Patent Publication Number: US-9835634-B2

Title: Coupled heterogeneous devices for pH sensing

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of International Application No. PCT/US13/41649 filed May 17, 2013, which claims the benefit of and priority to U.S. Provisional Application No. 61/648,261 filed May 17, 2012. This application also claims the benefit of and priority to U.S. Provisional Application No. 61/724,368, filed Nov. 9, 2012. Each of the above applications are hereby incorporated by reference in their entireties. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     This invention was made with government support under RO1-CA20003 awarded by the National Institutes of Health. The government has certain rights in the invention. 
    
    
     BACKGROUND OF INVENTION 
     The devices and methods disclosed herein are for use in pH measuring and monitoring applications. There is a need in the art for ultrasensitive detection of pH in a rapid and reliable manner. Conventional pH sensors are generally confined by the Nernstian limit of 59 mV/pH, and have a detection limit practically constrained by signal-to-noise interference. Provided herein are devices and methods that vastly improve the pH detection limit by effectively increasing the Nernstian limit by an amplification factor. In this manner, a pH sensitivity that is better than 0.02 pH units is achieved, including as good as 0.002 pH units. Such an improvement represents about an order of magnitude improvement over commercial pH sensors. 
     SUMMARY OF THE INVENTION 
     Provided herein are methods and devices that have improved pH sensitivity and ultrasensitive pH detection. This improvement is by specially selecting geometrical and/or electrical properties of two components of the device: a sensor and a transducer, so as to obtain an amplification factor that functions to provide an extrinsic pH sensor response that is increased dramatically beyond the Nernst limit, including by factors of 10, 20, 100 or more, or a range of between about 10 and 1000. 
     In an aspect, the invention is a method of amplifying a pH signal, such as by providing a sensor comprising a source electrode, a drain electrode, a sensor channel provided between the source and drain electrodes, and a sensing surface over at least a portion of the sensor channel, wherein the sensor channel has a first transconductance. A transducer is provided comprising a source electrode, a drain electrode, and a transducer channel provided between the source and drain electrodes, wherein the transducer channel has a second transconductance, and the second transconductance is greater than the first transconductance. A material is applied to the sensing surface, wherein a change in pH of the material generates a conductance modulation of the sensor channel. A bias of the transducer is adjusted to counterbalance the conductance modulation of the sensor channel, thereby amplifying the pH signal of the material. 
     In an aspect, the amplifying corresponds to selecting an amplification factor that is defined by: 
     
       
         
           
             
               
                 
