Patent Publication Number: US-8982528-B2

Title: Low consumption logic circuit and integrated circuit comprising at least one such logic circuit

Description:
TECHNICAL FIELD AND PRIOR ART 
     The present invention relates to a low consumption logic circuit and to integrated circuits comprising at least one such logic circuit. 
     Logic circuits of the prior art are produced in CMOS (Complementary Metal-Oxide Semiconductor) technology, which associates a pair of complementary transistors, one of N type, the other of P type, on a same support. 
     In particular due to the development of autonomous electronic systems, it is sought to control the consumption of integrated circuits in order to reduce said consumption. Several solutions may be implemented, one consisting in reducing the supply voltage of the circuits, indeed the consumption known as dynamic is proportional to the square of said voltage, the other solution consists in favoring the implementation of several circuits operating at relatively slow frequencies compared to a system operating at high frequency. However these solutions have limits due to the reduction in size of transistors. 
     There exists another solution called adiabatic logic, which consists in controlling in an optimal manner the charges and discharges of the capacitances of an integrated circuit, said capacitances being mainly those of the interconnecting lines, which are clearly superior to those of transistors. Adiabatic logic is described in the document of W C Athas, “ Low power digital systems based on adiabatic switching principles”, IEEE transactions on VLSI systems VOL  2, N04 December 1994. 
     In  FIG. 1A  may be seen a logic inverter in conventional CMOS technology. The logic inverter comprises a p transistor and an n transistor  102 ,  104 . G, S and D designate respectively the grid, the source and the drain of the transistors. A and its complement designates the control signals. In a more general manner,  FIG. 1C  shows how to produce any logic function as a function of the inputs, the associated circuit being a combination of transistors in series or in parallel. The inverter function is simply formed by a transistor, a PMOS for F and a NMOS for the complementary function. 
     In conventional logic, at each change of state, the capacitance C L  of the interconnecting lines is charged to the supply voltage V DD  then discharged to ground. An energy is thus dissipated thermally, which can be written for a cycle: 
     
       
         
           
             E 
             = 
             
               2. 
               ⁢ 
               
                 
                   1 
                   2 
                 
                 · 
                 
                   C 
                   L 
                 
                 · 
                 
                   V 
                   DD 
                   2 
                 
               
             
           
         
       
     
     It may be shown in a theoretical manner that to minimise the energy dissipated by Joule effect in the resistance in series with a capacitance, it is necessary to guarantee that the charge and discharge operations take place at constant current. In this case, it is easy to show that the energy dissipated during time T, during which the capacitance is charged or discharged is written: 
     
       
         
           
             E 
             = 
             
               
                 
                   RC 
                   L 
                 
                 T 
               
               · 
               
                 C 
                 L 
               
               · 
               
                 V 
                 DD 
                 2 
               
             
           
         
       
     
     The resistance R is the sum of the resistances between the supply and the input of the interconnecting line (resistance of the switch used+resistances of the connecting lines). To establish this result, it suffices to resolve the system of equations:
 
 Q=iT  
 
 Q=C   L   V   DD  
 
 E=Ri   2   T  
 
     Q is the charge stored in the capacitance of the interconnecting line (in fact it is this capacitance plus the input capacitance of the following stage but in general much lower). 
     The constant charge and discharge current is i. 
     The voltage to be established on the interconnecting line is the supply voltage (the charge being assumed quasi-total). 
     T is the time during which the interconnecting line is charged or discharged. 
     In practice, to come close to this ideal condition, the circuits proposed until now are based on a linear variation of the supply voltage during the operations of charging and discharging the capacitances, which amounts to the first order to working at constant current. The case of the inverter makes it possible to specify this operating mode. 
     In adiabatic logic, in the case of the inverter represented in  FIG. 1B , the supply voltage is no longer constant as in conventional logic, but is established relatively slowly at each change of state. The inputs are positioned then the supply voltage V alim  is progressively taken to the nominal voltage V DD  for a time T, which makes it possible to establish the output level then to transmit this level to the following gates. The opposite operation is then carried out to return the system to zero and treat another logic event. In the same way, the supply voltage V alim  is then relatively slowly lowered from V DD  to zero. The inputs are then also taken to zero potential while awaiting a new change of state. 
       FIG. 1D  represents a logic function equivalent to that of  FIG. 1C  produced in adiabatic logic. 
     Usually, adiabatic gates also perform the complementary function as is indicated in  FIGS. 1A to 1D  and as a result also use at input not only the logical variables but also their complements. This particular adiabatic logic is called “dual rail”. 
     In so far as the capacitance C L  is charged and discharged slowly compared to the typical time constant of the circuit RC L , R being the overall resistance associated with the charge and discharge process, which includes the output resistance of the transistor(s) performing the functions F as well as the resistance of the connections, the voltage at the terminals of the capacitance C L  can follow the voltage applied at input. The voltage at the terminals of the resistance is thus virtually zero and the thermal consumption may thus be reduced in a significant manner compared to conventional logic. 
     The energy dissipated during the charge may then be written as in the ideal case of the charge at constant current: 
     
