Paul Lee Smitesh Bakrania George Ioannou Wayne Fung EECS 598 Presentation 4 October 4 th, 2005

Paul LeeSmitesh BakraniaGeorge IoannouWayne Fung

EECS 598 Presentation 4October 4th, 2005

Background1. Theory on ballistic transport (Wayne)2. MBE Cleaved Edge Overgrowth (Smitesh)

Experimental Results3. 4-terminal resistance measurement (George)

Applications4. ballistic Analog-to-Digital converter (Smitesh) 5. ballistic CNTs (Paul)6. Quantum computing application (Paul)7. ballistic MOSFET (Wayne)

Outline

background

BackgroundLayer by layer growth of epitaxial layerscontrolled depositionideal for heterostructure fabrication

MBE - CEO

www.bell-labs.com www.specs.de

GaAs/Al-GaAs Heterostructures

uniformly versus modulation doped: great mobility due to lack of donor impurities

electrons confined in 2-dimensions on a single side plane of electrons

MBE - CEO

R. Dingle et al. Electron mobilities in modulation-doped semiconductor heterojunction superlattices, Applied

Physics Letters, Volume 33, Issue 7, pp. 665-667 (1997)

1D structure

Intersection of two planes

possible to get electrons confined in 2 directions

Challenges

need a clean, atomically smooth surface for growth – cleaved

cleaving to be performed inside the MBE chamber (UHV)

(110) growth surface difficulties

MBE - CEO

Pfieffer et al., Cleaved edge overgrowth for quantum wire fabrication, Journal of Crystal Growth 127 (1993) 849—857

Cleaved Edge Overgrowth must be conducted in situ, Tantalum bar is used for cleaving

doping performed simultaneously with Al in the Al-GaAs layers

MBE - CEO

experimental results

Experimental results of quantum wire resistance

measurementBuilding a quantum wire

Resistance measurement of the ballistic quantum wire

4 terminal2 terminal

4-terminal measurement

Quantum wire resistance(1)

Standard two-probe resistance measurement for single-mode ballistic quantum wire:

R ≈ 13 kΩ

But the nature of quantum wire implies that the resistance should be zero!


Quantum wire resistance(2)

We know that electrical resistance occurs because of scattering.

Supposedly, there is no scattering in a quantum wire, so why the huge resistance?

A better question would be, where is the resistance coming from?


Building a quantum wire

GaAs/AlGaAs heterostructure

Cleaved-edge overgrowth (CEO) technique

GaAs quantum well supports 2DEG


2-point resistance measuring

Straightforward measuring of the resistance between source and drain


4-point resistance measuring

Uses Probes A, B to make the measurement

Biasing gate 2 by itself allows for 2-point measurements

Biasing all 3 gates leads to 4-point measurements by separating probes A, B from source, drain


Resistance Measurements


Results

Little or no resistance along the wire for gate voltages up to -3.5 V

Standard measurement of 13 kΩ is due to contact resistance.


applications

Analog-to-Digital Converters (ADC) Direct conversion is necessary for communications, Radar, Digital Oscilloscopes.

Flash converters (Parallel conversion) uses brute force method. All possible quantization levels are simultaneously compared to the analog input signal.

Testing all possible values of N-bit A/D 2N-1 comparators are required.

Comparator values stored in thermometer code – height relates to value.

Ballistic ADChttp://www.maxim-ic.com

Demler, High-Speed analog-to digital conversion, Academic Press, Inc, 1991

Ballistic ADC

P. Debray et al., A BALLISTIC QUANTUM DEVICE FOR POTENTIAL USE IN ANALOG-TO-DIGITAL CONVERSION, IEEE (2000)

Fast ADCs limitations

low resolution (bits)high power consumption (heating)large die sizecircuit complexity (speed)

Speed is governed by the comparator switching speed and propagation delay of the logic in the encoder.

Still limiting as the trend is to digitize signals as early as possible – requires higher speeds (Giga-samples/second)

Need to replace on/off comparators with devices whose output conductance is a symmetric, periodic function of an input voltage.

http://www.maxim-ic.com

Ballistic ADC

P. Debray et al., A BALLISTIC QUANTUM DEVICE FOR POTENTIAL USE IN ANALOG-TO-DIGITAL CONVERSION, IEEE (2000)

Need to replace on/off comparators with devices whose output conductance is a symmetric, periodic function of an input voltage.

