A new type of logic gate that can be designed using a nonhysteretic Josephson weak link is proposed. The basic component of the proposed device is a one-junction interferometer, and a logic state is represented by either a zero or a single-flux-quantum. In contrast to the “Parametric Quantron,” this device is designed to operate without a three-phase clock and the dependence of the junction critical current on magnetic field is not used. The switching behavior of the device was simulated by computer and an analytical expression for the switching delay has been obtained

Okabe Yoichi

Sugano Takuo

Tamura Hirotaka

岡部 洋一

田村 泰孝

UTokyo Repository

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-27, NO. 10, OCTOBER 1980 2035 
[SI R. B. Laibowitz, A. N. Broers, J. T. C. Yeh, and J. M. Viggrano, 
“Josephson  effect in Nb nanobridges,” Appl .  Phys. Lett . ,  vol. 35, 
[6] R. A. Buhrman, .I. E. Lukens, L. D. Jackel, S. F. Strait, J. M. 
Warlaumont, and W. W. Webb, “SQUID techniques. 1. Obtain- 
ing  reliability  in point-contact SQUID’S,” J. Appl .  Phys., vol. 45, 
pp. 4045-4048, Sept. 1974. 
pp. 891-893,1979. 
Proposal of Single-Flux-Quantum Logic  Device 
HIROTAKA  TAMURA,  YOICHI  OKABE, AND 
TAKUO  SUGANO 
Abstract-A new type of logic gate that can be designed using a 
nonhysteretic  Josephson  weak  link  is  proposed.  The  basic  component 
of the proposed device is a one-junction interferometer, and a logic 
state is  represented by either a zero or a single-flux-quantum.  In  con- 
trast to the “Parametric  Quantron,” this device  is  designed to operate 
without a three-phase  clock  and the dependence of the junction critical 
current on magnetic field is not used. The switching behavior of the 
device was simulated by computer and an analytical expression for 
the switching  delay has been  obtained. 
I.  INTRODUCTION 
At  least two  types of Josephson-junction devices for digital 
use have been reported. One uses the voltage change of the 
Josephson  junction to represent logic state  and  the  other uses 
trapping or untrapping of a single-flux-quantum to represent 
binary  states. 
One  type of the device in  the  latter  group is the  “Parametric 
Quantron”  proposed  by  Likharev [ 11. The  “Parametric 
Quantron”  uses  the  magnetic  sensitivity of the  critical  current 
of Josephson junctions and is driven by three-phase control 
current. 
Here, we propose a new type of single-flux-quantum logic 
device, which is designed to operate in a mode that allows 
only a zero-to-one transition followed by a resetting of the 
logic network.  The device does  not use magnetically sensitive 
junctions  or  a  three-phase  clock.  Its  logical  operation  by com- 
puter  simulation  and  an  analytical  study of its  switching  char- 
acteristics  are  presented. 
11. PRINCIPLE OF LOGIC OPERATION 
Consider the circuit of Fig. l(a), which is a one-junction 
interferometer. If the  inductance of the  interferometer L 
and the critical current I, are chosen so that L I ,  - @,, a 
flux quantum, the flux in the interferometer is quantized in 
two stable states which correspond to a zero-flux-quantum 
mode and a one-flux-quantum mode, as shown in Fig. l(b). 
The zero-flux-quantum mode can be taken as a logical “0” 
state  and  the  one-flux-quantum  mode as  a  logical “1” state. 
Two  methods  can  be  used  for  switching  the  interferometer 
from  the logical “0” state  to  the  “1”  state.  One is to hold  the 
bias flux @b = Lib, where Ib is the bias current as shown in 
Fig. l(a), fixed and to reduce the critical flux a,, which is 
the maximum bias flux that leaves the interferometer in the 
logical “0” state as shown  in Fig. l(b), t o  less than @b by re- 
ducing the critical current I,. The other is to hold @, fixed, 
Manuscript  received  February 1, 1980; revised  May 5 ,  1980. 
The authors are with the Departments of Electrical and Electronic 
Engineering,  Faculty  of  Engineering,  University  of  Tokyo, 7-3-1, Hongo, 
Bunkyo-ku,  Tokyo 113, Japan. 
Fig. 1. (a) Schematic  drawing of the one-junction  interferometer. 
1, is the bias current, L is the inductance of the interferometer, 
Z is the current in the inductance, and Z ,  is the critical current of 
the Josephson junction. (b) Internal flux  versus  applied  flux  relation 
for the interferometer of Fig. l(a). (c) A configuration of the pro- 
posed single-flux-quantum logic. The coupling between the inter- 
ferometer is accomplished  by  mutual  inductance. (d) The  other 
coupling  scheme  in  which  mutual  inductance  is not required. 
i.e., I, fixed, and to increase to  larger than @, by adding a 
small magnetic flux to a b .  This will be called “flux switch- 
ing” hereafter.  To  switch  back  the  interferometer  in  the 
