1. Theory

Definition: Sensor FETs are field-effect transistors whose gate region is exposed to a gas or liquid, so a chemical or biological signal changes the channel current.
Scope: The ion-sensitive FET (ISFET), the chemical FET (ChemFET, general name for gas and liquid chemical sensors), the biological FET (BioFET, with a receptor layer for proteins or DNA) and the electrolyte-gated organic FET (EGOFET).
Standard transistor core: The channel follows the Long Channel MOSFET (or Thin-Film Transistor) page; only the sensing interface is new.
Electrolyte gate: In an ISFET the metal gate is replaced by an electrolyte and a reference electrode, so the solution itself acts as the gate.
Surface potential: Ions or molecules binding to the gate insulator change its surface potential, which shifts the threshold voltage.
Nernstian limit: The pH response cannot exceed about 59 mV/pH at 298 K; good insulators (e.g. $T a_{2} O_{5}$ , $A l_{2} O_{3}$ ) approach it.
Debye screening: Ions in the solution screen charges over the Debye length ( $\approx 0.8$ nm at 150 mM), the electrolyte analogue of a depletion width.

2. Working Principle

ISFET: Protons bind to amphoteric surface sites (site-binding model), changing the surface potential and $V_{T H}$ in proportion to pH.
BioFET: A captured charged biomolecule shifts $V_{T H}$ ; most of its charge is screened in high-salt solution unless low ionic strength, small receptors or high-frequency detection are used.
Enzyme FET (ENFET): An enzyme layer converts the target molecule into a pH change that an ISFET can read.
EGOFET: An electrolyte forms a very high-capacitance double layer on an organic channel, giving low-voltage operation limited by ionic response time.
Gas ChemFET: A catalytic Pd gate absorbs hydrogen, forming an interface dipole that shifts $V_{T H}$ .
Noise and detection limit: Small sensors (e.g. nanowires) give large relative signals but higher $1/ f$ noise; subthreshold operation boosts the signal.

3. Applications

Solid-state pH sensing: Glass-free, robust pH probes for food, beverage and in-line industrial monitoring.
Semiconductor DNA sequencing: Massive ISFET arrays detect the protons released as each nucleotide is added.
Hydrogen leak detection: Pd-gate FET sensors for fuel-cell and industrial safety.
Point-of-care biosensing and bioelectronics (emerging): BioFET and EGOFET devices for label-free biomarker detection and tissue interfacing.

Ion-Sensitive FET (ISFET)

