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Radio-frequency single-electron transistor (RF-SET) as a fast charge and position sensor

Radio-frequency single-electron transistor (RF-SET) as a fast charge and position sensor. 11/01/2005. I. V. D I. Single-Electron Transistor. q , offset charge. q = ne. q =(n-1/2) e. I and R SET sensitive to offset charge q. SET as charge sensor. I. island charge is quantized when:.

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Radio-frequency single-electron transistor (RF-SET) as a fast charge and position sensor

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  1. Radio-frequency single-electron transistor (RF-SET) as a fast charge and position sensor 11/01/2005

  2. I V DI Single-Electron Transistor q, offset charge q=ne q=(n-1/2)e I and RSET sensitive to offset charge q SET as charge sensor I island charge is quantized when: q n=0 -1 1 n= n= and kBT<< e2/C

  3. Ccable Limitations of SET Bandwidth Ideal circuit: R, C R, C Intrinsic time scale: output Cc V DUT Noise-limited bandwidth: Achievable bandwidth in a typical DC setup:

  4. vr t reflected voltage vout t after demodulation LCR tank circuit RF-SET as a Fast Electrometer Capacitance now part of the characteristic impedance! radio-frequency single-electron transistor inductor L, SET pad stray capacitance Cp, SET differential resistance Rd(q) form resonant tank circuit vr Z0 = 50 Ω L R,C R,C Cc Cp DUT V(w0t) changes in chargemodulates the amplitude of the reflected signal Dq(wmt)->DR(wmt) q1 q0 q0 Signal at wm detected after demodulation Schoelkopf, Science, 280, 1238 (1998)

  5. Demodulated: 0.05e offset excitation 20 15 -40 signal (mV) 10 -60 5 0 99.9 100.0 100.1 frequency (kHz) -80 0.05e offset exictation 1.0909 1.0910 1.0911 f (GHz) 0.11 0.10 0.09 0 10 20 30 40 50 60 m t ( S) Characterization of RF-SET sine wave modulation applied to the gate Frequency domain Time domain Lu, Nature, 422, 423 (2003) BW=1MHz

  6. N +1 vr N N T = 4 K to 1.5 K t reflected voltage N +1 vout N N t after mixer Experimental Set-up RF circuit: 1.0 GHz carrier w0 HEMT amplifier circulator GaAs FET amplifier Bipolar amplifier mixer To digital oscilloscope directional coupler LO w0 L Cp + SET QD Vbias Cc – Tmix =50 mK

  7. QD: Tunable, flexible Coulomb blockade nanostructure System RF-SET coupled to QD top view depletion gates side view Al tunnel junctions Al AlGaAs GaAs Cc QD QD tunable by gate voltage, capacitively coupled to SET SET: Excellent electrometer Charge detector

  8. Real time detection of individual electrons Number of tunneling events a direct measure of the tunneling rate G relatively open dot relatively closed dot

  9. Charge Occupation probability two level system near a charge degeneracy point dot switching between two charge states: Can directly measure the occupation probability of the N electron charge state

  10. Distribution Function charge occupation probabilities: Distribution function: Thermally broadened Fermi distribution Tunneling rate directly measured Lu, Nature, 422, 423 (2003)

  11. RF-SET as fast charge sensor Can see transition rate pick up as QD source/drain bias is increased. Can also monitor charge fluctuations. In principle, can acquire complete statistical information about current flow! Great potential applications for quantum computation, for example. Lu, Nature, 422, 423 (2003)

  12. RF-SET as displacement sensor RF-SET Mechanical resonator Q0=CgVg DQ0=VgDCgVgDd resonator Apply fixed voltage Vg to the beam, and the RF-SET output measures the beam’s motion (changes in d) d SET LaHaye, Science, 304, 74 (2004)

  13. RF-SET as displacement sensor LaHaye, Science, 304, 74 (2004) Ultrasensitive displacement detection achieved Detect the properties of the resonator by simply “listening”, without driving it (a factor of 4.3 away from the quantum limit)

  14. High BW particle/cell counter Wood, APL, 87, 184106 (2005) RF reflectance data taken for flowing 15 mm beads through the microfluid channel BW>10MHz Problems associated with large R, Cs solved by the RF resonant circuit Millions of beads (cells) can be counted per second

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