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

2. Single-Electron TransistorV DI
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: n= -1
n=0 n= 1 q
and kBT<< e2/C

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

4. 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
LCR tank circuit L
R,C
R,C Cc Cp
DUT
V(w0t) vr t
reflected voltage
changes in charge modulates the amplitude of the reflected signal
Dq(wmt)->DR(wmt) q1
vout t
after demodulation q0 q0
Signal at wm detected after demodulation
Schoelkopf, Science, 280, 1238 (1998)

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

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

7. QD tunable by gate voltage, capacitively coupled to SET
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
QD: Tunable, flexible Coulomb blockade nanostructure
System

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
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, (2005)
RF reflectance data taken for flowing 15 mm beads through the microfluid channel
Problems associated with large R, Cs solved by the RF resonant circuit
BW>10MHz
Millions of beads (cells) can be counted per second