Simulation study on electrical characteristic of AlGaN/GaN high electron mobility transistors with AlN spacer layer

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Simulation study on electrical characteristic of AlGaN/GaN high electron mobility transistors

with AlN spacer layer

View the table of contents for this issue, or go to the journal homepage for more 2014 Jpn. J. Appl. Phys. 53 04EF08

(http://iopscience.iop.org/1347-4065/53/4S/04EF08)

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Niraj Man Shrestha1_{, Yiming Li}2_{*, and Edward Yi Chang}1_*

1_{Compound Semiconductor Device Laboratory, Department of Material Science and Engineering,}

National Chiao Tung University, Hsinchu 300, Taiwan

2_{Parallel and Scienti}_{ﬁc Computing Laboratory, Department of Electrical and Computer Engineering,}

National Chiao Tung University, Hsinchu 300, Taiwan E-mail: ymli@faculty.nctu.edu.tw; edc@mail.nctu.edu.tw

Received September 24, 2013; revised November 20, 2013; accepted November 25, 2013; published online February 24, 2014

Two-dimensional electron gas (2DEG) property is crucial for the performance of GaN-based high electron mobility transistors (HEMTs). The 2DEG-related concentration and mobility can be improved as device’s performance booster. Electrical characteristics of AlGaN/AlN/GaN HEMT are numerically simulated and compared with conventional AlGaN/GaN HEMT. The main ﬁndings of this study indicate that 2DEG’s concentration level is increased when a spacer layer of AlN in the interface of AlGaN/AlN/GaN is inserted owing to large conduction band off set, high polarizationﬁeld, and high barrier. Notably, when a thin spacer layer of AlN is introduced, the 2DEG’s distribution virtually shifts away from the interface which reduces the interface scattering. The scattering appearing in conventional AlGaN/GaN HEMT includes alloy and interface roughness scatterings. They are reduced in AlGaN/AlN/GaN HEMT due to binary nature of AlN material. A critical thickness of spacer layer for mobility is 0.5 nm and the maximum drain current and transconductance (Gm) are at 1.5 and 1.2 nm thickness of AlN spacer layer. Increasing

thickness of AlN spacer layer deteriorates the ohmic resistance of source/drain contact and hence degrades the performance of device beyond 1.5-nm-thick AlN spacer layer. ©2014 The Japan Society of Applied Physics

1. Introduction

GaN-based high electron mobility transistors (HEMTs) have attracted a great deal of attention for high-frequency and high-power microwave applications because nitride-based material systems have desirable fundamental physical

proper-ties, such as a large band gap (3.4 eV), high breakdownﬁeld

(about 3© 106V/cm) and strong spontaneous and

piezo-electric polarization ﬁelds. A unique feature of GaN-based

HEMTs is high sheet carrier concentration (1© 1013cm¹2), which is achieved in the channel not only due to large band gap discontinuty1) _{at interface but also due to piezoelectric}

and spontaneous polarization effect without intentionally

doping barrier layer.2–4) Because of these advantageous

material properties, GaN and its related alloys have been used in a variety of light-emitting devices and electron devices on a commercial basis. Nevertheless, more techno-logical innovations are needed to realize high-efﬁciency, highly reliable and low-cost devices. High power density is one of key parameters for diverse power devices. In order to increase the power density, the product of electron

concen-tration and electron mobility should be maximized.5,6) To

improve device’s performance, various barrier and channel

alternatives have been studied in nitride-based HEMTs.7,8)

Carrier’s concentration level can be increased by increasing

Al mole fraction and AlGaN barrier layer thickness.9,10)

However, when the Al content of AlGaN layer increases, surface quality of AlGaN layer is degraded and then reduces

the two-dimentional electron gas (2DEG) mobility.9,11) _The

existence of the different scatterings, such as acoustic and optical phonons scattering,12,13) _{ionized impurity scattering,}

interface roughness scattering,14) _{dislocation scattering, and}

alloy disorder scattering15–18) play major role to limit the mobility of 2DEG in conventional AlGaN/GaN HEMT. These scatterings are unique to GaN-based HEMTs due to large dislocation density and strong polarization effects.