       
         
           
             E 
             = 
             
               
                 
                   RC 
                   L 
                 
                 T 
               
               · 
               
                 C 
                 L 
               
               · 
               
                 V 
                 DD 
                 2 
               
             
           
         
       
     
     During the discharge an equivalent energy is dissipated. 
     Consequently, the energy dissipated in adiabatic logic may be reduced in a significant manner provided that the period T is very much greater than the time constants RC L . 
     In practice, the trapeze form of the supply signal is often replaced by a sinusoidal or partly sinusoidal signal more easy to generate and constituting a suitable approximation. 
     This logic has not however given rise to any industrial realisation. In fact, the calculation exposed above ignores a characteristic of transistors produced in a technology based on semi-conductors, namely the threshold effect. To make the transistor (or the transistors) conductive in the charge or discharge phase of the capacitances, it is necessary that the control voltage applied to the grid exceeds a value called threshold voltage and noted V T  in CMOS technology. In general, the control voltage and the supply voltage are of the same value to simplify the architecture. In the case of the inverter of  FIG. 1B , when the input is at the state “0”, the PMOS transistor becomes conductive when the supply voltage is greater than the threshold voltage of the transistor. In this case, a voltage difference is going to appear at the terminals of the resistance R in the charge (or discharge) process as long as the transistor is not conductive. This value varies from 0 to V T  during the cycle. A non negligible current then appears at the terminals of the resistance and generates a thermal dissipation. 
     The energy dissipated in the charge process may be written as a first approximation: 
     
       
         
           
             E 
             = 
             
               
                 
                   
                     RC 
                     L 
                   
                   T 
                 
                 · 
                 
                   C 
                   L 
                 
                 · 
                 
                   V 
                   DD 
                   2 
                 
               
               + 
               
                 
                   1 
                   2 
                 
                 ⁢ 
                 
                   
                     C 
                     L 
                   
                   · 
                   
                     V 
                     T 
                     2 
                   
                 
               
             
           
         
       
