J Comput ElectronDOI 10.1007/s10825-013-0468-5

Analytical modeling and analysis of Alm Ga1−mN/GaN HEMTsemploying both field-plate and high-k dielectric stack forhigh-voltage operation

Mourad Kaddeche · Azzedine Telia · Ali Soltani

© Springer Science+Business Media New York 2013

Abstract In this paper, a new high-voltage AlmGa1−mN/GaN HEMT (High Electron Mobility Transistors) withField-Plate and high-k dielectric stack, Graded two-dimen-sional electron gas (2DEG) Channel Field-Plate Stack di-electric (GCFPS) HEMTs structure has been reported. Theproposed structure has shown enhancements of the perfor-mances of the GaN-based HEMTs taking into account theeffects of spontaneous and piezoelectric polarization fields.In order to analyze this structure, a 2D analytical model hasbeen developed where the expressions for 2D channel po-tential and electric field distribution have been derived. Itwas shown that the GCFPS design exhibits significantly re-duction of the electric field peaks along the 2DEG channel.Therefore, the breakdown voltage (BV) is greatly improvedin comparison with the standard AlGaN/GaN FP-HEMTs.The developed model is validated by the good agreementwith the 2D simulated data.

Keywords AlGaN/GaN heterostructure ·GCFPS-HEMTs · High-k dielectric · Field-plate (FP)

1 Introduction

Recently, many high-k materials such as Al2O3 [1], Gd(Ga2)O3 [2–4], HfO2 [5], SiNX [6], hexagonal Boron Ni-

M. Kaddeche (�) · A. TeliaLaboratoire de Microsystème et Instrumentation (LMI),Département d’Electronique, Université Constantine 1,Route de Ain El Bey, 25000 Constantine, Algeriae-mail: kaddeche@gmail.com

A. SoltaniIEMN-CNRS 8520, Université de Lille, Cité Scientifique,Avenue Poincaré, B.P. 69, 59652 Villeneuve d’Ascq Cedex,France

tride (hBN) [7, 8] and Si3N4 [9, 10] were widely used as gateinsulators and surface passivation layers in CMOS technol-ogy and HEMTs to reduce drain-to-source surface leakagecurrent, high-field trapping effect and increase the forwarddrain current for high power and microwave applications.However, the high dielectric constant of passivation layerincreases the gate-drain and gate-source capacitance whichdecreases AlGaN/GaN HEMTs switching speed [11]. In or-der to suppress the High-k passivation layer capacitance, theinsertion of SiO2 interfacial layer of (ε = 3.9) or anotherlow permittivity material layer has been used to limit thelarge gate stack capacitance [11–13]. In addition, an alterna-tive passivation approach for AlGaN/GaN HEMTs has beenproposed in [14] and has demonstrated an improvement indc, high-frequency and microwave power performance, bytwo-step passivation where both SiNx and SiOx effectivelysuppress trapping effect and increase the breakdown volt-age. A new device structure oxide stack with high-k dielec-tric grown on oxide layer has been proposed for MOSFET[5, 15, 16] to improve short-channel effects (SCEs), hot car-rier effect, drain induced barrier lowering (DIBL) also to re-duce the density of interface trap states and the influence ofthe doping concentration in the channel on breakdown volt-age enhancement [17–19]. A new structural concept basedon graded channel asymmetric gate stack (GCASYMGAS)MOSFET and graded channel symmetric gate stack (GCGS)double-gate (DG) MOSFET have been respectively pro-posed in [16] and [20] where the gate leakage and SCEshave been greatly improved.