Will need n such devices for n-bit output – low power, high-speed.

Ballistic Electron Tuner (BET)two identical ballistic wires, widths modulated by gate voltage

shift in one of the ‘staircases’

http://www.maxim-ic.com

Ballistic ADC

Device Concept output conductance is the difference G(Vg)=G1 – G2, which is a periodic, square wave. The regular, square-wave output conductance features of a BET can conceivably used for direct, binary analog-to-digital (A/D) conversion.

Device and experimental techniqueBET from 2DEG on Si-modulation doped Al-GaAs/GaAs (electron mfp = 6 m)

W = 250 nm L = 150 nm

Temp = 4.2 K

VDS = 100 V

Vg = -ve bias

Ballistic ADC

Measurement resultsapplying slight shift between top and bottom gates to get optimal periodic signal

Ballistic ADC

Device characteristics increasing temp causes smearing of electron distribution function at Fermi level – sharpness of steps

Ballistic ADC

Practical Device analog signal applied to either middle gate or top and bottom.

16GS/s without optimization – potentially 100GS/s!

TemperatureTarget for 77K for LN2

Since LM varies inversely with effective mass, high-temp operation needs low m* like InSb and InAs.

Ballistic ADC

• Carbon nanotubes can conduct electrons ballistically (without scattering) over thousands of nanometers between two electrodes

• The quantum wave nature of electrons can be seen when an electron wave hits two semi reflective barriers, which produce an interference pattern

• This creates regular oscillations in the intensity of the transmitted wave across the double barrier, as a function of wavelength.

• Transmitted intensity is directly related to the electrical current I flowing in a system under an applied voltage V between the electrodes.

• Smooth variations in the differential conductance G have been observed, where G = dI/dV as a function of V and the gate voltage Vg, confirming the validity of CNT ballistic transport.

Ballistic Carbon Nanotubes

http://carbon.as.wm.edu/laserfocus/HRTEM2.jpg

http://www.nanomedicine.com/NMI/Figures/2.16.jpghttp://www.nature.com/nature/journal/v411/n6838/full/411649a0.html

• When a wave, , hits two successive barriers B1 and B2:

– At B1, part of the wave is reflected back to form R1, while the rest reaches B2

– At B2, part of the wave is transmitted as T1, while the rest is reflected back to B1.

– At B1, part of the wave is transmitted, forming R2, while the rest is returned to B2, and etc.

• Each internal reflection reduces the amplitude and causes a fixed change in phase

• Such transmission of an electron wave has been seen in the experiment by Liang* of a quantum nantotube wire between two electrode contacts.

Experimental Results with CNT’s

Nature 411, 649-651 (7 June 2001)

*Liang, W. Nature 411, 665-669 (2001)

http://www.nature.com/nature/journal/v411/n6838/full/411649a0.html

• Nature has given us a mechanically robust and flexible electron waveguides

– Ballistic transport possible even with residual structural/chemical disorders

– The # of quantum states available for electron conduction through the tube is independent of the tube’s diameter

– Metallic SWNT’s stable against Peierls distortion (spontaneous symmetry breakdown), long-range disorders, and bending.

• The ballistic character of nanometer-diameter wires suggests resistance to electromigration, the atomic rearrangements and diffusion caused by current-induced forces on atoms in regions of electron scattering.

• Devices such as that created by Liang (especially those with larger separation between electrodes) could be used as

– Miniature strain gauges– Detectors of trace amounts of foreign chemical species

• The ability of metallic SWNT to transmit quantum-mechanical electron waves without losing information may be useful in quantum computing.

Applications of CNT transport

http://www.nature.com/nature/journal/v411/n6838/full/411649a0.html

• Goal of QC: Create a quantum computing device with (i) the definition of a well-characterized qubit by means of a two-state quantum system and (ii) the proposal of fundamental transformations on the single qubits and two-qubit states.

• Qubits are defined as the spin states of individual electrons trapped in an array of quantum dots

• The basic two-qubit gate is obtained by changing the height of the electrostatic barrier between the dots

• A basic quantum computing device is made of two parallel quantum wires, where the qubit is defined by the x-component of the wavefunction of an electron propagating along the couple of wires.

