110 Brazilian Journal of Physics, vol. 26, no. 1, March, 1996 Quantum Wires and Quantum Dots in Hetero junction Devices with Field-E ect Electro des W. Hansen, D. Schmerek and H. Drexler Ludwig-Maximilians-Universitat, Muchen Geschwister-Schol l Pl. 1, 80539 Munchen, Germany Received July 21, 1995 We generate in esp ecially designed hetero junction crystals one-dimensional electron wires and zero-dimensional electron dots with a eld-e ect controlled numb er of electrons o c- cupying the lowest quantum states. Very strong and well controlled con nement of one- dimensional quantum wires is achieved with patterned eld electro des, that allowusto study the electronic prop erties of quantum wires as function of the sti ness of the con ne- mentpotential. For exp eriments on smallest electron dots with very large energy spacing of the quantum dot levels we study structurally con ned electrons in self-assembled InGaAs islands that are grown in the Stranski-Krastanow mo de. The electron systems are char- acterized with capacitance sp ectroscopy and with far-infrared absorption exp eriments that prob e the electronic ground states and the fundamental excitations, resp ectively. [3] or quantum dots . Such systems are preferentially I. Intro duction prepared from a high mobilitytwo-dimensional elec- Manyphysical prop erties of an electron system are tron system at the interface of a mo dulation-dop ed critically dep endent on its dimensionality. This is hetero junction crystal. Their geometry is usually de- mainly due to mo di ed screening and di usion and the ned either byetching patterns into the crystal surface reduced density of states (DOS) in lower-dimensional or by means of patterned eld-e ect electro des biased electron systems. The latter arises from the fact that to deplete the areas b eneath the electro des of mobile [4] con nement of the electrons reduces the degree of free- electrons . Then electron strip es or discs are left in dom for free motion and thus the dimensionality of the the unetched areas or in the gaps b etween the elec- quasi-continuous regions in phase space. Thus energy tro des. Although these techniques have b ecome quite levels of electron systems con ned in one or two di- sophisticated and manyintriguing results are obtained, mensions form two- or one-dimensional subbands. Of imp ortant parameters like the energy quantization due course, con nementinto all three spatial dimensions to the lateral con nement and the numb er of electrons leads to a fully quantized energy sp ectrum likeinan o ccupying the one-dimensional subbands of the wires atom. So-called two-dimensional electron systems are or the energy levels of the dots is often not well known usually generated in the plane of a semiconductor- and determined quite indirectly if at all. Furthermore, insulator or semiconductor hetero junction interface and the in uence of the density of states on transp ort and [1] are well known for more than three decades . The optical prop erties is quite involved, so that in general tunability of the electron densityaswell as the advan- it is imp ossible to determine this fundamental quan- tages asso ciated with the reduced dimensionalityhave tity from such exp eriments. For instance, in transp ort given rise to a vast numberoftechnological applications exp eriments electron lo calization and in optical tran- among which the b est known are eld e ect transistors sitions selection rules as well as collective e ects are [2] and heterostructure lasers . imp ortant aside from pure density of states e ects. Within the last decade growing interest has b een The exp eriments on quantum wires and quantum devoted to the fundamental prop erties of one- and zero- dots describ ed in the following are p erformed with dimensional electron systems, so-called quantum wires present address: Center for Free Electron Laser Studies, University of California, Santa Barbara. H. Hansen et al. 111 nm, an undop ed GaAs spacer layerandanundoped devices esp ecially designed to havevery well de ned, barrier layer are grown. The highly dop ed GaAs con- strong con nement and a go o d control of the electron tains an electron system of low mobility, which is con- density. We present capacitance sp ectra that clearly ducting (sheet conductivitytypical 10mS) even at re ect the quantization of the electronic energies due the low temp eratures and high magnetic elds of our to the lateral con nement. Indeed, capacitance sp ec- exp eriments. It forms a back electro de buried in the troscopy has previously b een very successfully applied heterostructure sample. The front barrier is made of an to