Name	Formula	Related Formulae	Variables/Constants
ISFET threshold voltage	$V_{T H} = E_{r e f} - ψ_{0} + χ_{so l} - \frac{Φ _{S i}}{q} - \frac{Q _{o x} + Q _{ss} + Q _{B}}{C _{o x}} + 2 ϕ_{F}$		$E_{r e f} : p o t e n t ia l o f t h e r e f er e n ce e l ec t r o d e r e l a t i v e t o v a c uu m$ $ψ_{0} : p o t e n t ia l d r o p a t t h e e l ec t r o l y t e - in s u l a t or in t er f a ce, w hi c h d e p e n d s o n p H$ $χ_{so l} : s u r f a ce d i p o l e p o t e n t ia l o f t h e so l u t i o n$ $Φ_{S i} : s i l i co n w or k f u n c t i o n$ $Q_{o x}, Q_{ss}, Q_{B} : o x i d e, s u r f a ce s t a t e an d d e pl e t i o n c ha r g e p er u ni t a r e a$ $C_{o x} : c a p a c i t an ce p er u ni t a r e a o f t h e g a t e in s u l a t or$ $ϕ_{F} : F er mi p o t e n t ia l o f t h e s u b s t r a t e$
Site-binding model	$K_{a} = \frac{[ M O ^{-} ] a _{H, s}}{[ MOH ]}, K_{b} = \frac{[ MOH ] a _{H, s}}{[ MO H _{2}^{+} ]}$	$a_{H, s} = a_{H, b} exp (- \frac{q ψ _{0}}{k _{B} T}), p H_{p z c} = \frac{1}{2} (p K_{a} + p K_{b})$	$K_{a}, K_{b} : d i ssoc ia t i o n co n s t an t s o f t h e am p h o t er i c s u r f a ce h y d r o x y l g r o u p s$ $[MOH], [M O^{-}], [MO H_{2}^{+}] : s u r f a ce s i t e d e n s i t i es$ $a_{H, s}, a_{H, b} : p r o t o n a c t i v i t y a t t h e s u r f a ce an d in t h e b u l k o f t h e so l u t i o n$ $p H_{p z c} : p H o f t h e p o in t o f z er o c ha r g e, w h er e t h e s u r f a ce i s n e u t r a l$ $k_{B} : B o l t z mann co n s t an t$
pH sensitivity (Nernstian limit)	$\frac{\partial ψ _{0}}{\partial p H} = - 2.303 α \frac{k _{B} T}{q}$	$α = \frac{1}{\frac{2.303 k _{B} T C _{d l}}{q ^{2} β _{in t}} + 1}, α \leq 1$	$α : se n s i t i v i t y p a r am e t er, 1 f or an i d e a l N er n s t ian r es p o n se o f ab o u t 59 mV / p H a t 298 K$ $C_{d l} : d i f f er e n t ia l d o u b l e - l a y er c a p a c i t an ce$ $β_{in t} : in t r in s i c b u f f er c a p a c i t y o f t h e s u r f a ce (n u mb er o f s i t es t im es t h e i r r es p o n se t o p H)$ $k_{B} : B o l t z mann co n s t an t$
Debye length	$λ_{D} = \frac{ε _{r} ε _{0} k _{B} T}{2 N _{A} q ^{2} I}$	$λ_{D} \approx \frac{0.304 nm}{I [ M ]} (1:1 electrolyte in water at 25 C)$	$λ_{D} : D e b y e scr ee nin g l e n g t h o f t h e e l ec t r o l y t e$ $I : i o ni c s t r e n g t h in m o l / m^{3}$ $N_{A} : A v o g a d r o co n s t an t$ $ε_{r} : r e l a t i v e p er mi tt i v i t y o f t h e so l u t i o n$ $k_{B} : B o l t z mann co n s t an t$
Screened potential and double-layer capacitance	$ψ (x) = ψ_{0} exp (- \frac{x}{λ _{D}})$	$\frac{1}{C _{d l}} = \frac{1}{C _{H}} + \frac{1}{C _{GC}}, C_{GC} = \frac{ε _{r} ε _{0}}{λ _{D}} cosh (\frac{q ψ _{d}}{2 k _{B} T})$	$ψ (x) : p o t e n t ia l in t h e e l ec t r o l y t e a t d i s t an ce x f r o m t h e s u r f a ce (l in e a r i z e d D e b y e - H u c k e l, s ma l l ψ_{0})$ $C_{H} : H e l mh o l t z (S t er n) l a y er c a p a c i t an ce p er u ni t a r e a$ $C_{GC} : G o u y - C ha p man d i f f u se l a y er c a p a c i t an ce$ $ψ_{d} : p o t e n t ia l a t t h e o u t er H e l mh o l t z pl an e (t h e s t a r t o f t h e d i f f u se l a y er)$ $k_{B} : B o l t z mann co n s t an t$
Small-signal response	$Δ I_{D} = g_{m} Δ V_{T H}$	$\frac{Δ I _{D}}{I _{D}} \approx \frac{q Δ ψ _{0}}{m k _{B} T} (weak inversion)$	$Δ V_{T H} : t h r es h o l d s hi f t c a u se d b y t h e ana l y t e, f or e x am pl e 2.303 α (k_{B} T / q) p er p H u ni t$ $g_{m} : t r an sco n d u c t an ce o f t h e t r an s i s t or$ $m : b o d y f a c t or o f t h e t r an s i s t or$ $(the relative sensitivity is the largest in the subthreshold region)$ $k_{B} : B o l t z mann co n s t an t$

Biological FET (BioFET)

