Abstract:
Integrated circuits described herein implement an x-input logic gate. The integrated circuit includes a plurality of Schottky diodes that includes x Schottky diodes and a plurality of source-follower transistors that includes x source-follower transistors. Each respective source-follower transistor of the plurality of source-follower transistors includes a respective gate node that is coupled to a respective Schottky diode. A first source-follower transistor of the plurality of source-follower transistors is connected serially to a second source-follower transistor of the plurality of source-follower transistors.

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
       [0001]    This application is a continuation-in-part of and claims priority to PCT patent application Ser. No. PCT/US2015/055020, filed Oct. 9, 2015, entitled, “SUPER CMOS (SCMOS™) DEVICES ON A MICROELECTRONIC SYSTEM,” which claims priority to U.S. Provisional Patent Application No. 62/062,800, filed Oct. 10, 2014, entitled, “SUPER CMOS (SCMOS) DEVICES ON A MICROELECTRONIC SYSTEM,” both of which are hereby incorporated by reference in their entirety. This application also is a continuation-in-part of and claims priority to U.S. patent application Ser. No. 15/358,049, filed Nov. 21, 2016, entitled, “SUPER CMOS DEVICES ON A MICROELECTRONICS SYSTEM,” which is hereby incorporated by reference in its entirety. U.S. patent application Ser. No. 15/358,049 is a continuation of and claims priority to U.S. patent application Ser. No. 14/793,690, filed Jul. 7, 2015, now U.S. Pat. No. 9,502,379, entitled, “SUPER CMOS DEVICES ON A MICROELECTRONICS SYSTEM,” which claims priority to U.S. Provisional Patent Application No. 62/062,800, filed Oct. 10, 2014, all of which are hereby incorporated by reference in their entirety. U.S. patent application Ser. No. 14/793,690 is a continuation application of and claims priority to U.S. patent application Ser. No. 13/931,315, filed Jun. 28, 2013, now U.S. Pat. No. 9,077,340, entitled, “SUPER CMOS DEVICES ON A MICROELECTRONICS SYSTEM,” which is a divisional application of and claims priority to U.S. patent application Ser. No. 12/343,465, filed Dec. 23, 2008, now U.S. Pat. No. 8,476,689 entitled, “SUPER CMOS DEVICES ON A MICROELECTRONICS SYSTEM,” all of which are hereby incorporated by reference in their entirety. 
     
    
     TECHNICAL FIELD 
       [0002]    The present application relates to semiconductor devices and circuits, and more particularly, to analog, digital and mixed signal integrated circuits (ICs) that employ Super Complementary Metal-Oxide-Semiconductor (SCMOS™) devices and thereby exhibit improved device performance due to improvements in power consumption, operating speed, circuit area and device density. 
       BACKGROUND 
       [0003]    Since the introduction of integrated circuits (ICs), engineers have been trying to increase the density of circuits on ICs, which reduces the cost of manufacturing of said ICs. One approach has been to put more components/functionality onto a chip. A second approach has been to build more chips on a larger wafer to reduce IC costs. For example, silicon wafer sizes have grown from averaging 3 inches in diameter in the 1960s to 12 inches today. 
         [0004]    Various attempts were tried in the past to improve IC functionality, performance, and cost figures. Early IC implementations used bipolar junction transistors (BJTs), which have layers of various diffusion regions stacked vertically, and isolated transistor pockets containing the three switching terminals (base, emitter and collector), among other resistive (R) and capacitive (C) circuit elements. However, for the last decade of IC implementations, it was V-I signal and PHY parameter scaling that was used to house more components on a chip. 
         [0005]    CMOS technology came after and surpassed BJT technology, which was relatively bulky, provided poor transistor yield, and exhibited high DC power usage. Device complexity has grown to over billions of circuit elements with Complementary MOS (CMOS) constructs. For more than  30  years a reduction in cost and increase in performance of CMOS technology has been achieved by shrinking the physical dimensions of CMOS transistors. These dimensions have shrunken to a size that is only a few molecular layers thick in critical device parameters. However, further shrinking of CMOS is running against limits imposed by the laws of physics. In addition to trying to manufacture tens of billions of these CMOS circuit elements with “molecular” dimensions, these dramatically smaller circuits operate with very low signal (voltage) levels, making their signal integrity susceptible to noise and causing speed degradation, and or power/heat run-off. 