     
     To reduce this negative effect it would be necessary to reduce the threshold voltage V T  to a value close to 0, but in CMOS technology this solution is inapplicable because it would lead to an intolerable static consumption due to the current under the threshold. The static consumption is linked to the leakage current of the transistors (residual conduction below the threshold), it varies exponentially with the reduction of the threshold voltage and V T /V DD  ratios greater than 0.2 or even 0.3 in low consumption technologies are necessary. 
     Consequently, adiabatic logic, theoretically of considerable interest, is incapable of significantly reducing the consumption of circuits produced in a technology of switches based on semi-conductors, having threshold effects. 
     DESCRIPTION OF THE INVENTION 
     It is consequently the aim of the present invention to offer a logic circuit with very low energy consumption. 
     The aforementioned aim is attained by a logic circuit in adiabatic logic; i.e. supplied by a supply voltage source able to charge and discharge at quasi constant current an interconnecting line through mechanical switches, and implementing microelectromechanical switches or MEMS or nanoelectromechanical or NEMS instead of N and P transistors. 
     On the one hand, such mechanical switches do not have a threshold voltage in the sense of semi-conductors. When the contact is established, a very small value of the applied voltage is sufficient to make a current flow without having to overcome a threshold voltage. Moreover, they have a negligible static dissipation, contrary to transistors. Consequently, the energy dissipated is reduced compared to that dissipated by CMOS. 
     On the other hand, in a particularly interesting manner, the combination of mechanical switches with an electrostatic actuation and adiabatic logic makes it possible to obtain an integrated circuit in which the energy dissipated is to the first order independent of the supply voltage, which makes it possible to produce low consumption circuits without needing to implement very low supply voltages. The operating voltage may be chosen freely, which avoids having to work at very low voltages as in CMOS. 
     This effect is completely unexpected for those skilled in the art who generally associate low consumption with low supply voltage. 
     Thanks to the invention, in the case of ultra low consumption devices, it is no longer necessary to reduce the supply voltage, such a reduction having negative effects on reliability. 
     In the case of an integrated circuit that would implement one or more mechanical switches in conventional logic, the supply voltages would have to be lowered below 200 mV to be able to have an important advantage compared to CMOS integrated circuits. However, such supply voltages would impose clearances between the moving structure and the base of the switch of the order of several nanometers, which would imply very considerable technological production difficulties. 
     Thanks to the invention, such technological constraints are eliminated. A clearance comprised between 5 nm and 100 nm between the moving structure and the base in the switches may be implemented. 
     Although mechanical switches are considered by those skilled in the art in the field of integrated circuits as slow, having a high contact resistance in the case of switches of small dimensions and which are moreover capable of being subject to problems of sticking, the inventor of the present invention is going against the prejudices regarding mechanical switches by using them to produce logic gates in adiabatic logic and has obtained unexpected results from this combination. In particular, the independence to the first order of the energy dissipated compared to the supply voltage. It ensues that the supply voltage may be relatively high, which procures the unexpected advantage of resolving the problems of sticking, since said sticking is notably reduced when the applied voltage is low. 
     The present invention has the advantage of not being the seat of leakage current. In adiabatic logic, it is then possible to arbitrarily choose the operating frequency, which is impossible with MOS, since it is necessary to reach a static energy-dynamic energy compromise, which leads to an optimal operating frequency. 
     Moreover, mechanical switches do not have a threshold voltage, which leads to eliminating the non adiabatic residues in the dissipation, unlike MOS switches, which lead to terms dependent on the square of the threshold voltage. 
     The subject-matter of the present invention therefore is a logic circuit for integrated circuit comprising:
         a supply voltage source able to charge and discharge at quasi constant current an interconnecting line through mechanical switches:   an interconnecting line,   mechanical switches, said switches being microelectromechanical switches or nanoelectromechanical switches,   means of switching said switches.       

     In an advantageous embodiment, the supply voltage source is variable according to at least three successive phases, a first phase of increasing the voltage from a zero value to a nominal voltage, a second phase of maintaining the supply voltage at the nominal voltage and a third phase of reducing the supply voltage from the nominal voltage to a zero value, and at least two mechanical switches, said switches being microelectromechanical switches or nanoelectromechanical switches, and means of switching said switches. 
     For example, each switch comprises two electric conductive tracks, one of which is connected to the supply voltage source and a moving part intended to come into contact with the two tracks in a state of closing of the switch, and the switching means implementing a control voltage for displacing the moving part. 
     In a preferred manner, the switching means are of electrostatic type and comprise a fixed electrode facing a part at least of the moving part and means of applying the positive control voltage to attract the moving part towards the fixed electrode and place in contact the moving part with the conductive tracks. 
     Advantageously, the supply voltage is equal to the control voltage. 
     For example, the duration of the first phase is comprised between 1 and 100 ns, and the nominal supply voltage may be comprised between 100 mV and 10 V. 
     In a variant, the switching means are of magnetic, piezoelectric type. 
     The logic circuit according to the invention may be a logic inverter or a NOR or NAND or AND or OR circuit or a Toffoli gate or a Fredkin gate or a Feynman gate. 
     The subject-matter of the present invention is also an integrated circuit comprising at least a first and a second logic circuit according to the present invention. 
     In an embodiment, the output voltage of the first gate controls the second gate. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       The present invention will be better understood on reading the description that follows and by referring to the appended drawings in which: 
         FIGS. 1A to 1D  are logic gates of the prior art, 
         FIG. 2  is an example of logic inverter according to the present invention, 
         FIGS. 3A ,  3 B and  3 C are examples of NOR and NAND logic gates according to the present invention, 
         FIG. 4  is a complete view of a schematic representation of a mechanical switch that can be implemented in the present invention, 
         FIGS. 5A and 5B  are side views of the switch of  FIG. 4  in a closed state and in an open state respectively, 
         FIGS. 6A and 6B  are top and sectional views of an example of embodiment of a mechanical switch with magnetic control that can be used in the present invention, 
         FIGS. 7A and 7B  are longitudinal sectional views of an example of embodiment of a mechanical switch with piezoelectric control that can be used in the present invention, in a state in the course of closing and in an open state respectively. 
     