A physical correspondence between MOSFET andHEMT for analytical solutions, circuit designs and noiseanalysis has been widely reported by several authors inthe case of GaAs-based HEMTs [21–25] and GaN-basedHEMTs [26]. Based on this correspondence, an analyticalexpression of threshold voltage for InAlAs/InGaAs sym-

J Comput Electron

metric double-gate HEMT [25] and for Dual-Material Gate(DMG) AlGaN/GaN HEMT structure [26], have been inves-tigated. These structures have the advantage of improvingthe carrier transport efficiency and of reducing SCEs due to astep function in the channel potential. To enhance the deviceperformances for high-voltage power electronics and mi-crowave applications, GaN-Based HEMTs were elaboratedusing Field-Plate technology (FP) in which tremendous im-provement in the breakdown voltage and power densitieswere demonstrated [27–36]. They represent an extension ofthe gate deposited onto the passivation layer (over a uniforminsulator) on the drain side to reduce the electric field at theAlGaN surface leading to reduced dispersion [36] that en-hances DC and RF performance of devices by improving thebreakdown voltage. However, longer FP extension increasesthe main electric field peak under the FP edge that increasesthe gate capacitance (transit time) and decreases the break-down voltage [32]. In order to reduce the electric field mag-nitude at the two edges (gate and FP edge) of the drain sideand to increase the breakdown voltage, a new device designis suggested, in the present work, based on a graded 2DEGchannel FP stack dielectric HEMTs (AlGaN/GaN GCFPS-HEMTs). We have incorporated both advantages of dielec-tric stack structure (high-k dielectric on oxide layer) andgraded channel. The proposed structure is shown in Fig. 1.To suppress SCEs and to minimize the mobility degradationof the 2DEG channel, a high-k dielectric layer is used atthe gate edge under the FP close to the drain (Regions II)and the doping concentration is higher under the FP close todrain region (graded regions).

In order to analyze this structure, a two-dimensional an-alytical model has been developed and its advantages havealso been shown. This model is based on explicit solutionof two-dimensional (2D) Poisson’s equation in which ana-lytical expressions for the channel fields and potential dis-tribution of the structure are derived in terms of the appliedvoltage and the device parameters. The particularity of thismodel is the effects of spontaneous and piezoelectric polar-ization fields. The effects of various technological parame-ters of Field-Plate and High-k layer material (such as: op-timum FP extension length LFPE close to drain, distancedrain-gate separation LGD , thickness t2 and permittivity ε2)on the standard AlmGa1−mN/GaN FP-HEMTs performancehave been carefully examined. In addition, the effect of theinsulator thickness toxeff (stack oxide) on the breakdownvoltage has been also discussed.

Using the proposed structure the electric field profile, themaximum operation voltage capability and the breakdownvoltage have been greatly improved in comparison with thestandard AlGaN/GaN FP-HEMTs. The good agreement ofthe results provided by the 2D analytical model with thepublished 2D simulated data confirms the validity of the pro-posed model.

Fig. 1 AlmGa1−mN/GaN HEMT cross-section view incorporatingboth a Field Plate and a High-k layer (GCFPS-HEMTs structure) usedfor model calculation

2 Model descriptions

2.1 Two-dimensional potential analysis

The Field-Plate (FP) structure considered in this work isa gate extension above the passivation layers (high-k di-electric on SiO2) where the FP is directly connected to thegate, which then can be biased simultaneously. The devicecross-section incorporating both an FP and a high-k dielec-tric stack is shown in Fig. 1 where all the important deviceparameters have been defined, the source and the drain re-gions are uniformly doped at N+

d = 1025 m−3 respectively,while the gate electrode is a Schottky barrier placed on n-AlmGa1−mN layer.

The gate-drain spacing LGD and the insulator (high-kand SiO2) layer thickness under the FP are important de-sign parameters to achieve higher breakdown voltage. TheFP extension length LFPE is defined as the distance betweenthe gate and the FP edges with LFPE < LGD [32]. Thefront interface is located at y = d and the hetero-interfaceis located at y = 0, where the total AlGaN layer thicknessd = d1 + d2 + dc, with d1, d2 and dc are the thickness ofthe AlGaN spacer layer, doped AlmGa1−mN layer and caplayer, respectively. The electrons are confined to the hetero-interface (AlGaN/GaN). In order to analyze the effects of

J Comput Electron

the technological parameters, the structure is divided intotwo regions (see Fig. 1). The Region I is the area under thegate (0 ≤ x ≤ LG), the Region II is the area between the gateedge and drain terminals (LG ≤ x ≤ L).

