Surface Science 229 (1990) North-Holland
FIELD-EFFECT J. ALSMEIER,
E. BATKE and J.P. KOTTHAUS
Institut ftir Angewandte Physik, Universitiit Hamburg, Received
DOTS ON SILICON
11 July 1989; accepted
1 I. D-2000 Hamburg 36, Fed. Rep. of Germany
A versatile dual gate structure on silicon is presented in which a periodic array of electron disks with diameters in the 100 nm range can be induced by field effect. With far infrared spectroscopy at low temperatures we demonstrate that the disks containing 20 to 350 electrons can be tuned from quasi-two-dimensional behavior to quantum dot behavior by electric and magnetic fields.
The lateral confinement of originally two-dimensional (2D) electron layers to submicron dimensions has now made possible the realisation of quasione-dimensional ( 1D) [ 1 ] and quasi-zero-dimensional (OD) [ 2-4 ] electron systems. Here we demonstrate that field effect can be used to create small electron disks in which lateral confinement is tunable from classical to quantum behavior. The devices schematically shown in fig. 1 are prepared on p-Si ( 100) with doping N., x 6 x 1014 cmp3. The bottom gate is a thin NiCr mesh with period a = 400 nm embedded between two layers of SiOz on which a ho-
Fig. 1. Schematical cross section of a dual gate device on Si. The top gate is homogeneous, whereas the bottom gate is a NiCr mesh embedded between a thermal and a PECVD SiOa layer. Typical dimensions are a= 400 nm, t= 150 nm, d, = 50 nm and d2 = 150 nm. * Permanent address: Sektion Physik, Universitlt Miinchen, Geschwister-Scholl-Platz 1, 8000 Mtinchen 22, Fed. Rep. of Germany. 0039-6028/90/$03.50 (North-Holland)
0 Elsevier Science Publishers
mogeneous, semitransparent top gate is evaporated. The voltage at the top gate Vpt induces electrons at the Si-SiO, interface below the openings of the mesh and determines the electron number No per disk, whereas the voltage at the bottom gate is set to a threshold voltage l’&= l’, and serves to keep the disks isolated. At liquid-helium temperatures ( Tc 2 K) minority carriers are injected at gate voltage V,, via a substrate contact while illuminating the sample with band gap radiation. After charging, the band gap radiation is switched off and the electronic diameter W of the electron disks is reduced below the geometrical value t (see fig. 1) by the build-up of a depletion region with charge Ndepl in the substrate. The N depl can be further enhanced by a substrate bias voltage Vsn added to V,, in the dark [ 5 1. We measure the relative change in transmission of - AT/T= [ T( 0) - T( No) ] / far-infrared radiation T(0) as shown in fig. 2 and observe strong dimensional resonances characteristic for arrays of isolated electron disks. In the low signal limit appropriate here the strength of the resonances is proportional to the average area1 electron density No/a’. As is apparent in fig. 2a No is nearly independent of VsB but depends in a nonlinear fashion on VP,- V, yielding, e.g., N,- 30 at ( Vgt- V,) = 10 V. For vanishing N, the resonance energy fiw extrapolates to a finite value of about fioO = 6 meV at VsB = 0 V and AoO = 9 meV at VsB = 18 V, respectively. This is in contrast to the behavior expected for a classically confined disk with depolarisation frequency wi x No/ W3 [ 6 1. We in-
J. Alsmeier et al./F’ield-effect tunable quantum dots on Si
Fig. 2. Relative change in transmission -AT/T at 2 K of a periodic array of electron disks on p-Si( 100) for different average electron densities No/a2 and depletion charges NdcPl. (a) Quantum confined dots with Wg 50 nm (solid traces) and W< 40 nm (dashed traces). (b ) Dependence of the high frequency response on the bottom gate voltage V, at fixed Ndcpl.
