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Numerical simulation of the HTSC-single electron transistor amplifier
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Jj&&
PHYSICA E
’
i_
ELSEVIER
Physica C 282-287
(1997) 2507-2508
Numerical simulation of the HTSC-single electron transistor amplifier B. Shen, J.-F. Jiang and Q.-Y. Cai Microelectronic Centre, Shanghai Jiao Tong University, Shanghai, 200030, P. R. China
Based on a quasi-classical model, the intrinsic transconductance and output conductance of the capacitively coupled HTSC-single electron transistor are acquired, and properties of a simple amplifier are studied by means of numerical simulation. The results indicate the potential and possibility of the application in analog circuits of this kind of devices.
1. MTRODUCTION
coulomb blockade region of the device is [2]:
If the geometry of HTSC tunnel junctions is scaled to the range of nanometre, single electron tunneling effect will be distinct [l-2]. A HTSC-single electron transistor @lTSC-SET) consists of two serially connected HTSC junctions, with gate voltage and background voltage capacitively coupled to the interjunction area (island). Assuming that the junction is small enough to make the tunneling of single electron be possible, and the resistance of the junction is so large that the quantum noise can be negligible, we regard the discrete transfer of single electrons as the determiner of the current passing through the HTSC-SET [l]. For convenience, we take the direction of electron transmission as positive in after discussions.
[(C-C,)V&,V&k+1/2)e-2A(l)C’/e]
(2)
where C’=C,+C2+CG+CB , and k is an arbitrary integer. Accordingly, the transmission region is: [(C’-C,)V&,Vr&k+l/2)e-2A(l+)C’/e]>V&,>[(1/2k)e-C!,Vo-C,Vr,+2A(l)C’/e] (3) Let it be supposed that N is the net number of electrons on the island when one of the junctions is in the transmission state, and N-l is for the other junction. We use [x] to represent the maximum integer less than x, and N can be expressed as: (4)
2. THE INTRINSIC PROPERTIES According to the quasi-classical model, we consider a HTSC-SET with junction resistances Ri and R2 , junction capacitances C, and C2, gate capacitance CG and background capacitance Ca . While the source is connected. to the ground, the drain gate and background voltages are Vn , Vo and V, respectively. Since Vn is defined as: o
(1)
electrons will alternatively tunnel forward through the junctions when the device is passable. Here A(l) is the energy gap of HTSC material. ln this case, the 0921-4534/97/$17.00 0 Elsevier Science B.V. All rights reserved PI1 SO921-4534(97)01360-9
The potentials across two junctions in the transmission state are V,(N-1) and V,(N), so the drain current accurately is [3]: on condition (2), the device is blocked, I&; on condition (3),
The example parameters which will be used throughout the following discussions are chosen as: C1=2C2 , Cc=10C2 , Cr,=6C2 , R,=3R2 , V,=O, Ao=e/lOC’. The relations of ID , V, and VG are shown in Figure 1. Steps occur on the ID surface because of the energy gap of the superconducting material. While VG is on the increase, 1~ varies periodically with the cycle of elCG
2508
B. Shen et al./Physica
C 282-287
(1997)
2507-2508
g,,~=(1/C’){C,R2[V,(N-1)-e/2C’]2+(C’-C,)R,[V2(N)e/2C’]2}/(R2[V1(N-l)-e/2C’]+R,[V2(N)-e/2C’])2 (7) Figure 2 illustrates &n as a function of V, , three curves here correspond to different values of V, Figure 3 shows the relations of gdr , Vu and Vc , where each curve denotes a particular choice of Vc
3. PROPERTIES OF THE AMPLIFIER Figure 1. The relations of In, Vn and Vc
‘Gl ,, 0 M-2,
---v,=o2sv~, -vD~5vDmax - - - - vD=,,).75vD,,
Consider a single rank co-source amplifier with the load resistance RL and DC source potential Vs According to equation (5) we get In(Vn ,Vc) in case V, is definit. Provided that Vc is known, corresponding In can be acquired by the numerical method utilized to analyze normal amplifiers. Assuming R+kQ, C2=1.6E-19F, C1=0.1C2 , C,-1 0C2, CB=4C2,RI=R2, RL=200Rz, A(T)=3OmeV, V,=O and Vs=l .74V, we set DC working point in the region near the step of ID so as to get higher g, In this instance V&38mV, so V,=972mV, In=48OnA and g==O.O7mS. ‘Ihe gain of the amplifier is Kv=38.3, and the static power consumption is Ws=835nW.
Figure 2. Transconductance g, as a tunction of Ve 4. CONCLUSIONS The discussions above show that the HTSC-SET has advantages including high sensitivity, low power consumption etc. However, the device is restricted by the working envirenment as it is very sensitive to external disturbances. , ACKNOWLEDGMENT
Figure 3. The relations of gd, , Vu and VG Intrinsic transconductance g, and output conductance g, of HTSC-SET can be obtained by differentiation of equation (5). On condition (2), g,,=Oand gb=O; On condition (3), &n=(CG/C’)(R2[V,(N-l>e/2C’]2-R,[Vz(h+e/2C’]2) /(R2[V,(N-l>e/2C’]+R,[Vfi)-e/2C’]}2 (6)
This work was supported by the National Natural Science Foundation of China_ The authors would like to express sincere thanks.
REFERENCE3
1. 2. 3.
Likharev, IBM J. Res. Develop., 32 (1988) 144. M. Amman., K. Mullen and E. Ben-Jacob, J. Appl. Phys., 65 (1989) 339. J. R. Tucker, J. Appl. Phys., 72 (1992) 4399.