                   
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     wherein μ is the channel mobility, W is the channel width, L is the channel length, V DS  is the drain bias, C OX  is the gate oxide capacitance, and the subscripts 1 and 2 refer to the sensor and the transducer, respectively. Depending on the application of interest, an appropriate amplification factor is obtained by adjusting one or more of the parameters that define the amplification factor, including a geometry, mobility scaling, oxide thickness, and/or bias. In an aspect, the amplification factor is greater than or equal to 10, greater than or equal to 20, greater than or equal to 100, or selected from a range that is between about 20 and 20,000. 
     In an aspect, the selecting step comprises selecting a width and/or a length of: the transducer, the sensor, or both, so that (W/L) 1 /(W/L) 2  is greater than or equal to 20. 
     In an embodiment, any of the sensor channels provided herein is a nanoplate and any of the transducer channels is a nanowire. Such a configuration provides the ability to greatly vary the ratio of W 1 /W 2  in the above Eq&#39;n (A) so as to obtain a desired amplification factor. In an aspect, W 1 /W 2  is greater than or equal to 20 and less than or equal to 1×10 6 . Alternatively, any of the widths may be described in absolute terms, such as a nanoplate width (W 1 ) that is greater than or equal to 1 μm and less than or equal to 100 μm, and/or a nanowire width (W 2 ) that is greater than or equal to 1 nm and less than or equal to 100 nm. In an aspect, L 1 ≠L 2 . In an aspect, L 1 =L 2 . Although the term “nanoplate” has traditionally been used to describe objects with about 100 nm dimensions, here we use the term to describe a transistor, including a channel thereof, that is that is about 100 nm thick with width (W) that may be greater than nano scale, including widths on the order of about 1-20 μm wide, to emphasize its pairing with a NW transistor. Accordingly, the term “nanowire” refers to wires that have cross sections on the order of about 100 nm, such as diameters that are about 10 nm to 200 nm, or more specifically rectangular or square cross-sections that are (10 nm-200 nm)×(10 nm-200 nm), and any subranges thereof. The lengths of the nanoplate and nanowire can be on the order of many microns, such as greater than 1 μm, greater than 10 μm, or selected from a range of between about 1 μm and 100 μm. 
     In an embodiment, the selecting step comprises mobility scaling so that the sensor channel has a higher mobility than a transducer channel mobility. This selecting embodiment may be achieved by providing a first material for the sensor channel and a second material for the transducer channel, wherein the first material has a higher mobility than the second material. Examples of such sensor/transducer (first material/second material) pairs include, but are not limited to: AlGaN/Si; SiNW/Si; GaN/Si. In an aspect, the mobility scaling comprises providing the sensor as part of an n-channel metal-oxide-semiconductor field-effect transistor (nMOS) and the transducer as part of a p-channel metal-oxide-semiconductor field-effect transistor (pMOS). In any of these embodiments, effecting relative changes in sensor and transducer channel mobility provides a means for adjusting the amplification factor of Eq&#39;n (A). 
     In another embodiment, the selecting step comprises oxide thickness scaling, such as to obtain a C OX,1  that is greater than C OX,2  by at least a factor of 20. For example, the scaling may be achieved by a dual oxide process to provide an oxide layer thickness of the sensor that is greater than an oxide layer thickness of the transducer. Alternatively, the oxide thickness scaling may be by providing a sensor channel material having a higher k-dielectric than a transducer channel material k-dielectric. Examples of k-dielectric materials include those discussed in WO 2012/078340, hereby incorporated by reference. Alternatively, the oxide thickness scaling may comprise both the oxide layer thickness selection and the higher k-dielectric selection. 
     In another embodiment, the selecting step comprises bias scaling so that V DS,1  is greater than or equal to V DS,2  by a factor of at least 20. This bias scaling is particularly suited for applications where tuning of the device is desired, such as to change the dynamic range or the pH sensitivity as the other methods generally are fixed upon device manufacture. In an aspect, therefore, the bias scaling provides real-time tunability of sensor performance, such as a performance wherein the dynamic range of pH is tuned to cover a pH unit range that is between about 0.01 pH units to about 1 pH unit, or a sensitivity that is tuned to provide about 0.001 pH units sensitivity to about 0.02 pH units sensitivity. 
     In an aspect, any of the methods and devices provided herein may be described by one or more functional parameters, such as having a Nernst response that is greater than or equal to 0.5 V/pH, or that is greater than or equal to 10 V/pH, or that is between about 0.5 V/pH and 100 V/pH and any subranges thereof. In an aspect, the functional parameter is a dynamic pH range of up to 0.5 pH. In an aspect, the functional parameter is a pH sensitivity selected from a range that is greater than or equal to 0.001 pH units and less than or equal to 0.01 pH units. 
     In an aspect, the transducer channel is biased to a top gate or to a bottom gate. In an aspect, the sensor channel is biased to a fluid gate that is at least partially immersed in the material, such as a material that is a fluid. 
     In an aspect, the transducer further comprises a transducer surface and the material is provided on the transducer surface in addition to the sensing surface, wherein the second transconductance is substantially independent or is independent of pH, in contrast to the first transconductance. This may be achieved by coating or surface treating the nanowire with a chemically inert and/or non-interacting surface material so that the surface does not bind protons. Alternatively, the transducer may be positioned outside of a well in which the material is confined, in contrast to the sensor&#39;s sensing surface. 
     The methods and devices provided herein are suitable for use in a range of applications, such as nucleotide sequencing, environmental toxic monitoring, pharmaceutical testing, food testing, cancer monitoring, detection of enzyme activity, or any other application where a change in pH provides information about a process or status. 
     In an embodiment, the material comprises a fluid, such as an electrically-conductive fluid or an electrolyte. In an aspect, the fluid is a biological material, or a liquid in which a biological material is suspended. In an aspect, the material or fluid is defined by a sample volume that is applied to the device, such as a fluid well in which the sensing surface forms at least part of a surface. In an aspect, the sample volume that is applied to the device is a low volume sample, such as less than 1 mL, less than 1 μL, or selected from a range that is between about 0.1 μL and 10 mL, or any sub-ranges thereof. 
     In an aspect, the material comprises a biological cell and intracellular pH, extracellular pH, or both intracellular and extracellular pH is measured. In an aspect, the biological cell is lysed and the internal pH measured, such as by monitoring a change in pH of a fluid in which the cell is lysed. 
     Any of the methods and devices provided herein has a sensing surface that comprises an oxide surface, such as an oxide surface that interacts with a proton. For example, the oxide surface may comprise OH surface groups that react with protons to provide a sensor channel transconductance modulation that is pH dependent. 
     In an embodiment, the invention is a device for measuring changes in pH in a fluid, the device comprising: a sensor comprising a fluid gate, a source electrode, a drain electrode, a sensor channel provided between the source and drain electrodes, and a sensing surface over at least a portion of the sensor channel for receiving the fluid, wherein the sensor channel is a nanoplate in electrical contact with the fluid gate; a transducer comprising a top or a bottom gate, a source electrode, a drain electrode, and a transducer channel provided between the source and drain electrodes, wherein the transducer channel is a nanowire in electrical contact with the top or the bottom gate; wherein the sensor channel has a width (W 1 ) and the nanowire has a width (W 2 ). In one aspect, the ratio of W 1 /W 2  is greater than or equal to 20, or selected from a range that is greater than or equal to 20 and less than or equal to 1000. 
     In an aspect, any of the devices have an amplified Nernst response that is greater than or equal to 0.5 V/pH. 
     In an embodiment, any of the devices have the transducer channel or nanowire is electrically connected to the top gate, having a pH sensitivity that is greater than or equal to 1 V/pH. Alternatively, the transducer channel or nanowire is electrically connected to the bottom gate, having a pH sensitivity that is greater than or equal to 10 V/pH. 
     In an aspect, the nanoplate has a width to length ratio (W/L) 1  and the nanowire has a width to length ratio (W/L) 2 , wherein (W/L) 1 /(W/L) 2  is greater than or equal to 20 and less than or equal to 10,000. In an aspect, L 1 ≠L 2 . The methods and devices provided herein are compatible with a wide range of L, wherein L refers to either or both L 1  and L 2 . In an aspect, L 1  and L 2  are independently selected to be greater than or equal to 100 nm and less than or equal to 1 mm. In an aspect, L 1  and L 2  are independently selected to be greater than or equal to 1 μm and less than or equal to 100 μm. 
     Optionally, the nanoplate and the nanowire comprise Si. Alternatively, the nanoplate and the nanowire comprise materials that are different from each other, such as AlGaN/Si; SiNW/Si; GaN/Si. 
     In another aspect, the transducer further comprises a transducer surface that contacts the fluid, wherein a transducer channel conductance is not substantially affected by a change in pH of the fluid. In another aspect, the nanowire is physically isolated from the fluid. 
     Any of the devices provided herein are described in terms of a pH amplification factor, such as an amplification factor that is greater than or equal 20, thereby increasing the Nernst response by at least a factor of 20. 
     In an aspect, any of the devices described herein are tunable, such as to achieve a user-selected pH sensitivity, a user-selected pH dynamic range, or both a user-selected pH sensitivity and pH dynamic range, including over any of the ranges described herein. 
     In an aspect, the device has a pH sensitivity that is better than 0.01 pH units. 
     In an aspect, any of the devices provided herein have a sensor and the transducer with a common source and a common drain. Alternatively, the sensor and transducer are electrically connected to physically distinct sources and physically distinct drains. 
     Without wishing to be bound by any particular theory, there may be discussion herein of beliefs or understandings of underlying principles relating to the devices and methods disclosed herein. It is recognized that regardless of the ultimate correctness of any mechanistic explanation or hypothesis, an embodiment of the invention can nonetheless be operative and useful. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1 . (a) Schematic diagram of a standard ISFET pH sensor. The surface groups (OH) react with protons (H + ) in electrolyte, and the reaction products (OH 2   +  and O − ) create a net surface charge. (b) Changes in the pH of the electrolyte are reflected in the change of surface charge and eventually changes in channel current (I D ) from source (S) to drain (D). The change in fluidgate bias (ΔV G ) required to restore I D  to the original value defines the pH sensitivity of the ISFET. (c) Top view of a coupled nanoplate (NP)-nanowire (NW) pH sensor. NP is always biased by the fluid gate, but the NW can be biased via the top or bottom gate, illustrated as schematics in (d). (e, f) SEM images of a nanoplate (top view) and five nanowires (top view). Only one of the NWs is used as T 2  for the sensor scheme proposed. 
         FIG. 2 . (a, b) Measured transfer characteristics of a nanoplate (serves as T 1 ) and bottom-gated nanowire (T 2 ), respectively. (c) Transfer characteristics of combined response of (a) and (b)—NP coupled with bottom-gated NP—plotted as a function of V G,2 . (d) Transfer characteristics of combined currents of a pair of NP and top-gated NW sensor with varying pH and V G,1 . (e) Measured pH sensitivity (circles) of coupled NP-NW sensors depending on NW bias configurations: bottom gate (top of plot dots, extracted from (c)) and top gate (lower dots, extracted from (d)) sweep. The dashed lines indicate the corresponding theoretical estimates dictated by Eq (4). The solid shaded region represents the classical sensitivity regime below the Nernst limit (59 mV/pH). 
         FIG. 3 . The simulated pH sensitivity of GN scheme with various types of sensing devices (T 1  in  FIG. 1 c   ) in the literature: AlGaN 13  (squares), GaN 14  ( ), and SiNW 15  (⋄)-based ISFETs. Here a Si n-MOSFET serves as T 2 . The rest (black) symbols indicate the experimental data from several DGFET sensors in the literature. 6-8  The solid black line represents the theoretical limit of the DGFET sensors. 
         FIG. 4 . (a) The measured sensitivity (top of plot dots) of an isolated nanoplate (T 1 ) sensor and instrument noise (open circles) as a function of nanoplate gate bias (V G,1 ), as defined in  FIG. 1 d   . (b) Corresponding plot for the nanoplate-nanowire (T 1 -T 2 ) sensor scheme proposed in this paper. The measured sensitivity in (b) represents the top of plot dots in  FIG. 2 e   . The theoretical lower limit of 1/f noise are also shown (solid curve). 
         FIG. 5 . The theoretical calculation of pH sensitivity using Giant-Nernst scheme. The sensitivity is shown as a function of the bias applied to the fluid gate of the nanoplate (V G,1 ) subtracted by its flat band voltage (V FB ). Since the analytical simulation is consistent with the numerical simulation, we only use the analytical simulation to interpret the experiment data in the manuscript. 
         FIG. 6 . The calculation of 1/f noise in gate voltage (in log plot). The physical parameters are: W=2 μm, f 1 =1 Hz, f 2 =1 kHz, α=1.5×10 5  V s/C, λ=0.5 Å, N t =3×10 16  eV −1  cm −3 , C eff =4.73×10 −7  F/cm 2 , T=300K. 
         FIG. 7 . The conceptual description of current fluctuation in the nanoplate (T 1 , left) and nanowire (T 2 , right) due to pH changes (7 to 7.1) and their corresponding current noise. The current change in T 1  (ΔI) is compensated by T 2 . 
         FIG. 8 . Schematic of a device for amplifying a pH signal and measuring pH. 
         FIG. 9 . Schematic of a nanowire-nanoplate pH sensor configuration. A constant DC bias is applied to the gate of T 2 , the plate device. The gate of T 1 , the wire, is swept while the total current I is measured as a function of the pH over T 2 . 
         FIG. 10 . A—Transfer characteristics for the nanoplate (for 5 different pH values) and for the nanowire. B—Zoomed in region around the rectangle in part A. 
         FIG. 11 . The transfer characteristics of the combined nanowire-nanoplate device as a function of pH. The line associated with ΔV t  shows an example of how the shift in threshold voltage for the device is calculated. 
         FIG. 12 . Comparison of the minimum pH detection resolution to commercial sensors, to an individual nanoplate, and to an individual nanowire sensor. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In general, the terms and phrases used herein have their art-recognized meaning, which can be found by reference to standard texts, journal references and contexts known to those skilled in the art. The invention may be further understood by the following non-limiting examples. All references cited herein are hereby incorporated by reference to the extent not inconsistent with the disclosure herewith. Although the description herein contains many specificities, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of the invention. For example, the scope of the invention should be determined by the appended claims and their equivalents, rather than by the examples given. 
     Example 1 
     Coupled Heterogeneous Nanowire-Nanoplate Planar Transistor Sensors for Giant Nernst Response 
     Provided herein is a comprehensive theory of pH response of a coupled ISFET sensor to show that the maximum achievable response is given by: ΔV/ΔpH=59 mV/pH×α, where 59 mV/pH is the Nernst response and α is an amplification factor that depends on the geometrical and electrical properties of the sensor and transducer nodes. While the intrinsic Nernst response of an electrolyte/site-binding interface is fundamental and immutable, we show that by using channels of different materials, areas, and bias conditions, the extrinsic sensor response can be increased dramatically beyond the Nernst limit. We validate the theory by measuring pH response of Si nanowire-nanoplate transistor pair that achieves &gt;10V/pH response and show the potential of the scheme to achieve (asymptotically) the theoretical lower-limit of signal-to-noise ratio (SNR) for a given configuration. Even larger pH response can be obtained based on recent trends in heterogeneous integration on the Si platform. 
     The search for a miniaturized, highly integrated, and lower cost replacement of the Beckman pH meter 1  dates back to 1970s when Bergveld proposed the CMOS-compatible concept of ion-sensitive field effect transistor 2  (ISFETs,  FIG. 1 a   ). Modern variants of ISFETs, based on silicon nanowire (Si-NW) 3  and carbon nanotubes (CNTs) 4 , offer novel form factor, prospects of innovative integration, and broader applications, but the sensitivity of all ISFETs are still defined by 59 mV/pH—the Nernst limit associated with an electrolyte and a site-binding surface. Many modern applications of ISFETs, such as the label-free detection of biomolecules in human genome sequencing 5 , however, requires the ability to detect just a few hundred protons (ΔpH˜0.02) in rapid flux (milliseconds response). For those applications, ability to amplify the Nernst signal can simplify design and increase throughput. 
     A recent trend for such amplification is based on double-gate silicon-on-insulator FET (DGFET) and a “super” Nernst response of ˜1V/pH has been demonstrated 6-9 . As discussed below, the need to use high fluid gate bias, the poorer quality of bottom oxide, the high cost of silicon-on-insulator (SOI) wafer suggest opportunities to develop alternative techniques. In this example, an alternative is presented based on a highly integrated Si nanoplate (NP)-nanowire (NW) transistor pair that is compatible with planar Si processing technology, see  FIG. 1 c   . In this configuration, the nanoplate acts as the pH sensor node biased through the fluid gate, while the transducer node, defined by the NW, is biased either through the top-gate (top-gated NW) or the bottom gate (bottom-gated NW), as shown in  FIG. 1 d   . The configuration obviates the need for high fluid bias for the NP pH-sensor node, and yet achieves amplified Nernst response ˜1V/pH with top-gated NW and (even superior)&gt;10V/pH with bottom-gated NW. Even higher pH response is possible with transistors of different materials integrated onto a common substrate (in  FIG. 1 , both NW and NP are made of Si). The maximum sensitivity achievable by the scheme is defined by the fundamental trade-off between dynamic range and sensitivity, and practical requirements of the transistor technology. 
     Operation of Single and Double-Gated ISFETs. A classical ISFET pH sensor involves a simple modification of the standard metal oxide field effect transistor (MOSFET) with the poly-Si gate (on top of the gate oxide) replaced by an electrolyte and a fluid gate, as shown in  FIG. 1 a   . Instead of using poly-Si gate to control the channel current in Si, in ISFET fluid gate affects the source (S) to drain (D) channel current I D  via electrolyte. Any shift in pH of the electrolyte changes the surface charge at the electrolyte-oxide interface through the site-binding process. As shown in  FIG. 1 b   , that ISFET detects pH shifts in the electrolyte by monitoring changes in Si channel current due to charge modulation of surface group at electrolyte-oxide interface 10 . The pH sensitivity is obtained by measuring shift of fluid gate voltage (ΔV G ) at a given amount of pH changes in constant current operation. 
     The pH sensitivity of an ISFET is understood as follows (see Ref. [10] for detailed analysis): The amphoteric OH groups at gate oxide/buffer undergo protonation/deprotonation of interface as a function of surface proton density, [H + ] S  Assuming Boltzmann distribution for ions in buffer solution, we have
 
[ H   + ] S   =[H   + ] B   e   −q(ψ     0     −V     G     )/k     B     T   =e   −2.303pH−q(ψ     0     −V     G     )/k     B     T ,  (1)
 
where [H + ] S  is the bulk proton density, pH=−log 10 [H + ] S , and ψ 0  is the oxide/buffer interface potential, k B  is the Boltzmann constant, and T is the temperature. Accordingly, any change in buffer pH manifests as an effective change in surface potential (or an effective change in applied bias for constant current operation) as ΔV G ≈2.303(k B T/q)ΔpH. Hence the maximum pH sensitivity, known as the Nernst limit, is ΔV G /ΔpH=59 mV/pH in room temperature. In practice, the sensitivity is always less than the intrinsic Nernst limit (associated with electrolyte/oxide interface) due to the high electrolyte screening, protonation affinity of sensor surface, and most importantly, finite semiconductor capacitance of an ISFET 10 .
 