An additional thin AlN spacer between AlGaN and GaN

may improve the 2DEG concentration1) and the mobility at

low temperatures.18)_{It is found that, the carriers’ mobility in}

AlGaN/AlN/GaN HEMTs is comparatively higher than that of the conventional device without AlN spacer layer.18,19)_A

thin AlN spacer layer in AlGaN/GaN interface causes the reduction of alloy scattering which plays a dominant factor in the carriers’ mobility. Another effect of AlN spacer layer insertion is the reduction in the forward Schottky gate current, which makes it possible to apply a high gate voltage

in the transistor operation.20) The drain current of AlGaN/

AlN/GaN HEMTs is better than that of conventional AlGaN/

GaN HEMTs.21–23) Therefore, the AlN spacer layer is one

of the fascinating ways to achieve high speed, high power

switching device with low speciﬁc on resistance.

Addition-ally, the thickness of AlN is important for the mobility.19)

When the thickness is changed, the polarization ﬁeld and

the conduction band offset are changed which also affects the 2DEG-related concentration and mobility. Therefore, to know the potential thickness of spacer layer for high power device and to know the real cause of reduction of mobility at higher spacer layer thickness will be interesting studies.

In this study, the effect of AlN spacer layer thickness on electrical characteristic in AlGaN/AlN/GaN HEMT is numerically studied. The most potential spacer layer thick-ness for power device is discussed. In addition, effect of the AlN layer thickness on interface roughness scattering will be highlighted. This paper is organized as follows. In Sect. 2, we introduce the device structure and simulation settings used for studying the effect of AlN spacer layer thickness on AlGaN/AlN/GaN HEMT. In Sect. 3, we report our result and examine the transport property as determined by the thickness of AlN spacer layer. Finally, we draw our con-clusions and suggest future works in Sect. 4.

2. Simulation methodology

The epitaxial layer grown step and fabrication step is shown in Figs. 1(a)–1(f ). The physical device studied in this paper is grown on sapphire substrates by using metal organic chemical vapor deposition system at different temperatures.

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Entire growth process is conducted by using ammonia (NH3),

trimethylgallium (TMGa), trimethylaluminum (TMAl) as precursors and hydrogen as carrier gas. Following an AlN nucleation layer, a 2-µm-thick undoped GaN buffer is grown. A thin AlN spacer layer of varying thickness (0–2 nm) and a 25-nm-thick undoped AlGaN barrier layer are grown on top. The entire epitaxial layer is grown at high temperature. The Al mole fraction determined by using X-ray diffraction is around 30%. Figure 2 shows a scanning electron microscope (SEM) image of cross section of the fabricated AlGaN/AlN/ GaN HEMT structure.

The simulated device structures of AlGaN/GaN HEMT with and without the AlN spacer layer are shown in Figs. 3(a) and 3(b), where the parameters of simulated devices are tabulated in Table I. Figure 3(a) is the device is the conventional structure without the spacer layer and Fig. 3(b) with the AlN spacer layer and both structures use the same device parameters except the thickness of AlN spacer layer. As shown in Fig. 3(b), the thickness of AlN spacer layer varies from 0 to 2 nm while keeping the total thickness of AlN and AlGaN layers at 25 nm. Notably, an insertion of thin AlN layer between AlGaN and GaN can enhance the conﬁnement of 2DEG. Therefore, improvement of electron transport characteristic could be estimated. The spacer layer affects the transport carrier which is related to 2DEG’s concentration and mobility. The band gaps of the relevant binary compounds are computed, by Eqs. (1) and (2), as a function of temperature T: EgðGaNÞ ¼ 3:507 0:909 10 3_T2 T þ 830 ; ð1Þ EgðAlNÞ ¼ 6:23 1:799 103_T2 T þ 1462 : ð2Þ

The band gap of ternary compound depends on composition fraction x is given by

EgðAlxGa1xNÞ

¼ EgðAlNÞ þ EgðGaNÞð1 xÞ 1:3xð1 xÞ: ð3Þ

Polarization is one of key mechanisms in controlling the

formation of the 2DEG at the AlGaN/GaN interface. PPZof

Eq. (4) is piezoelectric polarization which is related to strain tensor: PPZ¼ 2as a0 a0 E31 C13 C33E33 ; ð4Þ

where E31 and E33 are piezoelectric constants, and C13 and

C33 are elastic constants. When an AlxGa1¹xN grown on

GaN, the piezoelectric polarization is expressed as

PPZðxÞ ¼ ð3:2x 1=9x2Þ106cm2: ð5Þ

In addition to strain induced polarization, cations and anions are spontaneously displaced with respect to each other, producing spontaneous polarization. Then total polarization is given by