In the present analysis, the doping concentration in Re-gion II (Nd2) is higher than in Region I (Nd1). Assum-ing that the charge densities in insulator layers (high-k andSiO2) are negligible and that the AlGaN barrier layer is fullydepleted under operating conditions, the 2D potential distri-bution can be obtained by solving the Laplace/Poisson equa-tions:

∇2ψi(x, y) =

⎧⎪⎪⎨

⎪⎪⎩

0 LG ≤ x ≤ LG + LGD

d ≤ y ≤ d + toxeff

− qNdi

εd0 ≤ x ≤ L, 0 ≤ y ≤ d

(1)

where ψi(x, y) is the potential distribution in each regionwhere i = 1, 2 corresponds to the Region I, II respectively,L = LG + LGD is the effective channel length, Ndi is thedoping concentration of the AlmGa1−mN layer in regions,εd is the AlGaN permittivity and q is the electronic charge.If a structure contains several dielectrics in series the lowestcapacitance layer will dominate the overall capacitance andwill limit the minimum achievable equivalent oxide thick-ness (EOT) value [12]. A dielectric structure is a stack oftwo layers where the top layer is the high-k dielectric (thick-ness t2, permittivity ε2) on the SiO2 layer (t1, ε1). The totalcapacitance of the insulator layer is given by

Coxtot = εox

toxeff(2)

with εox = ε1, toxeff is the effective stack oxide layer thick-ness of the insulator layer defined as

toxeff = t1 + αt2 (3)

where α = ε1/ε2.

2.1.1 Analysis in Region I (under the gate): 0 ≤ x ≤ LG

Under the gate (Region I), the potential profile along thechannel depth is expressed by a parabolic function [37–39].Hence, the potential profile along vertical direction underthe metal gate can be approximated by a simple parabolasuch as:

ψ1(x, y) = a1(x) + b1(x)y + c1(x)y2 for 0 ≤ y ≤ d (4)

where the coefficients a1(x), b1(x) and c1(x) are functionsof x only and they can be determined by the boundary con-ditions for ψ1(x, y) given below.

The electric flux and channel potential at the interface ofthe two regions are continuous [20, 26, 38–41] then:

dψ1(x, y)

dx

∣∣∣∣x=LG

= dψ2(x, y)

dx

∣∣∣∣x=LG

(4a)

ψ1 (0, 0) = ψc1(0) = Vbi (4b)

ψ1(LG,d) = ψ2(LG,d) = V1/2 (4c)

ψ1(LG,0) = ψ2(LG,0) ⇒ ψc1(LG) = ψc2(LG) = Vc1/2

(4d)

where Vbi = (kT /q) ln(Nd/ni) is the built in potential ofsource/drain and the 2DEG channel junction, ni is the in-trinsic carrier concentration, V1/2 is the electrostatic poten-tial along the vertical direction and Vc1/2 is the electrostaticchannel potential at x = LG (see Appendix).

At the interface of the gate/AlmGa1−mN (y = d), wehave:

ψ1(x, d) = VG1 = VGS − VFB1 (4e)

At the interface of AlGaN/GaN hetrojunction (y = 0), wealso have:

dψ1(x, y)

dx

∣∣∣∣y=0

= εd

εG

ψc1(x,0) − ψ1(x,0)

d1(4f)

where ψc1(x,0) is the channel potential at the AlGaN/GaNhetrojunction (2DEG channel), εG is the GaN permittivity,VGS is the gate to source bias voltage, VFB1 is the flat bandvoltage, VFB1 = ΦMS1 = ΦM1 − ΦS , ΦM1 is the metal gatework function and the semiconductor (AlmGa1−mN) workfunction ΦS is given as [26, 38]:

Φs = χd + Eg

2− ΦF (5)

where Eg is the AlmGa1−mN band gap, χd is the elec-tron affinity of AlmGa1−mN, ΦF = (kT /q) ln(Nd/ni) isthe Fermi potential and ψ1(x,0) = ψAlGaN(y) representsthe electrostatic potential in the AlmGa1−mN layer whichis given by [42]:

ψAlGaN(y) = PspAlGaN − PspGaN

ε′ y− qn(x)

ε′ y+2βγxxy (6)

with: β = (e31 − e33c13)/ε′c33, ε′ = εd + e2

33/c33, γxx =(aGaN − aAlGaN)/aAlGaN.

The material parameters that depend on the Al mole frac-tion (m) are listed in Table 1.

The parameter n(x) represents the 2DEG carriers con-centration at the AlmGa1−mN/GaN heterointerface which isgiven by [43, 44]:

n(x) = εd

qd

(VG − Vtheff − Vc(x)

)(7)

where VG is the applied gate to source voltage, Vc(x) isthe channel potential at x and Vtheff is the effective thresh-old voltage which depends on induced charges at the inter-face and is given by the following expression at T = 300 K

J Comput Electron

Table 1 Material parameterswhich are used in modelcalculation forAlmGa1−mN/GaN HEMTs(Refs. [42–46])

Parameter Signification Expression Unit

e31(m) piezoelectric constant ofAlmGa1−mN layer

−0.11m − 0.49 C/m2

e33(m) piezoelectric constant ofAlmGa1−mN layer

0.73m + 0.73 C/m2

C13(m) elastic constant 5m + 103 G/Pa

C33(m) elastic constant −32m + 405 G/Pa

αGaN lattice constant in GaN layer 3.189 Å

αAlGaN(m) lattice constant in AlmGa1−mNlayer

−0.077m + 3.189 Å

PspGaN spontaneous polarization in theGaN layer

−0.029 C/m2

PspAlmGa1−mN(m) spontaneous polarization in theAlmGa1−mN layer

−0.052m − 0.029 C/m2

m aluminum mole fraction ofAlmGa1−mN layer

0.25

[43, 45]:

Vtheff = φb(m) − E(m) − qNdd22

2εd(m)− σpz(m)d

εd(m)(8)

where φb(m) = 1.3m + 0.84 Ev [46] is the Schottky bar-rier height, E(m) is the conduction band discontinuity atthe AlGaN/GaN interface and σpz(m) is the polarization in-duced sheet charge density between the AlGaN barrier layerand the GaN layer given as

σpz(m) = 2

(a(0) − a(m)

a(m)

)(

e31(m) − e33(m)C13(m)

C33(m)

)

+ psp(m) − psp(0) (9)

a(0) and a(m) are the lattice constants of GaN andAlmGa1−mN respectively. In the case of GCFPS-HEMTstructure, Vc(x) = ψci(x) is the channel potential for eachregion which will be calculated later on. The 2DEG sheetcharge density is obtained by replacing Vc(x) with ψci(x)

in Eq. (7). Then the expression of 2DEG sheet charge den-sity can be expressed as:

ni(x) = εd

qd

(VG − Vtheffi − ψci(x)

)for i = 1,2 (10)

where ni(x) is the sheet charge density of the 2DEG ofeach region. The effective threshold voltage of each region(Vtheffi, i = 1, 2) is different (Nd1 �= Nd2).

The two-dimensional potential distribution in region I isgiven in the following expression as:

ψ1(x, y) = ψc1(x) + Cc

εd

(ψc1(x) − VG1

)y

−[

2Cc

εdd

(ψc1(x) − VG1

)

+ 3

d2

(ψc1(x) − ψAlGaN(y)

)]

y2 (11)

where ψc1(x) is the channel potential in region I and Cc =εd/dc is the cap layer capacitance. Substituting Eq. (11) inEq. (1) leads to a second-order differential equation in termsof the channel potential distribution in the region I at Al-GaN/GaN hetero-interface (2DEG channel) as follows:

d2ψc1(x)

dx2+ θ2

1 ψc1(x) = S1 (12)

where

θ1 =√

2CcC1

εdd, C1 = 1 + δ1,

δ1 = εd/Ccd, S1 = qNd1

εd

+ θ21 VFP

The solution of Eq. (12) in Region I is represented as:

ψc1(x) = A1 exp(θ1x) + B1 exp(−θ1x) − S1

θ21

(12a)

The constants A1 and B1 values are obtained using theboundary conditions of Eqs. (4a)–(4f) (see Appendix).

