Virtual Scanning Tunneling Microscopy: A Local Spectroscopic Probe of 2D Electron Systems
Adam Sciambi, Matthew Pelliccione, Seth R. Bank, Arthur C. Gossard, David Goldhaber-Gordon
aa r X i v : . [ c ond - m a t . m e s - h a ll ] A ug Virtual Scanning Tunneling Microscopy:A Local Spectroscopic Probe of 2D Electron Systems
A. Sciambi,
1, 2
M. Pelliccione,
S. R. Bank,
3, 4
A. C. Gossard, and D. Goldhaber-Gordon
5, 2 Department of Applied Physics, Stanford University, Stanford CA 94305-4045 USA Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, 2575 Sand Hill Road,Menlo Park, CA 94025 USA Materials Department, University of California Santa Barbara, Santa Barbara CA 93106 USA Electrical and Computer Engineering Department, University of Texas at Austin,Austin TX 78758 USA Department of Physics, Stanford University, Stanford CA 94305-4045 USA (Dated: 6 December 2018)
We propose a novel probe technique capable of performing local low-temperature spectroscopy on a 2Delectron system (2DES) in a semiconductor heterostructure. Motivated by predicted spatially-structuredelectron phases, the probe uses a charged metal tip to induce electrons to tunnel locally, directly belowthe tip, from a “probe” 2DES to a “subject” 2DES of interest. We test this concept with large-area (non-scanning) tunneling measurements, and predict a high spatial resolution and spectroscopic capability, withminimal influence on the physics in the subject 2DES.As semiconductor growth techniques advance, two-dimensional electron systems (2DESs) with ultra-low dis-order are revealing exotic new physics. For instance,anisotropic transport in high mobility quantum Hall sys-tems suggests a striped mixture of electron phases.
Transport in other high quality samples shows metal-insulator transitions whose intermediate states areconjectured by some to be microemulsions of metallicand crystallized electron phases driven by strong elec-tron interactions. Unfortunately, the exact organizationof such phases is hard to discern with spatially-averagedtransport measurements. Scanned probes have greatlyenhanced our understanding of 2DESs but have yetto directly map the mixed phases. One hindrance is thatthe transport evidence for these phases appears only inthe lowest-disorder 2DESs, which reside at interfaces atleast a hundred nanometers from the surface, behind alarge Schottky barrier.Scanning tunneling microscopy (STM), the dominantprobe of local electronic properties on surfaces, wouldbe a powerful tool for studying buried semiconductor2DESs were the tip close enough to allow tunneling.With this in mind, we suggest a novel probe where tun-neling comes not from a metal tip but rather from a“probe” 2DES grown above the “subject” 2DES (Fig 1a).The weakly-coupled 2DESs are separated by a wide butvery low potential barrier (Fig. 1b). The barrier is solow that we can induce interlayer tunneling by applying avoltage to a surface gate, modifying the interlayer barrierand thus allowing the wave function of the probe 2DES topenetrate deeper into the barrier. Were this surface gatereplaced by a metallic tip scanned above, inter-2DES tun-neling would occur preferentially below the tip, forminga “virtual tip” that moved with the physical tip. Hence,we call this proposed method Virtual STM (VSTM).The novelty of this probe is not in its scanning system,which is well established, but in its heterostructure thatpermits modulation of tunneling between layers. We have recently developed and characterized such a heterostruc-ture, incorporating it into a non-scanning device: theWavefunction Extension Transistor (WET). The het-erostructure (Fig 1a, left) uses a 145 nm-wide AlGaAsbarrier with an Al gradient of 0-1.5% from top to bot-tom, and is described in more detail in Ref. 13. In thisletter, we use a WET as proof of the VSTM principle,implementing fixed, large-area ( ∼ µ m ) surface gatesin place the scanned VSTM tip. Based on simulation andWET measurements, we predict fully-realized VSTM willhave high tunneling spatial resolution, spectroscopic ca-pability, and little probe influence on the subject 2DES.Before discussing VSTM attributes, we briefly addresstunnel modulation, the central effect giving rise to theWET and VSTM. FIG. 1. (a) Right: VSTM schematic shows a scanned, chargedtip inducing local tunneling from a “probe” 2DES into the“subject” 2DES. Left: Layer composition of heterostruc-ture. (b) Simulated conduction band edge (black), havingquantum wells separated by a low and wide barrier, with cal-culated bound wavefunctions (blue) . (c) A negative probegate voltage (-0.3 V) induces tunneling by pushing the probelayer into the barrier to overlap the subject layer. Induced tunneling is a dramatic increase in inter-2DEStunneling conductance brought about by nearly depletingthe probe layer with a negatively-biased gate. A negativevoltage raises the band edge in the subband of the probelayer, effectively lowering the relative barrier height. Thiscauses the probe wavefunction to