Ptot¼ PPZþ PSP: ð6Þ

The Schottky barrier height estimated is 1.4 V. A 2D quantum mechanically corrected device simulation is per-formed, where the quantum mechanical correction is considered with a density-gradient approach. Performance

of device mainly depends on the carriers’ mobility which is

affected by various types of scattering mechanism; such as, the phonon scattering (at room temperature), the alloy disorder scattering (potential disorder from ternary alloy, at low and room temperatures), the surface roughness scattering (at low temperature), the ionized impurities scattering, the dislocation scattering, and the dipole scattering. Among these scattering mechanisms, the alloy disorder scattering is the

limiting factor14) at low and room temperatures when the

carrier’s concentration is high. Binary nature of AlN makes comparatively low alloy disorder scattering. Notably, the

Fig. 1. (Color online) Epilayer grown and processﬂow of the studied AlGaN/AlN/GaN HEMT.

GaN AlGaN

AlN

1 μm

Fig. 2. (Color online) A SEM image of the AlGaN/GaN structure with the AlN spacer layer.

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Fig. 3. (Color online) Schematic plots of the AlGaN/GaN HEMT. (a) Conventional device is without the AlN spacer layer and (b) the explored device which is with the AlN spacer layer.

Table I. Parameters used for the simulated devices.

Gate width (µm) 15

AlGaN layer thickness (nm) 25

GaN layer thickness (µm) 2

Al composition in AlGaN (%) 30

Gate length (µm) 1

AlN thickness (nm) 0, 0.3, 0.5, 1, 1.2, 1.5, 2

Jpn. J. Appl. Phys. 53, 04EF08 (2014) N. M. Shrestha et al.

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one is the lowﬁeld mobility model and the other is the nitride

specific high field dependent mobility model. The first low

ﬁeld mobility model consists of the interface roughness scattering and alloy scattering. The expression for the interface roughness scattering is given by24)

1 I

0ðND; TÞ

¼ aðND=1017Þ lnð1 þ 2cwÞ=ðT=300Þ1:5

þ bðT=300Þ1:5_{þ c=expð=T 1Þ;} _ð7Þ

where ¼ h!LO=kB is related to the phonon scattering

resulting from the scattering of interface roughness, 2cw¼

3ðT=300Þ2_ðN

D=1017Þ2=3, ND (cm¹3) is ionized donor

con-centration, T (K) is absolute temperature. Notably, the interface roughness scattering is one of the most important factors to determine the longitudinal optical phonons; in particular, for binary compound quantum wells where the

contribution from the alloy scattering is absent.25,26) _The

expression for the alloy scattering, is given by27)

A₀ðND; TÞ ¼ min ðT=300Þ1

þ ðmax minÞ ðT=300Þ2

1 þ ½ND=1017 ð300=TÞ3ðT=300Þ4

; ð8Þ

where min and max are the minimum and maximum

mobility for the materials.

Therefore, the nitride speciﬁc high ﬁeld dependent mobility model is27)

ðEÞ ¼

A

0ðND; TÞI₀ðND; TÞ=½A₀ðND; TÞ þ I₀ðND; TÞ þ vsatðEn11=En₀1Þ

1 þ ðE=E0Þn2þ ðE=E0Þn1 ; ð9Þ

where I0ðND; TÞ and A0ðND; TÞ are calculated from Eqs. (7)

and (8), vsat is the saturation velocity, E is electric ﬁeld, and the other parameters used in Eqs. (7)–(9) are tabulated in Tables II and III. The current characteristics of device can be evaluated through Schrödinger equation into a self-consistent computation with the Poisson equation.28–31)

3. Results and discussion

Simulation study of electron transport and DC characteristic of the purposed AlGaN/AlN/GaN HEMT is performed in this section. We compare the results with that of conventional AlGaN/GaN HEMT to show the advantage of the spacer layer of AlN in the interface of the AlGaN/AlN/GaN of the explored device. In Sect. 3.1, we show and discuss the physical characteristic of the device. In Sect. 3.2, we report the electrical characteristics including the transport current and the transconductance.