Jj&&
PHYSICA E
’
i_
ELSEVIER
Physica C 282-287
(1997) 2507-2508
Numerical simulation of the HTSC-single electron transistor amplifier B. Shen, J.-F. Jiang and Q.-Y. Cai Microelectronic Centre, Shanghai Jiao Tong University, Shanghai, 200030, P. R. China
Based on a quasi-classical model, the intrinsic transconductance and output conductance of the capacitively coupled HTSC-single electron transistor are acquired, and properties of a simple amplifier are studied by means of numerical simulation. The results indicate the potential and possibility of the application in analog circuits of this kind of devices.
1. MTRODUCTION
coulomb blockade region of the device is [2]:
If the geometry of HTSC tunnel junctions is scaled to the range of nanometre, single electron tunneling effect will be distinct [l-2]. A HTSC-single electron transistor @lTSC-SET) consists of two serially connected HTSC junctions, with gate voltage and background voltage capacitively coupled to the interjunction area (island). Assuming that the junction is small enough to make the tunneling of single electron be possible, and the resistance of the junction is so large that the quantum noise can be negligible, we regard the discrete transfer of single electrons as the determiner of the current passing through the HTSC-SET [l]. For convenience, we take the direction of electron transmission as positive in after discussions.
[(C-C,)V&,V&k+1/2)e-2A(l)C’/e]
(2)
where C’=C,+C2+CG+CB , and k is an arbitrary integer. Accordingly, the transmission region is: [(C’-C,)V&,Vr&k+l/2)e-2A(l+)C’/e]>V&,>[(1/2k)e-C!,Vo-C,Vr,+2A(l)C’/e] (3) Let it be supposed that N is the net number of electrons on the island when one of the junctions is in the transmission state, and N-l is for the other junction. We use [x] to represent the maximum integer less than x, and N can be expressed as: (4)
2. THE INTRINSIC PROPERTIES According to the quasi-classical model, we consider a HTSC-SET with junction resistances Ri and R2 , junction capacitances C, and C2, gate capacitance CG and background capacitance Ca . While the source is connected. to the ground, the drain gate and background voltages are Vn , Vo and V, respectively. Since Vn is defined as: o
(1)
electrons will alternatively tunnel forward through the junctions when the device is passable. Here A(l) is the energy gap of HTSC material. ln this case, the 0921-4534/97/$17.00 0 Elsevier Science B.V. All rights reserved PI1 SO921-4534(97)01360-9
The potentials across two junctions in the transmission state are V,(N-1) and V,(N), so the drain current accurately is [3]: on condition (2), the device is blocked, I&; on condition (3),
The example parameters which will be used throughout the following discussions are chosen as: C1=2C2 , Cc=10C2 , Cr,=6C2 , R,=3R2 , V,=O, Ao=e/lOC’. The relations of ID , V, and VG are shown in Figure 1. Steps occur on the ID surface because of the energy gap of the superconducting material. While VG is on the increase, 1~ varies periodically with the cycle of elCG
2508
B. Shen et al./Physica
C 282-287
(1997)
2507-2508
g,,~=(1/C’){C,R2[V,(N-1)-e/2C’]2+(C’-C,)R,[V2(N)e/2C’]2}/(R2[V1(N-l)-e/2C’]+R,[V2(N)-e/2C’])2 (7) Figure 2 illustrates &n as a function of V, , three curves here correspond to different values of V, Figure 3 shows the relations of gdr , Vu and Vc , where each curve denotes a particular choice of Vc
3. PROPERTIES OF THE AMPLIFIER Figure 1. The relations of In, Vn and Vc
‘Gl ,, 0 M-2,
---v,=o2sv~, -vD~5vDmax - - - - vD=,,).75vD,,
Consider a single rank co-source amplifier with the load resistance RL and DC source potential Vs According to equation (5) we get In(Vn ,Vc) in case V, is definit. Provided that Vc is known, corresponding In can be acquired by the numerical method utilized to analyze normal amplifiers. Assuming R+kQ, C2=1.6E-19F, C1=0.1C2 , C,-1 0C2, CB=4C2,RI=R2, RL=200Rz, A(T)=3OmeV, V,=O and Vs=l .74V, we set DC working point in the region near the step of ID so as to get higher g, In this instance V&38mV, so V,=972mV, In=48OnA and g==O.O7mS. ‘Ihe gain of the amplifier is Kv=38.3, and the static power consumption is Ws=835nW.
Figure 2. Transconductance g, as a tunction of Ve 4. CONCLUSIONS The discussions above show that the HTSC-SET has advantages including high sensitivity, low power consumption etc. However, the device is restricted by the working envirenment as it is very sensitive to external disturbances. , ACKNOWLEDGMENT
Figure 3. The relations of gd, , Vu and VG Intrinsic transconductance g, and output conductance g, of HTSC-SET can be obtained by differentiation of equation (5). On condition (2), g,,=Oand gb=O; On condition (3), &n=(CG/C’)(R2[V,(N-l>e/2C’]2-R,[Vz(h+e/2C’]2) /(R2[V,(N-l>e/2C’]+R,[Vfi)-e/2C’]}2 (6)
This work was supported by the National Natural Science Foundation of China_ The authors would like to express sincere thanks.
REFERENCE3
1. 2. 3.
Likharev, IBM J. Res. Develop., 32 (1988) 144. M. Amman., K. Mullen and E. Ben-Jacob, J. Appl. Phys., 65 (1989) 339. J. R. Tucker, J. Appl. Phys., 72 (1992) 4399.