So, Eq. (12a) can be expressed as

ψc1(x) = S1

θ21

+(Vc1/2 − S1

θ21) sinh θ1x

sinh θ1LG

−( S1θ2

1+ Vbi) sinh θ1(LG − x)

sinh θ1LG

(12b)

2.1.2 Analysis in Region II (at gate edge close to drainterminal): LG ≤ x ≤ L

The region between the gate edge and drain terminals (Re-gion II) is the most important region of the proposed struc-

J Comput Electron

ture because it’s the highest electric field region (at the gateedge). To explain the effect of oxide field (stack dielectriclayer effect) on channel potential profile, the potential dis-tribution along the insulator is assumed as linear and it isderived using the approach reported in [49, 50] by the fol-lowing expression:

ψox(x) =

⎧⎪⎨

⎪⎩

0 x ≤ LG

VD(x−LG)LGD

LG ≤ x ≤ L

VD x ≥ L

(13)

where ψox(x) represents the potential distribution along theinsulator layer (stack oxide layer) in this region and LGD =L − LG is the length of the stack oxide layer. In order toachieve a precise potential profile definition, an electric fielddistribution and to increase the accuracy of the 2D analyti-cal model a third-order polynomial for approximating thepotential profile under the FP has been adopted. So, from[25, 40], the third-order polynomial is given by:

ψ2(x, y) = a2(x) + b2(x)y + c2(x)y2 + d2(x)y3

for 0 ≤ y ≤ d (14)

where the coefficients a2(x), b2(x), c2(x) and d2(x) can beexpressed by applying the following boundary conditions:

Electric flux at the FP oxide/AlmGa1−mN layer interfaceis continuous, hence we have

dψ2(x, y)

dx

∣∣∣∣y=d

= εox

εd

ψs2(x, d) − ψ2(x, d)

toxeff(14a)

dψ2(x, y)

dx

∣∣∣∣y=0

= εd

εG

ψc2(x,0) − ψ2(x,0) − ψox(x)

d1(14b)

where ψs2(x, d) and ψc2(x,0) are, respectively, the surfaceand channel potential at the AlmGa1−mN/oxide interfaceand the AlGaN/GaN hetrojunction (2DEG channel).

ψ2(x,0) = ψAlGaN(y) represents the electrostatic poten-tial in the AlmGa1−mN layer in Region II.

ψ2(x, d) = VG2 = VFP = VGS − VFB2 (ΦM1 = ΦM2)

(14c)

The electric flux and channel potential at the interface of thetwo zones are continuous [39–41, 47, 48]. So, we have

dψ1(x, y)

dx

∣∣∣∣x=LG

= dψ2(x, y)

dx

∣∣∣∣x=LG

(14d)

ψ2(LG + LGD,0) = ψc2(LG + LGD) = ψc2(L)

= Vbi + VD (14e)

The two-dimensional potential distribution in region II isgiven by the following expression:

ψ2(x, y) = ψc2(x) + Coxtot

εd

(ψc2(x) − VFP

)y

−[

2Coxtot

εdd

(ψc2(x) − VFP

)

+ 3

d2

(ψc2(x) − ψAlGaN(y)

)]

y2

+(

Coxtot

εdd2+ 2

d3

)(ψc2(x) − Vox(x)

