SimulationofthepHSensingCapabilityofanOpen-GateGaN-basedTransistor

M.Sciullo,E.E.Patrick,andM.E.Law

GaN HEMTBiosensorTechnology

Source:bccResearch,GlobalMarketsandTechnologies forSensors, Published: April2013bccResearch ReportCode:IAS006E

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GaNHE

MTBiosen

sors

• Matureexperimentalstudies• Noexistingcommercial

softwarepackageforthispurpose

• Needforsensoroptimizationviasimulation

Approach

3

• SimulationofpHSensor• UsingFLorida Object-OrientedDeviceSimulator(FLOODS)

BulkSemiconductor

Contacts Bulk Electrolyte Electrolyte/SemiconductorInterface

Electron/holetransport

Source/Drain-Ohmic

Iontransport Surfacereactions

Electrostaticpotential

Electrostaticpotential

Adsorbedmolecularcharge

Polarizationcharge

Physics

GaN

AlGaNS D2DEG

SiN

Electrolyte

SiN

Approach:BulkElectrolyte

! !"!!" = !∇ !!!"! !"! ∇! + !!"!! ∇ !"! !!!!!!

!! !"!!" = !∇ −!!!"! !"! ∇! + !!"!! ∇ !"! !!!!!!!!

! !!

!" = !∇ !!!! !! ∇! + !!!! ∇ !! !!!!!!!

! !!!" = !∇ −!!!! !! ∇! + !!!! ∇ !! !!!!!!!!!!

Substrate

GaN

AlGaNDoubleLayer

NitrideElectrolyte

Nitride

2DEG

Source Drain

1μm1.5μm 1.5μmConservationofCharge(PoissonEq.)

MassBalance(ContinuityEq.)

Approach:BulkSemiconductor

Substrate

GaN

AlGaNDoubleLayer

NitrideElectrolyte

Nitride

2DEG

Source Drain

1μm1.5μm 1.5μm

!∇!! = ! ! − ! + !! − !! !!!

!"!" = !−!"!!∇

!!!! !!!!!! !"!" = !!"!!∇!!!! !!!! ! = !!!! !!!!!" !! ! = !!!! !!"!!! !!

ConservationofCharge(PoissonEq.)

MassBalance(ContinuityEq.)

Approach:DoubleLayer/Oxide/Nitride

!∇!! = 0!!!

!/!

ConservationofCharge(PoissonEq.)

MassBalance(ContinuityEq.)

Substrate

GaN

AlGaN

NitrideElectrolyte

Nitride

2DEG

Source Drain

1μm1.5μm 1.5μm

DoubleLayer

DoubleLayer d

Approach:SurfaceAdsorption

7

contain N types of ions is governed by the potential !!z" thatis determined by the Poisson–Boltzmann equation,12

"r"0d2

dz2!!z" = #!z" , !1"

#!z" = ! e#i

N

zini,0 exp$! zie%!!z" ! UG&kBT

' , !2"

where zi is the ion valency, e is the positive elementarycharge, ni,0 is the concentration of ion species i, and "r is therelative dielectric constant of the entire solvent. We use SIunits except where specified otherwise and kBT is the thermalenergy at temperature T.

In order to determine $adsorbed, we employ the so-calledsite-binding model for amphoteric oxide surfaces.1,13 Thismodel characterizes the surface reactions by two dissociationconstants K1 and K2 that reflect the following reactions:

SOH2+ ! SOH + H+, !3"

SOH! SO! + H+. !4"

Here, S denotes an oxide molecular site (GaxOy in thepresent case) with the bonded hydroxyl group OH. Thesetwo types of reactions lead to an amphoteric behavior. Whena proton gets attached to the hydroxyl group, the site getspositively charged. A dissociation, on the other hand, createsa negatively charged site. The net surface charge density isgiven by

$adsorbed = e!%SOH2+ ! %SO!" , !5"

where %SOH2+ and %SO! are the charge densities of the positive

and negative sites, respectively. The total number of surfacegroups per unit area is then given by nS=%SOH+%SOH2

+

+%SO!, where %SOH denotes the density of electrically neutralsites. As shown in Healy et al.,13 the resulting dissociationconstants K1 and K2 are given by

K1 =%SOH%SOH2

+exp(! e!!ox ! UG"

kBT! cpH) , !6"

K2 =%SO!

%SOHexp(! e!!ox ! UG"

kBT! cpH) , !7"

with K1 referring to Eq. (3) and K2 to Eq. (4), and cpH=pH ln 10. We note that the pH value equals the negativedecadic logarithm of the H+ concentration, divided by M,i.e., by mole per liter. By combining expressions Eqs.(5)–(7), we finally obtain the net surface charge at the am-photeric oxide–electrolyte interface as

$adsorbed = enSexp!! y0 ! cpH" ! K1K2 exp!y0 ! cpH"

K1 + exp!! y0 ! cpH" + K1K2 exp!y0 ! cpH",

!8"

where we have introduced the abbreviation y0=e!!ox!UG" /kBT.

