JARA FIT Ferienprakticum Nanoelektronik Experiment: Resonant tunneling in quantum structures

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1 JARA FIT Ferienprakticum Nanoelektronik 2013 Experiment: Resonant tunneling in quantum structures Dr. Mihail Ion Lepsa, Peter Grünberg Institut (PGI 9), Forschungszentrum Jülich GmbH 1. Introduction The experimental study of resonant tunneling in semiconductors is possible only by using high quality thin epitaxial layer structures. Molecular Beam Epitaxy (MBE) is the most appropriate method to grow such heterostructures because of the perfect control of the layer thickness down to one monolayer, high quality of the grown material, good control of the layer doping, atomically sharp interfaces between layers etc. Double barrier quantum well structure (DBQW) realized with GaAs-AlGaAs material system represents the most common system by means the resonant tunneling process can be studied at room temperature using the electronic transport in quantum heterostructures. During this experiment some aspects related to the MBE growth and electrical characterization of the GaAs-AlGaAs DBQW structures will be investigated. 2. Experimental setups MBE system The MBE system is a Varian MOD GEN II equipment dedicated mainly to the growth of GaAs based material layers. It consists in Load-Lock- (Fig. 1), Buffer- (Fig. 1c) and Growth (Figs. 1a, b) chambers. Two racks contain the control equipment (Fig. 1d). The growth process is PC controlled. The chambers are from stainless steel and are kept constantly under ultra high vacuum (UHV) conditions at a background pressure of mbar and lower using ion getter pumps, titanium sublimation pumps and cryo-pumps. The Load-Lock chamber enables the transfer of the substrates from air in the Buffer chamber (UHV). The substrates (2 or 3 diameter) are mounted on molybdenum specimen blocks which are then fixed on a trolley. In the Buffer chamber, the GaAs substrate is deoxidized using a heating station (Fig. 1a). Afterwards, this is transferred into the growth chamber using a transfer rod (Fig. 1a). Both the trolley and transfer rod movements are magnetically controlled from outside. In the Growth chamber, the substrate is mounted in the middle, on rotatable stage or CAR. The CAR contains a heating station for substrate heating. The effusion cells are mounted symmetrically on a source flange (Fig. 1b) opposite to the Buffer chamber. Except As, the other MBE materials, Ga, In, Al (a) 1

2 (a) (b) (c) (d) Fig.1. Varian MOD GEN II MBE system: (a) Buffer and Growth (front) chambers; (b) Growth (back) chamber; (c) Load-lock chamber; (d) Control equipment. 2

3 used for growth), Si and Be (used for doping) are evaporated from pyrolytic boron nitride (PBN) crucibles. For As, a valve controlled cracker is used, to obtain both As 2 and As 4 molecules. Each cell is surrounded by a cryo shield that is continually cooled with liquid nitrogen (LN) at a temperature of 77K (-196 C). A second cryo panel forms an inner shield, also using LN, so that the main MBE area is surrounded by cold walls at 77K, operating as additional pumping units. The precise temperature control of each cell guaranties the desired constant beam flux of the material. Shutters in front of the effusion cells open the atomic or molecular vapor flux and enable the growth of the material. For calibration, the pressure of the specific material can be measured with a Bayert-Alpert ionization gauge mounted on the CAR, opposite to the substrate. This pressure is often referred as the beam equivalent pressure (BEP) since the absolute value of the ionization gauge reading is dependent on the geometry of the beam with respect to the ionization gauge entrance slit and other properties, like the ionization probability of the material. Therefore this reading does not reflect the absolute pressure but it can be used to calibrate the beam flux. With this respect, the total thickness of an epitaxial layer grown at a certain BEP value will be measured ex-situ after the growth. As in-situ analyzing tool, a Reflection High Electron Energy Diffraction (RHEED) system is mounted on the Growth chamber. Using RHEED specular intensity oscillations, the growth rate can be monitored in-situ during the growth.the background residual gases content can be determined with a quadrupole mass spectrometer (QUAD). Contrast optical microscope The surface morphology of the grown wafers is checked with a Jenatech optical microscope (Fig. 2). The microscope can be used in both contrast and dark field modes and has a magnification of more than1000x. Fig. 2. Jenatech optical microscope. 3

4 Hall effect measurement system The doping concentration and carrier mobility in the grown structures are determined by Hall measurements using a van der Pauw contact configuration. A Keithley 926B automatic Hall profiling system (Fig. 3) is used. The contacts are realized by alloying Sn or In small balls on the sample in a BioRAD RC 2400 alloying furnace (Fig. 4). For measurements, the four contact sample is mounted in a special holder (see inset of Fig. 3). The measurements can be done at room temperature or 77K (using LN). Fig. 3. Keythley 926B automatic Hall measurement system. Inset: special sample holder. Fig. 4. BioRAD RC 2400 alloying furnace. 4