       SUMMARY 
       [0006]    In various embodiments, Schottky-CMOS (also referred to herein as “Super CMOS” and SCMOS™) technology is employed to build circuit blocks using Schottky Barrier diodes (SBDs), such as low threshold Schottky Barrier Diodes (LtSBD™s), thereby addressing the above deficiencies and problems associated with an increasing demand for higher semiconductor efficiency and upcoming physical limits on CMOS transistor dimensions. 
         [0007]    In some embodiments, an integrated circuit implements a NAND gate system. The integrated circuit includes a first input coupled to a cathode of a first p-type Schottky diode and x additional inputs coupled to x respective cathodes of x additional p-type Schottky diodes. The integrated circuit additionally includes a first n-type transistor including a gate node that is coupled to an anode of the first Schottky diode and x respective anodes of the x additional Schottky diodes. The integrated circuit additionally includes a p-type transistor including a gate node that is coupled to the anode of the first Schottky diode and x respective anodes of the x additional Schottky diodes. The integrated circuit additionally includes a second n-type transistor including a gate node that is coupled to the cathode of the first p-type Schottky diode and x additional n-type transistors including x respective gate nodes that are coupled to the x respective cathodes of the x additional p-type Schottky diodes. An output is coupled to a non-gate node of the first n-type transistor and a non-gate node of the p-type transistor. 
         [0008]    In some embodiments, an integrated circuit implements a NOR gate system. The integrated circuit includes a first input coupled to an anode of a first n-type Schottky diode and x additional inputs coupled to x respective anodes of x additional n-type Schottky diodes. The integrated circuit additionally includes a first p-type transistor including a gate node that is coupled to a cathode of the first n-type Schottky diode and a cathode of x additional n-type Schottky diodes. The integrated circuit additionally includes an n-type transistor including a gate node that is coupled to the cathode of the first n-type Schottky diode and the cathodes of the x additional n-type Schottky diodes. The integrated circuit additionally includes a second p-type transistor including a gate node that is coupled to the anode of the first n-type Schottky diode and x additional p-type transistors including x respective gate nodes that are coupled to the x respective anodes of the x additional n-type Schottky diodes. An output is coupled to a non-gate node of the first p-type transistor and a non-gate node of the n-type transistor. 
         [0009]    In some embodiments, an integrated circuit implements an x-input logic gate. The integrated circuit includes a plurality of Schottky diodes that includes x Schottky diodes and a plurality of source-follower transistors that includes x source-follower transistors. Each respective source-follower transistor of the plurality of source-follower transistors includes a respective gate node that is coupled to a respective Schottky diode. A first source-follower transistor of the plurality of source-follower transistors is connected serially to a second source-follower transistor of the plurality of source-follower transistors. 
         [0010]    Various advantages of the disclosed technology will be apparent in light of the descriptions below. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0011]    The aforementioned features and advantages of the disclosure as well as additional features and advantages thereof will be more clearly understood hereinafter as a result of a detailed description of preferred embodiments when taken in conjunction with the drawings. 
           [0012]    To illustrate the technical solutions according to the embodiments of the present disclosure more clearly, the accompanying drawings needed for the embodiments are introduced briefly below. The appended drawings, however, merely illustrate the more pertinent features of the present disclosure and are therefore not to be considered limiting, for the description may admit to other effective features. 
           [0013]      FIG. 1  is a circuit diagram of a two-input Schottky-CMOS NAND gate, in accordance with some embodiments. 
           [0014]      FIG. 2  is a circuit diagram of an eight-input Schottky-CMOS NAND gate, in accordance with some embodiments. 
           [0015]      FIG. 3  is a circuit diagram of an 8-input CMOS NAND gate. 
           [0016]      FIG. 4  is a circuit diagram of a two-input Schottky-CMOS NOR gate, in accordance with some embodiments. 