)y3 (15)

where ψc2(x) represents the channel potential in region II.Substituting Eq. (15) in Eq. (1), we will get a second-orderdifferential equation that involves only the channel potentialdistribution in the region II at AlGaN/GaN hetero-interface(2DEG channel) and can be expressed as:

d2ψc2(x)

dx2+ θ2

2 ψc2(x) = S2 (16)

where

θ2 =√

2CoxtotC2

εdd, C2 = 1 + δ2,

δ2 = εd/Coxtotd, S2 = qNd2

εd

+ θ22 VFP

The solution of Eq. (16) in Region II is given as

ψc2(x) = A2 exp(θ2(x − LG)

)

+ B2 exp(−θ2(x − LG)

) − S2

θ22

(16a)

The constants A2 and B2 values are obtained using theboundary conditions of Eqs. (4a) and (14a)–(14e) (seeAppendix).

Equation (16a) can be expressed as

ψc2(x) = S2

θ22

+ VD(x − LG)

C2LGD

+((VD + Vbi)

δ2C2

− S2θ2

2) sinh θ2(x − LG)

sinh θ2LGD

+(Vc1/2 − S2

θ22) sinh θ3(L − x)

sinh θ2LGD

(16b)

2.2 Analysis of electric field distribution

The electric field profile along the 2DEG channel deter-mines the electron transport velocity through the 2DEG

J Comput Electron

channel. It can be calculated by differentiating the poten-tial distribution and using the boundary conditions for eachregion.

In the case of AlGaN/GaN GCFPS-HEMTs structure, themain factor considered is the value of the y-component ofthe electric field perpendicular to the growth direction whichdependent on the polarization field in AlmGa1−mN barrierlayer. The x and y components of the electric field distri-bution along 2DEG channel in Regions I and II, (derivedby differentiating Eqs. (12b) and (16b) for the x-componentand by using the boundary conditions in Eqs. (4f), (14b) fory-component) are given by:

Ex1(x) = −∂ψx1(x, y)

∂x

∣∣∣∣y=0

= −dψc1(x,0)

dx(17a)

Ey1(x) = −∂ψ1(x, y)

∂y

∣∣∣∣y=0

= εd

εG

ψ1(x,0) − ψc1(x,0)

d1

= εd

εG

ψAlGaN(y) − ψc1(x)

d1(18a)

Ex2(x) = −∂ψx2(x, y)

∂x

∣∣∣∣y=0

= −dψc2(x,0)

dx(17b)

Ey2(x) = −∂ψ2(x, y)

∂y

∣∣∣∣y=0

= εd

εG

ψox(x) + ψ2(x,0) − ψc2(x,0)

d1

= εd

εG

ψox(x) + ψAlGaN(y) − ψc2(x)

d1(18b)

3 Results and discussion

The potential profile variations along the 2DEG channelfor graded channel Field-Plate stack dielectric AlGaN/GaNHEMTs have been studied taking into account several tech-nological parameters with the same condition of biases(VG = −3 V and VD = 120 V). The effect of high-k di-electric permittivity (ε2) on potential profile is shown inFig. 2(a). We can observe that the channel potential de-creases when the dielectric constant (ε2) of the high-k layerincreases. This is mainly due to the structure capacitanceincrease. However, from Figs. 2(b) and 2(c), the channelpotential is enhanced with the increase of both the high-klayer thickness (t2) and the AlmGa1−mN layer doping con-centration Nd . This behavior is due to the decrease of thegate-drain capacitance. Therefore, the designed Field-Platestack dielectric provides an excellent control of the channelbarrier and a significant improvement in the potential distri-bution profile along the LGD distance. So, the high-k layer

Fig. 2 Potential distribution variation along the 2-DEG channelfor AlGaN/GaN GCFPS-HEMT as function of: (a) high-k dielec-tric permittivity ε2, (b) thickness t2 and (c) doping concentrationNd of AlGaN layer (t1 = 0.1 µm, t2 = 0.3 µm, LG = 0.4 µm,LFPE = 2.2 µm, LGD = 4.7 µm, dc = 4 nm, d1 = 5 nm, d2 = 20 nm,Nd1 = 1 × 1021 m−3 and Nd2 = 2 × 1022 m−3)