two-dimensional electron systems in order to obtain undop ed short p erio d AlAs/GaAs sup erlattice (SPS), information ab out the two-dimensional thermo dynamic [58] [7] eachlayer typically 10 epitaxial monolayers thick. Such DOS . There with a re ned metho d it was even a barrier exhibits a lowleakage current and serves here p ossible to determine quantitatively many-particle cor- as an undop ed insulator. The thickness of the SPS is rections to the single particle DOS, which are found to typically 32 nm and covered with a 10 nm thickun- be very imp ortant at small electron densities or in high dop ed GaAs layer to protect the AlAs against oxida- magnetic elds. For technical reasons, that will b ecome tion. On this hetero junction crystal a metal gate (typ- obvious in the following, this re ned metho d cannot ically 30 nm Ti) is thermally evap orated. b e applied to one- or zero-dimensional electron systems and a sophisticated quantitative analysis is only p os- sible with self-consistentnumelical calculations basing on parameters that are less well controlled. Neverthe- less, the substructures observed in the di erential ca- pacitance can b e interpreted on basis of very simple mo dels yielding a go o d notion ab out imp ortant param- eters suchasquantization energies, electron o ccupa- tion and typical widths of the structures. Furthermore, the electron wires realized in our exp eriments are of such good quality, that unlike in previous exp eriments the substructures are clearly observed in the direct ca- pacitance signal rather than in the derivativemaking a comparison to self-consistentnumerical calculations less ambiguous. The parameters obtained from the capacitance sp ec- tra are used to understand the high frequency conduc- tivity of the quantum wires. These exhibit characteris- tic resonances in the Far-Infrared (FIR) that are asso ci- ated with transitions b etween the one-dimensional sub- bands of the wire or the energy levels of the dot. Com- parison of the subband spacing extracted from the ca- pacitance data to the resonance energies tells us ab out the collective contributions to the intersubband transi- tions, and in the case of the quantum dots it substan- tiates our interpretation of the capacitance data. Figure 1. (a) Cross section through the epitaxially grown layers of a MIS-dio de. The distances b etween back elec- I I. Samples tro de and hetero junction interface z as well as top gate z b t are indicated. The thickness of the GaAs spacer layer on top of this electro de is typically z = 100 nm. (b) Sketchof The samples of our exp eriments are basically metal- b the conduction band edge as function of the co ordinate in [9] insulator hetero junction (MIS) dio des . The hetero- growth direction at gate voltage b elow and ab ove a thresh- junction is grown by molecular b eam epitaxy.Atypical old voltage Vtll as describ ed in the text. epitaxial layer sequence and an idealized band structure are sketched in Fig. 1a and 1b. On the [100] surface Note that unlike in a conventional mo dulation- of a GaAs substrate wafer an undop ed GaAs bu er, a [10] highly dop ed GaAs layer with typical thickness of 20 dop ed hetero junction our MIS- dio des generally do 112 Brazilian Journal of Physics, vol. 26, no. 1, March, 1996 not contain mobile electrons at the hetero junction in- strip es is 150 nm so that at V 6= 0 the p erio d of the d terface at zero gate voltage as indicated in Fig. 1b. surface p otential is a=500 nm. Like in a Si metal-oxide-semiconductor dio de the car- riers have to b e eld induced by a p ositive gate volt- age applied b etween the back electro de and the front gate. If the gate voltage V is larger than a threshold g voltage V the conduction band edge forms a mini- th mum at the interface b etween the GaAs spacer layer and the front barrier into which electrons are injected from the back electro de. In all exp eriments discussed in the following charge injection through the shallowtun- Figure 2. Sketch of the electro de con guration for the gen- nel barlier formed by the undop ed spacer layer happ ens eration of eld-induced quantum wires. The gate voltage V g is applied b etween the back electro de in the heterostructure suciently fast that we can assume equilibrium with re- crystal and one of the interdigital electro des. The voltage sp ect to charge exchange b etween the electron system V is applied b etween the twointerdigital electro des. d at the hetero junction interface and the back electro de. The advantage of our MIS-dio des is that no intentional dopants are contained in the layers b etween the eld induced electron system and the front gate.