     Recently many recent experimental 6-8  and theoretical works 9  suggest this response can be ‘amplified’ through innovative device geometry, and in fact, a super-Nernst sensitivity ˜1V/pH can be achieved by using the double-gate SOI structures (DGFET). There are two gates (top and bottom one) in a DGFET sensor. And the key is to restore the change in I D  due to pH change not by the fluid gate (as in ISFET), but rather through the bottom gate. The conductance change at the top surface of the channel (due to pH shift) is compensated by the change in conductance at the bottom surface to maintain constant current operation. The corresponding pH sensitivity of a DGFET sensor is 
                       Δ   ⁢           ⁢       V   G   DGFET     /   ΔpH       =       (     59   ⁢           ⁢   mV   ⁢     /     ⁢   pH     )     ×     (       C   tox       C   box       )     ×     α   SN         ,           (   2   )               
where C tox  and C box  are the top and bottom gate oxide capacitance, so that the amplification factor α=(C tox /C box )α SN &gt;&gt;1(α SN ≦1). For DGFET sensors, the bias and geometry dependent factor α SN &lt;1. Note that the intrinsic Nernst limit (59 mV/pH), associated with electrolyte and site-binding layer is fundamental and cannot be changed by new device configurations (ISFET or DGFET) or novel transducers. The amplified extrinsic Nernst response, however, simplifies detection and improves the practical signal-to-noise ratio (SNR), and is utilized herein to obtain high-sensitivity pH sensors.
 
     For maximum sensitivity, α SN →1, of a DGFET sensor (Eq. 2), the top channel of the device must be biased in inversion through the fluid gate. Biasing the fluid gate at high voltage is challenging because (i) large fluidic bias often leads to significant leakage current and reduced device lifetime 11 , and (ii) if the bias exceeds the formal potential of the electrode, a Butler-Volmer reaction 12  at the fluidic electrode may make the fluid gate potential undefined. Moreover, a shared bottom gate electrode of the DGFET technology makes it difficult to integrate multiple, individually accessible sensors within a common platform, as required in applications such as Ref. [5]. Finally, applying too high a bias on the poorer-quality bottom oxide may lead to hysteresis and unstable device operation. Hence, a super-Nernst sensor that does not require high fluid bias, is not constrained by the geometric/material features of the DGFET, and can be integrated better with the traditional planar technology, is desirable. 
     “Giant” Nernst (GN) scheme. Consider an accumulation-mode NP-NW transistor pair shown in  FIG. 1 c   . Here, the NP FET acts a sensor transistor T 1  and is exposed to the buffer solution for pH sensing, while the NW FET T 2  acts as a transducer and is isolated from the buffer, or is not reactive to the buffer. Since the transistors are compatible with planar top-down technology and are processed simultaneously, the process is simple and no additional masks are necessary. 
     For the accumulation-mode devices, the drain current modulation in T 2  is given as
 
Δ I   D,2 =μ 2   C   OX,2 ( W/L ) 2   V   DS,2   ΔV   G,2 ,  (3)
 
where μ 2  is the channel mobility, C OX,2  is the gate oxide capacitance, W and L is the channel width and length, V DS,2  is the drain bias, and ΔV G,2  is the gate bias modulation. Since T 1  and T 2  are in accumulation regime, the band bending at the channel surface is very small. Hence the current modulation of T 1  due to any pH-induced modulation of top-oxide/buffer interface potential is given by ΔI D,1 =μ 1 C OX,1 (W/L) 1 V DS,1 ΔV G,1  (note that ΔV G,1  is limited by the Nernst limit). The scheme requires adjustment of the bias of T 2  to counterbalance the conductance modulation of T 1 , so that
 
     
       
         
           
             
               
                 
                   
                     
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     Equation (4) suggests that GN scheme achieves significant amplification over DGFET sensors (i.e., α GN &gt;&gt;α SN ) by (i) Scaling of device dimension, so that W/L of T 1  far exceeds that of T 2  (and hence the use of NP and NW transistor couple). (ii) Mobility scaling so that T 1  has higher mobility than T 2 . This can be achieved by using NMOS/PMOS pair for T 1 /T 2  or by using different channel materials. (iii) Oxide thickness scaling—this option is similar to the DGFETs. For maximum amplification, C OX,1 &gt;&gt;C OX,2 . This is achieved through oxide thickness scaling in a dual oxide process or by using higher-k dielectrics for T 1  compared to T 2  or a combination thereof. And finally, (iv) Bias scaling so that V DS  of T 2  is smaller than that of T 1 . This option of bias scaling provides a post-process, point-of-care option to tune the sensor performance. Since the geometry of DGFET precludes the use of device, bias, and mobility scaling, the response is typically limited to ˜1V/pH. 
       FIG. 2  demonstrates the experimental validation of Giant Nernst (GN) scheme, with the maximum GN response of &gt;10V/pH. Let us consider two different biasing configurations for the NW (T 2 ) illustrated in  FIG. 1 d    and compare their performances. In the first configuration, the nanowire T 2  is operated through the bottom (BG) gate, and in the second one, through its top gate (TG) (Note T 1  is always biased via the fluid gate). 
     To understand the overall response of first configuration (bottom gate operation of T 2 ) we first characterize the T 1 -T 2  responses independently ( FIGS. 2 a  and 2 b   ). The pH sensitivity of a stand-alone nanoplate (T 1 ) is obtained by the measuring transfer characteristics (I D,1  vs. V G,1 ) of a nanowire in solution for various pH values, as shown in  FIG. 2 a   . The responses are stable and repeatable over many hours of operation. We find that stand-alone response of T 1  is 46 mV/pH, always below the Nernst limit, as expected. For the GN amplification, T 1 -T 2  coupling is essential, as predicted by Eq. (4).  FIG. 2 b    shows the isolated transfer characteristics (I D,2  vs. V G,2 ) of the nanowire (T 2 ) measured in dry air with bottom gate operation. 
     Recalling the current change in T 1  (ΔI D,1 ) needs to be compensated by T 2  (ΔI D,2 =ΔI D,1 ), we obtain the “combined” transfer characteristics (I D  vs. V G,2  shown in  FIG. 2 c   ), where the total current (I D ) is the sum of individual currents of T 1  (I D,1 ) and now top-gated T 2  (I D,2 ).  FIG. 2 c    shows combined current vs. the NW gate bias (V G,2 ) with different V G,1  and pH. Since the current changes in T 1  needs to be compensated by T 2  (i.e., ΔI D,1 +ΔI D,2 =0 or I D =I D,1 +I D,2  is fixed), the NW gate bias V G,2  needs to be shifted versus pH changes (ΔpH) at the constant current level of I D  vs. V G,2  in  FIG. 2 c   . For each V G,1  we measure the shift of curves (ΔV G,2 ) for a constant current level. This measured sensitivity (ΔV G,2 /ΔpH) of the first configuration is shown in  FIG. 2 e    as dots at the top of the plot. Since T 2  is operated via bottom gate and the channel lengths of T 1  and T 2  are the same (L 1 =L 2 ), the theoretical estimate of α GN  equals to (W/L) 1 /(W/L) 2 ×(C OX,1 /C OX,2 )=(W 1 /W 2 )×(EOT OX,2 /EOT OX,1 )=(2 μm/50 nm)×(145 nm/7.3 nm)≈794, so the sensitivity is 46 mV/pH×794≈36V/pH, shown as the dashed line in  FIG. 2 e   , which is consistent with our measurement. This NP-NW sensitivity is significantly better than that of DGFET sensors (i.e., α GN &gt;&gt;α SN ). This amplification reflects the fact that the current level of T 1  ( FIG. 2 a   ) is 1-2 orders of magnitude higher than that of T 2  ( FIG. 2 b   ) since the nanoplate (T 1 ) FET has much higher (W/L) ratio compared to that of the nanowire (T 2 ) FET (i.e., (W/L) 1 =40×(W/L) 2  for these particular devices). Note that it is not possible to obtain such high gain from DGFET sensors reported in the literature, because the oxide area, mobility, and drain-bias of the sensor and transducer channels are coupled by common substrate of DGFET, so that α SN ≈1. 
     To measure the pH sensitivity in the second configuration of NW biasing (top gate operation of T 2 , sensitivity shown as dots in the middle and bottom of the plot in  FIG. 2 e   ) we also measure “combined” transfer characteristics (I D  vs. V G,2  shown in  FIG. 2 d   ) of a nanoplate and a top-gated nanowire. We follow the same procedure to extract the corresponding pH sensitivity as in the first configuration (with bottom-gated nanowire).  FIG. 2 e    show the pH sensitivity (ΔV G,2 /ΔpH) measured in T 2  as a function of NP fluid gate bias (V G,1 ). Since both T 1  and T 2  are biased via the top gate and have the same top oxide dimension, the sensitivity amplification is achieved by different (W/L) ratios. The effective transistor width of the NW sensor is W 2   eff =W 2 +2H 2 ≈3W 2 , because the height of nanowire (H 2 ) is similar to W 2  and the gate bias couples to all three surfaces electrostatically. The estimated sensitivity of 46 mV/pH×(W 1 /W 2   eff )≈0.613V/pH, shown as dashed lines in the middle of the plot of  FIG. 2 e   , matches well with the experimental data in the accumulation regime. This result implies that the amplification comparable to DGFET can be easily achieved with conventional top-gated MOSFETs with proper design of device geometries. Although the bottom-gated NW (top of plot dots,  FIG. 2 e   ) gives higher sensitivity compared to top gated NW configuration (middle to lower plot dots,  FIG. 2 e   ) due to its thicker (bottom) oxide, in practice one cannot scale the bottom oxide arbitrarily without introducing excessive defects that leads to device instability and hysteresis. Also, the availability of top contact simplifies interconnection in a massively parallel circuit. Therefore, there may be many practical reasons to prefer the top-gated NW configuration for device application. 
     Eq. (4) suggests that the sensor response could be further improved if the NP and NW sensors are made of different channel materials, so that their mobility asymmetry (μ 1 /μ 2 &gt;&gt;1) can be used for the amplified sensor response. To estimate the possible gain in sensitivity by combing transistors of different materials, we first measure the transfer characteristics of a set of Si n-MOSFET devices, which would serve as the transducer node, T 2 . Next, we extract the slopes of pH responses (ΔI D IΔpH) of devices with different channel materials 13-15  reported in the literature, each of which may potentially serve as the sensor node, T 1 . Finally, we calculate the combined pH sensitivity of these heterogeneous T 1 -T 2  pairs.  FIG. 3  compares the responses so obtained with those from DGFET and ISFETs sensors reported in the literature. As expected, regardless the material characteristics or device dimensions, all the data from the literature based on DGFET and ISFET sensors (black symbols) lie below α SN ≈1 line (the solid black line). In DGFET sensors 6-8 , pH response of ˜1V/pH is can be achieved. For the proposed GN scheme based on T 1 -T 2  pair, the corresponding pH sensitivity far exceeds DGFET response (α GN &gt;&gt;1), especially with high-mobility devices (such as GaN, AlGaN) serving as T 1 , and one can achieve even higher sensitivity (up to 100V/pH regime) by pairing planar FETs with different materials and dimensions into a single sensing entity. Eq. (4) therefore defines the fundamental upper limit of pH sensing for NW-NP based sensors. In practice, this upper limit may not be achieved due to fundamental and practical issues, as discussed in the next section. In an aspect, any of the T 1 /T 2  pairs provided in  FIG. 3 , or the literature associated herein, are utilized in any of the methods and devices provided herein to further increase the amplification factor. 
     Considerations of Dynamic Range, SNR, and minimum pH resolution In contrast to ISFET pH sensor showing wide dynamic range of pH sensing 16 , the high sensitivity of the GN scheme is realized at the expense of reduced dynamic range (analogous to the gain-bandwidth product of a traditional transistor). For many applications in healthcare, where the dynamic range of interest is small (7.35-7.45 for human blood pH; ΔpH˜0.02 for Ref. Error! Reference source not found.), the tradeoff of higher sensitivity for reduced dynamic range is fully justified. However, excessive gain requires repeated changing of DC bias to cover the pH-range of interest, which is cumbersome and counterproductive. In addition, practical concerns of applying high-bias on gate oxide (for the bottom-gated NW corresponding to top plot dots in  FIG. 2 e   ) that may lead to leakage and hysteresis may also limit the maximum gain achievable from a NP-NW sensor combination. 
     Regarding the signal-to-noise ratio (SNR), another key parameter of pH sensor, it is important to realize that the theoretical lower limit of SNR and minimum pH-resolution (ΔpH min ) of the GN scheme are still defined by those of its detector (T 1 ). In practice, however, fundamental considerations of measurement noise and biasing configuration ensure that the GN-scheme achieves better ΔpH min  far more easily than either NP or NW sensor could in isolation, as discussed below. 
     The 1/f noise is the dominant source of noise at frequencies relevant for pH sensors 17  and its power-spectrum is given by S V     G   ˜ δV G     2 ∝1/A (A is a device area), or 
                     〈     δ   ⁢           ⁢     V   G       〉     2       ~   γ     /     A           
is a preractor). For a typical single NW pH sensor this noise-floor makes the pH-resolution limited to
 