extend into the barrier(Fig 1c) and overlap more with the subject layer. This isseen empirically as an increase in the tunneling: for tem-peratures below 1K, gating the WET can raise tunnelconductance by more than two orders of magnitude (Fig2a). Because tunnel modulation relies on the extent ofthe probing wavefunctions and not on the subject layer,it is present across a wide range of subject 2DES densitiesin the WET. Furthermore, the tunnel modulation is ob-served to grow roughly exponentially as the probe 2DESis depleted, though reproducible tunnel resonances likelyrelated to quantum interference in the barrier region are superimposed on this behavior.This strong dependence of tunneling on gate voltageshould give VSTM a high spatial resolution, similar tothe high resolution of STM that arises from sensitivityto tip proximity. In case of VSTM, the falloff of the elec-tric field away from the tip at the probe 2DES should bematched by a sharp decline in tunneling. We can esti-mate this resolution using large-area tunneling measure-ments. The negatively-gated WET has its peak value oftunnel conductance halved when the field at the probelayer is only slightly reduced to 97% of its optimal value(Fig 2a). This reduction can be compared to the modeledfield profile of a tip with a 20 nm radius positioned 20 FIG. 2. (a) Induced tunneling measured in a WET (inset), asa function of the calculated electric field from the probe gateat the probe layer. Tunnel conductance increases by overtwo orders of magnitude from no field to the optimal field,and is at less than half its peak value at 97% of this field.By calculating the potential profile of a (b) tip suspended invacuum over a grounded 2DES in GaAs, we find where thetip electric field at the 2DES (purple) is similarly reduced to97%. There, tunneling should be more than halved, giving usan estimate of VSTM resolution of 40 nm. nm above a sample surface, and a further 80 nm abovea grounded probe 2DES (Fig 2b). We calculate that thefield at the probe 2DES from such a tip falls to 97%at 20 nm off-center, yielding a tunnel full-width at half-maximum of 40 nm. This serves as a reasonable estimateof the spatial resolution, a value which broadens to 130nm if tunneling is more conservatively required to fall toone tenth of the maximum.This analysis relies on a direct relationship betweenlocalized field and similarly localized tunneling. For thisto be so, the confined tunneling region must have withinit a sharp subband edge to give the barrier-penetratingsubband wavefunction definite energy and form. It is notobvious, however, how the constituent energy eigenstatesof a subband will respond to a sharp potential perturba-tion in position-space. Our simulations show that forperturbations spatially larger than λ F , there is a sharpspectral divide between high-energy states with weightin the perturbed region, and excluded low-energy states.Hence, treating that region as a depleted subband con-taining only higher-energy states is valid. In a regionsmaller than λ F , we find that all states have weight inthe local region and that there is no well-defined subbandedge. Using this as a guide, for probe 2DES densities of2 or 4 × cm − , the resolution could be as fine as λ F ≈
56 nm or 40 nm, respectively.We note we have yet to actually measure tunnel mod-ulation from a small region of 2DES, though for regionslarger than λ F the signal size should simply scale withtunneling area. A small local induced tunneling signalshould be measurable as long as it is not obscured byweak parallel conduction everywhere else. For a 10 µ m × µ m scan area and a 0.1 µ m × µ m modulated area,the modulated signal at 300 mK should be a 1% changeagainst a 1 GΩ background, assuming a tip makes thesame 100-fold increase locally that we see for the large-area WET in Fig 2a. Another WET device with a nar-rower interlayer barrier would yield a 1% change on a100 MΩ background based on large area measurements.For this device, a momentum conservation tunneling res-onance is seen in large-area devices but this resonanceshould not be present for tip-induced tunneling. Thesmall expected changes in tunneling can be observed byoscillating the tip voltages and using standard lock-intechniques.An important concern beyond resolution and signalstrength is that probing might perturb the physics be-ing studied. For VSTM, we want the electric field fromthe VSTM tip to modify the probe layer without chang-ing the carrier density of the subject 2DES. In bilayerswith narrower interlayer barriers than ours, this indepen-dent gating of 2DESs is not always easy. We evaluatethe influence on the subject 2DES by varying a WETprobe gate voltage ( V p ) and tracking the subject densityas measured by Shubnikov-de Haas (SdH) oscillationsin longitudinal conductance (Fig 3a). For each V p , weFourier transform the oscillations to find a period in in-verse perpendicular magnetic field (B), indicating a sheet FIG. 3. (a) Fourier transform of SdH oscillations reveals thesheet density of each layer as a function of V p . In region1, the subject layer density is constant to within 1% due toscreening by the probe layer. More negative V p couples to thesubject 2DES since the probe 2DES is localized (region 2) orfully depleted (region 3). (b) Spectroscopy of excited/filledLandau levels (filling factor ∆ ν = 0 , , ,
