SET Single Electron Transistor
SET Single Electron Transistor
SET Single Electron Transistor
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Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
<strong>SET</strong><br />
<strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong><br />
Jürgen Wurm, Teresa Lermer<br />
Universität Regensburg<br />
27. Juni 2006<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Setup<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Coulomb Blockade<br />
◮ Equilibrium Charge<br />
Q0 = CL · VL + CR · VR + Cg · Vg<br />
◮ Total energy of the island with n electrons<br />
(Q − Q0) 2<br />
Ech(Q) =<br />
2CΣ<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Transition Rates and Master Equation<br />
◮ Rates Γ can be calculated via Fermi golden rule<br />
◮ pn: propability to find the system in a state with n electrons<br />
◮ → Masterequation<br />
d<br />
dt pn = Γn+1→npn+1 + Γn−1→npn−1 − (Γn→n+1 + Γn→n−1)pn<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Steady State and Current<br />
◮ Condition of Detailed Balance<br />
◮ ⇒ pn<br />
Γn→n+1pn = Γn+1→npn+1<br />
◮ Current through the left junction<br />
I = −e <br />
pn(Γ L n→n+1 − Γ L n→n−1)<br />
n<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Stability Diagram for T = 20mK<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Conservation of Energy - Tunneling<br />
◮ from left junction onto island<br />
<br />
ɛi =<br />
k L max<br />
<br />
ɛf =<br />
k<br />
kL max<br />
k<br />
ɛk + Ech(n) +<br />
R max<br />
ɛk<br />
k<br />
ɛk − ɛk ′ + Ech(n<br />
k<br />
+ 1) +<br />
R max<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong><br />
k<br />
k<br />
ɛk
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
◮ ɛi = ɛf<br />
∆Ech = ɛk ′ ≤ ɛ k L max<br />
◮ from island to right junction<br />
◮ from right junction onto island<br />
◮ from island to left junction<br />
∆Ech ≥ −e V<br />
2<br />
∆Ech ≤ −e V<br />
2<br />
∆Ech ≥ e V<br />
2<br />
= e V<br />
2<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Tunneling condition - straight lines in stability diagram<br />
◮ calculate ∆Ech for positive population n and consider equal<br />
signs<br />
◮ from left to island and v.v.<br />
(2n + 1)e<br />
V =<br />
CΣ<br />
◮ from right to island and v.v.<br />
− 2Cg<br />
CΣ<br />
(2n + 1)e<br />
V = − +<br />
CΣ<br />
2Cg<br />
CΣ<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong><br />
· Vg<br />
· Vg
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
◮ calculate ∆Ech for negative population -n and consider equal<br />
signs<br />
◮ from left to island and v.v.<br />
(2n + 1)e<br />
V =<br />
CΣ<br />
◮ from right to island and v.v.<br />
+ 2Cg<br />
CΣ<br />
(2n + 1)e<br />
V = − −<br />
CΣ<br />
2Cg<br />
CΣ<br />
◮ slope and axis intercept yield CΣ and Cg<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong><br />
· Vg<br />
· Vg
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Coulomb Oscillations for V = 1nV<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
I vs. V = VR − VL<br />
for Vg = 0<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Stability Diagram for T = 0.15K<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Stability Diagram for T = 2K<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Different resistance: RR = 100Ω, RL = 10Ω<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
Coulomb Blockade Stability Diagram Coulomb Oscillations I vs. V Higher Temperatures different resistance Conclusion<br />
Conclusion<br />
◮ We learned the basics of the Coulomb Blockade Effect and<br />
the concept of the <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong><br />
◮ We gained insight into numerical working with matlab and its<br />
graphical features<br />
Jürgen Wurm, Teresa Lermer Universität Regensburg<br />
<strong>SET</strong> <strong>Single</strong> <strong>Electron</strong> <strong>Transistor</strong>
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