5 DC electrical measurement setup The I-V characteristics of processed resonant tunneling diodes (RTD) is measured with an HP 4145 Semiconductor Parameter Analyzer (Fig. 5a) using a probe station (Fig. 5b). (b) (a) Fig. 5. DC measurement setup: (a) HP4145 Semicondcutor Parameter Analyzer and (b) probe station. 3. RHEED oscillations RHEED oscillations of a specular beam spot can be used to determine the growth rate during the epitaxial process. This is illustrated in Fig. 6. The steady state period corresponds precisely to the growth of a single molecular layer (ML), i.e. of Ga(Al)+As atoms ML Δt Fig. 6. Principle of appearance of RHEED intensity oscillations 5

6 4. Hall effect measurements The Hall measurement technique is used for determining the carrier concentration and mobility in semiconductor materials. The basic physical principle underlying the Hall effect is the Lorentz force. This is illustrated in Fig. 7. for n-type semiconductors. When an electron moves along a direction perpendicular to an applied magnetic field, it experiences a Fig. 7. Schematic of the Hall effect in a long, thin bar of semiconductor with four ohmic contats. force acting normal to both directions and moves in response to this force and the force effected by the internal electric field. Electrons subject to the Lorentz force initially drift away from the current line toward the negative y-axis, resulting in an excess surface electrical charge on the side of the sample and correspondingly the Hall voltage, V H. This transverse voltage is the Hall voltage V H and its magnitude is equal to IB/qnd, where I is the current, B is the magnetic field, d is the sample thickness, and q (1.602 x C) is the elementary charge. Instead of bulk density, it is convenient to use layer or sheet density (n s = nd). One then obtains the equation: n s = IB/q V H. (1) Thus, by measuring the Hall voltage V H and from the known values of I, B, and q, one can determine the sheet density n s of charge carriers in semiconductors. The Hall voltage is negative for n-type semiconductors and positive for p-type semiconductors. The sheet resistance R S of the semiconductor can be conveniently determined by use of the van der Pauw resistivity measurement technique. Since sheet resistance involves both sheet density and mobility, one can determine the Hall mobility from the equation: µ = V H /R S IB = 1/(qn S R S ). (2) If the conducting layer thickness d is known, one can determine the bulk resistivity (ρ = R S d) and the bulk density (n = n S /d). In order to determine both the mobility µ and the sheet density n s, a combination of a resistivity measurement and a Hall measurement is needed. These measurements are based on the van der Pauw technique. 6

7 The objective of the resistivity measurement is to determine the sheet resistance R S. Two characteristic resistances R A and R B, associated with the corresponding terminals shown in Fig. 8., are related to the sheet resistance R S through the van der Pauw equation: exp(-πr A /R S ) + exp(-πr B /R S ) = 1 (3) which can be solved numerically for R S. Fig. 8. Schematic of a van der Pauw configuration used in the determination of the two characteristic resistances R A and R B. The objective of the Hall measurement in the van der Pauw technique is to determine the sheet carrier density n s by measuring the Hall voltage V H. As illustrated in Fig. 9., to measure the Hall voltage V H, a current I is forced through the opposing pair of contacts 1 and 3 and the Hall voltage V H (= V 24 ) is measured across the remaining pair of contacts 2 and 4. Once the Hall voltage V H is acquired, the sheet carrier density n s can be calculated via n s = IB/q V H from the known values of I, B, and q. Fig. 9. Schematic of a van der Pauw configuration used in the determination of the Hall voltage V H. There are practical aspects which must be considered when carrying out Hall and resistivity measurements. Primary concerns are (1) ohmic contact quality and size, (2) sample uniformity and accurate thickness determination, (3) thermomagnetic effects due to nonuniform temperature, and (4) photoconductive and photovoltaic effects which can be minimized by measuring in a dark environment. Also, the sample lateral dimensions must be large 7

8 Current Density [x10 3 A/cm 2 ] compared to the size of the contacts and the sample thickness. Finally, one must accurately measure sample temperature, magnetic field intensity, electrical current, and voltage. 5. I-V characteristics of the DBRT diode A typical experimental I-V characteristics is shown in Fig. 10. The characteristic parameteres are: the peak density current (J p ) and voltage (V p ), the valley density current (J v ) and voltage (V v ) and the peak to valley ratio, PVR = J p /J v (a) J p, V p J v, V v Voltage [V] Fig. 10. Experimental I-V characteristics of an RTD. 6. Activities and tasks Basics related to the MBE equipment should be explained. The students should perform growth rate calibration of GaAs and AlGaAs using RHEED oscillations. The students should perform N-doping calibration using Hall measurements on already Si doped samples. The students should annalyse the surface morphology of a grown structure by means of the contrast optical microscope. The growth recipe for a typical DBRT structure should be generated within the MBE control software. The students should measure the I-V characteristics of a typical DBRT diode and determine the characteristic parameters. 8