logical “1” state to the logical “0” state, the interferometer 
should  be  reset  by  reducing  the bias flux @b below  some 
critical value. This is similar to   the resetting commonly used 
in  Josephson-tunneling logic  gate. 
The  key idea of the design for flux-switching  logic  is  shown 
schematically in Fig. 1 (c). One-junction interferometers are 
coupled  to  each  other  by  mutual  inductances. If the  currents 
of the preceding interferometers generate a magnetic flux to 
make  the  total  magnetic  flux  coupled  to  the  next  interferom- 
eter  larger  than  the  next  interferometer will be  switched 
from the “0” state to the “1” state and latched in the “1” 
state.  Then,  in  the  same  manner,  the  next  interferometer 
triggers the  interferometer  after  the  next.  The  preceding 
interferometers still remain in the state “1” because of their 
latching  property.  This  latching  property  ensures  the  uni- 
lateral  propagation of signals in  the  same  manner as “Domino 
Toppling.”  The  direction of the  propagation is determined  by 
the  positions of the interferometers which are first triggered, 
and  a  three-phase  clock  is not  required  to  determine  the  direc- 
tion. After each logic cycle, the interferometers are reset to 
“0” in  the  same  manner as conventional Josephson-tunneling 
logic gate. The basic operation, AND, OR, and NOT can be 
realized using this logic scheme, and confirmed by numerical 
calculations. Fig. l (d)  shows an alternative coupling scheme, 
called the current injection scheme, which does not require 
the mutual inductance. Fig. 2 shows the result of the com- 
puter simulation of an AND gate using the current injection 
scheme. The parameters of the interferometers used in the 
simulation  are  listed  in  the  figure  caption. 
111. CALCULATION OF SWITCHING DELAY 
To analyze the switching delay of the proposed device, it 
is useful to replace Josephson weak links by their resistively 
shunted-junction model in the limit of heavy damping. The 
resulting circuit equations for the circuit shown in Fig. l(a) 
can be  written 
0018-9383/80/1000-2035$00.75 O 1980 IEEE 
2036 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. ED-21, NO. 10, OCTOBER 1980 
0 , 1 , 0 ’ ? - 1 0 ,  
1 L c L  
L R IC 
I $i& L L L C  
(b) 
Fig.  2.  (a)  Simulation  of the time  dependence  of the flux in the inter- 
ferometers forming AND gate illustrated in Fig. 2(b). The parameter 
values are: L = 0.33 pH, R the normal resistance of the junction 
(0.2 a),  C the capacitance  of the junction (0.1 pF), andZ, the critical 
current (1 mA). The total inductance of an interferometer LT is 
4 L and 2nL74, is equal to 4.000 in this case. The bias current of 
each interferometer is clocked by a bipolar trapezoidal signal. (b) 
The  configuration  of the AND gate  used for simulation. 
( l /R)(d@/dt) = [ab - {@ + LI,  sin (2n@/(a0))I / L  (1) 
and 
@ = (@0/2n) 8. (2) 
Here, 8 is the  quantum  phase  change  across  the  junction  and 
R is the normal resistance. The switching delay r for Gb(t < 
0) = @, - A@ and @b(t  > 0) = @, + A@ is expressed  by  the 
following  equation: 
dt  -)X 0.9 - d @ = -  
CP ( t  = 0 )  d@ R cP(t=o) 
8 %  
. 
\ 
\ 
I I 
0.01 01 1 
A@/L,/Llc 
Fig. 3. Switching  delay  versus  overdrive for the interferometer of 
Fig. l(a). Solid  line:  numerical  calculations.  Dashed  line:  (4). 
Equation (4) agrees with the numerical calculation of (3) within 
about 15 percent for overdrives A@/LZ, below about 20 percent, 
and for values  of LZ, ranging  from about 0.3CPo to 1.300. 
This  can  be well approximated by 
( 3 / 4 2 / 2 ) ( @ 0 / V ~ )  (A@/LI,)-”’ (4) 
where VJ = R * I,. In Fig. 3, the  turn-on delay  obtained  from 
the  numerical  calculation  of (3) and  the  delay  calculated  from 
(4) are  indicated  by  a  solid-line  curve  and  a dashed-line  curve, 
respectively. It can be seen that the result calculated from 
(4) agrees with the numerical calculation of (3) within about 
15  percent  for overdrives A@/LI, below  about 20 percent,  and 
for values of LI, ranging  from  about 0.3Q0 to 1  .3Q0. 
If the Josephson junction with VJ = 0.3 mV is used and 
A@/LI,  = 0.1,  about  10 ps is obtained  for r from  (4). 
IV. CONCLUSION 
We have proposed  a  new  single-flux-quantum  Josephson- 
logic  device. Magnetic  sensitivity of the critical  current of 
Josephson junctions is not required in this logic  device. It 
is predicted theoretically that a switching delay of about 10 
ps is feasible. 
REFERENCES 
[ I ]  K. K. Likharev, “Dynamics of some single flux quantum devices: 
I. Parametric Quantron,” ZEEE Trans. Mugn., vol. MAG-13, pp. 
242-244,  Jan.  1977. 


PROPOSAL OF SINGLE-FLUX-QUANTUM LOGIC DEVICE

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