3.1 Physical characteristic

Figure 4 illustrates the patterns of conduction band proﬁle of

the proposed AlGaN/AlN/GaN HEMT and the conventional

AlGaN/GaN device. A thin AlN spacer layer in the hetero-interface of AlGaN/GaN produces large effective conduction band offset because of the potential drops across the spacer layer due to large piezoelectric and spontaneous polarization

ﬁeld.32) _{The increase in the conduction band offset when}

using the thin AlN spacer layer inside the structure of AlGaN/GaN is explained by EAlN c EcAlGaN¼ exp AlN N2D "AlN dAlN; ð10Þ

whereEAlN_c andEAlGaN_c are the effective conduction band offsets between the AlGaN/AlN/GaN and the AlGaN/GaN,

respectively; N2D is the sheet carrier concentration of the

AlGaN/AlN/GaN structure, ¾AlN is dielectric constant,·AlN

is the polarization induced charge at the AlN/GaN inferface, and dAlNis the thickness of AlGaN.10)Effect of the thickness

of AlN spacer layer on the conduction band offset was analyzed by means of device simulation and results are plotted as shown in Fig. 5(a). The conduction band offset becomes large when the thickness of AlN spacer layer increases. Numerically calculated values of the quantum well depth with respect to the thickness of AlN spacer layer is tabulated in Table IV. Figure 5(b) shows the quantum well depth for the device with respect to different thickness of AlN

c (V s¹1cm¹2) 1.7© 10¹2 Vsat_(cm_/s) _1.9064_{© 10}7 ¡ 6.12 n1 7.2 n2 0.786 E0(kV/cm) 220.89

Table III. The adopted parameters in Eq. (8).27)

¢1 ¢2 ¢3 ¢4 £

GaN ¹1.02 ¹3.84 3.02 0.81 0.66

AlGaN ¹1.33 ¹1.75 6.02 1.44 0.29

AlN ¹1.82 ¹3.43 3.78 0.86 1.16

Fig. 4. (Color online) Illustration of the pattern of band diagram for the (a) AlGaN/GaN and (b) AlGaN/AlN/GaN HEMTs.

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spacer layer. The results show that 2DEG’s depth has 50% increases when the AlN spacr layer is 1.5 nm thick in the

AlGaN/AlN/GaN HEMT.

2DEG, created at the hetero-interface on growing high band gap material Al0.3Ga0.7N on comparatively small band

gap material GaN, is crucial mechanism to conﬁne electrons

in quantum well which leads to high electron concentration

and high mobility. It is found that large polarization ﬁelds

in the AlN barrier layer in the AlN/GaN

heterostruc-ture results in high values of the 2DEG sheet density. The 2DEG’s concentration in the AlGaN/AlN/GaN structure is given by10) N2D¼ AlNþ "AlN "AlGaN dAlGaN dAlN AlGaN1 e "AlN dAlN

½Efþ ’sþ EcðAlGaN=AlNÞ EcðAlN=GaNÞ

1 þ "AlN "AlGaN dAlGaN dAlN ; ð11Þ

where·AlGaNis the polarization charge at AlGaN surface,¤s

is the depth of the Fermi level at the AlGaN surface with respect to its conduction band edge;¾AlGaNand dAlGaNare the

dielectric constant and the thickness of AlGaN, respectively.

High level of 2DEG’s concentration is owing to the large

conduction band offset and reduced wave propagation into

the AlGaN layer33)_{caused by large band gap of the inserted}

AlN spacer layer. Device simulation results listed in Table IV and plotted in Fig. 6(a) show dependency of the conduction band offset on the thickness of AlN spacer layer improves the level of 2DEG’s concentration. As shown in Fig. 6(a), the level of 2DEG’s concentration increases with respect to the thickness of the AlN spacer layer. The level of 2DEG’s concentration is improved by 63% when the thickness of the AlN spacer layer is 1.5 nm thick in the AlGaN/AlN/GaN

interface. The electron concentration distribution for the device with respect to different thickness of the AlN spacer

layer at Vg= 0 V, plotted in Fig. 6(b), shows the 2DEG

distribution. Using the simulated data of electron density,

the averaged position of 2DEG’s distribution is further

calculated by hxi ¼ Z n x dx Z n dx ; ð12Þ

where n is the 2DEG’s concentration and x is respective position.

Figure 7 shows the average position of 2DEG distribution. The results show that the averaged position of 2DEG’s

AlN Spacer Layer Thickness (nm)

0.0 0.5 1.0 1.5 2.0 2.5

Quantum W

ell Depth (eV)

0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 (a) Distance (_μm) 0.295 0.300 0.305 0.310 Quantum W

ell Depth (eV)

-0.15 -0.10 -0.05 0.00 0.05 0.10 (b)

Fig. 5. (Color online) (a) Variation of the quantum well depth for the device at zero bias with respect to the different thickness of the AlN spacer layer. (b) Plot of the quantum well depth for the device at zero bias varying with the thickness of the AlN spacer layer.

