Quantum dots on the InAs(110) cleavage surface created by atom manipulation

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Semiconductor quantum dots play a central role in optoelectronic device applications [1].At the level of fundamental research, they make it possible to explore superimposed and entangled quantum states [2,3], semiconductor qubits [4], electron correlation in artificial lattices [5], and electronic quantum transport [6], to mention only a few.Aside from their fabrication in the form of colloidal crystals [7], quantum dots are typically created in semiconductor heterostructures by growing vertically and laterally aligned nanocrystals [2,3,8,9], by imposing lateral confinement using electron-beam lithography [5,10], or by depleting a two-dimensional electron gas (2DEG) using external gates [11,12] and local oxidation [13].
The method of 2DEG depletion using external gates exploits the electric field effect to spatially modulate the carrier density.In our previous work [14], we followed a similar idea of spatially controlling the electrostatic surface potential, however, at the level of single atoms: we used the tip of a scanning tunneling microscope (STM) to assemble short atomic chains on an InAs(111)A surface by atom manipulation [15].The chains consisted of six positively charged In adatoms leading to electronic confinement, and hence, the emergence of a bound state with discrete energy the fingerprint of a quantum dot.We showed that these dots can be arranged and thereby coupled in various ways, yielding quasi-molecular electronic states which can be described by a tightbinding Hamiltonian assuming a single s orbital on each site [14,16].
Here, we extend this concept to the (110) cleavage surface of indium arsenide.First, the adsorption and charge state of an In adatom on InAs(110) are investigated by STM and complementary density-functional theory (DFT) calculations.It is then demonstrated that an assembly of six adatoms confines electrons and thus behaves like a quantum dot.The resulting bound state has an intrinsic linewidth of ~4 meV which is remarkably small for confined electronic states at surfaces.Finally, it is shown that quantum-dot dimers can be created, leading to bonding and antibonding states as verified by scanning tunneling spectroscopy (STS).The present findings are important because they facilitate the STM-based construction of quantum structures on a new InAs platform: a cleaved (110) surface is significantly easier to prepare than a (111)A-terminated surface requiring a dedicated growth facility for molecular beam epitaxy (MBE) [17].Moreover, working in (110) surface orientation offers the prospect of exploring cleaved III-V semiconductor heterostructures in cross-sectional geometry to ultimately be able to create electrical gating of the STM-generated nanostructures.
The STM investigations were carried out in ultrahigh-vacuum (UHV) at a sample temperature of 5 K.We used undoped and (001)-oriented InAs wafers cleaved in UHV to obtain the InAs(110) surface.The left panel in Fig. 1(a) shows a constant-current topography image of an In adatom adsorbed on the InAs(110) surface.At the sample bias of 0.1 V as applied here, the surface As atoms are imaged as protrusions arranged in rows along the in-plane direction [18]; the spacing between the rows is a0=6.06Å, the cubic lattice constant of InAs.The adatom in the center of the image is located in the channel in between of the rows, consistent with previous work [19,20] predicting interstitial configurations in which the adatom is bonded either to two cations and one anion (labeled Ii1) or to two anions and one cation (Ii2).In agreement with the findings by Weber et al. [20], our DFT calculations confirm that Ii2 is the most stable configuration, as illustrated by the right hand-side panel showing a close-up view together with an overlaid structure model.(The orientation of the structure model with respect to the (001) plane is confirmed experimentally by the chemical contrast between surface anions and cations (Supplementary Material, Fig. S1) first revealed by the atom-selective STM imaging of GaAs(110) [21].) We performed DFT calculations to determine the equilibrium geometry of InAs(110) with and without adsorbed In adatoms, as well as the potential-energy surface for surface diffusion of those adatoms (general details on the calculations are given in Ref. [14]). Figure 1(b) shows the DFT potential-energy surface for an In adatom diffusing on the InAs(110) cleavage surface and provides quantitative information on the adsorption behavior: the metastable configuration Ii1 is 0.2 eV higher in energy than the stable configuration Ii2.The diffusion barrier along the channel is 0.3 eV (the minimum energy path is sketched as a solid curve); this barrier can be overcome above ~120 K. On the other hand, the barrier across the channel is about 0.6 eV (dotted curve) and can be overcome above ~240 K.However, this pathway is probably preempted by exchange between the adatom and a surface In atom, similar to the exchange reaction previously observed for Mn substitutional impurities on InAs(110) [22].