12) using an inter-layer bias ( V b ). The spin-degenerate Landau level spacings ofthe density-matched layers (white lines) are linear in field asexpected, and a single level ( ν = 24) is also shown. density n = (2 e/h )[∆(1 /B )] − . We see that the popu-lated probe layer (region 1) screens the probe gate fromthe subject layer and leaves the density of the latter con-stant to within 1%.The SdH oscillations, a result of Landau levels (LLs)appearing in an otherwise flat 2DES density of states(DOS), can also be used to test out-of-equilibrium spec-troscopy in the sample. To simplify the measurement, weuse the probe gate to match the layer densities and hencelevel filling. By applying a bias between layers, we cantunnel from filled into excited LLs (Fig 3b). We confirmthat the LL spacing is linear in field and we see up to thetwelfth excited/filled filling factor, comparable to statesprobed by capacitive measurements of tunneling into a2D quantum Hall system from a 3D electrode. The large-area gate characterization of a WET indi-cates VSTM is in good position to see complex electronphases. To further help, the probe layer can be givena much higher density than the subject layer to smooththe DOS of the former and weaken its interactions. Un-like capacitive measurements of 2DES tunneling, whichhave enabled impressive spectroscopy of localized and de-localized states,
VSTM will need an exit path forthe tunneling current to be measured. Thus, it can mapthe borders of large regions of localized electrons but notthe local DOS within. With finite bias, however, elec-trons can be injected into localized states from whichthey could then escape into nearby metallic or delocal-ized states.We have shown many benefits of VSTM, namely its spectroscopic capability, predicted high spatial resolu-tion, and minimal effect on the subject 2DES. These fea-tures are all due to the novel heterostructure design withits especially wide and low barrier. The design gives ver-satility too, as the VSTM may also be used to map wavefunctions inside lithographically-defined structures likequantum point contacts and quantum dots. With futureheterostructure design iterations, it should be possible togreatly increase tunnel modulation and mobility, thoughVSTM appears a viable probe technique even with thesamples at hand.We thank C.X. Liu for theoretical discussions, andM.P. Lilly for help with bilayer device fabrication. Thiswork is supported by DOE-BES, DMS&E at SLAC (DE-AC02-76SF00515), with the original concept developedunder the Center for Probing the Nanoscale (NSF NSECGrant No. 0425897) and a Mel Schwartz Fellowship fromthe Stanford Physics Department. This work was per-formed, in part, at the Center for Integrated Nanotech-nologies, a DOE-BES user facility at Sandia NationalLabs (DE-AC04-94AL85000). A.S. acknowledges sup-port from an NSF Fellowship, and M.P. from a HertzFellowship, an NSF Fellowship, and a Stanford Gradu-ate Fellowship. D.G.-G. recognizes support from a Davidand Lucile Packard Fellowship. A. A. Koulakov, M. M. Fogler, and B. I. Shklovskii, Phys. Rev.Lett. , 499 (1996). M. P. Lilly, K. B. Cooper, J. P. Eisenstein, L. N. Pfeiffer, and K.W. West, Phys. Rev. Lett. , 394 (1999). G. Sambandamurthy, R. M. Lewis, Han Zhu, Y. P. Chen, L. W.Engel, D. C. Tsui, L. N. Pfeiffer, and K. W. West, Phys. Rev.Lett. , 256801 (2008). A metal-insulator transition review: E. Abrahams, S. V.Kravchenko, and M. P. Sarachik, Rev. Mod. Phys. , 251 (2001). S. Ilani, A. Yacoby, D. Mahalu, and H. Shtrikman, Science ,1354 (2001). M. Baenninger, A. Ghosh, M. Pepper, H. E. Beere, I. Farrer, andD. A. Ritchie, Phys. Rev. Lett. , 016805 (2008). R. Jamei, S. Kivelson, and B. Spivak, Phys. Rev. Lett. , 056805(2005). M. A. Topinka, B. J. LeRoy, R. M. Westervelt, S. E. J. Shaw, R.Fleischmann, E. J. Heller, K. D. Maranowski, and A. C. Gossard,Nature , 183 (2001). S. Chakraborty, I. J. Maasilta, S. H. Tessmer, and M. R. Melloch,Phys. Rev. B , 073308 (2004). S. Ilani, J. Martin, E. Teitelbaum, J. H. Smet, D. Mahalu, V.Umansky, and A. Yacoby, Nature , 328 (2004). G. A. Steele, R. C. Ashoori, L. N. Pfeiffer, and K. W. West,Phys. Rev. Lett. , 136804 (2005). H.-J. G¨untherodt and R. Wiesendanger (eds.), Scanning Tunnel-ing Microscopy, Vol I (Springer, 1992). Paper submitted in parallel. M. Heiblum and M. V. Fischetti, IBM J. Res. and Develop. ,530 (1990). J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Appl. Phys.Lett. , 2324 (1990). ∼ gsnider/), and by C.X. Liu, Ts-inghua University (unpublished). I. B. Spielman, PhD Thesis, Cal. Tech, pg. 58 (2004). O. E. Dial, R. C. Ashoori, L. N. Pfeiffer, and K. W. West, Nature448