Electron Transport of Metal Gated Devices in GaAs/AlGaAs Heterostructure K. M. Liu() , W. R. Chen(), Y. M. Lin (), and S. Y. Hsu ()Low Temperature Laboratory, Department of Electrophysics, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.

OutlineIntroductionGaAs/AlGaAs HeterostructureTransport in mesoscopic systemQuantum Point ContactGate Defined Quantum DotFabricationDouble quantum point contacts in seriesElectron PumpingAdiabatic Quantum PumpingSummary

Introduction-GaAs/AlGaAs Heterostructure There is a very thin layer called 2-Dimensional Electron Gas(2DEG) at the interface of GaAs and AlGaAs. Which is a conducting layer. The mean free path is much larger than the limit length scale of modern technology. Thus we can obtain a system where the transport of electron is coherent and ballistic through lithographic fabrications.

GaAs/AlGaAs 0.3K(5-70)carrier density ns1.88x1011 cm-2mobility 0.8x106 cm2/VsFermi wavelength f57.8 nmmean free path le5.9m

Transport in Mesoscopic System A Theoretical DescriptionFor an Ideal 1D system with one conducting channelCurrent passing through a conductor can be expressed asv(k): electron velocityf(k): distribution functionT(E): Transmission In the limit of low temperature, small (1- 2), and assume T(E) independent with E2Transport is conductance!

Quantum Point Contact Applying a negative voltage on the metal split-gates fabricated above a 2DEG, depleting the electron gas, a quasi-1D quantum wire is formed. And the electron state in the conductor is quantized.xy Each plateau corresponds to an additional mode as integer multiples of half the Fermi wavelength.

Gate Defined Quantum Dote-sourcedrainThe modeled circuit: The energy is quantized as soon as the quasi-0D dot is formed. And the transport is blocked as shown: The energy potential of QD can be tuned by varying Vg, and electron tunneling occurs when there is a state aligning with the Fermi level at source or drain.Coulomb Blockade0.5me2/Ceq charging energyNN+1VgsD

PRL. 80, 4522(1998)Coulomb Staircase For the I-V curve of the QD, the value of current corresponds to the number of states in the energy window Vsd and is quantized.Z. Phys. 85, 367(1991)Weak LocalizationCoulomb Oscillation6-102a-I2Number of electrons~1500

FabricationsPart I. Photolithographymesacontact padsmetal gates

MesaEtch the wafer with solution H2SO4:H2O2:H2O=1:8:160Ohmic ContactDeposit Ni/Au/Ge/Ni=100/2000/1000/700Annealing:450o for 13minGateDeposit Au/Ti =1200/100

Part II. E-beam lithography

-J. Phys. C 21, L887 (1988)g1g2The second channel must impose a more severe constriction on the transverse momentum (Collimation) additional geometry resistance As both QPCs are confined, the plateau index start from the smallest number among themthe resistance through two QPCs is determined by the narrowest of the two constrictions.Double QPCs in SeriesChannel length:0.3m1 mRemove the anomalous resistance

Phys. Rev. B 39, 10445 (1989)QPC constrictionWith zero magnetic field: Tr=Tl=0 If Td=0Ohmic addition of conductance.For direct transmission(Td>1) (h/2e2)Gseries =Td=Ns-Rs G N (2e2/h)Gseries is identical to single QPCLTlTrTdNonadditivity of point contact resistances in seriesFrom Landauer-Bttiker formula describing current in a lead of a four-terminal conductorset Ir=Il=0 and Is=-Id=I

Preliminary Summary Transport through single QPC demonstrates quantized conductance in units of 2e2/h. If the transport is ballistic, the total conductance across double QPCs is determined by the smallest one. The values are also integer multiples of 2e2/h.It is theoretically predicted that: When one of the QPC is in the tunneling regime (N

L=0.8mThe traces have fewer plateaus with narrower qpc2.It has only 1 plateaus with qpc2 set in N=2. Its ballistic when L=0.8m.Destruction of coherence in double quantum point contacts (QPCs) in series

L=1mThe number of plateaus doesnt relate to the channel width of qpc2.The transport doesnt behave ballistically. Ohmic addition.

For larger L, subtracting the contribution from qpc2, the single QPCs conductance quantization is restored. These two QPCs are almost independent with each other.

L=2.9m

When the separation L is much larger than the mean free path, identical traces were obtained. These two QPCs are completely independent with each other.L=20m

As the transmission mode is set to zero (N

SummaryTransport through double QPCs in series :The transport behaviors are determined by two factors: (a) separation between two QPCs, L. (b) number of transmission modes N. As L is larger than a specific length, order of e, the transport behaves completely as that of two independent QPCs. As L is less than e and N is less than one , the quantized conductance vanishes. Coherence between QPCs can be destroyed.

Electron Pumping-Photon-assisted Tunneling Etched narrow wire with width ~0.8m. Use gate 1 and 2 to define a quantum dot containing about 100 electrons. Couple a microwave signal to gate via a capacitor near the sample.The electron can tunnel through the dot by absorption or emission with a photona shoulder along with a Coulomb Oscillation peakCurves in different Excitation amplitudeCurves in different Excitation frequency The position of shoulder is independent with excitation amplitude but scaling with frequency.PRL. 73, 3443(1994)

Turnstile PumpingI:used gatesConfigure the barriers to oscillate with a phase difference . Exactly one electron passes in one cycle. While Increasing the bias V increases number of electron states between l and rI=nefquantized currentThe pumped current scales with frequency and quantized with respect to Vsd.PRL. 67, 1626(1991)

Adiabatic Quantum PumpingSystem: Electron reservoirs are held at same voltage.(zero bias)Each QPC have N channels at the Fermi level EF.The scattering matrix of the system has dimension 2N2N and is a function of X1 and X2X1 and X2 are two parameters modifying the wavefunction of the open dots. Which may be magnetic field or gate voltage.Small harmonic variation:The charge Q(m) entering or leaving the cavity through contact m(m=1,2) in an infinitesimal time: For two parameters X1 and X2 Integrate over one period and use Greens TheoremorPRB, 58, 10135(1998)emissivity

For a phase coherent quantum system, the out-of-phase variation will give rise to a dc current.The current scales as the area enclosed by X1 and X2 in phase space or say the current varies as sin.Science 283, 1905(1999)Experiments:Isd=0

Pumped current in different dot sizeOpen dotClosed dotqpc3qpc4The pumped current reduces with increasing barrier height between dot and reservoirs.

Pumped current with different excitation amplitudeThe pumped current enhances with increasing excitation amplitude. Non-sinusoidal form when Vpp becomes too large.

Pumped current with different frequencyThe pumped current is roughly linear with frequency.

SummaryA mesoscopic system is easily achieved through GaAs/AlGaAs heterostructures due to its long mean free path.The transport of electrons in such systems is characterized by transmission or conductance.Quantum phenomenon: Quantized Conductance in QPC, periodic Coulomb Oscillations, Weak Localization.Double QPCs in series is also studied, where the behavior is characterized by distance between QPCs.Adiabatic Pumping can generate a DC voltage or current without external bias.

The transmission probability Tr and Tl are normalized as Td+Tl+Tr=Ns-Rs. Ns:the number of spin degenerate quantum channels. Rs:probability for electrons to be scattered back source. f=Td/N fraction of the injected current which does miss the opening of the opposite point contact

The anomolous resistance is caused by the collimation of the injected electrons.Both the original and the subtracted data cant align well on N(2e2/h)Partial adiabatic and ohmic transportFor separation between two QPCs is larger then 1.8um, the series conductance behaves almost ohmic addition.