Ch 7 – Coulomb Blockade and the Single-Electron Transistor EE 315/ECE 451 N ANOELECTRONICS I From notes by R Munden - 2010.

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Ch 7 – Coulomb Blockade and the Single-Electron Transistor EE 315/ECE 451 N ANOELECTRONICS I From notes by R Munden

O UTLINE  7.1 Coulomb Blockade  7.2 The Single-Electron Transistor  7.3 Other SET and FET Structures  7.4 Main Points 10/14/ J. D ENENBERG - F AIRFIELD U NIV. - EE315

7.1 C OULOMB B LOCKADE 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 3

C APACITOR P ROPERTIES 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 4

7.1.1 N ANOCAPACITOR 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 5 Tunnel one electron Classical Model of Capacitance This leads to:

C OULOMB B LOCKADE IN N ANOCAPACITOR 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 6 So, Energetically, We only notice the Blockade effect for very small capacitors And temperature plays a role k b = 86 μeV/K -> k b RT ~ K For || C, let d = L/10 C or T must be very small!

T UNNEL J UNCTIONS 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 7

T EMPERATURE D EPENDENCE 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 8

T EMPERATURE D EPENDENCE OF N ANOPARTICLE C LUSTERS 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 9

7.1.2 T UNNEL J UNCTIONS 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE Rt represents the ability of the electron to tunnel (the distance between the plates), while C is the capacitor that we are charging up. Rt cannot be too large, therefore, simply increasing d to decrease C does not make Coulomb Blockade a visible effect Uncertainty: Generally R>>Ro ~ 26kOhms

7.1.3 T UNNEL J UNCTION E XCITED BY C URRENT S OURCE 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE Classically: But when we allow tunneling: Hard to achieve experimentally

7.1.4 Q UANTUM D OT C IRCUITS 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE Using to TJ to achieve a small quantum dot (QD), or island, between them makes it easier to control the behavior. Where electron tunneling allows nq electrons to accumulate on the island

QD S TORED E NERGY 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 13

QD T UNNELING E VENT 10/14/2015 J. DENENBERG - F AIRFIELD U NIV. - EE315 14

QD E NERGY B AND D IAGRAMS 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 15

E NERGY B ANDS (2) 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 16

E NERGY B ANDS (3) 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 17

E NERGY B ANDS (4) 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 18

C OULOMB S TAIRCASE 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE Tunneling

STM C OULOMB S TAIRCASE 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 20

7.2 S INGLE -E LECTRON T RANSISTOR 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 21

SET E NERGY D IAGRAM 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 22

C OULOMB D IAMONDS 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE Use the gate to adjust the potential on the island Tunneling occurs when both conditions are met. Tunneling Onto the islandTunneling Off the island

C OULOMB D IAMONDS 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 24

G ATE V OLTAGE C ONTROL FOR T RANSISTOR E FFECT 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE For very small C the effect is visible at Room Temp.

7.2.1 SET L OGIC 10/14/2015 J. D ENENBERG - F AIRFIELD U NIV. - EE315 26

SET INVERTER 10/14/2015 J. DENENBERG - F AIRFIELD U NIV. - EE315 27

SET L OGIC 10/14/2015 J. DENENBERG - F AIRFIELD U NIV. - EE315 28

7.3 SET & FET S TRUCTURES 11/1/2010 R.M UNDEN - F AIRFIELD U NIV. - EE315 29

7.3.1 CNT FET S AND SET S 11/1/2010 R.M UNDEN - F AIRFIELD U NIV. - EE315 30

CNT FET P ROPERTIES 11/1/2010 R.M UNDEN - F AIRFIELD U NIV. - EE315 31

7.3.2 S EMICONDUCTOR N ANOWIRE FET S 11/1/2010 R.M UNDEN - F AIRFIELD U NIV. - EE315 32

S EMICONDUCTING NW SET 11/1/2010 R.M UNDEN - F AIRFIELD U NIV. - EE315 33

7.3.3 M OLECULAR SET S AND M OLECULAR E LECTRONICS 11/1/2010 R.M UNDEN - F AIRFIELD U NIV. - EE315 34

M OLECULAR RTD AND SET 11/1/2010 R.M UNDEN - F AIRFIELD U NIV. - EE315 35

M AIN P OINTS 11/1/2010 R.M UNDEN - F AIRFIELD U NIV. - EE  the Coulomb blockade effect  current-biased tunnel junctions  the influence of capacitance and energy on tunneling and Coulomb blockade  basic Coulomb blockade structures  tunnel junction models, tunneling in quantum dot circuits, and the Coulomb Diamond  the SET and its applications  electronic channels based on carbon nanotubes and semiconducting nanowires  the basic idea of molecular electronics

7.5 P ROBLEMS 11/1/2010 R.M UNDEN - F AIRFIELD U NIV. - EE315 37