    
    
     DETAILED DESCRIPTION OF PARTICULAR EMBODIMENTS 
     In  FIGS. 2 and 3  may be seen two examples of logic gates according to the present invention. In  FIG. 2  it is a logic inverter and in  FIG. 3A  it is an example of a NOR gate. In  FIG. 3B  may be seen another example of NOR gate and in  FIG. 3C  may be seen an example of embodiment of NAND gate. 
     Said logic gates comprise, instead of transistors, mechanical switches, more particularly nanoswitches or microswitches produced by NEMS (Nanoelectromechanical Systems) or MEMS (Microelectromechanical Systems) technology. The closing and sometimes the opening of said switches may be controlled by electrostatic means, by application of a magnetic field, by piezoelectric effect, by thermal effect, etc. 
     For reasons of simplicity, “nano and microswitches” will be designated uniquely by “mechanical switches”. 
     On the circuit of  FIG. 2  are shown schematically the two mechanical switches  2 ,  4 , one of them  2  performing the function F and the other  4  performing the complementary function  F . 
     The capacitors  6 ,  8  of capacitance C L  symbolise the capacitances of the interconnecting lines. 
     The supply voltage designated V alim  is applied at input of the two mechanical switches  2 ,  4 . 
     In the case of switches with electrostatic control, a control voltage V assures the closing of the switches  2 ,  4 . 
     According to the invention, the gate of  FIG. 2  functions in adiabatic logic, i.e. the supply voltage source is such that it makes it possible to charge and discharge at quasi constant current an interconnecting line through the mechanical switches. 
     For example, the voltage supply source is such that the supply voltage V alim  is not constant and varies according to a trapezoidal profile. The variation in the voltage V alim  is represented schematically in  FIGS. 2 and 3 . In a first phase I, the supply voltage rises progressively from 0 until it reaches the nominal voltage V DD , during a time T, which makes it possible to establish the output level then to transmit the level to the following gates. In a second phase II, the supply voltage V alim  is maintained for a certain time at the nominal voltage V DD  and then, during a third phase III, the supply voltage V alim  decreases during the time T to return the system to zero and treat another logic event. The inputs are then also taken to zero potential while awaiting a new change of state. 
     The time of increasing the voltage and the time of reducing the voltage are preferably substantially equal. Moreover, the time during which the voltage is constant is substantially constant. In practice, the trapezoidal profile is approximated by a demi-sinusoid. 
     In adiabatic logic, also called “energy recovery logic”, the energy stored in the capacitance of the interconnection is not discharged to ground as in CMOS logic, which necessarily introduces a dissipation, but to the supply that has served to charge it. A large part of the energy is thus recovered by the supply. Adiabatic logic is also called energy recovery logic. 
     In  FIG. 4  may be seen, in top view, an example of embodiment of a mechanical switch  2  adapted to the present invention. 
     The switch is intended to electrically connect two tracks  10 ,  12  formed on the surface of the integrated circuit, the switch comprises a means of connection formed by a moving part  14  provided with a control electrode  15  arranged above two tracks  10 ,  12  and a fixed electrode  16  on the fixed part  11  of the integrated circuit and a part of which at least is facing the moving part  14 . In the example represented, the moving part  14  is of cantilever type. It could be formed by a membrane. 
     In the example represented, the two tracks  10 ,  12  are aligned and comprise two free ends  10 . 1 ,  12 . 1  respectively facing, the fixed electrode  16  is situated between the free ends  10 . 1 ,  12 . 1  of the two tracks  10 ,  12 , and the moving part  14  overlaps the two ends  10 . 1 ,  12 . 1  of the tracks  10 ,  12  and is perpendicular to the fixed electrode. 
     The moving part  14  is, in the absence of applied positive voltage, between the moving part  14  and the fixed electrode  16  maintained suspended above the tracks by beam type elastic elements. When a sufficient control voltage is applied, the moving part comes closer to the tracks under the effect of the electric force and enters into contact with them so as to assure the electrical connection therewith. For example, the moving part is of the cantilever type. 