     
       
         
           
             
               
                 
                   
                     
                       
                         Δ 
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                         pH 
                       
                       min 
                       NW 
                     
                     ~ 
                     3 
                   
                   ⁢ 
                   
                     
                       
                         
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                             δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               
                                 G 
                                 , 
                                 NW 
                               
                             
                           
                           〉 
                         
                         2 
                       
                     
                     / 
                     
                       0.059 
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                       3 
                     
                   
                   ⁢ 
                   
                     
                       γ 
                       NW 
                     
                     / 
                     
                       
                         ( 
                         
                           0.059 
                           ⁢ 
                           
                             
                               A 
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                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     Indeed, a key concern for typical NW pH sensor is that such low resolution due to small A NW  might be unacceptable for many physiological applications 18 . 
     On the other hand, if the larger area NP sensor (T 1 ) is used in the ISFET configuration, the noise floor (solid line,  FIG. 4( a ) ) and improves the pH resolution considerably, i.e., 
                           Δ   ⁢   pH     min   NP     ~   3     ⁢           〈     δ   ⁢           ⁢     V     G   ,   NP         〉     2       /     0.059   ~   3       ⁢       γ   NP     /     (     0.059   ⁢       A   NP         )         ,           (   6   )               
as defined by the vertical gap (in log plot) between the top dots and the bottom line in  FIG. 4 a   . For the NP-NW sensor used in the GN scheme, pH sensitivity is amplified (0.059×α GN , dots in  FIG. 4 b   ) and so is the voltage noise (curve in  FIG. 4 b   ). However, its pH resolution is still fundamentally limited by NP (T 1 ) noise because if an instantaneous pH signal unresolved in NP-sensor probe due to noise, it will also remain unresolved in NP-NW combination, thus ΔpH min   NP-NW =ΔpH min   NP . Nevertheless, since A NP &gt;&gt;A NW , the pH-resolution is considerably improved compared to single NW sensor: this improvement reflects the reduction in noise-floor due to larger area of NP sensor itself (T 1 ), not due to the NP-NW (T 1 -T 2 ) combination.
 
     The additional SNR advantage of T 1 -T 2  combination becomes apparent, however, when the noise of the measurement instrument, δV Ins , is taken into account. If δV NP &lt;δV Ins —as can always be conveniently arranged by increasing the size of the NP (T 1 ) transistor, we find that the pH resolution for the NP alone would have been limited by instrument noise, i.e., 
                     Δ   ⁢   pH     min   ins     ⁢     ❘   NP     ⁢       ~   3     ⁢           〈     δ   ⁢           ⁢     V   ins       〉     2       /   0.059         &gt;&gt;       Δ   ⁢   pH     min   NP       ,         
and therefore the signal from the NP alone will remain poorly resolved. However, the same signal can still be detected by the T 1 -T 2  combination as
 
                 Δ   ⁢   pH     min   ins     ⁢     ❘     NP   -   NW       ⁢       ~   3     ⁢           〈     δ   ⁢           ⁢     V   ins       〉     2       /     (     0.059   ×     α   GN       )               
if δV ins  is larger than δV NW  and δV NP  thus ΔpH min   ins | NP &gt;&gt;ΔpH min   ins | NP-NW  (See Table S1). This is illustrated by the increasing gap between instrument noise (middle band) and sensitivity (top dots) in  FIG. 4( a )  vs.  4 ( b ), respectively. This is because in the GN scheme the sensitivity is amplified by the area-ratio, while the noise depends on the square-root of the area. Note that this improvement cannot be obtained by simply adding an amplifier following a sensor node, because the SNR ratio remains unchanged in that case.
 
     In this example, we establish a framework of a new class of ISFET-sensors that achieves high sensitivity by physically decoupling the sensor from the transducer node. This principle is used to design a nanoplate-nanowire transistor pair, which shows (consistent with theoretical prediction) sensitivity&gt;10V/pH, which is significantly higher than previous reports based on DGFET pH sensors. Furthermore, we show that pH sensitivity close to 100V/pH may be achieved by incorporating high mobility materials as a sensor node coupled to a low-mobility traducer. The high sensitivity improves pH-resolution as well as signal-to-noise ratio, especially when sensor precision is limited by the noise of the measurement instrument. The improvement of sensitivity, however, must be counter-balanced against the requirement of dynamic range for pH sensing and practical requirements of device scaling. This generic nature of the concept, combined with its compatibility to conventional top-down CMOS processing technology, should make the concept relevant for applications in biomedical areas such as proton-based genome sequencers, environmental toxin monitoring, pharmaceutical testing, etc., in which precise pH monitoring is critical to its sequencing accuracy. 
     Example 2 
     Fabrication Methods of Nanowire and Nanoplate Devices 
     The devices are fabricated using top down fabrication, starting with bonded SOI wafers. 8″ bonded SOI wafers (SOITECH) doped p-type at 10 15 /cm 2  with BOX thickness of 145 nm and superficial silicon thickness of 55 nm were first laser cut into 4″ wafers by Ultrasil Corp. Wafers were then oxidized for 11 minutes at 1000° C. to grow 30 nm of oxide and placed into buffered oxide etch (BOE) to thin down the top silicon to around 350 Å. Wafers were doped with boron at 10 KeV at a dose of 10 14  cm −2  and a tilt of 7°. Next, the gate dielectric was formed. For SiO 2  devices, the wafers are dry oxidized for 1 minute at 1000° C. to form a gate oxide of around 50 Å, which was measured via ellipsometry on monitor wafers also present during the oxidation run. This also serves as a dopant activation step. For HfO 2  devices, after a brief BOE dip and dopant activation in nitrogen for 3 minutes at 1000° C., the wafers were placed into an atomic layer deposition (ALD) machine for 150 cycles of HfO 2  for a target thickness of 150 Å. Wafers were then subjected to a Rapid Thermal Anneal (RTA) for 1 min at 950° C., followed by a Forming Gas Anneal (FGA) for 30 minutes at 450° C. in 5% H 2  in N 2  to reduce interfacial trapped charge, mobile charge, and fixed charge. Next, vias were formed in the silicon mesas with optical lithography and subsequent BOE etch to make solid, crack-free connection between metal interconnects and the silicon layers. AFM was performed over these regions to determine the silicon thickness (≈300 Å) and the gate dielectric thickness (≈50 Å for SiO 2 , 150 Å for HfO 2 ). 
     Device Measurement in pH Environment. The pH measurements utilized two separate devices. The main sensing chip with the nanoplate device (2 μm wide) had a 150 Å thick HfO 2  dielectric, while the device exhibiting the GN response (a 50 nm wide nanowire device) contained a 50 Å thick SiO 2  dielectric. Both chips were fitted with open PDMS wells for containing the fluid. The values for the pH for each solution were measured separately with a commercial pH meter. The fluidic environments over the two separate chips were biased with two leak-free Ag/AgCl reference electrodes purchased from Warner Instruments. A 1× phosphate buffer saline (PBS) solution at pH 7.4 was used for the nanowire device for the entire experiment to enable normal transfer characteristics. Robinson buffers (0.04 M of phosphoric, boric, and acetic acid) with titrated HCl and NaOH, which have good buffering capacity over wide pH ranges, were manually pipetted and rinsed in the PDMS well over the nanoplate device, followed by a 5 minute settling time to allow the surface charge to equilibrate. Transfer characteristics were measured using a Keithley 4200 semiconductor characterization system. The source and drain nodes of the devices were shorted together to create the full GN response sensor, and current was measured at the shorted source nodes of the devices. 
     References 
     