Name	Formula	Related Formulae	Variables/Constants
Threshold shift due to bound charge	$Δ V_{T H} \approx - \frac{q z N _{b}}{C _{d l}} exp (- \frac{d}{λ _{D}})$	$C_{d l} \approx \frac{ε _{r} ε _{0}}{λ _{D}} \Rightarrow Δ V_{T H} \approx - \frac{q z N _{b} λ _{D}}{ε _{r} ε _{0}} exp (- \frac{d}{λ _{D}})$	$Δ V_{T H} : f i r s t - or d er t h r es h o l d s hi f t f or a c ha r g e d l a y er o f bi o m o l ec u l es$ $z : c ha r g e n u mb er o f e a c h b o u n d m o l ec u l e$ $N_{b} : s u r f a ce d e n s i t y o f b o u n d m o l ec u l es$ $C_{d l} : d o u b l e - l a y er c a p a c i t an ce p er u ni t a r e a t ha t scr ee n s t h e s u r f a ce c ha r g e (n o t t h e m u c h s ma l l er o x i d e c a p a c i t an ce p er u ni t a r e a 1/ C_{o x})$ $d : d i s t an ce o f t h e c ha r g e f r o m t h e g a t e in s u l a t or$ $λ_{D} : D e b y e scr ee nin g l e n g t h$
Limit of detection	$L O D = \frac{3 σ _{n o i se}}{S}$	$S = \frac{\partial V _{T H}}{\partial c}$	$L O D : l o w es t ana l y t e co n ce n t r a t i o n t ha t g i v es a s i g na l t h r ee s t an d a r d d e v ia t i o n s ab o v e t h e n o i se$ $σ_{n o i se} : s t an d a r d d e v ia t i o n o f t h e n o i se r e f er r e d t o t h e g a t e$ $S : se n s i t i v i t y o f t h e t h r es h o l d v o l t a g e t o t h e ana l y t e co n ce n t r a t i o n c$
Low-frequency noise (Hooge)	$\frac{S _{I}}{I _{D}^{2}} = \frac{α _{H}}{N _{c} f}$		$S_{I} : c u r r e n t n o i se p o w er s p ec t r a l d e n s i t y$ $α_{H} : H oo g e p a r am e t er$ $N_{c} : t o t a l n u mb er o f c a r r i er s in t h e c hann e l, s ma l l f or nan o w i r es so t ha t t h e n o i se i s l a r g er$ $f : f r e q u e n cy$
Enzyme-modified FET (ENFET)	$v = \frac{V _{ma x} [ S ]}{K _{M} + [ S ]}$		$v : r a t e o f t h e e n z y m e r e a c t i o n w hi c h c han g es t h e l oc a l p H se n se d b y t h e I S F E T$ $V_{ma x} : ma x im u m r e a c t i o n r a t e$ $K_{M} : M i c ha e l i s co n s t an t$ $[S] : s u b s t r a t e co n ce n t r a t i o n$

Electrolyte-Gated Organic FET (EGOFET)

Name	Formula	Related Formulae	Variables/Constants
Electrolyte-gated transistor current	$I_{D} = μ C_{d l} \frac{Z}{L} [(V_{GS} - V_{T H}) V_{D S} - \frac{V _{D S}^{2}}{2}]$	$C_{d l} \approx 1 to 10 μ F/c m^{2}$	$C_{d l} : e l ec t r i c d o u b l e - l a y er c a p a c i t an ce p er u ni t a r e a, m u c h l a r g er t han f or a so l i d o x i d e so t ha t t h e d e v i ce w or k s b e l o w 1 V$ $μ : c a r r i er m o bi l i t y o f t h e or g ani c se mi co n d u c t or$ $V_{GS} : p o t e n t ia l o f t h e g a t e e l ec t r o d e in t h e e l ec t r o l y t e r e l a t i v e t o t h e so u r ce$
Ionic response time	$τ_{i o n} \approx R_{e l} C_{d l} A$		$τ_{i o n} : c ha r g in g t im e o f t h e d o u b l e l a y er, w hi c h l imi t s t h e s w i t c hin g s p ee d$ $R_{e l} : r es i s t an ce o f t h e e l ec t r o l y t e b e tw ee n t h e g a t e an d t h e c hann e l (in o hm)$ $A : a r e a o f t h e c hann e l$