     In  FIG. 5A  may be seen from the side the switch of  FIG. 4 , in an open state (logic state  2 ), in the absence of a positive control voltage applied between the fixed electrode and the moving part and in  FIG. 5B , the switch is in a closed state (logic state  1 ) by application of a positive control voltage between the fixed electrode  16  and the moving part  14 , the two tracks  10 ,  11  are connected and the current can flow between the two tracks  10 ,  12 . 
     The switch structure represented in  FIGS. 4 ,  5 A and  5 B is only an example of embodiment and is in no way limiting. 
     A switch with magnetic actuation is represented in  FIGS. 6A and 6B , this comprises a moving part  514  of cantilever type and the control means are formed by a permanent magnet  524  and a coil  526  separated by a substrate  528 . 
     In  FIGS. 7A and 7B  may be seen an example of embodiment of a switch with piezoelectric control. The moving part  614  is also of cantilever type, this comprises two portions  630 ,  632  of piezoelectric material, for example AlN, in which the application of a positive voltage V causes for one an expansion  630  in the plane and for the other  632  a contraction, closing the switch, and conversely the application of a negative voltage V causes for one  630  a contraction and for the other an expansion  632 , opening the switch. 
     The switch structures represented in  FIGS. 6A to 7B  are examples of embodiments and are in no way limiting. 
     In  FIGS. 3A and 3B  may be seen examples of embodiments of NOR gates according to the present invention. In  FIG. 3A , the gate comprises two branches supplied in parallel by V alim , one comprising two switches in series  210 ,  212  and the other comprising two switches in parallel  220 ,  222 . Each branch is charged by its own capacitance C L . A capacitance C L  is provided between the two switches in series and the switches in parallel. The voltages V at the terminals of A and B are also represented. 
     The switches may be similar to those represented in  FIGS. 4 ,  5 A and  5 B. 
     In  FIG. 3B , the gate comprises two switches  310 ,  312  in parallel performing the controls A and B, in series with two switches in parallel  320 ,  322  performing the complemented controls and B. The voltage source is connected to the switches  310 ,  312 . A capacitance C L  is provided between the two switches in series and the switches in parallel. When the switches  310  and  312  are open, the switches  320  and  322  are closed. The complemented control A and the complemented control B may be replaced by the controls A and B with different switches, i.e. closed without application of control voltage and opened by application of a control voltage. 
     In  FIG. 3C  may be seen an example of NAN gate according to the present invention implementing four mechanical switches  410 ,  412 ,  420 ,  422 . The voltages V at the terminals of A and B are also represented. 
     Preferably, all of the switches of a same logic circuit are similar or identical in order to simplify the production and the control of the circuit. 
     We are now going to determine the energy dissipated for a mechanical switch with electrostatic control and in the case of a logic inverter according to the present invention. 
     The inverter according to the present invention consumes energy uniquely during switchings, this consumption is designated dynamic consumption, the static consumption thereof being negligible. 
     In fact, the mechanical contact being established by positioning of the inputs, the switch is conductive whatever the value of voltage applied between the two conductive tracks  10 ,  12  and a voltage however small is transmitted between the input and the output. 
     The current flowing between the two tracks is independent of the control voltage value, unlike a CMOS switch in which the current between the source and the drain depends on the threshold voltage value. The closing of the mechanical switch is effective from a certain control voltage value, however this is not comparable to the threshold voltage of a MOS transistor because its value does not intervene on the current value that flows through the switch and thus does not introduce any non adiabatic dynamic consumption. In addition, since the control electrode is electrically isolated, there is no static consumption. 
     The energy dissipated may then be written: 
     