• The computed sum/difference of two lower energy eigenfunctions is nearly entirely localized in one of the couple of wires and represents the |0> (|1>) state.

• The single-qubit transformation occurs by introducing a coupling window between the wires, where the potential barrier is lowered to produce a E between the two lower eigenstates.

Quantum Computing

Bertoni and Reggiani, Semicond. Sci. Technol. 19 (2004)

• When the electron reaches the end of the coupling window, the oscillation process ends and the wavefunction is split into two parts along the left and right wires: transformation = rotation matrix Rx()

• Introducing a potential barrier on one of the two wires can delay the propagation of the wavefunction and introduce a phase shift: transformation = Rz()

• To implement a two-qubit gate, two couples of wires are designed in such a way that the 1-state wire of the first qubit and the 0-state wire of the second qubit get close to each other.

• This creates a Coulomb coupler that gives an effective Coulombic interaction between two electrons running along the inner two wires.

• The |10> state of the two-particle system undergoes a mutual phase shift from the spatial delay of the two electrons crossing the coupler

Coulomb Coupler


Coulomb coupler

• Ideal quantum-wire structure implemented onto the realistic profile of the conduction band inside a modulation-doped 2DEG (see Figure 2)

• The physical model here assumes that the electron injected into a wire can coherently propagate without any dephasing processing within the duration of quantum elaboration

• The Coulomb coupler is able to entangle the two qubits by introducing a phase factor to the |10> state

Physical Realization


• Electrons can be injected and transported along wires based on surface acoustic waves (SAW)

• Electrons are captured from a 2DEG and placed into the minima of a SAW that propagates along the device

• The 2DEG region is connected to the wire region in which a single electron must be injected: when the SAW minimum reaches the wire, the trapped electrons go through even more confinement from the potential of the wire.

• This creates a 1D moving quantum dot

• Figure 3 shows two 1D simulations

• The wavefunction undergoes the transformations Rx(/2)Rx(/2) in the top graph (A), and Rx(/2)Rz()R=(/2) in the lower graph

Modeling surface acoustic waves in Quantum wires


Entangling Qubits

• Figure 4 shows two electron wavefunctions injected along two adjacent wires with the same velocity, while Figure 5 shows opposite velocity. The amount of entanglement is computed.• For two electrons propagating in the same direction along two parallel wires, their entanglement is higher for smaller distance between the wires. • With two electrons moving in opposite directions: as the distance between the wires goes to zero, the entanglement between the two wavefunctions increases as the particles are approaching each other, then reach a maximum at collision. After the collision, the entanglement decreases as the particles recede from each other.


Ballistic MOSFET

IEEE Transactions on Electron Devices (50) 9, September 2003.Journal of Applied Physics (76) 8, 15 October 1994.

Source Drain

-k states are injected from Drain

Ballistic MOSFET

IEEE Transactions on Electron Devices (50) 9, September 2003.

+k states are injected from Source

Ballistic MOSFET


DSFFD qVEIEII

VDS small

DSEI qVIIF

DEI

D qVIF

Total drain current:

Ballistic MOSFET


F

C

E

E

x dEEvEDqWI FxFEI EvEDqWF

221

mED

EvdEvvx

21 2

2

cosE m

EEv 2

where

the 2D density of states for right-moving electrons

the average x-component of velocity

DShq

DShqkW

DSEI

D VMVqVI F

F

22 22

Ballistic MOSFET


Velocity Saturation in Ballistic MOSFET

•Occurs at top of potential barrier (where E-field = 0) instead of near the drain.

•Not due to scattering, but to thermal-equilibrium hemi-Fermi-Dirac distribution

•e.g. for nondegenerate statistics (E >> EF),

)19.0(

/102.1

0

7821

mmmwhere

scmv

t

mTk

TB

Ballistic MOSFET


Linear region: conductance quantization

II onD )(

T = O K:

conclusionAn emerging field whose full potential has not been realized

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Paul Lee Smitesh Bakrania George Ioannou Wayne Fung EECS 598 Presentation 4 October 4 th, 2005