We probed the electronic surface properties by STS measurements of the tunnel conductance dI/dV which provides an approximate measure of the electronic density of states.The spectrum shown blue in Fig. 2(a) was recorded with the tip probing the bare surface.It reveals the energy band gap of InAs (0.42 eV at the measurement temperature of 5 K [23]) and, most prominently, Fermi-level pinning in the conduction band.(The residual conductance observed within the band gap is due to the so-the filled conduction-band states located near the band edge [24].)Fermi level pinning in the conduction band is a generic feature of InAs surfaces, indicating charge accumulation at the surface [20].In agreement with previous STS work on cleaved InAs(110) [18], we observe conductance peaks near the conduction-band minimum just below the Fermi level (at sample bias V=0) which are a manifestation of conduction-band states that undergo vertical confinement and thereby quantization because of the downward band bending near the surface.In the blue spectrum in Fig. 2(a), these states show up as two peaks at -30 and -11 mV, respectively, reflecting the two lowest subbands of the accumulation layer (denoted s1 and s2).The actual energy and magnitude of the peaks observed depends on the location probed by the tip, see Fig. S2 in the Supplementary Material.We attribute this spatial variation to the effect of electrostatic disorder due to defects [25,26,27] in the surface-near region.
The red spectrum in Fig. 2(a) was recorded with the tip probing a single In adatom on InAs(110) and reveals a conductance peak at a sample bias of 0.85 V.The corresponding state derives predominantly from 5p atomic orbital states of the adatom as evident from the density of states calculated by DFT, see Fig. 2(b).It is noted that a similar adatom-induced state was observed previously for In adatoms on InAs(111)A [28] and GaSb(110) [29].
Similar to the situation observed on InAs(111)A, In adatoms on InAs(110) are positively charged.This is evident from the increased apparent height around the charged adatom when imaged at positive sample bias as in the upper panel of Fig. 3(a).The increased height is due to the screened Coulomb potential induced by the charged adatom which locally increases the density of states available for the tunnel process [30,31].It is noteworthy that the hillock produced by the local potential is not symmetric about the adatom position.This asymmetry is clearly evident from the topographic line scan in the lower panel of Fig. 3(a) taken along the dashed line.
To explain this observation, we consider the DFT electrostatic potential in a plane just above the surface.A contour plot of the potential, 3 Å above the surface and within the rectangular area marked in the STM image, is shown in the upper panel of Fig. 3(b).Far from the adatom, the local potential reflects the fact that electrons are transferred from surface In atoms to surface As atoms in accordance with the electron counting rule 32 33 34 Hence, the hexagon acts as a quantum dot that creates a bound state of discrete energy.(It is noted that electron confinement was reported recently also for Cs adatom structures created by atom manipulation on the InSb(110) surface [35].)It is tempting to interpret the present spectra in the way that the dot gives rise to a lateral confinement of accumulation-layer states with the bound state at -75 meV deriving from the lowest subband.This alone, however, provides no conclusive picture why the lowest subband would be confined in the first place rather than higher-lying subbands.(All spectral features observed here were reproduced for various independently assembled dots in different experimental runs.)It remains to be established precisely which surface states are confined in the present case; the central finding of this work is that quantum dots can be assembled from charged In adatoms on the cleaved InAs(110) surface.