           [0017]      FIG. 5  is a circuit diagram of an eight-input Schottky-CMOS NOR gate, in accordance with some embodiments. 
           [0018]      FIG. 6  is a circuit diagram of an 8-input CMOS NOR gate. 
           [0019]      FIG. 7  is a circuit diagram of a Schottky-CMOS implementation of a 4-to-1 multiplexer circuit, in accordance with some embodiments. 
           [0020]      FIG. 8  illustrates a CMOS implementation of a 4-to-1 multiplexer circuit. 
           [0021]      FIG. 9  is a chart that compares layout areas of NAND gates implemented using 
           [0022]    Schottky-CMOS with layout areas of NAND gates implemented using CMOS, in accordance with some embodiments. 
           [0023]      FIG. 10  is a chart that compares a root mean square (RMS) power draw for NAND gates implemented using Schottky-CMOS with the power draw of NAND gates implemented using CMOS, in accordance with some embodiments. 
           [0024]      FIG. 11  is a chart that compares propagation delay of NAND gates implemented using Schottky-CMOS with propagation delay of NAND gates implemented using CMOS, in accordance with some embodiments. 
           [0025]      FIGS. 12A-12G  illustrate CMOS implementations of NAND gates that have various numbers of inputs. 
       
    
    
       [0026]    Like reference numerals refer to corresponding parts throughout the several views of the drawings. 
       DESCRIPTION OF EMBODIMENTS 
       [0027]    Reference will now be made in detail to embodiments, examples of which are illustrated in the accompanying drawings. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the subject matter presented herein. But it will be apparent to one skilled in the art that the subject matter may be practiced or designed without these specific details. In other instances, well-known methods, procedures, components, and circuits have not been described in detail so as not to unnecessarily obscure aspects of the embodiments. Trademarks designated herein with the “TM” symbol are the property of Schottky LSI, Inc. 
         [0028]    The technical solution of the present disclosure will be clearly and completely described in the following with reference to the accompanying drawings. It is obvious that the embodiments to be described are examples and only a part rather than all of the embodiments of the present disclosure. All other embodiments obtained by persons skilled in the art based on the described embodiments of the present disclosure shall fall within the protection scope of the present disclosure. 
         [0029]    The Schottky-CMOS technology described herein implements logic using a 
         [0030]    Schottky Barrier diode (also referred to herein as “SBD” and “Schottky diode”). In comparison with prior CMOS implementations, various embodiments of the Schottky-CMOS described herein use Schottky diodes in lieu of p-type metal-oxide-semiconductor (PMOS) field effect transistors and/or n-type metal-oxide-semiconductor (NMOS) field effect transistors. Particularly as the number of logic inputs to a logic gate increases, replacing PMOS and NMOS transistors with Schottky diodes increases the efficiency of the implemented logic in various ways, including reduced area consumed by the circuit layout, reduced propagation delay, and reduced power required for switching. 
         [0031]    The following description is presented to enable one of ordinary skill in the art to make and use the invention and is provided in the context of a patent application and its requirements. Various modifications to the preferred embodiment and the generic principles and features described herein will be readily apparent to those skilled in the art. Thus, the present invention is not intended to be limited to the embodiment shown but is to be accorded the widest scope consistent with the principles and features described herein. 
         [0032]      FIG. 1  is a circuit diagram of a two-input Schottky-CMOS NAND gate, in accordance with some embodiments. The two-input Schottky-CMOS NAND gate includes two p-type Schottky diodes  102  and  104  and a source follower tree  106  that includes two n-type transistors  108  and  110 . The transistors in the source follower tree  106  are connected in series, as indicated by the connection  112 . Input A 0  is coupled to a cathode of p-type Schottky barrier diode (SBD)  102  and to a gate node of n-type transistor  108 . Input A 1  is coupled to a cathode of p-type SBD  104  and a gate node of n-type transistor  110 . An anode of SBD  102  and an anode of SBD  104  are coupled to the gates of result transistors  114  and  116 . Result transistor  114  is an n-type transistor and result transistor  116  is a p-type transistor. Output  118  is coupled to non-gate nodes of the result transistors  114  and  116 . Specifically, output  118  is coupled to the drain node of n-type transistor  114  and output  118  is coupled to the drain node of p-type transistor  116 . 
