Circuits and Applications
Single-electronics needs applications which make good use of inherent properties of the Coulomb blockade, tunnel junctions, and quantum dots. Many problems that plague single-electronics today can be removed or alleviated by intelligent circuit design. In
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Single-electronics needs applications which make good use of inherent properties of the Coulomb blockade, tunnel junctions, and quantum dots. Many problems that plague single-electronics today can be removed or alleviated by intelligent circuit design. In order to capture the status quo of single-electronic circuit design a fairly complete list of devices and circuits is presented . We will look at fundamental building blocks, such as the ubiquitous single-electron transistor, pump, and turnstile, we will analyze metrological applications like supersensitive electrometers and primary thermometers, and we will study single-electron memories and logic applications. Finally we will assess the merits of neuronal networks, Boltzmann machines, and other specialized circuits.
4.1 Fundamental Circuits Single-electron transistors, turnstiles, pumps, one- and two-dimensional arrays are devices on their own but are frequently building blocks for more elaborate circuits. A large portion of all possible single-electron circuits can be understood in terms of these fundamental circuits. The only other circuits which one would call fundamental circuits which are not explained in this section but in Sect. 4.3 are the electron box and trap.
4.1.1 Single-Electron Transistor The single-electron transistor (SET) is the most studied single-electron device . The first experimental SETs were fabricated by Fulton and Dolan [109] and Kuzmin and Likharev [194] in 1987. A SET is conceptually simple and shows several interesting features in its electrical characteristic. One can distinguish between a C-SET, R-SET, and RC-SET, according to the coupling of the gate to the central island (see Fig . 52).
S. Selberherr ed., Computational Microelectronics © Springer-Verlag/Wien 2001
148
4 Circuits and Applications
V¥, R,
R2
Y
RR
VR
a
c
b
Fig. 52 . a C-SET, b R-SET, c RC-SET
For the C-SET the voltages across junctions one and two are
J;( _
o
V' _ Vi C, 2 -
T'2( c, + Cg ) + VgCg - ne + qo , C 1 + C2 + Cg
(4.2)
with Va the voltage of the central island, qo a noninteger offset charge on the central island, and n the number of excess elementary charges on the central island . The changes in free energy for forward (to the right, superscript +) and backward (to the left , superscript - ) tunneling in the junctions are
A.F,± _ e[e/2 ± (Vi (C2 I
A.F± 2
-
=
+ Cg) - T'2C2 CI + C2 + Cg
VgCg + ne - qo)]
e[e/2 ± (ViC, - T'2(C, + Cg ) + VgCg C, + C2 + Cg
-
(4.3) ,
ne + qo)] .
(4.4)
At zero temperature only events with a negative change in free energy can happen. By setting A.F,± and A.Fl equal to zero one derives the linear equations for boundaries of stable regions. Each region is bounded by four lines forming a diamond-shaped area. The precise shape and position of these stable regions depends on the capacitances, background charges, and form of biasing (symmetric, VI = Vb/2 and V2 = - Vb/2 ; asymmetric, Vi = Vb and T'2 = 0). The general form of the four tunnel event boundaries are 1+ :
1- : 2+ :
T:
- e(n + !) + qo = e(n
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