J Comput Electron

Fig. 3 Comparison of electric field profile along 2-DEG chan-nel for standard and AlGaN/GaN GCFPS-HEMTs as a function ofField Plate Extension Length LFPE and High-k layer thickness t2 at(a) VD = 123 V and (b) VD = 630 V (VG = −2.8 V, t1 = 0.1 µm,t2 = 0.7 µm, LG = 0.4 µm, LGD = 4.7 µm, dc = 4 nm, d1 = 5 nm,d2 = 20 nm, Nd1 = 1 × 1021 m−3 and Nd2 = 2 × 1022 m−3)

exhibits a change in the potential profile (the potential slopechanges) along the 2-DEG channel between the gate and thedrain terminals which enables the channel barrier control.The introduction of GCFPS design can lead to the suppres-sion of short-channel effects (SCEs) due to a step-functionin the channel potential profile which screens the drain po-tential variations [20, 26, 38].

Figures 3(a) and 3(b) present the module electric fielddistribution profile along the 2DEG channel for standardFP-HEMTs (ε = ε1 = ε2 = 7) and the proposed GCFPS-HEMTs structure (ε1 = 3.9, ε2 = 9) at the biases conditionVG = −2.8 V, VD = 123 V for the FP extension length,LFPE = 2 µm, t = t1 + t2 = 0.3 µm and VD = 630 V for the

Fig. 4 Variation of 2-DEG density with Al mole fraction for variousvalues of doping concentration Nd of AlGaN barrier layer

FP extension length, LFPE = 2.2 µm, t = t1 + t2 = 0.8 µmrespectively. For standard AlGaN/GaN FP-HEMTs our re-sults are comparable to those obtained in Ref. [32]. How-ever, the presence of both, GC and high-k dielectric on oxidelayer (ε1 = 3.9, ε2 = 9) effectively reduce the magnitude ofthe electric field at the two edges (gate and FP edges).

It can be observed [Figs. 3(a) and 3(b)] a significant re-duction in the secondary peak of electric field at the FP edgeand a slight decrease in the first peak. The second peak hasbeen considerably reduced at the FP edge by nearly 40 %[Fig. 3(b)]. In the present work, the breakdown voltage (BV)is defined as the drain-source voltage at which the maximumelectric field peak reaches 2.15 MV/cm under the given con-ditions [32]. Due to the impacts of both the high-k layer andthe large drain side doping concentration, the device break-down voltage (BV) has been improved. This observation canbe explained by the important effect of the GCFPS structurewhich enables the electrical field control and efficiently re-duces its high value in the 2DEG channel. This result maybedue to the decrease in the gate leakage current because of theoxide stacks high-k. Kumar et al. [26] has argued that theelectric field reduction near the drain terminal leads as wellto the reduction in hot carrier effects and suppressed SCEs,resulting in improved carrier transport efficiency.

The variations of 2DEG density versus Al mole frac-tion for different doping concentrations are shown in Fig. 4.It can be seen that the 2DEG density increases with theincrease in Al mole fraction of the AlGaN barrier layerand the doping concentration Nd . From this figure, it isnoted that the effect of doping concentration is more sig-nificant at lower mole fractions. Figure 5 represents thebreakdown voltage enhancement in the AlmGa1−mN/GaNGCFPS-HEMTs. It is clear that the introduction of the stackoxide (high-k Ga2O3/SiO2) in a standard AlGaN/GaN FP-HEMTs results in an increase in breakdown voltage from

J Comput Electron

Fig. 5 Comparison of the ATLAS simulation and analytical break-down voltages with Field- Plate extensions length LFPE for standardand GCFPS-HEMTs

Fig. 6 Variation of Breakdown Voltage with insulator layer thicknesstoxeff

630 V to 830 V representing an improvement of about 30 %in the BV. A Significant higher Breakdown voltage can beachieved using higher insulator dielectric constant [32], thiswill lead to a safe and reliable device operation up to thisbias and then it will make it suitable for high-power applica-tions. This enhancement maybe due to the decrease of gate-drain capacitance induced by the increase of the gate-draindepletion region width [29].