For the present application, we have taken into acountthree different types of ions, namely (i) singly charged cat-

ions and (ii) singly charged anions with a fixed concentrationof 100 mM that represent dissolved NaCl, (iii) a Hepes so-lution consisting of doubly charged cations with a concentra-tion of 10 mM plus 20 mM singly charged anions to guaran-tee electrical neutrality. Any change of the pH value iscompensated by a corresponding increase in the concentra-tion of singly charged anions. Since we consider a symmetricmonovalent salt and a high concentration of asymmetric di-valent Hepes, a closed-form solution of the Poisson–Boltzmann equation in the electrolyte region is not possible.However, the numerical effort required to solve this equationis negligible.

B. Model of GaN heterostructure

The potential at the surface exposed to the electrolytesets the boundary value for the potential distribution and theresulting spatial dependence of the band edge within thesemiconductor device. As mentioned before, variations of thechemical features of the electrolyte, i.e., the pH value or theionic composition, lead to detectable changes of $adsorbed and!ox. The relevant part in the semiconductor is the 2DEG thatresponds sensitively to slight changes in the spatial variationof the conduction band edge.

We consider a nitride heterostructure, grown along thehexagonal [0001] direction, that is of either Ga-face orN-face polarity. In this section, we focus on the Ga-facestructure with a schematic cross section shown in Fig. 1. Thestructure consists of a 5-nm-thick oxide on top of a 3 nmstrain-relaxed GaN layer, followed by 35 nm of anAl0.28Ga0.72N barrier, grown on top of a 1.5 &m strain re-laxed GaN layer. The latter is assumed to be homogeneouslydoped with a carrier concentration of n=1016 cm!3. Thisstructure is a fairly typical design for GaN-based sensors thathave been fabricated by several groups.14,15 The most signifi-cant features of AlGaN/GaN heterostructures are the hugespontaneous and piezoelectric polarization fields. Both typesof polarizations are included in our present calculations. Thedivergence of the total polarization across the interface be-tween adjacent layers is equivalent to a fixed interfacial sheetcharge density. There is a positive polarization charge at theleft AlGaN/GaN interface near the 2DEG in Fig. 1 with atheoretical value of $polarization=1.37'1013 cm!2 that is com-pensated at the right AlGaN/GaN interface.16,17 The result-

FIG. 1. Schematic layout of the calculated heterostructure including theinterface charge densities. Their magnitudes, in units of 1013 e /cm2, areindicated by closed symbols and the axis to the left.

033703-2 Bayer, Uhl, and Vogl J. Appl. Phys. 97, 033703 (2005)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:128.227.183.120 On: Fri, 07 Nov 2014 16:18:28

Site-bindingModel(oxide/electrolyteinterface)

=neutralsurfacesite

contain N types of ions is governed by the potential !!z" thatis determined by the Poisson–Boltzmann equation,12

"r"0d2

dz2!!z" = #!z" , !1"

#!z" = ! e#i

N

zini,0 exp$! zie%!!z" ! UG&kBT

' , !2"

where zi is the ion valency, e is the positive elementarycharge, ni,0 is the concentration of ion species i, and "r is therelative dielectric constant of the entire solvent. We use SIunits except where specified otherwise and kBT is the thermalenergy at temperature T.

In order to determine $adsorbed, we employ the so-calledsite-binding model for amphoteric oxide surfaces.1,13 Thismodel characterizes the surface reactions by two dissociationconstants K1 and K2 that reflect the following reactions:

SOH2+ ! SOH + H+, !3"

SOH! SO! + H+. !4"

Here, S denotes an oxide molecular site (GaxOy in thepresent case) with the bonded hydroxyl group OH. Thesetwo types of reactions lead to an amphoteric behavior. Whena proton gets attached to the hydroxyl group, the site getspositively charged. A dissociation, on the other hand, createsa negatively charged site. The net surface charge density isgiven by

$adsorbed = e!%SOH2+ ! %SO!" , !5"

where %SOH2+ and %SO! are the charge densities of the positive

and negative sites, respectively. The total number of surfacegroups per unit area is then given by nS=%SOH+%SOH2

+

+%SO!, where %SOH denotes the density of electrically neutralsites. As shown in Healy et al.,13 the resulting dissociationconstants K1 and K2 are given by

K1 =%SOH%SOH2

+exp(! e!!ox ! UG"

kBT! cpH) , !6"

K2 =%SO!

%SOHexp(! e!!ox ! UG"

kBT! cpH) , !7"

with K1 referring to Eq. (3) and K2 to Eq. (4), and cpH=pH ln 10. We note that the pH value equals the negativedecadic logarithm of the H+ concentration, divided by M,i.e., by mole per liter. By combining expressions Eqs.(5)–(7), we finally obtain the net surface charge at the am-photeric oxide–electrolyte interface as

$adsorbed = enSexp!! y0 ! cpH" ! K1K2 exp!y0 ! cpH"

K1 + exp!! y0 ! cpH" + K1K2 exp!y0 ! cpH",

!8"

where we have introduced the abbreviation y0=e!!ox!UG" /kBT.