terpret the observed resonances as OD intersubband resonances with frequency w= (w$ +Q2) 1/2 shifted by collective phenomena from the OD subband spacing rioo. Assuming parabolic confinement we deduce dot diameters for low N,5 30 of W= 50 nm for VsB= 0 V and Wz 40 nm for VsB= 18 V, respectively. Thus via depletion build-up we are able to continuously tune W to values far below the geometrical openings t without significantly changing N,,. In addition we are able to vary the confining potential at fixed Vs, and V,, via the voltage V,, at the bottom gate as demonstrated in fig. 2b. Here increasing Vgb from a value where the Fermi level below the bottom gate is located at the top of the valence band by a voltage equivalent to the band gap we increase No whereas the resonance energy decreases. This we interpret as an increase of W by a factor of 1.6 by fringing field effects. In a magnetic field B applied perpendicularly to the sample surface the dimensional resonance splits into two modes as has been demonstrated for both classical disks [ 6-8 ] and quantum confined dots [ 4 ] with resonance frequencies w*= *c&/2+ [(w~/~)~+w~=~]‘/~ and w,=eB/m*. For a large No = 240 this is shown in fig. 3a. At large magnetic fields the mode o, becomes cyclotron resonance-like, whereas the resonance with o_ is an edge-like mode. The line shapes of the spectra can only qualitatively be described by a classical model for a parabolically confined electron system [ 9 1. To analyse the oscil-
Fig. 3. Relative change in transmission AT/T of an array of electron dots on Si at Vss= 18 V in magnetic fields B applied perpendicularly to the sample surface. (a) Dots containing about 240 electrons. (b) Dots with a number of electrons in the regime
lator strength S, and S_ we approximate the lineshapes of the o+ and w_ resonances with Lorentzian profiles. A relative oscillator strength different from the classical and quantum mechanical prediction S, /S_ = w, /w_ are observed at medium magnetic field strength if we establish flat band conditions below the mesh by choosing the appropriate I’& thus generating a confining potential for electrons with depth close to the band gap as shown in fig. 3b. For No in the regime 20 5 No 5 170 we obtain from fits to the lineshapes a ratio of oscillator strength S, / S_ N 3w,/2w_. This is a general trend found at low electron numbers No 5 170 if the depth of the confining potential is close to the band gap. At higher magnetic fields Bz 10 T S+/S_ approaches the predicted ratio. Generally this happens in a magnetic field regime where the diameter of the cyclotron orbit at the Fermi energy is less or equal to the diameter of the dots. This we attribute to relate to the strong quantum confinement in our dots. A more detailed discussion will be given elsewhere. In summary we present a dual gate structure on silicon, which allows us to create a periodic array of small electron disks with diameters tunable below 100 nm. Infrared spectroscopy is used to measure the high-frequency conductivity and demonstrates strong quantum confinement. We would like to acknowledge
J. Alsmeier et al/Field-effect tunable quantum dots on Si
by Stiftung Volkswagenwerk Forschungsgemeinschaft.
References [ 1 ] W. Hansen, M. Hors& J.P. Kotthaus, U. Merkt, Ch. Sikorski and K. Ploog, Phys. Rev. Lett. 58 (1987) 2586.  M.A. Reed, J.N. Randall, R.J. Aggatwal, R.J. Matyi, T.M. Moore and A.E. Wetsel, Phys. Rev. Lett. 60 (1988) 535.  W. Hansen, T.P. Smith III, K.Y. Lee, J.A. Brum, C.M. Knoedler, J.M. Hong and D.P. Kern, Phys. Rev. Lett. 62 (1989) 2168.
 Ch. Sikorski and U. Merkt, Phys. Rev. Lett. 62 ( 1989) 2164. [ 5 ] E. Batke and D. Heitmann, Infrared Phys. 24 ( 1984) 189.  S.J. Allen, Jr., H.L. Stiirmer and J.C.M. Hwang, Phys. Rev. B28 (1983) 4875.  D.B. Mast, A.J. Dahm and A.L. Fetter, Phys. Rev. Lett. 54 (1985) 1706.  D.C. Glattli, E.Y. Andrei, G. Deville, J. Pointrenaud and F.I.B. Williams, Phys. Rev. Lett. 54 (1985) 1710.  B.A. Wilson, S.J. Allen, Jr. and D.C. Tsui, Phys. Rev. B 24 (1981) 5887.