       
         
           
             
               
                 
                   
                     E 
                     meca 
                   
                   = 
                   
                     
                       
                         
                           R 
                           meca 
                         
                         ⁢ 
                         
                           C 
                           L 
                         
                       
                       T 
                     
                     · 
                     
                       C 
                       L 
                     
                     · 
                     
                       V 
                       DD 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   I 
                   ) 
                 
               
             
           
         
       
     
     With C L  the capacitance of the interconnections,
         R meca  the electrical resistance of the interconnections and contacts.       

     By way of comparison, the switching energy of an MOS based adiabatic inverter is: 
     
       
         
           
             
               
                 
                   
                     E 
                     MOS 
                   
                   = 
                   
                     
                       
                         
                           
                             R 
                             mos 
                           
                           ⁢ 
                           
                             C 
                             L 
                           
                         
                         T 
                       
                       · 
                       
                         C 
                         L 
                       
                       · 
                       
                         V 
                         DD 
                         2 
                       
                     
                     + 
                     
                       
                         C 
                         L 
                       
                       · 
                       
                         V 
                         T 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   II 
                   ) 
                 
               
             
           
         
       
     
     Assuming that the period T is chosen so that the first term of the expression (II) in the case of a CMOS inverter is negligible, one may compare: 
     
       
         
           
             
               E 
               meca 
             
             = 
             
               
                 
                   
                     
                       
                         R 
                         meca 
                       
                       ⁢ 
                       
                         C 
                         L 
                       
                     
                     T 
                   
                   · 
                   
                     C 
                     L 
                   
                   · 
                   
                     V 
                     DD 
                     2 
                   
                 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 and 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 
                   E 
                   mos 
                 
               
               = 
               
                 
                   C 
                   L 
                 
                 · 
                 
                   V 
                   T 
                   2 
                 
               
             
           
         
       
     
     For example, R meca  may be as low as 1000 Ohms for a voltage V DD  of 1 V. 
     The time T of raising the polarisation signal may be chosen at 10 ns. 
     The typical capacitance of the connecting line is 10 fF. 
     The threshold voltage of an advanced low consumption CMOS technology is of the order of 300 mV. 
     The two energies are then C L ·V T   2  for CMOS and 10 −3  C L ·V DD   2  for the NEMS solution. 
     As has been explained previously, the threshold voltage of CMOS technology cannot be reduced due to the static consumption and since it is possible to envisage voltages of several volts for the supply voltage V DD , it may be noted that the logic circuit according to the invention makes it possible to reduce the energy dissipated by a factor of the order of 100 compared to a logic circuit in advanced CMOS technology. 
     For example, taking typical values of 300 mV for the threshold voltage and 1 V for the supply voltage of the logic circuit according to the invention, a factor 100 is obtained. 
     This factor would be between 100 and 1000 for a time T of 100 ns. 
     Consequently, thanks to the invention, a low consumption logic circuit is obtained. 
     Moreover, thanks to the combination of an operation in adiabatic logic and of mechanical switches according to the invention, it is possible to produce low consumption integrated systems without having to use low supply voltages. Being able to use relatively high voltages (of the order of a volt) is a major advantage because circuits operating at low voltage (100 mV or less) are particularly sensitive to electrical perturbations. The fact of having the switching energy quasi independent of the voltage used gives a large flexibility to the design of electronic systems. In addition, the possibility of varying the supply voltage in a vast range enables an easier optimisation of the mechanical switches, for example by eliminating more easily the problems of sticking or problems of electrical breakdown. 
     As indicated above, a high supply voltage makes it possible moreover to resolve the problem of the sticking of mechanical switches. 
     In the case of electrostatic actuation, the force F applied between the moving part and the fixed electrode when the contact is established is written: 
     
       
         