Figure 6 shows the breakdown voltage behavior ofAlmGa1−mN/GaN heterostructure FP-HEMTs (with andwithout GCFPS) as a function of insulator layer thickness.As can be seen, the breakdown voltage is improved by 40 %when increasing the insulator layer thickness toxeff compara-tively to the standard FP-HEMTs due to the double effects ofstack oxide thickness and FP extension length. In addition, itis clear from the Fig. 6, there is an optimal value of the oxide

Fig. 7 Breakdown voltage as a function of LGD distance

thickness toxeff is equal to 1.1 µm for which the breakdownvoltage is maximum (BV = 1092 V for LFPE = 1.8 µm)beyond which the BV would become lower. It means thatthe high-voltage devices need appropriate thickness insu-lators [33, 36]. Therefore, the implemented GCFPS designimproves the breakdown voltage and enhances the devicereliability. The BV as a function of LGD distance is shownin Fig. 7. It can be seen that the increase of LGD from 5 µmto 10 µm leads to an increase of the BV by up to 10 %when other parameters are fixed. Finally, the graded 2DEGchannel Field-Plate stack dielectric design improves Field-Plate controllability by reducing significantly the electricfield peaks along the 2DEG channel, resulting in the en-hancement of the breakdown voltage (BV) by up to 40 %.

4 Conclusion

In this paper, a new device design based on the use ofa Field-Plate combined with high-k material on top of anoxide layer, a graded 2DEG channel FP stack dielectricAlGaN/GaN HEMTs (GCFPS-HEMTs) structure has beenpresented. An analytical model that can be used for esti-mating several technological parameters of GCFPS-HEMTsbased on AlmGa1−mN/GaN heterostructure has been devel-oped. It was shown that the incorporation of GCFPS designimproves the reliability of the AlGaN/GaN FP-HEMT by re-ducing significantly the electric field peaks along the 2DEGchannel. This leads to a higher drain bias operation as com-pared to standard FP-HEMTs. The high-k layer parameterssuch as the permittivity (ε2) and thickness (t2), which con-trol the potential profile, have a significant influence on thedevice electric field. The obtained results are in good agree-ment with the published 2D-simulated data, which confirmsthe validity of the proposed model. The studied structure

J Comput Electron

seems to be promising for BV enhancement and conse-quently an improvement on device performances in high-power applications.

Appendix

The electrical flux and channel potential at the interface ofregion I/region II are continuous as indicated by the bound-ary conditions (Eqs. (4a) and (4d)). So, the value of channelpotential Vc1/2 calculated at x = LG of low doping channel(region I) and high doping channel (region II) can be derivedfrom

dψc1(x)

dx

∣∣∣∣x=LG

= dψc2(x)

dx

∣∣∣∣x=LG

The constant coefficients Ai and Bi are represented as

A1 =[(

S1

θ21

+ Vbi

)

exp(−θ1LG)

−(

S1

θ21

+ Vc1/2

)

exp(2θ1LG)

]

· F1 (19a)

B1 =[(

S1

θ21

+ Vbi

)

−(

S1

θ21

+ Vc1/2

)

exp(−θ1LG)

]

· F1

(19b)

A2 =[(

S2

θ22

+ Vbi + VD

)

exp(−θ2L)

−(

S2

θ22

+ Vc1/2

)

exp(−2θ2LG)

]

· F2 (20a)

B2 =[(

S2

θ22

+ Vbi + VD

)

exp(−θ2L)

−(

S2

θ22

+ Vc1/2

)

exp(−θ2LG)

]

· F2 (20b)

where

F1 = [− exp(2θ1LG) + 1]−1 (21)

F2 = [exp(−θ2LG) − exp(2θ2L) + 1

]−1 (22)

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