         [0033]    In some embodiments, the two-input Schottky-CMOS NAND gate includes feedback logic that receives the output signal as an input at gate nodes of n-type transistor  120  and p-type transistor  122 . 
         [0034]    Whereas a CMOS implementation of a two-input NAND gate would use a p-type transistor and an n-type transistor coupled to each input of the NAND gate, in some embodiments, the Schottky-CMOS implementation of the two-input NAND gate uses a p-type SBD and an n-type transistor coupled to each input (replacing a p-type transistor of the CMOS implementation with a p-type SBD in the Schottky-CMOS implementation). As the number of inputs in the NAND gate increases, the efficiencies attained by replacing transistors with SBDs increases, e.g., as illustrated by the CMOS and Schottky-CMOS performance comparisons of  FIGS. 9-11 . 
         [0035]      FIG. 2  is a circuit diagram of an eight-input Schottky-CMOS NAND gate, in accordance with some embodiments. The eight-input Schottky-CMOS NAND gate includes eight p-type Schottky diodes,  202 - 216  and a source follower tree  218  that includes eight n-type transistors  220 - 234 . Transistors  220 - 234  in the source follower tree  218  are connected in series (e.g., the drain node of transistor  220  is coupled to the source node of transistor  224 , the drain node of transistor  224  is coupled to the source node of transistor  228 , and so on). Input A 0  is coupled to a cathode of p-type SBD  202  and to a gate node of n-type transistor  220 . Input A 1  is coupled to a cathode of p-type SBD  204  and a gate node of n-type transistor  222 . Input A 2  is coupled to a cathode of p-type SBD  206  and to a gate node of n-type transistor  224 . Input A 3  is coupled to a cathode of p-type SBD  208  and a gate node of n-type transistor  226 . Input A 4  is coupled to a cathode of p-type SBD  210  and to a gate node of n-type transistor  228 . Input A 5  is coupled to a cathode of p-type SBD  212  and a gate node of n-type transistor  230 . Input A 6  is coupled to a cathode of p-type SBD  214  and to a gate node of n-type transistor  232 . Input A 7  is coupled to a cathode of p-type SBD  216  and a gate node of n-type transistor  234 . 
         [0036]    Anodes of SBDs  202 - 216  are coupled to the gates of result transistors  236  and  238 . Result transistor  236  is an n-type transistor and result transistor  238  is a p-type transistor. Output  240  is coupled to non-gate nodes of the result transistors  236  and  238 . Specifically, output  240  is coupled to the drain node of n-type transistor  236  and output  240  is coupled to the drain node of p-type transistor  238 . 
         [0037]    In some embodiments, the eight-input Schottky-CMOS NAND gate includes feedback logic that receives the output signal as an input at gate nodes of n-type transistor  242  and p-type transistor  244 . 
         [0038]    It will be recognized that the scaling illustrated with regard to  FIGS. 1-2  can be extended to other numbers of NAND gate inputs. For each additional input, an additional SBD is coupled to the additional input, and an additional source-follower transistor that is complementary to the SBD (e.g., an n-type transistor complementary to a p-type SBD) is added to the source follower tree (e.g., as illustrated by source-follower tree  106  of  FIG. 1  or source-follower tree  218  of  FIG. 2 ). The additional input is coupled to the additional SBD (e.g., to the cathode of a p-type SBD) and to the gate node of the additional source-follower transistor. The additional SBD is coupled (e.g., the anode of a p-type SBD) to the gate nodes of a set of result transistors (e.g., as illustrated by result transistors  114 - 116  of  FIG. 1  or result transistors  236 - 238  of  FIG. 2 ). 
         [0039]    For example, a four-input Schottky-CMOS NAND gate includes four inputs A 0 -A 3 , four p-type SBDs (e.g., configured as illustrated by SBDs  202 - 208  of  FIG. 2 ) and four n-type transistors (e.g., transistors as illustrated at  220 ,  222 ,  224 , and  226  of  FIG. 2  connected in series). 