         
         [1] Arnold O. Beckman, Henry E. Fracker, Apparatus for Testing Acidity, U.S. Pat. No. 2,058,761 (1936). 
         [2] Piet Bergveld, Sens. Actuators B: Chem. 88, pp. 1-20 (2003). 
         [3] Fernando Patolsky, Gengfeng Zheng and Charles M. Lieber, Anal. Chem. 78, pp. 4260-4269 (2006). 
         [4] Alexander Star, Jean-Christophe P. Gabriel, Keith Bradley, and George Grüner, Nano Lett. 3, pp. 459-463 (2003). 
         [5] Jonathan M. Rothberg, Wolfgang Hinz, Todd M. Rearick, Jonathan Schultz, William Mileski, Mel Davey, John H. Leamon, Kim Johnson, Mark J. Milgrew, Matthew Edwards et al., Nature 475, pp. 348-352 (2011). 
         [6] Mark-Jan Spijkman, Jakob J. Brondijk, Tom C. T. Geuns, Edsger C. P. Smits, Tobias Cramer, Francesco Zerbetto, Pablo Stoliar, Fabio Biscarini, Paul W. M. Blom, and Dago M. de Leeuw, Adv. Funct. Mater. 20, pp. 898-905 (2010). 
         [7] M. Spijkman, E. C. P. Smits, J. F. M. Cillessen, F. Biscarini, P. W. M. Blom, and D. M. de Leeuw, Appl. Phys. Lett. 98, 043502 (2011). 
         [8] O. Knopfmacher, A. Tarasov, Wangyang Fu, M. Wipf, B. Niesen, M. Calame, and C. Schonenberger, Nano Lett. 10, pp. 2268-2274 (2010). 
         [9] Jonghyun Go, Pradeep R. Nair, Bobby Reddy, Brian Dorvel, Rashid Bashir, and Muhammad A. Alam, Electron Devices Meeting (IEDM), 2010 IEEE International (2010). 
         [10] Luc Bousse, Nico F. De Rooij, and Piet Bergveld, Electron Devices, IEEE Transactions on, 30, pp. 1263-1270 (1983). 
         [11] Eric Stern, James F. Klemic, David A. Routenberg, Pauline N. Wyrembak, Daniel B. Turner-Evans, Andrew D. Hamilton, David A. LaVan, Tarek M. Fahmy, and Mark A. Reed, Nature, 445, pp. 519-522 (2007). 
         [12] A. J. Bard and L. R. Faulkner, Electrochemical Methods: Fundamentals and Applications, John Wiley, New York, 1980. 
         [13] Takuya Kokawa, Taketomo Sato, Hideki Hasegawa, and Tamotsu Hashizume, J. Vac. Sci. Technol. B 24, pp. 1972-1976 (2006). 
         [14] G. Steinhoff, M. Hermann, W. J. Schaff, L. F. Eastman, M. Stutzmann, and M. Eickhoff, Appl. Phys. Lett. 83, 177 (2003). 
         [15] X. T. Vu, R. GhoshMoulick, J. F. Eschermann, R. Stockmann, A. Offenhäusser and S. lngebrandt, Sens. Actuators B:Chem. 144, pp. 354-360 (2010). 
         [16] Songyue Chen, Johan G. Bomer, Edwin T. Carlen, and Albert van den Berg, Nano Lett. 11, pp. 2334-2341 (2011). 
         [17] C. G. Jakobson and Y. Nemirovsky, Electron Devices, IEEE Transactions on, 46, pp. 259-261 (1999). 
         [18] Xueji Zhang, Huangxian Ju, and Joseph Wang, Electrochemical Sensors, Biosensors and their Biomedical Applications, Academic Press, 2007. 
       
    
     I. Theoretical Frameworks of Giant-Nernst (GN) Scheme 
     To understand the Giant-Nernst pH response, let us first develop a general model to predict the pH response for decoupled T 1 -T 2  platform and then compare the analytical results with numerical simulations and experimental results. Assume that T 1 -T 2  is the accumulation-type device. Under such linear operating regimes, the drain current modulation in T 2  is given as
 
Δ I   DS,2 =μ 1   C   OX,2 ( W/L ) 2   V   DS,2   ΔV   G,2   (S1)
 
     We now consider two operation regimes of GN scheme: If T 1  is in accumulation regime, the band bending at the channel surface is very small. Hence the current modulation of T 1  due to any pH induced modulation of top-oxide/buffer interface potential (ΔV G,1 ) is given by, ΔI DS,1 =μ 1 C OX,1 (W/L) 1 V DS,1 ΔV G,1 . The proposed scheme ( FIG. 1 c   ) requires that the bias of T 2  should be adjusted to counterbalance the conductance modulation of T 1 , so that 
     
       
         
           
             
               
                 
                   
                     
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         
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                           , 
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                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         
                           GS 
                           , 
                           1 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           
                             
                               μ 
                               1 
                             
                             
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                               2 
                             
                           
                           ⁢ 
                           
                             
                               
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                                 , 
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                         ) 
                       
                       ⁢ 
                       
                         
                           C 
                           
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                             , 
                             1 
                           
                         
                         
                           C 
                           
                             OX 
                             , 
                             2 
                           
                         
                       
                     
                     = 
                     
                       
                         α 
                         GN 
                       
                       ⁢ 
                       
                         
                           
                             C 
                             
                               OX 
                               , 
                               1 
                             
                           
                           
                             C 
                             
                               OX 
                               , 
                               2 
                             
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   S2 
                   ) 
                 
               
             
           
         
       
     
     Appropriate design can achieve α GN &gt;&gt;1 while the maximum amplification of current DGFET schemes is limited by the condition α SN =1. 
     On the other hand, if T 1  is in the depletion regime, its conductance modulation is due to the changes in depletion charge. Semi-classical analysis 0 indicates that the depletion charge is given as Q 1 =Q 0 (1−√{square root over (1+V G,1 /V 0 )}) where Q 0  ≡∈ Si qN A /C OX,1  and V 0 ≡∈ Si qN A N A /2C OX,1   2 , respectively. Correspondingly the pH induced current modulation of T 1  is equal to
 
Δ I   DS,1 =μ 1 ( W/L ) 1   V   DS,1   Q   0 (√{square root over (1 +V   G,1   /V   0 )}−√{square root over (1+( V   G,1   +ΔV   G,1 )/ V   0 )}).  (S3)
 
     Thus the corresponding sensing signal from T 2  can be expressed as 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       V 
                       
                         G 
                         , 
                         2 
                       
                     
                   
                   = 
                   
                     
                       α 
                       GN 
                     
                     ⁢ 
                     
                       
                         Q 
                         0 
                       
                       
                         C 
                         
                           OX 
                           , 
                           2 
                         
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             
                               1 
                               + 
                               
                                 
                                   V 
                                   
                                     G 
                                     , 
                                     1 
                                   
                                 
                                 
                                   V 
                                   0 
                                 
                               
                             
                           
                           - 
                           
                             
                               1 
                               + 
                               
                                 
                                   
                                     V 
                                     
                                       G 
                                       , 
                                       1 
                                     
                                   
                                   + 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       
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                                         , 
                                         1 
                                       
                                     
                                   
                                 
                                 
                                   V 
                                   0 
                                 
                               
                             
                           
                         
                         ) 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   S4 
                   ) 
                 
               
             
           
         
       
     
     Clearly, the pH response is a function of the gate bias in T 1  in contrast to the accumulation regime. Equation (S4) can be simplified such that ΔV G,2 ≈α GN  (Q 0 /2C OX,2 √{square root over (V 0 )})ΔV G,1 /√{square root over (V G,1 )} if V G,1 &gt;&gt;ΔV G,1 ,V 0 . This analytical expression implies the decrease of sensitivity as the bias (V G,1 ) increases. However, the GN scheme still offers significant amplification over DGFET sensors as α GN &gt;&gt;1. 
     Although Eqs. (S2) and (S4) clearly indicate that significant amplification can be achieved through the GN scheme, the above analysis is not complete as the pH dependent modulation of top-oxide/buffer interface potential of T 1  (ΔV G,1 ) is not an independent parameter. Hence, we numerically solve for the electrostatics of the sensor-buffer system, as described by the following equations:
 
−∇(∈ w ∇Ψ)= qn   0 (exp(−βΨ)−exp(βΨ)),  (S5)
 
−∇(∈ Si ∇Ψ)= q ( n   i (exp(−βΨ)−exp(βΨ))− N   A ),  (S6)
 
∈ OX ∇Ψ−∈ w ∇Ψ=ρ OH     2+   −ρ O     −   .  (S7)
 
     Here Ψ represent the electrostatic potential. Equation (S5) represents the electrostatics of the buffer (n 0 —ion concentration), while eq. (S6) describes the semiconductor (n i —intrinsic carrier concentration and N A  is the p-type doping density). Eq. (S7) describes top oxide/buffer interface whose RHS denotes the pH dependent charge due to the protonation/de-protonation of surface OH groups. This charge is modeled as function of buffer H +  concentration through the well-known site binding model 0 and will not be discussed in detail here. We self-consistently solve the system of non-linear equations, (S5)-(S7), with appropriate boundary conditions to estimate the charge modulation (and hence the conductance modulation, assuming constant mobility) in the semiconductor due to changes in pH, bias conditions, etc. 
       FIG. 5  shows the bias-dependent amplification for GN scheme (symbols indicate numerical simulation results while solid lines indicate analytical results). Here we assume that T 2  is in linear regime while the bias applied to T 1  is varied. With appropriate design of device geometry, GN scheme achieves ˜10V/pH in accumulation regime, which is many orders of magnitude better than the current DGFET sensors (0.1˜1V/pH). While in depletion mode of T 1  the sensitivity is slightly reduced but still much higher than that of DGFET. In general, therefore one should operate the sensing device in accumulation regime to achieve maximum sensitivity. 
     II. Noise Consideration of Giant-Nernst (GN) Scheme: We address the noise and its ratio to the signal (SNR) of our GN scheme, which consists of a nanoplate (NP, T 1 ) and a nanowire (NW, T 2 ). Although there are several sources of noises in ISFET-based pH sensor, we assume that the noise is dominated by the FET&#39;s 1/f noise, not by the electrolyte noise (I 0 ˜10 mM), which was demonstrated in Ref [3] As we define the sensitivity in terms of the shift in gate voltage (V G ) due pH changes, its corresponding noise in V G (√{square root over (&lt;δV G   2 &gt;)}) dictates SNR. 
     If the sensor is operated in its linear regime, its noise in terms of the voltage fluctuation is given by the following equations [3]: 
     
