well heterostructures grown by molecular-beam epitaxy on a GaAs substrate. The procedure is schematically shown in Fig. 1. The as-grown 2D electron-gas structure consists of a 250-A-thick GaAs quantum well, separated from the surface by a 1000-A-thick /z-type delta-doped Alo.3Gao.7As layer and a 40-A-thick GaAs cap layer.