Gas-Sensitive ChemFET

Name	Formula	Related Formulae	Variables/Constants
Hydrogen-sensitive Pd-gate response	$θ = \frac{K p _{H_{2}}}{1 + K p _{H_{2}}}$ $Δ V_{T H} = Δ V_{ma x} θ$		$θ : h y d r o g e n co v er a g e o f t h e p a l l a d i u m - in s u l a t or in t er f a ce f or d i ssoc ia t i v e a d sor pt i o n$ $K : e q u i l ib r i u m co n s t an t o f h y d r o g e n a d sor pt i o n$ $p_{H_{2}} : p a r t ia l p r ess u r e o f h y d r o g e n$ $Δ V_{ma x} : s a t u r a t e d s hi f t o f t h e t h r es h o l d v o l t a g e c a u se d b y t h e d i p o l e l a y er a t t h e in t er f a ce$ $(Lundstrom, Shivaraman and Svensson, J. Appl. Phys. 46, 3876 (1975))$

Important Questions

Ques: Why does the pH response of an ISFET not exceed 59 mV/pH?

The surface potential is set by the balance between the protons bound to the amphoteric surface groups and the screening charge in the electrolyte. In the ideal case the surface groups are so numerous that the surface potential follows the Nernst equation, $\partial ψ_{0} / \partial p H = - 2.303 k_{B} T / q \approx - 59 mV/pH$ at 298 K. The parameter $α = 1/ [2.303 k_{B} T C_{d l} / (q^{2} β_{in t}) + 1]$ is always below 1, and approaches 1 only when the buffer capacity of the surface $β_{in t}$ is much larger than the double-layer capacitance, so the Nernst value is a ceiling. Insulators such as Ta $_{2}$ O $_{5}$ and Al $_{2}$ O $_{3}$ have a higher $β_{in t}$ than SiO $_{2}$ and respond closer to the limit. Reference: R.E.G. van Hal, J.C.T. Eijkel, and P. Bergveld, “A novel description of ISFET sensitivity with the buffer capacity and double-layer capacitance as key parameters,” Sens. Actuators B 24, 201 (1995); P. Bergveld, “Thirty years of ISFETOLOGY,” Sens. Actuators B 88, 1 (2003).

Ques: Why can a BioFET not detect charge in a high-salt solution?

Charges in the electrolyte are screened over the Debye length, and the potential from a bound molecule decays as $exp (- d / λ_{D})$ . In physiological solution (ionic strength about 150 mM) $λ_{D} \approx 0.8 nm$ , much shorter than the size of an antibody (about 10 nm), so most of the charge of a captured protein is screened and the threshold shift is small. This is the Debye screening problem: it is reduced by working at low ionic strength, using smaller receptors such as aptamers or antibody fragments, or detecting at a high frequency where the screening layer cannot follow. Reference: E. Stern et al., “Importance of the Debye screening length on nanowire field effect transistor sensors,” Nano Lett. 7, 3405 (2007); Y. Cui, Q. Wei, H. Park, and C.M. Lieber, “Nanowire nanosensors for highly sensitive and selective detection of biological and chemical species,” Science 293, 1289 (2001).

Ques: Why are nanowire sensors both more sensitive and noisier?

A nanowire has a high surface-to-volume ratio, so a surface charge changes the potential of a large fraction of the carriers and the relative change in current is large. Its small number of carriers $N_{c}$ also raises the low-frequency noise through the Hooge relation $S_{I} / I_{D}^{2} = α_{H} / (N_{c} f)$ . The limit of detection, $L O D = 3 σ_{n o i se} / S$ , is therefore set by the ratio of the signal to the noise and does not necessarily improve with size; operating in the subthreshold region increases the signal because $Δ I_{D} / I_{D} \approx q Δ ψ_{0} / (m k_{B} T)$ . Reference: F.N. Hooge, “1/f noise sources,” IEEE Trans. Electron Devices 41, 1926 (1994); Y. Cui, Q. Wei, H. Park, and C.M. Lieber, Science 293, 1289 (2001).

Quartz 5

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Sensor Field Effect Transistors (ISFET, ChemFET, BioFET, EGOFET)