           
             F 
             = 
             
               
                 
                   ɛ 
                   0 
                 
                 · 
                 S 
                 · 
                 
                   V 
                   2 
                 
               
               
                 2 
                 ⁢ 
                 
                   
                     ( 
                     
                       g 
                       - 
                       
                         g 
                         d 
                       
                     
                     ) 
                   
                   2 
                 
               
             
           
         
       
     
     The contact resistance is conventionally calculated by the Sharvin formula: 
     
       
         
           
             R 
             = 
             
               2 
               ⁢ 
               
                 
                   4 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   ρ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   λ 
                 
                 
                   3 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   A 
                 
               
             
           
         
       
         
         
           
             V is the control voltage of the switches of the inverter, 
             R is the contact resistance between the moving part and the tracks, 
             ρ is the resistivity of the metal used in the moving part, 
             S is the surface facing the fixed electrode (noted  16  in  FIG. 5A ) and the corresponding electrode for the moving part, 
             λ is the average free path of the electrons in the metal, 
             A is the contact surface between the moving part and the tracks, 
             g is the clearance in the open state between the moving part and the fixed electrode (represented in  FIG. 5A ), 
             g d  is the clearance, in the open state, between the moving part and the base at the level of the zones intended to enter into contact (represented in  FIG. 5A ). 
           
         
       
    
     Moreover, the contact surface A may be calculated as follows: 
     
       
         
           
             A 
             = 
             
               F 
               
                 H 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 ξ 
               
             
           
         
       
         
         
           
             H being the hardness of the metal 
             ξ being the elasticity coefficient of the order of 0.3. 
           
         
       
    
     In a preferential manner, the control voltage V is also the output or nominal supply voltage, its value is thus V DD , which makes it possible to simplify the architecture of the integrated circuit as a whole, since one logic gate controls another. If not, the output voltage of a logic gate would be transformed in order that it forms a control voltage of another logic gate. 
     The switching energy in adiabatic logic for a stage gate is then, assuming that the contact resistances are the main contributions to the total resistance, which is confirmed by the literature: 
     
       
         
           
             E 
             = 
             
               
                 
                   32 
                   ⁢ 
                   
                       
                   
                 
                 3 
               
               ⁢ 
               
                 
                   ρ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   λ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   H 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   ξ 
                 
                 
                   
                     ɛ 
                     0 
                   
                   ⁢ 
                   S 
                 
               
               ⁢ 
               
                 
                   ( 
                   
                     g 
                     - 
                     
                       g 
                       d 
                     
                   
                   ) 
                 
                 2 
               
               ⁢ 
               
                 
                   C 
                   L 
                   2 
                 
                 T 
               
             
           
         
       
     
     It is thus noted in a very surprising manner that the energy dissipated is independent of the control voltage and thus of the nominal supply voltage, contrary to the prejudices of those skilled in the art who generally consider that a low consumption imposes a low supply voltage. 
     The preceding demonstration applies in the case of electrostatic control switches. For other types of control, there is also a compensating effect of the same type. In fact, the contact resistance depends on the actuation and thus on the control voltage, but not necessarily according to a law inversely proportional to the square of the voltage as in the electrostatic control switch. 
     The time taken by the structure to enter into contact with the substrate when a voltage is applied can also be calculated as a function of the applied voltage and the characteristics of the switch. This time should be less than the time T chosen in conventional logic architectures and thus should be of several nanoseconds if T is 10 ns. The miniaturisation of mechanical switches could lead to such values. In all cases, logic architectures more adapted to mechanical switches make it possible however to become free of this constraint for example by producing more complex logic functions at the level of elementary gates. 
     It is then possible to calculate the ratio between the energy dissipated in a circuit based on transistors in adiabatic logic and that dissipated in a circuit according to the invention, which represents the figure of merit of the invention compared to existing circuits. 
     Said factor is written: 
     
       
         
           
             η 
             = 
             
               
                 3 
                 32 
               
               ⁢ 
               
                 
                   
                     V 
                     T 
                     2 
                   
                   ⁢ 
                   
                     ɛ 
                     0 
                   
                   ⁢ 
                   S 
                 
                 
                   ρ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   λ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   H 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     
                       ξ 
                       ⁡ 
                       