       
         
           
             
               
                 
                   
                     
                       S 
                       
                         V 
                         G 
                       
                     
                     = 
                     
                       
                         
                           S 
                           
                             V 
                             FB 
                           
                         
                         ⁡ 
                         
                           [ 
                           
                             1 
                             + 
                             
                               ( 
                               
                                 
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                                   eff 
                                 
                                 ⁢ 
                                 
                                   C 
                                   eff 
                                 
                                 ⁢ 
                                 
                                   
                                     I 
                                     D 
                                   
                                   
                                     g 
                                     m 
                                   
                                 
                               
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                           ] 
                         
                       
                       2 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   where 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       S 
                       
                         V 
                         FB 
                       
                     
                     = 
                     
                       
                         
                           q 
                           2 
                         
                         ⁢ 
                         
                           kTN 
                           t 
                         
                         ⁢ 
                         λ 
                       
                       
                         f 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         W 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         L 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           C 
                           eff 
                           2 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   and 
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       g 
                       m 
                     
                     = 
                     
                       
                         
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             I 
                             D 
                           
                         
                         
                           d 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             V 
                             G 
                           
                         
                       
                       = 
                       
                         
                           μ 
                           eff 
                         
                         ⁢ 
                         
                           C 
                           eff 
                         
                         ⁢ 
                         
                           W 
                           L 
                         
                         ⁢ 
                         
                           
                             V 
                             DS 
                           
                           . 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   S8 
                   ) 
                 
               
             
           
         
       
     
     For a given low (f 1 ) and high frequency cutoff (f 2 ) in the measurement bandwidth, the voltage noise √{square root over (&lt;δV G   2 &gt;)} is given by 
                       〈     δ   ⁢           ⁢     V   G   2       〉       =               q   2     ⁢     kTN   t     ⁢   λ       W   ⁢           ⁢   L   ⁢           ⁢     C   eff   2         ⁢     ln   ⁡     (       f   2       f   1       )           ⁡     [     1   +     (       αμ   eff     ⁢     C   eff     ⁢       I   D       g   m         )       ]               (   S9   )               
where N t  is the volume trap density in the gate oxide layer, λ is the tunneling parameter, C eff  is the capacitance per area, and a is the coulomb scattering coefficient. Since the noise is given by √{square root over (&lt;δV G   2 &gt;)}˜1/√{square root over (W)}. And the spectral density of the current is S 1 =g m   2 S V     G   , therefore the current noise is √{square root over (&lt;δI 2 &gt;)}=∫ f     2     f     2   S 1 (f)df˜√{square root over (W)}. The calculated voltage noise versus V G  is shown in  FIG. 6 .
 
       FIG. 7  shows how the DC current and its noise changes in a nanoplate (T 1 , left)-nanowire (T 2 , right) pair. The sum of two DC currents is constant: I 1 +I 2 =I. The initial noise of T 1  and T 2  is proportional to their widths: W 1  and W 2 , respectively. As the current of T is altered by pH changes its noise magnitude is also changed by a factor of γ, which is independent of W, where γ is defined as 
     
       
         
           
             
               
                 
                   
                     
                       γ 
                       1 
                     
                     = 
                     
                       
                         [ 
                         
                           1 
                           + 
                           
                             ( 
                             
                               
                                 αμ 
                                 eff 
                               
                               ⁢ 
                               
                                 C 
                                 eff 
                               
                               ⁢ 
                               
                                 
                                   
                                     I 
                                     1 
                                   
                                   + 
                                   
                                     Δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     I 
                                   
                                 
                                 
                                   g 
                                   m 
                                 
                               
                             
                             ) 
                           
                         
                         ] 
                       
                       / 
                       
                         [ 
                         
                           1 
                           + 
                           
                             ( 
                             
                               
                                 αμ 
                                 eff 
                               
                               ⁢ 
                               
                                 C 
                                 eff 
                               
                               ⁢ 
                               
                                 
                                   I 
                                   1 
                                 
                                 
                                   g 
                                   m 
                                 
                               
                             
                             ) 
                           
                         
                         ] 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   S10a 
                   ) 
                 
               
             
             
               
                 
                   
                     γ 
                     2 
                   
                   = 
                   
                     
                       [ 
                       
                         1 
                         + 
                         
                           ( 
                           
                             
                               αμ 
                               eff 
                             
                             ⁢ 
                             
                               C 
                               eff 
                             
                             ⁢ 
                             
                               
                                 
                                   I 
                                   2 
                                 
                                 - 
                                 
                                   Δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   I 
                                 
                               
                               
                                 g 
                                 m 
                               
                             
                           
                           ) 
                         
                       
                       ] 
                     
                     / 
                     
                       
                         [ 
                         
                           1 
                           + 
                           
                             ( 
                             
                               
                                 αμ 
                                 eff 
                               
                               ⁢ 
                               
                                 C 
                                 eff 
                               
                               ⁢ 
                               
                                 
                                   I 
                                   2 
                                 
                                 
                                   g 
                                   m 
                                 
                               
                             
                             ) 
                           
                         
                         ] 
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   S10b 
                   ) 
                 
               
             
           
         
       
     
     The ratio of current and voltage noise between the nanoplate (T 1 ) and nanowire (T 2 ) can be expressed as 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           〈 
                           
                             δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               I 
                               2 
                               2 
                             
                           
                           〉 
                         
                       
                       
                         
                           〈 
                           
                             δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               I 
                               1 
                               2 
                             
                           
                           〉 
                         
                       
                     
                     = 
                     
                       
                         
                           γ 
                           2 
                         
                         
                           γ 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             W 
                             2 
                           
                         
                         
                           
                             W 
                             1 
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           〈 
                           
                             δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               
                                 G 
                                 , 
                                 2 
                               
                               2 
                             
                           
                           〉 
                         
                       
                       
                         
                           〈 
                           
                             δ 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               V 
                               
                                 G 
                                 , 
                                 1 
                               
                               2 
                             
                           
                           〉 
                         
                       
                     
                     = 
                     
                       
                         
                           γ 
                           2 
                         
                         
                           γ 
                           1 
                         
                       
                       ⁢ 
                       
                         
                           
                             
                               W 
                               1 
                             
                           
                           
                             
                               W 
                               2 
                             
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   S11 
                   ) 
                 
               
             
           
         
       
     
     Thus the voltage noise signal is inversely proportional to the square root of width ratio: a nanowire (T 2 ) shows higher noise than that of a nanoplate (T 1 ) 
             (           〈     δ   ⁢           ⁢     V     G   ,   2         〉     2       &gt;&gt;         〈     δ   ⁢           ⁢     V     G   ,   1         〉     2         )         
since W 1 &gt;&gt;W 2 . This implies that the signal measured at T 2  is amplified from signal of T 1  by factor of W 1 /W 2  whereas the corresponding voltage noise ratio is √{square root over (W 1 /W 2 )} (as γ 1 /γ 2 ≈1): Suppose
 
                 W   1     /     W   2       =     100   ⁢           ⁢   and   ⁢           ⁢         〈     δ   ⁢           ⁢     V     G   ,   1         〉     2               
is 1 mV, then the noise ratio is 10 thus T 2  noise is 10 mV, which is the dominant one in the GN scheme (T 1 -T 2 ). However, even though the noise ratio (√{square root over (W 1 /W 2 )}) is smaller the signal amplification factor (W 1 /W 2 ), the noise of GN sensor (T 1 -T 2 ), denoted as δV noise   NP-NW  is fundamentally equal to that of a single nanoplate pH sensor since any signal buried under the noise of NP (T 1 ) in GN scheme (T 1 -T 2 ) would not be also detectable in T 2 .
 
     The noise and SNR of pH sensor is directly correlated to the minimum pH resolution, ΔpH min , such that ΔpH min =3×δV noise /(ΔV/ΔpH). For any pH sensor we have noise sources from device and measurement instrument as well: for instance, there are two noise sources (δV noise   NP  and δV noise   Ins ) in a single nanoplate sensor and its SNR is limited by a larger one between two competitors. Depending on the magnitude of δV noise   NP  and δV noise   Ins  we have two situations for the pH resolution of a single nanoplate sensor: 
     
       
         
           
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       pH 
                     
                     min 
                     NP 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               3 
                               ⁢ 
                               δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   V 
                                   noise 
                                   NP 
                                 
                                 / 
                                 0.059 
                               
                             
                           
                           
                             
                               ( 
                               
                                 
                                   if 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     Ins 
                                   
                                 
                                 &lt; 
                                 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     NP 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               3 
                               ⁢ 
                               δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   V 
                                   noise 
                                   Ins 
                                 
                                 / 
                                 0.059 
                               
                             
                           
                           
                             
                               ( 
                               
                                 
                                   if 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     Ins 
                                   
                                 
                                 &gt; 
                                 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     NP 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   S12 
                   ) 
                 
               
             
           
         
       
     