Table IV. Simulated results of transport and DC characteristics for the device with respect to different thickness of AlN spacer layer. AlN spacer layer

thickness (nm) 2DEG depth (eV) Electron concentration (©1019_cm¹3₎ Mobility

(cm2_v1_s¹1₎ Drain current_(mA_/mm)

Maximum transconductance (mS/mm) 0.0 0.095 0.89 1495 417 170 0.3 0.125 1.02 1673 451 180 0.5 0.128 1.11 1675 473 188 1.0 0.1346 1.31 1670 518 194 1.2 0.1378 1.37 1665 533 195 1.5 0.14213 1.45 1653 551 194 2.0 0.14614 1.58 1637 550 163

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concentration shift away from the interface on inserting AlN spacer layer, which indicates that the interface scattering is reduced. It has been known that the interface roughness is the main scattering mechanism when the level of 2DEG’s concentration closes to the hetero-interface with the increase

of the level of 2DEG’s concentration.34) _{As summarized in}

Table V, the average position of 2DEG’s distribution shift

away from interface attains on inserting thin AlN spacer layer in AlGaN/GaN interface which implies that the low

interface roughness scattering on the AlGaN/AlN/GaN

HEMTs in comparison with the conventional HEMTs. For

the ﬁrst time, the averaged position of 2DEG’s distribution

with respect to different thickness of the AlN spacer layer is calculated. Distance of averaged position of 2DEG’s distribution attains its maximum when AlN thickness is 0.5 nm. Beyond this thickness, sufﬁciently high electron concentration leads the 2DEG position back toward the interface. Notably, the interface scattering reaches the minimum when the thickness of the AlN spacer layer is 0.5 nm thick and increase again on further increase the thickness. Therefore, mobility increase on increasing the AlN thickness, become maximum at the critical thickness and decrease beyond this thickness. The device simulation result depending on the electron mobility is affected by the thickness of the AlN spacer layer, as shown in Fig. 8.

Simulation result shows that the 2DEG’s mobility increases

when the thickness increases from 0 to 0.5 nm. Our result shows that the mobility is increased by 12% when the 0.5-nm-thick AlN spacer layer is introduced in the AlGaN/GaN heterointerface. Low interface roughness and low alloy scattering mechanism increase the mobility. However, high carrier concentration at a thicker AlN spacer layer leads to moving 2DEG distribution toward the interface. It results in increase of the interface roughness scattering and coulomb scattering in 2DEG. Consequently, the mobility is decreased beyond 0.5-nm-thick AlN space layer.

0.0 0.5 1.0 1.5 2.0 2.5 Electron Concentration (x10 0.0 0.2 0.4 0.6 0.8 1.0 (a) Distance (μm) 0.520 0.525 0.530 0.535 0.540 Electron Concentration (/cm 3 ) 0.0 2.0e+18 4.0e+18 6.0e+18 8.0e+18 1.0e+19 1.2e+19 1.4e+19 1.6e+19 1.8e+19 (b) 2 nm 0 nm Vg= 0 V Vd= 10 V

Fig. 6. (Color online) (a) Electron concentration for the device with different thickness of the AlN spacer layer at Vg= 0 V. (b) Electron

concentration distribution for the device with respect to the thickness of the AlN spacer layer at Vg= 0 V.

0.0 0.5227 0.3 0.5245 1.8 0.5 0.5261 3.4 1.0 0.5251 2.4 1.2 0.5251 2.4 1.5 0.5251 2.4 2.0 0.5250 2.3

0.0 0.5 1.0 1.5 2.0 2.5

A

v

eraged 2DEG Position (

μ m) 0.5225 0.5230 0.5235 0.5240 0.5245 0.5250 0.5255 0.5260 0.5265 Vg= 0 V Vd= 10 V ∫ ∫ ndx ndx x. Averaged 2DEG position 〈x〉 =

Fig. 7. (Color online) Averaged position of 2DEG’s distribution calculated by using Eq. (11) with respect to the thickness of the AlN spacer layer.

0.0 0.5 1.0 1.5 2.0 2.5 Mobility (cm 2/Vs) 1480 1500 1520 1540 1560 1580 1600 1620 1640 1660 1680 1700 Vg= 0 V Vd= 10 V

Fig. 8. (Color online) Plot of the variation of mobility versus the thickness of the AlN spacer layer.