         [0040]    In some embodiments, a Schottky-CMOS NAND gate includes a number of inputs between two inputs and sixteen inputs, such as twelve inputs. 
         [0041]      FIG. 3  is a circuit diagram of an 8-input CMOS NAND gate. The CMOS 8-input NAND gate requires three NAND gates  302 ,  304 , and  306 , a NOR gate  308 , and inverters  310  and  312 . In comparison with the Schottky-CMOS eight-input NAND gate described with regard to  FIG. 2 , the stacked configuration of the NAND gates  302 - 306  that feed into NOR gate  308 , as shown in  FIG. 3 , requires increased power and increased supply current, and causes an increased layout area, increased switching time, and increased propagation delay (as described further below with regard to  FIGS. 9-12 ). 
         [0042]      FIG. 4  is a circuit diagram of a two-input Schottky-CMOS NOR gate, in accordance with some embodiments. The two-input Schottky-CMOS NOR gate includes two n-type Schottky diodes  402  and  404  and a source follower tree  406  that includes two p-type transistors  408  and  410 . The transistors in the source follower tree  406  are connected in series. Input A 0  is coupled to an anode of n-type Schottky barrier diode (SBD)  402  and to a gate node of p-type transistor  408 . Input A 1  is coupled to an anode of n-type SBD  404  and a gate node of p-type transistor  410 . A cathode of SBD  402  and a cathode of SBD  404  are coupled to the gates of result transistors  414  and  416 . Result transistor  414  is an n-type transistor and result transistor  416  is a p-type transistor. Output  418  is coupled to non-gate nodes of the result transistors  414  and  416 . Specifically, output  418  is coupled to the drain node of n-type transistor  414  and output  118  is coupled to the drain node of p-type transistor  416 . 
         [0043]    In some embodiments, the two-input Schottky-CMOS NOR gate includes feedback logic that receives the output signal as an input at gate nodes of n-type transistor  420  and p-type transistor  422 . 
         [0044]    Whereas a CMOS implementation of a two-input NOR gate would use a p-type transistor and an n-type transistor coupled to each input of the NOR gate, in some embodiments, the Schottky-CMOS implementation of the two-input NOR gate uses a n-type SBD and a p-type transistor coupled to each input (replacing an n-type transistor of the prior CMOS implementation with an n-type SBD in the Schottky-CMOS implementation). As the number of inputs in the NOR gate increases, the efficiencies attained by replacing transistors with SBDs increases. 
         [0045]      FIG. 5  is a circuit diagram of an eight-input Schottky-CMOS NOR gate, in accordance with some embodiments. The eight-input Schottky-CMOS NOR gate includes eight n-type Schottky diodes,  502 - 516  and a source follower tree  518  that includes eight n-type transistors  520 - 534 . Transistors  520 - 534  in the source follower tree  518  are connected in series (e.g., the drain node of transistor  520  is coupled to the source node of transistor  524 , the drain node of transistor  524  is coupled to the source node of transistor  528 , and so on). Input A 0  is coupled to an anode of n-type SBD  502  and to a gate node of p-type transistor  520 . Input A 1  is coupled to an anode of n-type SBD  504  and a gate node of p-type transistor  522 . Input A 2  is coupled to an anode of n-type SBD  506  and to a gate node of p-type transistor  524 . Input A 3  is coupled to an anode of n-type SBD  508  and a gate node of p-type transistor  526 . Input A 4  is coupled to an anode of n-type SBD  510  and to a gate node of p-type transistor  528 . Input A 5  is coupled to an anode of n-type SBD  512  and a gate node of p-type transistor  530 . Input A 6  is coupled to an anode of n-type SBD  514  and to a gate node of p-type transistor  532 . Input A 7  is coupled to an anode of n-type SBD  516  and a gate node of p-type transistor  534 . 
         [0046]    Cathodes of SBDs  502 - 516  are coupled to the gates of result transistors  536  and  538 . Result transistor  536  is an n-type transistor and result transistor  538  is a p-type transistor. Output  540  is coupled to non-gate nodes of the result transistors  536  and  538 . Specifically, output  540  is coupled to the drain node of n-type transistor  536  and output  540  is coupled to the drain node of p-type transistor  538 . 
