Virtual Scanning Tunneling Microscopy

Contact Matt Pelliccione (pellim@) or John Bartel (jbartel@) for more information.

The two-dimensional electron gas (2DEG) that forms at the interface of GaAs and AlxGa1-xAs has received intense interest in recent years because it exhibits a very low amount of disorder, which allows it to support many exotic physical states that are highly sensitive to scattering. Most investigations into the physics of these systems have focused on electrical transport measurements. However, transport measurements alone can sometimes give an incomplete picture of the physics because they often are not sensitive to local electron ordering in the 2DEG. Many of the most interesting states in these systems, including fractional quantum hall states, Wigner crystallization and other correlated phases, are either highly anisotropic or are expected to exhibit local order. The virtual scanning tunneling microscopy (VSTM) project is aimed at developing a probe that can measure local spectroscopic information in these high mobility 2D electron systems.

VSTM vs. STM

A number of local probes have been developed to measure spatial effects with the aim of complementing transport measurements; including the scanning single electron transistor (SET), scanning capacitance microscopy (SCM), and scanning gate microscopy (SGM). These probes, however, are incapable of directly measuring the local density of states of the 2DEG, a measurement which can be achieved in other materials systems with a scanning tunneling microscope (STM). To date, STM has not been used to measure high mobility 2DEGs (μ > 106 cm2 V-1 s-1) because it is a surface-sensitive technique, and typically 2DEGs that exist at a surface have a significantly lower mobility that those found at an III-V interface, as is the case in GaAs/AlGaAs. However, the Schottky barrier of GaAs prevents one from measuring a tunnel current directly from an STM tip in a traditional STM measurement.



Figure 1: Diagram of an STM measurement on a buried 2DEG (left) and a VSTM measurement on a bilayer 2D system (right) in GaAs. The Schottky barrier prevents a measurable tunnel current from flowing from the STM tip to the interesting buried 2D layer. By intentionally growing a second 2D layer in the sample, tunneling can occur across an energy barrier that is tunable by a scanned gate. The "virtual" STM tip is then formed by the probe 2D electron layer in the region directly underneath the tip.


Sample Design

We have developed a bilayer GaAs/AlGaAs heterostructure that allows for local tunneling between two 2DEGs, where the tunnel coupling between the two 2D layers can be tuned with a gate on the surface of the device, as depicted in Figure 1. This avoids the surface energy barrier present in STM because the tunneling is occurring between two interfaces where the Schottky barrier does not factor in. By appropriately designing the heterostructure, we can tune the tunnel conductance between the layers by up to 4 orders of magnitude when a gate voltage is applied. This allows the device to function as a novel transistor [1], where the current flows vertically between two quantum wells, as opposed to horizontally across a doped channel as is the case with most FETs. Because the transistor is designed with quantum mechanics in mind, it continues to operate well even when its critical dimensions approach the Fermi wavelength of electrons in the 2DEG. This is contrary to typical MOSFETs which suffer significant performance limitations when built on this scale due in part to the fact that the transistor operates on semi-classical assumptions that break down at this length scale.




Figure 2: Typical VSTM device used in scanning measurements. The gray area is the GaAs/AlGaAs where the bilayer 2D electron system resides. Gates are fabricated on top of and beneath the device to allow both 2D layers to be tuned, and define an active tunneling area in the center of the image that is 5 μm x 5 μm.


One way to take advantage of the favorable scaling of this device is to use a gate with dimensions on the order of the Fermi wavelength of electrons in the 2DEG, which can be realized with conductive AFM tips that typically have a 15 - 30 nm tip radius. If one uses a conductive AFM tip as the gate, as is common in SGM, one can significantly enhance the tunneling between the two 2D layers directly beneath the tip. By scanning the tip around, the active tunneling area can be moved around the device, effectively mapping out the tunneling density of states. This is the key to the VSTM measurement, where the "virtual" STM tip is formed by the 2D layer closest to the conductive AFM tip. We have shown that we can realize this behavior in large-scale devices in GaAs [2], and recently shown that this behavior translates to a SGM measurement.

System Design

However, to access the physically interesting correlated electron phases, one needs to perform measurements at very low temperatures, typically less than 100 mK, and in high magnetic fields. Therefore, to carry out VSTM one must be able to perform atomic force microscopy with a conductive tip in this environment. To achieve this, we have constructed an AFM in a "cryogen-free" dilution refrigerator that is capable of operating at temperatures as low as 20 mK.




Figure 3: Cold finger (left) and scanning stage (right) of the low temperature AFM built for this project. The scanner operates inside a cryogen-free dilution refrigerator from Leiden Cryogenics. The base temperature of the system is 20 mK, and we can apply magnetic fields up to 9 T perpendicular to the sample and 3 T in plane.


The system is "cryogen-free" in the sense that no liquid helium is used for cooling, and instead a closed cycle cryocooler is used to reach 3 K, where a traditional dilution circuit then cools the sample to base temperature. Building an AFM in a system with a cryocooler is challenging because there are significantly larger mechanical vibrations introduced by the cryocooler as compared to a liquid helium bath. This makes performing scanning probe measurements difficult because one typically needs a very low vibration environment to maintain small displacements between the tip and sample. The vibrations normal to the sample in this system are 0.8 nm RMS from DC to 1 kHz, which are small enough for VSTM measurements. Pictured in Figure 3 is the cold finger and scanning stage of the instrument.

References

[1] A. Sciambi, M. Pelliccione, M. P. Lilly, S. R. Bank, A. C. Gossard, L. N. Pfeiffer, K. W. West, and D. Goldhaber-Gordon, "Vertical field-effect transistor based on wave-function extension," Phys. Rev. B 84, 085301 (2011).

[2] A. Sciambi, M. Pelliccione, S. R. Bank, A. C. Gossard, and D. Goldhaber-Gordon, "Virtual scanning tunneling microscopy: A local spectroscopic probe of two-dimensional electron systems," App. Phys. Lett. 97, 132103 (2010).