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3.2 DC characteristics

Note that the AlGaN/AlN/GaN HEMTs show better DC

characteristic in comparison with the conventional AlGaN/

GaN devices21,35) _{owing to excellent 2DEG property}

appearing in the AlGaN/AlN/GaN structures. Figure 9

shows that the simulated Ids–Vds curves for the AlGaN/

AlN/GaN HEMT varing with the thickess of the AlN spacer layer at zero gate bias. We know that drain current is the result of the combined effect of mobility and electron concentration. Result shows that the drain current increases up to 0.5 nm spacer layer thickness due to increase of both electron concentration and mobility with spacer layer thickness. On increasing the spacer layer thickness from 0.5 to 1.5 nm, the drain current enhances due to the carrier concentration. Beyond the thickness of 1.5 nm, the drain

current is lowered owing to decrease in the carrier’s

mobility. Our result shows that the drain current increases by 32% on using 1.5-nm-thick AlN spacer layer. Corre-spondingly, Fig. 10(a) shows the distribution of the trans-conductance with respect to the gate voltage. Figure 10(b) is the variation of the maximum transconductance with

respect to the thickness of the AlN spacer layer.

Figure 10(b) shows that the transconductance increases on the insertion of the AlN spacer layer in the AlGaN/ GaN interface; it increases with the thickness is increased to 1.2 nm thickness of the AlN spacer layer. It slightly decreases from 1.2 to 1.5 nm thickness of the AlN spacer layer and rapidly decreases beyond this thickness. The maximal transconductance of 195 mS/mm is observed at the 1.2-nm-thick AlN space layer which is 15% increase,

compared with the conventional the AlGaN/GaN HEMT.

Beyond the 1.5-nm-thick AlN spacer layer, there is sizeable degradation of ohmic contact resistance because an AlN spacer layer with an extremely wide band gap decreases

the contact resistance signiﬁcantly.20) _{The extremely high}

ohmic resistance in drain and source contacts degrade the device performance.

4. Conclusions

For the GaN HEMT with AlN spacer layer, the engineering ﬁndings of this study indicate that the 2DEG transport properties and DC characteristic of the AlGaN/AlN/GaN

HEMTs are strongly affected by the thickness of the AlN spacer layer. The electron concentration signiﬁcantly in-creases on the insertion of AlN spacer layer and is dependent on the thickness of the AlN spacer layer. The level of 2DEG’s concentration is virtually moved away from the interface on inserting the AlN space layer. Distance between the 2DEG concentration and the interface attains its maximum at 0.5-nm-thick AlN space layer. This exhibits that the lowest interface scattering is observed at 0.5-nm-thick AlN space layer. The carrier mobility increases as the thickness of the AlN spacer layer and reaches its maximum at the thickness of 0.5 nm and decreases on further increase of thickness. Furthermore, drain current increases with the thickness is increased to 1.5 nm. Beyond this thickness, the drain current decreases owing to decrease in mobility. As the thickness of the AlN spacer layer is thicker than a critical thickness, the source and drain ohmic contacts are degraded and the drain current decreases. The maximum trans-conductance is observed at 1.2-nm-thick AlN spacer layer. High ohmic resistance makes lower transconductance

beyond 1.5-nm-thick AlN space layer and ﬁnally degrades

the device performance. Notably, 1.5-nm-thick AlN spacer layer can be used for high speed, high power switching device.

Drain Voltage (V)

0 2 4 6 8 10 12

Drain Current (mA/mm)

-100 0 100 200 300 400 500 600 Vg= 0 V 2 nm 1.5 nm 1.2 nm 1 nm 0.5 nm 0.3 nm No spacer

Fig. 9. (Color online) Id–Vdcurves for the device with respect to the

different thickness of the AlN spacer layer (they are 0.0, 0.3, 0.5, 1.0, 1.2, 1.5, and 2.0 nm, respectively). Gate Voltage (V) -7 -6 -5 -4 -3 -2 -1 0 T ransconductance (mS/mm) 0 50 100 150 200 250 (a) Vd= 2 V 2 nm 1.5nm 1.2nm 1nm 0.5nm 0.3nm No spacer

0.0 0.5 1.0 1.5 2.0 2.5 The Maximum T ransconductance (mS/mm) 140 150 160 170 180 190 200 (b) Vd= 2 V

Fig. 10. (Color online) Plots of the (a) distribution of transconductance with respect to the gate voltage and (b) variation of transconductance with respect to the spacer layer thickness.

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Contracts Nos. NSC 2221-E-009-161 and NSC 102-2911-I-009-302. Mr. N. M. Shrestha would like to thank Mr. T.-T. Luong for the sample grown.

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