         [0047]    In some embodiments, the eight-input Schottky-CMOS NOR gate includes feedback logic that receives the output signal as an input at gate nodes of n-type transistor  542  and p-type transistor  544 . 
         [0048]    It will be recognized that the scaling illustrated with regard to  FIGS. 4-5  can be extended to other numbers of NOR gate inputs. For each additional input, an additional SBD is coupled to the additional input, and an additional source-follower transistor that is complementary to the SBD (e.g., a p-type transistor complementary to an n-type SBD) is added to the source follower tree (e.g., as illustrated by source-follower tree  406  of  FIG. 4  or source-follower tree  518  of  FIG. 5 ). The additional input is coupled to the additional SBD (e.g., to the cathode of an n-type SBD) and to the gate node of the additional source-follower transistor. The additional SBD is coupled (e.g., the anode of a p-type SBD) to the gate nodes of a set of result transistors (e.g., as illustrated by result transistors  414 - 416  of  FIG. 4  or result transistors  536 - 538  of  FIG. 5 ). 
         [0049]    For example, a four-input Schottky-CMOS NOR gate includes four inputs A 0 -A 3 , four n-type SBDs (e.g., configured as illustrated by SBDs  502 - 508  of  FIG. 5 ) and four p-type transistors (e.g., transistors as illustrated at  520 ,  522 ,  524 , and  526  of  FIG. 5  connected in series). 
         [0050]    In some embodiments, a Schottky-CMOS NOR gate includes a number of inputs between two inputs and sixteen inputs, such as twelve inputs. 
         [0051]      FIG. 6  is a circuit diagram of an 8-input CMOS NOR gate. The CMOS 8-input NOR gate requires four two-input NAND gates  602 ,  604 ,  606 , and  608 , two two-input NAND gates  610  and  612 , two-input NOR gate  614 , and inverters  616  and  618 . In comparison with the Schottky-CMOS eight-input NOR gate described with regard to  FIG. 5 , the stacked configuration of the NOR gates  602 - 608  that feed into NAND gates  610  and  612 , that in turn feed into NOR gate  614 , as shown in  FIG. 6 , requires increased power and increased supply current, and causes an increased layout area, increased switching time, and increased propagation delay. 
         [0052]      FIG. 7  is a circuit diagram of a Schottky-CMOS implementation of a 4-to-1 multiplexer circuit (MUX), in accordance with some embodiments. The Schottky-CMOS MUX couples input I 1  to a p-type SBD  702  and a gate node of an n-type transistor  704 . Inputs I 2 , I 3 , and I 4  are similarly each coupled to a p-type SBD and a gate node of an n-type transistor. The output of the p-type SBD  702  and transistor  704  is coupled to n-type SBD  706  and a p-type transistor  708 . The outputs of the SBDs and transistors that receive input from I 2 , I 3 , and I 4  are similarly each coupled to an n-type SBD and a p-type transistor. The outputs of the n-type SBDs are coupled to a gate node of a p-type result transistor  710  and a gate node of an n-type result transistor  712 . The output of the result transistors is received by output  714 . 
         [0053]      FIG. 8  illustrates a CMOS implementation of a 4-to-1 multiplexer circuit. 
         [0054]    In some embodiments, the Schottky-CMOS logic described with regard to  FIG. 1 ,  FIG. 2 ,  FIG. 4 ,  FIG. 5  and/or  FIG. 7  is configured for asynchronous (e.g., static) operation. For example, a size of one or more components is selected such that the operation of the circuit is asynchronous or substantially asynchronous. In some embodiments, a size of one or more components of Schottky-CMOS logic is selected to reduce and/or minimize switching noise immunity. 