For the present application, we have taken into acountthree different types of ions, namely (i) singly charged cat-

ions and (ii) singly charged anions with a fixed concentrationof 100 mM that represent dissolved NaCl, (iii) a Hepes so-lution consisting of doubly charged cations with a concentra-tion of 10 mM plus 20 mM singly charged anions to guaran-tee electrical neutrality. Any change of the pH value iscompensated by a corresponding increase in the concentra-tion of singly charged anions. Since we consider a symmetricmonovalent salt and a high concentration of asymmetric di-valent Hepes, a closed-form solution of the Poisson–Boltzmann equation in the electrolyte region is not possible.However, the numerical effort required to solve this equationis negligible.

B. Model of GaN heterostructure

The potential at the surface exposed to the electrolytesets the boundary value for the potential distribution and theresulting spatial dependence of the band edge within thesemiconductor device. As mentioned before, variations of thechemical features of the electrolyte, i.e., the pH value or theionic composition, lead to detectable changes of $adsorbed and!ox. The relevant part in the semiconductor is the 2DEG thatresponds sensitively to slight changes in the spatial variationof the conduction band edge.

We consider a nitride heterostructure, grown along thehexagonal [0001] direction, that is of either Ga-face orN-face polarity. In this section, we focus on the Ga-facestructure with a schematic cross section shown in Fig. 1. Thestructure consists of a 5-nm-thick oxide on top of a 3 nmstrain-relaxed GaN layer, followed by 35 nm of anAl0.28Ga0.72N barrier, grown on top of a 1.5 &m strain re-laxed GaN layer. The latter is assumed to be homogeneouslydoped with a carrier concentration of n=1016 cm!3. Thisstructure is a fairly typical design for GaN-based sensors thathave been fabricated by several groups.14,15 The most signifi-cant features of AlGaN/GaN heterostructures are the hugespontaneous and piezoelectric polarization fields. Both typesof polarizations are included in our present calculations. Thedivergence of the total polarization across the interface be-tween adjacent layers is equivalent to a fixed interfacial sheetcharge density. There is a positive polarization charge at theleft AlGaN/GaN interface near the 2DEG in Fig. 1 with atheoretical value of $polarization=1.37'1013 cm!2 that is com-pensated at the right AlGaN/GaN interface.16,17 The result-

FIG. 1. Schematic layout of the calculated heterostructure including theinterface charge densities. Their magnitudes, in units of 1013 e /cm2, areindicated by closed symbols and the axis to the left.

033703-2 Bayer, Uhl, and Vogl J. Appl. Phys. 97, 033703 (2005)

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP:128.227.183.120 On: Fri, 07 Nov 2014 16:18:28

![!"#!!]!" = !! !! − !! − !!! !!

AlGaNS D

=hydrogenion=otherions

[SO− ]= NS −[SOH2+ ]

![#$% ]!' = )* +, − ./ −)* ./

BoundaryConditions

Substrate

GaN

AlGaNDoubleLayer

NitrideElectrolyte

Nitride

2DEG

Dirchlet BC:ψ,Φn,Φp =fixed

Dirchlet BC:ψ,Φn,Φp =fixed

Dirchlet BC:[Na],[Cl],[H],[A]=fixed

PSP PPE

PSP+σ(PSP)

+σ(PPE)

-σ(PSP+PPE)-/+σ(adsorbed)

pHSensorSimulationResults

Double layeronly,Vds=5V

TheoreticalNernstian sensitivityψ0=2.303kT/qΔpH =59.2mV/pH

pHSensorSimulationResults

Effectofoxidelayers

0.8$

0.85$

0.9$

0.95$

1$

1.05$

1.1$

1.15$

1$ 2$ 3$ 4$ 5$ 6$ 7$ 8$ 9$ 10$

I ds/I

ds,0'

pH'

Double$layer$+$5nm$oxide$

Double$layer$+$3nm$oxide$

Double$layer$only$

ReductioninSensitivity

DL+3nmoxide=63%DL+5nmoxide=77%

Needfor2-DSimulation

Double layeronly,Vds=5V

Resultsfora1µmgatedevice

“Gate”LengthTrend

Double layeronly,Vds=5V

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6 7 8 9 10 11

PeakSensitvity(mA/mm-pH)

DrainVoltage, VDS(V)

EffectofDrainBias(Vds=2V)

EffectofDrainBias(Vds =5V)

Summary

• Mathematical frameworkforsimulationofAlGaN/GaN-basedBiosensors

• Firstsimulationof2-Deffects– Importantforhighbiasconditions

• Trends– Highersensitivityforhigherdrainbias

• Maybelimitedbyvelocitysaturationofcarriers(futurework)

– Highersensitivityforlonger“gate”length

GaN

AlGaNS D2DEG