Returning to the 36
The bound state of the quantum dot reflected by peak a in Fig. 4(b) has an exceptionally small line width as deduced from tunnel conductance measurements at varying energy resolution.We recorded corresponding peak profiles at different root-mean-square values Vmod of the lock-in modulation voltage and found that the profile steadily sharpens as Vmod is reduced.At successively small modulation, the measured peak width (the full width at half maximum [37]) converged to a value well below 5 mV as evident from the data points collected in Fig. 4(c).The theoretical energy resolution [38] is , where the two terms in the square root take into account the broadening due to temperature and lock-in modulation, respectively.The black dashed line in Fig. 4(c) shows the quantity at the measurement temperature of 5 K. On the other hand, a state with intrinsic line width is expected to be observed at a total energy broadening of .The quantity defined by the latter expression yields an excellent fit of the data points at an intrinsic line width of =4.3 meV as shown by the full red curve in Fig. 4(c).
Next, we demonstrate that quasi-molecular electronic states can be created by bound-state coupling in quantum-dot dimers created on the InAs(110) cleavage surface.In the topography image displayed in Fig. 5(a), we started from the same dot as in Fig. 4(a) and added an identical dot at a center-to-center spacing of 17a0/ 2=72.85Å along yielding a quantumdot dimer.The corresponding spectra in Fig. 5(b) were recorded with the tip placed above (blue) and in between of the dots (red).They reveal the emergence of a bonding ( ) and an antibonding state ( ) as expected for the symmetric and antisymmetric superposition of the bound states belonging to the two dots.The observed splitting measures =75 mV.Note also that the doublet is downshifted from the energy of the single dot indicated by the dashed line; this shift arises from the electrostatic potential change that each dot experiences from the other as previously observed in quantum-dot dimers on InAs(111)A [16].Aside from the dominant and peaks in the conductance spectra, we again observe a set of smaller peaks at higher and lower energies as detailed in the lower panel of Fig. 5(b).Again, the spectra feature inelastic replicas consistent with the excitation of surface phonons [36]; this is evident from the bias-voltage differences of 31, 33, and 30 mV found for the conductance-peak pairs ( ,g), ( ,n), and ( ,t), respectively.Finally, to further analyze the bonding and antibonding states, Fig. 5(c) displays spatial conductance maps recorded at the corresponding bias voltages of the and peaks in panel (b), respectively.These maps are consistent with the symmetric ( ) and antisymmetric ( ) wave-function character of the bonding and antibonding states.
In conclusion, we employed cryogenic STM and STS measurements in combination with DFT calculations to perform an in-depth study of individual In adatoms on the InAs(110) cleavage surface.The adatom is found to adsorb in the channel between the rows of surface atoms along the in-plane two anions and one cation (Ii2 configuration), in agreement with previous theoretical work [20].The Ii1 configuration ( two cations and one anion) is metastable and 0.2 eV higher in energy.It is found that the adatom together with its neighboring surface In atom along the in-plane direction are positively charged, with a net charge of +1e.By arranging these charged adatoms into groups with atomic precision, we have created quantum dots that laterally confine electrons in surface states.For the bound state resulting from this confinement we found an intrinsic line width of only ~4 meV.(The linewidths observed in conductance spectra of confined electrons on metal surfaces are typically larger by a factor of 10 to 10 2 [39,40].)Finally, it was demonstrated that the quantum coupling between two identical dots placed side by side leads to the emergence of a bonding and an antibonding state indicating the symmetric and antisymmetric superposition of the dot wave functions.
The comparably small intrinsic line width observed for the bound state of atomic-scale quantum dots on InAs(110) will open the way to resolve the energy level spectrum of more elaborate quantum-dot arrays hosting exotic electronic states [41,42].The system presented here has the practical advantage that large-scale and atomically flat surface terraces are readily prepared by cleavage in UHV and no extra deposition of material is required to generate charged adatoms, making it a promising platform for the creation of semiconductor quantum structures by scanningprobe techniques.