         [0055]    In some embodiments, one or more SBDs of the Schottky-CMOS logic described with regard to  FIG. 1 ,  FIG. 2 ,  FIG. 4 ,  FIG. 5  and/or  FIG. 7  has a threshold forward voltage that is lower than the threshold forward voltage of a transistor that has a gate coupled to the SBD (e.g., wherein both the transistor and the SBD are coupled to an input of the gate). For example, referring to  FIG. 1 , in some embodiments, SBD  102  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  108  and/or SBD  104  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  110 . Referring to  FIG. 2 , in some embodiments, SBD  202  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  220 , SBD  204  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  222 , and/or SBD  206  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  224 , and so on. Referring to  FIG. 4 , in some embodiments, SBD  402  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  408  and/or SBD  404  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  410 . Referring to  FIG. 5 , in some embodiments, SBD  502  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  520 , SBD  504  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  522 , and/or SBD  506  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  524 , and so on. Referring to  FIG. 7 , in some embodiments, SBD  702  has a threshold forward voltage that is lower than the threshold forward voltage of transistor  704 . 
         [0056]      FIG. 9  is a chart that compares layout areas of NAND gates implemented using 
         [0057]    Schottky-CMOS (e.g., as shown in  FIGS. 1-2 ) with layout areas of NAND gates implemented using CMOS (e.g., as shown in  FIG. 3 ), in accordance with some embodiments. As can be seen from  FIG. 9 , compared with the increase in the area of CMOS NAND gates as the number of inputs increase, the area of Schottky-CMOS NAND gates increases at a lower rate.  FIG. 9  indicates that a required layout area for a four-input Schottky-CMOS NAND gate is less than 2.0 μm 2 , which is significantly less than the area required for a four-input CMOS NAND gate. The reduction in area required for Schottky-CMOS NAND gates with three or more inputs in comparison with CMOS NAND gates with the same number of inputs is caused by, e.g., a reduced number of signal lines and/or circuit nets required to implement the logic, and the relatively small size of a source-follower tree (e.g., as shown at  106 ,  218 ,  406 , and  518 ) in comparison with the layouts of CMOS NAND gates (e.g., as shown at  FIG. 3  and  FIG. 6 ). 
         [0058]      FIG. 10  is a chart that compares a root mean square (RMS) power draw for NAND gates implemented using Schottky-CMOS (e.g., as shown in  FIGS. 1-2 ) with the power draw of NAND gates implemented using CMOS (e.g., as shown in  FIG. 3 ), in accordance with some embodiments. As can be seen from  FIG. 10 , compared with the increase in the power required for CMOS NAND gates as the number of inputs increase, the power required for Schottky-CMOS NAND gates increases at a lower rate.  FIG. 10  indicates that the RMS power requirement for a four-input Schottky-CMOS NAND gate is less than 50.0 microwatts, which is significantly less than the power required for a four-input CMOS NAND gate. 
         [0059]      FIG. 11  is a chart that compares propagation delay of NAND gates implemented using Schottky-CMOS (e.g., as shown in  FIGS. 1-2 ) with propagation delay of NAND gates implemented using CMOS (e.g., as shown in  FIG. 3 ), in accordance with some embodiments.  FIG. 11  indicates that a four-input Schottky-CMOS NAND gate has a propagation delay of less than 80 picoseconds, which is significantly less than the propagation delay of a four-input CMOS NAND gate. 
         [0060]    As can be seen from  FIG. 11 , the propagation delay of CMOS NAND gates exhibits particularly pronounced increases as the number of inputs increases from three inputs to four inputs and from six inputs to seven inputs. The pronounced increases in required area, power draw, and propagation delay that occur in CMOS implementations of NAND gates as the number of inputs increases can be understood with reference to  FIGS. 12A-12G . 
         [0061]      FIGS. 12A-12G  illustrate CMOS implementations of NAND gates that have various numbers of inputs. 
         [0062]      FIG. 12A  illustrates two-input NAND logic implemented using a single two-input NAND gate  1202 .  FIG. 12B  illustrates three-input NAND logic implemented using a single three-input NAND gate  1204 . 
         [0063]      FIG. 12C  illustrates four-input NAND logic implemented using two NAND gates  1206  and  108  and a NOR gate  1210 . When the number of NAND inputs increases from three inputs, as shown in  FIG. 12B , to four inputs, as shown in  FIG. 12C , the use of two NAND gates  1206  and  1208  (rather than the single NAND gate  1204  of  FIG. 12B ) and the addition of NOR gate  1210  increases the propagation delay through the circuit. This increase is reflected in the jump in propagation delay from less than 80 picoseconds for a three-input CMOS NAND to a propagation delay of more than 120 picoseconds for a four-input CMOS NAND, as shown in  FIG. 11 . 
         [0064]      FIGS. 12D-12E  illustrate five-input and six-input CMOS NAND gates, respectively. Like the four-input CMOS NAND shown in  FIG. 12C , the five-input and six-input CMOS NAND gates feed the output of two NAND gates to a NOR gate. The CMOS NAND gate of  FIG. 12D  feeds the outputs of NAND gates  1212  and  1214  to NOR gate  1216 . The CMOS NAND gate of  FIG. 12E  feeds the outputs of NAND gates  1218  and  1220  to NOR gate  1222 . 
         [0065]      FIG. 12F  illustrates seven-input NAND logic implemented using three NAND gates  1224 ,  1226 , and  1228  and a NOR gate  1230 . When the number of NAND inputs increases from six inputs, as shown in  FIG. 12E , to seven inputs, as shown in  FIG. 12F , the use of three NAND gates ( 1224 ,  1226 , and  1228 ), rather than the two NAND gates ( 1218 ,  1220 ) of  FIG. 12E , increases the propagation delay through the circuit. This increase is reflected in the jump in propagation delay from less than 140 picoseconds for a six-input CMOS NAND to a propagation delay of nearly 180 picoseconds for a seven-input CMOS NAND, as shown in  FIG. 11 . 
         [0066]      FIG. 12G  illustrates an eight-input CMOS NAND gate, which has a similar circuit structure to the eight input CMOS NAND gate described with regard to  FIG. 3 . The CMOS NAND gate of  FIG. 12G  feeds the output of NAND gates  1232 ,  1234 , and  1236  to NOR gate  1238 . 
         [0067]    As described above with regard to the CMOS NAND gates of  FIGS. 12A-12G , increasing the number of inputs of CMOS NAND gate requires increasing a number of NAND gates and/or adding a NOR stage. In some embodiments (e.g., as described with regard to  FIGS. 1-2  and  FIGS. 4-5 ), increasing the number of inputs of a Schottky-CMOS NAND gate includes increasing a number of SBDs and increasing a number of corresponding transistors in a source follower tree. In some embodiments, compared with CMOS approaches, the Schottky-CMOS approaches described herein result in lower increases in power draw, layout area, and propagation delay as a number of logic inputs increases. 
         [0068]    While particular embodiments are described above, it will be understood it is not intended to limit the disclosure to these particular embodiments. On the contrary, the disclosure includes alternatives, modifications and equivalents that are within the spirit and scope of the appended claims. Numerous specific details are set forth in order to provide a thorough understanding of the subject matter presented herein. But it will be apparent to one of ordinary skill in the art that the subject matter may be practiced without these specific details. In other instances, well-known methods, procedures, components, and circuits have not been described in detail so as not to unnecessarily obscure aspects of the embodiments. 
         [0069]    The terminology used in the description of the disclosure herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the disclosure. As used in the description of the disclosure and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and/or” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. It will be further understood that the terms “includes,” “including,” “comprises,” and/or “comprising,” when used in this specification, specify the presence of stated features, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, operations, elements, components, and/or groups thereof. 
         [0070]    As used herein, the term “if” may be construed to mean “when” or “upon” or “in response to determining” or “in accordance with a determination” or “in response to detecting,” that a stated condition precedent is true, depending on the context. Similarly, the phrase “if it is determined [that a stated condition precedent is true]” or “if [a stated condition precedent is true]” or “when [a stated condition precedent is true]” may be construed to mean “upon determining” or “in response to determining” or “in accordance with a determination” or “upon detecting” or “in response to detecting” that the stated condition precedent is true, depending on the context. 
         [0071]    The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or to limit the disclosure to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles of the disclosure and its practical applications, to thereby enable others skilled in the art to best utilize the disclosure and various embodiments with various modifications as are suited to the particular use contemplated.