                         ( 
                         
                           g 
                           - 
                           
                             g 
                             d 
                           
                         
                         ) 
                       
                     
                     2 
                   
                 
               
               ⁢ 
               
                 T 
                 
                   C 
                   L 
                 
               
             
           
         
       
     
     It may be noted that the present invention has as much interest when T increases and C L  diminishes. 
     T is advantageously comprised between 1 and 100 ns. 
     The figure of merit of the invention may be written for typical values of the physical constants brought into play: 
     
       
         
           
             η 
             = 
             
               
                 2 
                 · 
                 
                   10 
                   
                     - 
                     6 
                   
                 
               
               ⁢ 
               
                 
                   V 
                   T 
                   2 
                 
                 
                   C 
                   L 
                 
               
               ⁢ 
               TF 
             
           
         
       
     
     The shape factor of the mechanical switch is defined by: 
     
       
         
           
             F 
             = 
             
               S 
               
                 
                   ( 
                   
                     g 
                     - 
                     
                       g 
                       d 
                     
                   
                   ) 
                 
                 2 
               
             
           
         
       
     
     This relation gives the area of applicability of the invention. A figure of merit greater than 100 is sought for a given form factor, 1000 for example. 
     Typical values of 10 fF for the capacitance, 10 ns for T and 200 mV for the threshold voltage of the MOS circuit lead to values of the order of:
 
η=8·10 −2   F  
 
     To obtain a significant gain of 80, the form factor is of 1000. A switch of 10 nm gap with an electrostatic control surface of 300 nm×300 nm would be compatible, which leads to a reasonable size. 
     Let us return to the theoretical value of the energy dissipated for an electrostatic actuation. 
     
       
         
           
             E 
             = 
             
               
                 
                   32 
                   ⁢ 
                   
                       
                   
                 
                 3 
               
               ⁢ 
               
                 
                   ρ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   λ 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   H 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   ξ 
                 
                 
                   
                     ɛ 
                     0 
                   
                   ⁢ 
                   S 
                 
               
               ⁢ 
               
                 
                   ( 
                   
                     g 
                     - 
                     
                       g 
                       d 
                     
                   
                   ) 
                 
                 2 
               
               ⁢ 
               
                 
                   C 
                   L 
                   2 
                 
                 T 
               
             
           
         
       
     
     For an interconnection capacitance of 10, 10 −15  F and for a value of T equal to 10 ns, one obtains for metal layer devices by expressing the energy in kTa as is frequent in the low consumption field. 
     
       
         
           
             
               E 
               = 
               0 
             
             , 
             
               
                 75 
                 · 
                 
                   
                     10 
                     6 
                   
                   F 
                 
               
               ⁢ 
               
                 kT 
                 a 
               
             
           
         
       
         
         
           
             k being the Boltzmann constant. 
             Ta being the absolute temperature in Kelvin. 
           
         
       
    
     A value of 750 kTa is thus possible for F equal to 1000, which is exceptional compared to CMOS. 
     This value would be 75 kTa for a value of T of 100 ns. 
     The examples of logic gates represented in  FIGS. 2 and 3  are in no way limiting and apply to any type of logic gate architecture. The NOR gate has been given as example but conventional NAND, AND and OR gates are also realisable according to this principle. The same is true for the functions obtained by combination of elementary gates (adders, registers, SRAM or DRAM memory cells). It should also be noted that the gates used in reversible calculation (Fredkin, Toffoli and Feynman gates) are also realisable according to this principle. 
     The logic circuits thereby produced are particularly adapted to applications requiring very low consumption, for example portable autonomous systems. 
     The present invention is also particularly adapted to systems with a high degree of “parallelisation”, i.e. systems comprising a large number of circuits operating at relatively slow frequencies, thus requiring quite low operating frequencies per block. 
     The circuits according to the present invention may be produced by conventional microelectronics technologies used to produce MEMS or NEMS systems, for example by silicon technology, by layer deposition and etching, but any other technology making it possible to produce miniaturised mechanical switches is applicable.