     On the other hand, for our GN scheme, we have three noise sources: δV noise   NP , δV noise   NW  and δ noise   Ins . Since δV noise   NW &gt;&gt;δV noise   NP , in principle there are three different cases depending on the magnitude of the measurement instrument noise δV noise   Ins . 
     (1) δV noise   Ins ≦δV noise   NP &lt;δV noise   NW : Since the signal under the noise (δV noise   NP ) in NP (T 1 ) cannot be detected in NW side, the SNR of NP-NW sensor is limited by the NP noise and thus the ideal pH resolution is ΔpH min   NP-NW ˜3δV noise   NP /0.059 where the pH sensitivity=0.059V/pH. 
     (2) δV noise   NP &lt;δV noise   Ins &lt;δV noise   NW : First in a NP-alone sensor, its pH resolution is clearly equal to 3δV noise   Ins /0.059. In a NP-NW sensor, the pH resolution of NP (T 1 ) itself is ΔpH min   NP ˜3δV noise   NP /0.059. On the other hand, NP-NW pair-wise, a voltage signal (from NP) larger than δV noise   NP  can be amplified by the factor α GN  (where α GN =W 1 /W 2 &gt;&gt;1), thus the additional competing factor is ΔpH min   NW ˜3δV noise   NW /(0.059×α GN ). The ratio of pH resolution between two competing factors is given by ΔpH min   NP /ΔpH min   NW ˜α GN  (δV noise   NP /δV noise   NW ). Since (δV noise   NP /δV noise   NW )˜1/√{square root over (W 1 /W 2 )}, ΔpH min   NP /ΔpH min   NW ≈√{square root over (W 1 /W 2 )}&gt;1. Since the overall pH resolution is limited by larger (i.e., worse) one among two competing factors, where ΔpH min   NP &gt;ΔpH min   NW  in this case, ΔpH min   NP-NW =ΔpH min   NP ˜3δV noise   NP /0.059. 
     (3) δV noise   NP &lt;δV noise   NW &lt;δV noise   Ins : This case is similar to Case (2), but here the competing resolution in NW side is ΔpH min   NW ˜3δV noise   Ins /(0.059×α GN ) since now δV noise   Ins &gt;δV noise   NW . Again, the ratio of pH resolution between two competing factors is given by ΔpH min   NP /ΔpH min   NW ˜α GN (δV noise   NP /δV noise   Ins ). Since δV noise   NW &lt;δV noise   Ins , ΔpH min   NP /ΔpH min   NW ˜α GN (δV noise   NP /δV noise   Ins )=√{square root over (α GN )}(δV noise   NW /δV noise   Ins ). Depending on the magnitude of δV noise   Ins  we have two different answers: 
     
       
         
           
             
               
                 
                   
                     
                       
                         Δ 
                         ⁢ 
                         pH 
                       
                       min 
                       NP 
                     
                     / 
                     
                       
                         Δ 
                         ⁢ 
                         pH 
                       
                       min 
                       NW 
                     
                   
                   ⁢ 
                   
                     { 
                     
                       
                         
                           
                             
                               &gt; 
                               1 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   
                                     if 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       Ins 
                                     
                                   
                                   &lt; 
                                   
                                     
                                       
                                         α 
                                         GN 
                                       
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       NW 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                     α 
                                     GN 
                                   
                                   ⁢ 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     NP 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               &lt; 
                               1 
                             
                           
                           
                             
                               ( 
                               
                                 
                                   
                                     if 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       Ins 
                                     
                                   
                                   &gt; 
                                   
                                     
                                       
                                         α 
                                         GN 
                                       
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       NW 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                     α 
                                     GN 
                                   
                                   ⁢ 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     NP 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   S13 
                   ) 
                 
               
             
           
         
       
     
     The corresponding overall pH resolution has also two different answers: 
     
       
         
           
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       pH 
                     
                     min 
                     
                       NP 
                       - 
                       NW 
                     
                   
                   = 
                   
                     
                       max 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               Δ 
                               ⁢ 
                               pH 
                             
                             min 
                             NP 
                           
                           , 
                           
                             
                               Δ 
                               ⁢ 
                               pH 
                             
                             min 
                             NW 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       { 
                       
                         
                           
                             
                               
                                 
                                   3 
                                   ⁢ 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     NP 
                                   
                                 
                                 0.059 
                               
                             
                             
                               
                                 ( 
                                 
                                   
                                     
                                       if 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         V 
                                         noise 
                                         Ins 
                                       
                                     
                                     &lt; 
                                     
                                       
                                         
                                           α 
                                           GN 
                                         
                                       
                                       ⁢ 
                                       δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         V 
                                         noise 
                                         NW 
                                       
                                     
                                   
                                   = 
                                   
                                     
                                       α 
                                       GN 
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       NP 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                           
                             
                               
                                 
                                   3 
                                   ⁢ 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     Ins 
                                   
                                 
                                 
                                   0.059 
                                   × 
                                   
                                     α 
                                     GN 
                                   
                                 
                               
                             
                             
                               
                                 ( 
                                 
                                   
                                     
                                       if 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         V 
                                         noise 
                                         Ins 
                                       
                                     
                                     &gt; 
                                     
                                       
                                         
                                           α 
                                           GN 
                                         
                                       
                                       ⁢ 
                                       δ 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       
                                         V 
                                         noise 
                                         NW 
                                       
                                     
                                   
                                   = 
                                   
                                     
                                       α 
                                       GN 
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       NP 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   ( 
                   S14 
                   ) 
                 
               
             
           
         
       
     
     If we compare the ratio of ΔpH min   NP-NW  and ΔpH min   NP , 
     
       
         
           
             
               
                 
                   
                     
                       
                         Δ 
                         ⁢ 
                         pH 
                       
                       min 
                       
                         NP 
                         - 
                         NW 
                       
                     
                     
                       
                         Δ 
                         ⁢ 
                         pH 
                       
                       min 
                       NP 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               δ 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   V 
                                   noise 
                                   NP 
                                 
                                 / 
                                 δ 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 V 
                                 noise 
                                 Ins 
                               
                             
                           
                           
                             
                               ( 
                               
                                 
                                   
                                     if 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       Ins 
                                     
                                   
                                   &lt; 
                                   
                                     
                                       
                                         α 
                                         GN 
                                       
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       NW 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                     α 
                                     GN 
                                   
                                   ⁢ 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     NP 
                                   
                                 
                               
                               ) 
                             
                           
                         
                         
                           
                             
                               1 
                               / 
                               
                                 α 
                                 GN 
                               
                             
                           
                           
                             
                               ( 
                               
                                 
                                   
                                     if 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       Ins 
                                     
                                   
                                   &gt; 
                                   
                                     
                                       
                                         α 
                                         GN 
                                       
                                     
                                     ⁢ 
                                     δ 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     
                                       V 
                                       noise 
                                       NW 
                                     
                                   
                                 
                                 = 
                                 
                                   
                                     α 
                                     GN 
                                   
                                   ⁢ 
                                   δ 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     V 
                                     noise 
                                     NP 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   S15 
                   ) 
                 
               
             
           
         
       
     
     For the first case of eq. (S15) √{square root over (α GN )}δV noise   NP &lt;δV noise   Ins &lt;α GN δV noise   NP , thus 
               1     α   GN       &lt;       δ   ⁢           ⁢     V   noise   NP         δ   ⁢           ⁢     V   noise   Ins         &lt;     1       α   GN         &lt;   1.         
So, in the Case (3), regardless of the magnitude of δV noise   Ins  we always achieve smaller (i.e., better) pH resolution in GN (NP-NW) scheme compared to a single NP sensor.
 
     We summarize pH resolution of a single NP sensor (ΔpH min   NP ) and GN scheme (ΔpH min   NP-NW ) for the three possible cases in the following table: 
     
       
         
           
               
             
               
                 TABLE S1 
               
             
            
               
                   
               
               
                 The comparison of pH resolution for NP 
               
               
                 sensor alone and proposed GN scheme. 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 Comparison 
               
               
                   
                 NP alone (T 1 ) 
                 GN scheme (T 1 -T 2 ) 
                 of ΔpH min   
               
               
                   
                   
               
            
           
           
               
               
               
               
            
               
                 δV noise   Ins  &lt; 
                 3δV noise   NP /0.059 
                 3δV noise   NP /0.059 
                 ΔpH min   NP  = 
               
               
                 δV noise   NP  &lt; 
                   
                   
                 ΔpH min   NP-NW   
               
               
                 δV noise   NW   
               
               
                 δV noise   NP  &lt; 
                 3δV noise   Ins /0.059 
                 3δV noise   NP /0.059 
                 ΔpH min   NP  &gt; 
               
               
                 δV  noise   Ins  &lt; 
                   
                   
                 ΔpH min   NP-NW   
               
               
                 δV noise   NW   
               
               
                 δV noise   NP  &lt; 
                 3δV noise   Ins /0.059 
                 3δV noise   NP /(0.059 × 
                 ΔpH min   NP  &gt;&gt; 
               
               
                 δV noise   NW  &lt; 
                   
                 α GN ) or 3δV noise   NP /0.059 
                 ΔpH min   NP-NW   
               
               
                 δV noise   Ins   
               
               
                   
               
            
           
         
       
     
     Among all the three possible cases, GN scheme has its advantage over NP-alone sensor in terms of pH resolution in Cases (2) and (3) in which the pH resolution of GN scheme is much smaller than that of a single NP sensor. Since Cases (2) and (3) are the dominant situation especially for the point-of-care devices whose measurement instrument is not sophisticated enough (δV noise   NP ˜1-10 μV in general), the GN scheme always enhance the minimum pH resolution by the factor of α GN  for the sensors with relatively low-precision instruments. 
     An example of one embodiment of a device  10  for measuring pH, including monitoring a change in pH over time, is schematically illustrated in  FIGS. 1( c ), 1( d )  and  FIG. 8 . The device has a sensor  20  and a transducer  200 . The sensor  20  comprises a fluid gate  30  and corresponding fluid gate bias  40  (V G,1 ). The fluid gate  30  is at least partially immersed in a material or fluid  50  in which pH is measured. A sensor channel  60  is positioned between a source electrode  70  and a drain electrode  80  along with a sensing surface  65  that physically contacts and supports the fluid  50 . The sensor channel may further comprise a layer  62  that interacts with the fluid to generate a detectable electrical property, such as transconductance that is modulated based on the pH of the fluid. The layer  62  may be an oxide layer, as illustrated in  FIG. 1( a ) . In an embodiment, the sensor channel  60  is a nanoplate (labeled NP in  FIG. 1( d ) ). 
     The transducer  200  comprises a top or bottom gate  210  (see  FIG. 1( d )  top panel for bottom gate embodiment and bottom panel for top gate embodiment) and corresponding gate bias  240  (V G,2 ). In this embodiment, source and drain electrodes are illustrated as corresponding to the source  70  and drain  80  electrodes of the sensor. Optionally, source and drain electrodes used with the transducer  200 , are separate and distinct from those used with the sensor  20 . A transducer channel  260  is positioned between the source and drain electrodes. The illustrated embodiment depicts fluid droplet  50  that is not in contact with the transducer  200 . Optionally, the sensor and transducer channels from a fluid well for receiving a fluid  50 , in which case the transducer is configured such that the transconductance of the transducer is substantially independent or is independent of pH changes in the fluid and the transducer may have a transducer surface in contact with the fluid. “Substantially independent” refers to a transconductance that varies less than 10%, less than 5%, less than 1%, or less than 0.1%, with a selected change in pH. Referring to  FIGS. 1( c ), ( d ) , and  8 , the transducer channel may be nanowire (NW). The sensor and transducer channel widths are W 1  and W 2 , respectively. Similarly, L 1  and L 2  defines the sensor and transducer channel lengths. The illustrated embodiment shows those lengths as equal and corresponding to the distance between the source and drain. Optionally, the lengths are not equal. Optionally, any of the lengths may be less than the separation distance between the source and drain, such as by patterning of sensor, transducer, source or drain shape, including by one or more channel ends that are separated from source and drain, but electrically connected thereto by an electrical interconnection. In use, a channel current  300  (I D ), including a source-drain current for each of the sensor (I D,1 ) and transducer (I D,2 ) is monitored along with drain bias  400  (V DD ), including the drain bias of the sensor (V D,1 ) and the transducer (V D,2 ), thereby measuring pH, including detecting changes in pH, by the amplification factor arising from the unique sensor and transducer configurations. 
     References 
     
         
         [1] Y. Taur and T. H. Ning,  Fundamentals of Modern VLSI Devices , Cambridge University Press, Cambridge, UK, 1998. 
         [2] S. L. David E. Yates and T. W. Healy, “Site-binding model of the electrical double layer at the oxide/water interface,”  Journal of the Chemical Society, Faraday Transactions  1 : Physical Chemistry in Condensed Phases , vol. 70, pp. 1807-1818, 1974. 
         [3] M. J. Deen, M. W. Shinwari, J. C. Ranuárez, and D. Landheer, “Noise considerations in field-effect biosensors,”  Journal of Applied Physics , vol. 100, p. 074703 (2006). 
       
    
     Example 3 
     Ultrasensitive pH Detection by Nanowire-Nanoplate Combination Sensor 
     A schematic demonstrating the nanowire-nanoplate combination sensor is shown in  FIG. 9 . Two devices of varying width are biased in parallel. T 1  is a nanoplate device with width of 2 μm, and T 2  is a nanowire device with width of 50 nm. The output current is measured at the shorted drain nodes of the devices as indicated. This current is the sum of the source-drain current for both devices: I=I DS1 +I DS2 . 
     The two transistors have separate fluid wells and separate reference electrodes, which can be used to control the separate fluid potentials separately. T 1  is considered to be the sensing element, and is exposed to solutions of varying pH with a fixed gate bias, V FG2 . T 2  is the “transducer” element, and is exposed to only a reference solution throughout the experiments. Transfer characteristics of T 2  are used as the output characteristic (by sweeping V FG1 ), while the pH of the solutions over T 2  is the input characteristic. As the pH is changed over T 1 , large changes in the total current I will be induced due to the surface potential changes over T 1 . In order to counterbalance these large changes in current to preserve the same total current I, very large shifts in the I-V FG2  are required, as illustrated in  FIG. 11 . These large shifts are amplified by a factor of approximately W 2 /W 1 (about 40 in this case). This leads to a dramatic decrease in the smallest pH shift that is detectable by the system. 
     Individual transfer characteristics of the nanowire device and the nanoplate device at five different pH values are shown in  FIG. 10 . The nanowire current is seen to be significantly lower (≈20×) than the current through the plate. A blown up view of the nanoplate as a function of changing pH is shown in  FIG. 10B . Values around physiological pH are selected for higher relevance, and pH points are designed very close to one another, since this scheme lends itself well for very high sensitivity but low dynamic range measurements. The current through T 1 , the nanoplate in the pH solutions, I DS1 , can be seen to monotonically increase with increasing pH, at about 12-13 nA per 0.1 pH increase. We highlight the vertical line at V FG1 =−0.9V, since this is the low constant bias applied to T 1  to keep it in accumulation during the experiments. 
     The two devices are then connected as shown in  FIG. 9 , and exposed to the different pH solutions. Transfer characteristics are extracted by sweeping V FG1  and measuring the total current I total . Results are shown in  FIG. 11 . The method for determining the shift in “threshold voltage” is also demonstrated, where essentially we take a constant current, and determine where each curve intersects a horizontal line through this current. Five sweeps are taken per pH point to quantify the average noise of the nanoplate (3.45 mV), the nanowire (2.63 mV), and of the combined system. Results for each shift, including the noise of the combined system are shown in Table 2. Volts per pH is the sensitivity factor previously discussed, given by: 
     
       
         
           
             
               
                 
                   S 
                   = 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         t 
                       
                     
                     ΔpH 
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     This sensitivity factor is approximately equal to:
 
 S =α(0.059 V/pH)  (2)
 
     Using this sensitivity factor and the extracted noise for each point, we can calculate the minimum detectable pH resolution, given by: 
     
       
         
           
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       pH 
                     
                     min 
                   
                   = 
                   
                     3 
                     
                       
                         α 
                         / 
                         δ 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         V 
                         t 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
     These values are plotted in Table 2. For the four shifts noted, the highest ΔpH min  observed is less than 0.002 pH units, around an order of magnitude better than any pH sensor currently available. A comparison of this minimum pH resolution to individual nanoplate, nanowire, and commercial devices is shown in  FIG. 12 . This technique has very small dynamic range, which is limited by the window in which the transfer characteristics are swept (for example, from +1 to −2 V in  FIG. 11 ). It is intended as a very sensitive measurements of pH values that will not change significantly over time—for example, for use as intracellular or extracellular pH detectors in tumor cell environments. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Summary of sensitivity and achievable minimum pH resolutions. 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Sensitivity: 
                 Noise: 
                 Signal to 
                 pH Resolution 
               
               
                 pH Shift 
                 S (V/pH) 
                 δV t  (mV) 
                 Noise Ratio 
                 pH min   
               
               
                   
               
               
                  6.85 to 6.97 
                 4.24 
                 2.36 
                 1798 
                 0.00167 
               
               
                 6.97 to 7.1 
                 4.51 
                 1.28 
                 3525 
                 0.00085 
               
               
                  7.1 to 7.24 
                 3.72 
                 2.01 
                 1848 
                 0.00162 
               
               
                 7.24 to 7.4 
                 3.94 
                 1.10 
                 3582 
                 0.00084 
               
               
                   
               
            
           
         
       
     
     In conclusion, we demonstrate the use of a nanowire-nanoplate combination sensor for the detection of pH units down to 0.002, which is an order of magnitude better than commercial sensors and is, to our knowledge, the most sensitive bioFET pH sensor reported to date. An increase in the observed signal is achieved by a huge difference in the source-drain currents of the two devices, which is used to induce a large threshold shift for the nanowire device due to pH changes on the nanoplate device. The measured noise is not enhanced in this process due to an environmental noise factor that is larger than the intrinsic nanoplate and nanowire noise. As long as the intrinsic nanoplate noise is kept to lower than the environmental noise divided by α, the amplification factor, the resulting pH sensitivity will be α(0.059 mV/pH). This method for ultrasensitive detection can be used for many applications. 
     All references throughout this application, for example patent documents including issued or granted patents or equivalents; patent application publications; and non-patent literature documents or other source material; are hereby incorporated by reference herein in their entireties, as though individually incorporated by reference, to the extent each reference is at least partially not inconsistent with the disclosure in this application (for example, a reference that is partially inconsistent is incorporated by reference except for the partially inconsistent portion of the reference). Various patent documents are specifically referred to for the various electronic devices and processes related thereto, including FETs and related components for use in various applications, including: US 20110086352; WO 2012/078340; US 20080280776; WO 2010/037085; WO 2011/163058; WO 2013/016486. 
     The terms and expressions which have been employed herein are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. Thus, it should be understood that although the present invention has been specifically disclosed by preferred embodiments, exemplary embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims. The specific embodiments provided herein are examples of useful embodiments of the present invention and it will be apparent to one skilled in the art that the present invention may be carried out using a large number of variations of the devices, device components, methods steps set forth in the present description. As will be obvious to one of skill in the art, methods and devices useful for the present methods can include a large number of optional composition and processing elements and steps. 
     When a group of substituents is disclosed herein, it is understood that all individual members of that group and all subgroups, are disclosed separately. When a Markush group or other grouping is used herein, all individual members of the group and all combinations and subcombinations possible of the group are intended to be individually included in the disclosure. Specific names of compounds are intended to be exemplary, as it is known that one of ordinary skill in the art can name the same compounds differently. Every formulation or combination of components described or exemplified herein can be used to practice the invention, unless otherwise stated. 
     Whenever a range is given in the specification, for example, a ratio range, a size range, a pH range, a sensitivity range, a temperature range, a time range, or a composition or concentration range, all intermediate ranges and subranges, as well as all individual values included in the ranges given are intended to be included in the disclosure. It will be understood that any subranges or individual values in a range or subrange that are included in the description herein can be excluded from the claims herein. 
     All patents and publications mentioned in the specification are indicative of the levels of skill of those skilled in the art to which the invention pertains. References cited herein are incorporated by reference herein in their entirety to indicate the state of the art as of their publication or filing date and it is intended that this information can be employed herein, if needed, to exclude specific embodiments that are in the prior art. For example, when composition of matter are claimed, it should be understood that compounds known and available in the art prior to Applicant&#39;s invention, including compounds for which an enabling disclosure is provided in the references cited herein, are not intended to be included in the composition of matter claims herein. 
     As used herein, “comprising” is synonymous with “including,” “containing,” or “characterized by,” and is inclusive or open-ended and does not exclude additional, unrecited elements or method steps. As used herein, “consisting of” excludes any element, step, or ingredient not specified in the claim element. As used herein, “consisting essentially of” does not exclude materials or steps that do not materially affect the basic and novel characteristics of the claim. In each instance herein any of the terms “comprising”, “consisting essentially of” and “consisting of” may be replaced with either of the other two terms. The invention illustratively described herein suitably may be practiced in the absence of any element or elements, limitation or limitations which is not specifically disclosed herein. 
     One of ordinary skill in the art will appreciate that starting materials, biological materials, reagents, synthetic methods, purification methods, analytical methods, assay methods, and biological methods other than those specifically exemplified can be employed in the practice of the invention without resort to undue experimentation. All art-known functional equivalents, of any such materials and methods are intended to be included in this invention. The terms and expressions which have been employed are used as terms of description and not of limitation, and there is no intention that in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention claimed. Thus, it should be understood that although the present invention has been specifically disclosed by preferred embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims.