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GaN heterostructures
Accepted Manuscript Optical phonon scattering on electronic mobility in Al2O3/AlGaN/AlN/GaN heterostructures
X.J. Zhou, Y. Qu, S.L. Ban, Z.P. Wang PII:
S0749-6036(17)31207-7
DOI:
10.1016/j.spmi.2017.08.042
Reference:
YSPMI 5217
To appear in:
Superlattices and Microstructures
Received Date:
17 May 2017
Revised Date:
16 August 2017
Accepted Date:
23 August 2017
Please cite this article as: X.J. Zhou, Y. Qu, S.L. Ban, Z.P. Wang, Optical phonon scattering on electronic mobility in Al2O3/AlGaN/AlN/GaN heterostructures, Superlattices and Microstructures (2017), doi: 10.1016/j.spmi.2017.08.042
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ACCEPTED MANUSCRIPT Optical phonon scattering on electronic mobility in Al2O3/AlGaN/AlN/GaN heterostructures X. J. Zhou,1,2 Y. Qu,1 S. L. Ban,1 and Z. P. Wang1, a) 1
Department of Physics, School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China
2
Ordos Institute of Technology, Ordos 017000, Inner Mongolia, China
Abstract: Considering the built-in electric fields and the two-mode property of transverse optical phonons in AlGaN material, the electronic eigen-energies and wave functions are obtained by solving Schrödinger equation with the finite difference method. The dispersion relations and potentials of the optical phonons are given by the transfer matrix method. The mobility of the two dimensional electron gas influenced by the optical phonons in Al2O3/AlGaN/AlN/GaN heterostructures is investigated based on the theory of Lei-Ting force balance equation. It is found that the scattering from the half-space phonons is the main factor affecting the electronic mobility, and the influence of the other phonons can be ignored. The results show that the mobility decreases with increasing the thicknesses of Al2O3 and AlN layers, but there is no definite relationship between the mobility and the thickness of AlGaN barrier. The mobility is obviously reduced by increasing Al component in AlGaN crystal to show that the effect of ternary mixed crystals is important. It is also found that the mobility increases first and then decreases as the increment of the fixed charges, but decreases always with increasing temperature. The heterostructures constructed here can be good candidates as metal-oxide-semiconductor highelectron-mobility-transistors since they have higher electronic mobility due to the influence from interface phonons weakened by the AlN interlayer. Keywords:
Electronic
mobility;
Optical
phonon
scattering;
Al2O3/AlGaN/AlN/GaN
heterostructure 1. Introduction At present, III-N compound heterojunctions are basic elements for manufacturing various types of high-end electronic and optoelectronic devices. The key for these devices working with high power, high frequency and high speed is to improve the density and mobility of the two dimensional electron gas (2DEG). In recent twenty years, it has been reported that a high density of 2DEG with high mobility can be achieved in the AlGaN/GaN heterostructures even without a)Author
to whom correspondence should be addressed. Electronic mail: [email protected] 1
ACCEPTED MANUSCRIPT being doped due to the large band gap and the strong polarization [1-3]. As a result, the high electronic mobility transistors (HEMTs) based on these heterostructures have a good prospect of application. However, it is found that the traditional HEMTs even those consisting of AlGaN/GaN have the problems of a large leakage current and a small breakdown voltage. These problems not only reduce the device performance [4,5], but also lead to leakage current collapse [6]. Another defect of these structures is that the scatterings from alloy disorder and interface roughness greatly affect the mobility and the sheet density of 2DEG [7,8]. In order to improve the performance of the devices, a lot of efforts have been made to design AlGaN/GaN heterostructures [9-11]. Firstly, an oxide material is usually cultivated as a passivation layer on the surface of AlGaN barrier to form the so-called metal-oxide-semiconductor (MOS) HEMTs, which can not only reduce the leakage current [12-14], but also can improve the on-state drain current performance [15]. Despite the result of remote charge scattering [16-17], it can increase the 2DEG’s density and mobility [18]. Many materials can be used as a passivation layer, but Al2O3 is considered to be one of the most suitable for AlGaN material because of its thermal and chemical stabilities with a high breakdown field and a large band-gap [19]. Secondly, some results showed that two kinds of scattering from alloy disorder and interface roughness are the main factors affecting the mobility with the increase of Al component [20]. Fortunately, the effect of the disorder scattering can be well reduced if a thin AlN layer is introduced between the AlGaN and GaN layers [21]. Thus, Al2O3/AlxGa1-xN/AlN/GaN heterostructures were fabricated and investigated. For example, a high threshold voltage was achieved in Al2O3/Al0.25Ga0.75N/AlN/GaN MOS HEMTs by the combination of the fluorine-based treatment technique and an Al2O3 film as the gate oxide layer, the 2DEG’s mobility and density were reached to 1900cm2/Vs and 8.8×1012cm-2, respectively [22]. Subsequently, it was reported that these structures had a lower gate leakage current and a better small signal radio frequency (RF) performance compared with the structure of SiN passivation [23], and the electronic mobility was demonstrated up to 2361cm2/Vs. Although some studies have shown that there are many factors affecting the electronic mobility in these structures such as interface roughness, acoustic and optical phonons, alloy disorder, and remote interface charge scatterings, it is the optical phonon scattering at high temperature and high electronic density that plays the most important part [24,25]. Unfortunately, the study on optical 2
ACCEPTED MANUSCRIPT phonon scattering in Al2O3/AlxGa1-xN/AlN/GaN heterostructures is still lack. In our previous work, electronic mobility affected by optical phonons in Al2O3/AlGaN/GaN structure was investigated, it is found that the influence from interface (IF) phonons is great in any case, even replaces the half space (HS) phonon modes as a main factor when Al component is smaller than 0.3 [26]. This conclusion motivates us to think of improving electronic mobility by decreasing the scattering from IF phonons. It was known that the introduction of an AlN interlayer not only changes the built-in electric field and the strain between materials, but also modulates the fine structure of optical phonons [27]，so the optical phonons in an Al2O3/AlGaN/AlN/GaN structure may be completely different from those in an Al2O3/AlGaN/GaN structure. This also implies that introducing an AlN interlayer between AlGaN and GaN materials may modulate the mobility in HEMTs. In this paper, the optical phonons and electronic states are analyzed in details by means of the transfer matrix method and the finite difference method considering the two-mode property of transverse optical phonons in AlGaN material [28]. Electronic mobility determined by the electron-phonon interaction is calculated numerically for Al2O3/AlxGa1-xN/AlN/GaN multilayers to show how to optimize the properties of HEMTs based on these kinds of heterostructures. 2. Model and theory Figure 1 shows a schematic diagram of the Al2O3/AlxGa1-xN/AlN/GaN MOS HEMT considered in this paper. The growth direction is considered to be the z axis, and the x-y plane of the AlxGa1xN/GaN
interface perpendicular to the z direction is denoted as ⊥. For convenience, materials
Al2O3, AlxGa1-xN, AlN and GaN are labeled as 1, 2, 3 and 4, respectively.
Fig. 1. Structure diagram of an Al2O3/AlGaN/AlN/GaN MOS HEMT. 3
ACCEPTED MANUSCRIPT 2.1. Electronic states Considering the band offsets and built-in electric fields induced by the polarization, the Schrödinger equation of a single electron in the heterostructure can be expressed as 2 1 VC z eF z z z E z , 2 z m j z z
(1)
where ħ is Planck’s constant, m j z is the position-dependent effective mass of the electron in material j along the z axis. VC (z), which can be expressed as VC12 at Al2O3/AlxGa1-xN interface,
VC23 at AlxGa1-xN/AlN interface and VC34 at AlN/GaN interface, is the potential caused by conduction-band offset given by Ref. [29]. Electronic wave function z and corresponding energy level E can be obtained using the finite difference method to solve Eq. (1). The built-in electric field F (z) was given by Refs. [30,31]. 2.2. Potentials of optical phonons Because the Al2O3 layer is far away from the 2DEG, the influence of optical phonons in this layer can be ignored, this is equivalent to considering phonon modes in AlxGa1-xN /AlN/GaN structure, in which the optical phonons are mainly IF, HS, and local modes. The previous results showed that the IF and HS phonons in GaN channel play a major role in the mobility [26], therefore only these two factors are considered here. Based on the continuum dielectric model and Loudon’s uniaxial model, the potential of optical phonons with frequency ω in material j along the z direction is obtained by [32]
j q, z c j e
ik j z
c je
ik j z
,
(2)
here q is the component of wave vector q along the x-y plane, and cj+ and cj- are the normalization constants. kjω is given by k j j / jz q (j = 2, 3, and 4), the frequency-dependent dielectric function εjk of material j in directions k (k = z or ⊥) can be calculated by
jk jk 2 2jkL / 2 2jkT [33], in which jk ， jkL and jkT represent the highfrequency dielectric constant，frequencies of the longitudinal and transverse optical phonons, respectively, they were given by Refs. [34,35] for AlN and GaN materials. Considering the twomode property of transverse optical phonons, these parameters related to AlxGa1-xN material can 4
ACCEPTED MANUSCRIPT be calculated using the weight model [28]. The dispersion relation of each phonon mode can be obtained by the transfer matrix method using boundary condition according to the continuum dielectric model, and the frequency ω of optical phonons can be derived by solving the equation of dispersion relation [32,36]. 2.3. Sheet density and mobility of 2DEG Charges with a high sheet density will gather at the AlN/GaN interface due to the piezoelectric and spontaneous polarizations in an Al2O3/AlxGa1-xN/AlN/GaN heterostructure. Considering the fixed charges at Al2O3/ AlxGa1-xN interface, the sheet density ns of 2DEG can be written as [21]
ns nfix
net e
1 2
e d1
VC12
2z 2
e d2
VC23
3z 2
e d3
VC34
1 2 z 2 z 3 z
e d1 d 2 d3 2
e B EF ,
(3)
where nfix is the sheet density of the fixed charge. σnet represents the total induced net polarization density [37]. And e is the absolute value of the electron charge. The dielectric constant ε1 of Al2O3 can be obtained by Ref. [38]. dj is the thickness of material j (j = 1, 2, 3 or 4). The Schottky-barrier of a gate contact e B was also given by Ref. [38]. EF is the Fermi energy [39]. According to the force-balance equation [40], the electronic mobility of 2DEG influenced by optical phonons with the frequency of ω can be expressed as
1
2 ns ekBT
q
2 x
M q , 02 q , 2
q
exp / kBT 1 exp / kBT
2
,
(4)
where kB is the Boltzmann’s constant, and variable T represents temperature. qx is the component of wave vector q along the x axis. Π02 is the imaginary part of the zero-order two-dimensional density-density correlation function whose specific form was depicted by Ref. [40] in detail. And the Fröhlich interaction matrix M q , can be given by
M q , e † z j (q , z ) z dz .
(5)
3. Results and discussion Eq. (4) shows that the mobility of 2DEG is directly related to the electronic density, wave function, fixed charge and phonon’s potential. Therefore, it is necessary to analyze the influence 5
ACCEPTED MANUSCRIPT of size and ternary mixed crystals (TMCs) effects on these parameters for investigating the mobility. 3.1. Effects of size and TMCs 3.1.1. Sheet density of 2DEG
Fig. 2. Sheet densities ns of 2DEG vs (a) Al2O3 thickness d1, Al0.3Ga0.7N thickness d2, AlN thickness d3 and (b) Al component x for different thicknesses of passivation Al2O3. The asterisk in (a) represents the experimental value of ns for a 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure [41].
Without losing generality, the fixed charge nfix in 2DEG’s density ns calculated by Eq. (3) is taken as 1.0×1013 cm-2, and the dependences of ns on the size of each layer and Al component x are shown in Figs. 2(a) and (b). The three curves in Fig. 2(a) represent the variation of density with thicknesses of Al2O3, Al0.3Ga0.7N and AlN layers for 2~20nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN, 2nm Al2O3/ 2~20nm Al0.3Ga0.7N/1nm AlN/GaN and 5nm Al2O3/20nm Al0.3Ga0.7N/ 2~20nm AlN/GaN heterostructures, respectively. It can be clearly seen from the figure that electronic density increases with increasing the thickness of barrier Al0.3Ga0.7N, while decreases with passivation layer Al2O3 and interlayer AlN. This conclusion is in accord with Refs. [21,42], especially with Ref. [43]. The asterisk in Fig. 2(a) denotes the experimental value which is 1.4×1013 cm-2 for 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure given by Ref. [41], the corresponding theoretical value calculated by Eq. (1) is 1.48×1013 cm-2, which is very close to the experimental one. The dependence of ns on x is given in Fig. 2(b) for Al2O3/10nm AlxGa1-xN/1nm AlN/GaN structures with different thicknesses of Al2O3 layer. As depicted in the figure, the rise of x will lead to a decrease of ns, but a slower pace of decline appears when the Al2O3 thickness d1 increases gradually. This result can be attributed to the changes of the frequency-dependent dielectric functions and the polarization, as shown in Eq. (3). 6
ACCEPTED MANUSCRIPT 3.1.2. Conduction bands and electronic wave functions
Fig. 3. Band diagrams and wave functions vs (a) Al2O3 thickness d1, (b) Al0.3Ga0.7N thickness d2, (c) AlN thickness d3, and (d) Al component x.
Figure 3 displays the conduction band profiles and electronic wave functions varying with the size of each layer and Al component x, obtained using the finite difference method to solve Eq. (1). As seen in Fig. 3(a), a pure translation of the ground state wave functions is observed for Al2O3/13nm Al0.3Ga0.7N/1nm AlN/GaN structures as d1 increases from 2 to 6nm, which originates from the ignorance of passivation layer’s influence on the built-in electronic field. However, the effective barrier height increases obviously with increasing the thicknesses of d2 (in 16nm Al2O3/6~10nm Al0.3Ga0.7N/1nm AlN/GaN structures), d3 (in 16nm Al2O3/13nm Al0.3Ga0.7N/ 1~3nm AlN/GaN structures) and x (in 16nm Al2O3/13nm AlxGa1-xN/1nm AlN/GaN structures with x = 0.1, 0.3, 0.5, 0.7 and 0.9), as shown in Figs. 3(b), (c), and (d), especially in the last two figures. This will undoubtedly lead to a larger localization degree of 2DEG and a stronger interaction between an electron and phonons, and hence reduced electronic mobility as discussed later. 3.1.3. Potentials of HS phonons
7
ACCEPTED MANUSCRIPT
Fig. 4(a) Dispersion relations of HS phonons oscillating in GaN channel, (b) potentials of eight branches of highfrequency phonon modes and (c)low-frequency phonon modes, (d) potentials of one branch of low-frequency phonon modes for different thicknesses d2 of Al0.3Ga0.7N , (e) d3 of AlN and (f) Al component x.
It is found that the influence from the HS phonons oscillating in GaN channel is higher than that from the IF phonons by at least one order of magnitude under the same condition. Thus, only HS phonon modes are considered here. In theory, there are countless HS phonon modes satisfying the required dispersion relations, which can be divided into two kinds by the transfer matrix method as shown in Fig. 4(a): high- and low-frequency phonon modes. The dispersion relations of the first eight branches of low-frequency phonon modes and the last eight branches of high-frequency
8
ACCEPTED MANUSCRIPT phonon modes are displayed in Fig. 4(a). It can be seen that when wave vector q increases, the two kinds of phonon modes tend to display the maximum and minimum frequencies, respectively, which are same as the results of Ref. [25]. Figures 4(b) and (c) show the potentials of eight branches of the high- and low-frequency phonon modes depicted in Fig. 4(a) when wave vector q is taken as 0.0529nm-1. It can be found that the curves in the two figures are similar in trend, but the potentials of low-frequency phonons (Fig. 4(c)) are higher than those of high-frequency ones (Fig. 4(b)) near AlN/GaN interface, so their influences on the mobility is comparatively larger. It also can be seen from Fig. 4(b) that the potential reduces obviously with decreasing the frequency of high-frequency phonons (or increasing the low-frequency phonons shown in Fig. 4(c)), hence their influences of scattering on electrons become weaker and weaker so that they can be neglected when their frequencies are less (or greater for the low-frequency phonons) than a certain value. Figs. 4(d), (e) and (f) show the size and TMCs effects on the potential of one branch of low-frequency phonon modes given in Fig. 4(c). As shown in Figs. 4(e) and (f), the potential increases with increasing d3 and x. However, it shows a regular fluctuation with increasing d2 as shown in Fig. 4(f) where d2 varies from 1to 5nm, and the interval is 0.1nm. 3.1.4. Mobility of 2DEG
Fig. 5. 2DEG’s mobility μ vs Al component x for
a 16nm Al2O3/13nm AlxGa1-xN/AlN/GaN
structure.
Fig. 6. 2DEG’s mobility μ vs thickness d1 of Al2O3 layer for
different
structures.
Triangles
represent
the
experimental results of the mobility for 4nm Al2O3/20nm Al0.3Ga0.7N/1nm
AlN/GaN
[44],
5nm
Al2O3/20nm
Al0.3Ga0.7N/1nm
AlN/GaN
[41],
16nm
Al2O3/13nm
Al0.25Ga0.75N/1nm AlN/GaN [22] and 20nm Al2O3/17.6nm Al0.25Ga0.75N/2nm AlN/GaN [23] structures, respectively. 9
ACCEPTED MANUSCRIPT From the preceding discussion, it is clear that the sheet density, wave function and phonon’s potentials are greatly affected by the size and TMCs effects, so the mobility must be also affected according to Eq. (4). Fig. 5 shows the electronic mobility versus x for 16nm Al2O3/13nm AlxGa1xN
/1nm AlN/GaN structures. The blue and red curves represent the individual contribution from
high- and low-frequency phonon modes in GaN channel. The black curve denotes the total mobility. As described in the picture, the mobility is mainly determined by the low-frequency phonons due to their larger potentials near the interface shown in Fig. 4(c), and the influences from the two kinds of modes become larger and larger when x increases. This is because the confinement of 2DEG and the potentials of phonons have been obviously enhanced with increasing x (as illustrated in Figs. 3(d) and 4(f)), so that the total mobility declines gradually when x increases according to Eqs. (4) and (5). This downward trend is similar to the result given in Ref. [27] for AlxGa1-xN/AlN/GaN heterostructures. The numerical results show that the mobility declines from 2781 cm2/Vs to 392 cm2/Vs when x varies from 0.2 to 1, so a smaller component is better for fabricating the device with high electronic mobility. In fact, the experimental values of Al component are typically 0.25 and 0.3. Table 1. The calculated and experimental values of fixed charge and 2DEG sheet densities and mobility at different tempratures in some structures. Structure
Temprature
d1/d2 (x) /d3 (nm)
T (K)
nfix (cm-2)
ns (cm-2)
μ ( cm2/Vs)
ns (cm-2)
μ ( cm2/Vs)
5/20 (0.3) /1
300
1.0×1013
1.19×1013
2450
1.4×1013
1500 [41]
16/13 (0.25) /1
200
1.0×1013
1.12×1013
12134
300
1.0×1013
1.12×1013
2496
8.8×1012
1900 [22]
400
1.0×1013
1.12×1013
1091
500
1.0×1013
1.12×1013
700
600
1.0×1013
1.12×1013
522
200
1.0×1013
6.03×1012
1556
300
1.0×1013
6.03×1012
954
400
1.0×1013
6.03×1012
566
500
1.0×1013
6.03×1012
408
16/13 (0.25) /2
Calculation
10
Experiment
ACCEPTED MANUSCRIPT 600
1.0×1013
6.03×1012
321
20/17.6 (0.25) /2
300
1.0×1013
5.99×1012
2388
4/20 (0.3) /1
300
4.0×1012
1.18×1013
2403
3.0×1012
2000 [44]
300
1.0×1013
1.23×1013
2717
7.5×1012
2210 [44]
300
2.0×1013
1.3×1013
3294
1.0×1013
742 [44]
2361 [23]
Figure 6 illustrates the electronic mobility as a function of d1 for the Al2O3/17.6nm Al0.25Ga0.75N/2nm AlN/GaN, Al2O3/13nm Al0.25Ga0.75N/1nm AlN/GaN, Al2O3/20nm Al0.3Ga0.7N/ 1nm AlN/GaN and Al2O3/13nm Al0.25Ga0.75N/GaN heterostrutures at 300K when nfix is taken as 1.0×1013 cm-2. As shown in the figure, the mobility decreases with increasing d1, but varies irregularly with d2. This is because that increasing d1, though not changing electronic wave functions (shown in Fig. 3(a)) and phonon’s potentials, will reduce ns (see Fig. 2(a)). And this reduction leads to a decrease of mobility according Eq. (4). However, although a wave function increases slightly (seeing Fig. 3(b)), the change of mobility is irregular with raising d2 due to the fluctuation of potential shown in Fig. 4(d). In addition, the 2DEG’s mobility was calculated for an Al2O3/13nm Al0.25Ga0.75N/GaN structure without AlN interlayer for comparison. The results show that the mobility will be steeply improved if an AlN interlayer is introduced. The reason is that the impact of IF phonons is comparable to that of HS phonons in an Al2O3/AlGaN/GaN structure which has been proved in our previous work [26]. However, it can be ignored when AlN layer is inserted between AlGaN barrier and GaN channel. This means that the rise of mobility is not only due to the decreases of interface roughness and alloy disorder scatterings considered by other authors, but also because the effect of IF phonons is weakened after introducing the interlayer. It is believed that the latter is the main reason at high temperatures. The asterisks in Fig. 6 represent the experimental values of mobility which are 2210 cm2/Vs for 4nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN [44], 1500 cm2/Vs for 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN [41], 1900 cm2/Vs for 16nm Al2O3/13nm Al0.25Ga0.75N/1nm AlN/GaN [22] and 2361cm2/Vs for 20nm Al2O3/17.6nm Al0.25Ga0.75N/2nm AlN/GaN structures [23], the corresponding values calculated in this paper are 2715, 2450, 2496 and 2388 cm2/Vs, respectively. For clarity, these values of mobility and the corresponding charge densities are also listed in Table 1. 11
ACCEPTED MANUSCRIPT
Fig. 8. 2DEG’s mobility μ as a function of the Fig. 7. 2DEG’s mobility μ vs thickness d3 of AlN layer at different temperatures.
fixed charge density nfix in comparison with the experimental values [44].
Figure 7 describes the mobility as a function of d3 for a 16nm Al2O3/13nm Al0.25Ga0.75N/1~2.3nm AlN/GaN structure at temperatures of 200, 300, 400, 500 and 600K. Similar to the effect of d1, the mobility declines obviously when d3 varies from 1nm to 2.3nm. The reason of this result can be found from the above three figures. It can be seen from Figs. 3(c) and 4(e) that as d3 increases, both electronic wave functions and phonon’s potentials are strengthened to induce an intensive interaction between electrons and phonons. Meanwhile, a decrease of ns with increasing d3 is shown in Fig. 2(a). According to Eq. (4), all these changes result in a downward trend of the mobility, and the same trend was reported in Refs. [27] and [45] for AlGaN/AlN/GaN and AlInN/AlN/GaN structures. In combination with the previous comparison between the two cases with and without the interlayer in Fig. 6, this result reveals that an AlN interlayer helps to increase the mobility when its thickness is thin enough. This is the reason why the 1 or 2nm wide interlayer is commonly used in previous studies [22,23,41,44]. It is also found from Fig. 7 that the mobility is significantly reduced as increasing temperature due to the enhancement of thermal vibration amplitude of atoms [21,44]. The calculated mobilities are also given by Table 1 for 16nm Al2O3/13nm Al0.25Ga0.75N/1 or 2 nm AlN/GaN structures at different temperatures. 3.2. Influence of fixed charges on the mobility Many studies suggest that the fixed charges at the interface between passivation layer Al2O3 and barrier AlGaN affect the mobility of 2DEG in MOS HEMTs due to the remote charge scattering. But their influence on the mobility of Al2O3/AlxGa1-xN/AlN/GaN heterostructures has not been investigated, so it is necessary to study it for deeply understanding of properties in these 12
ACCEPTED MANUSCRIPT structures. The mobility as a function of nfix is given in Fig. 8 for 4nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure. It can be seen that the mobility reaches a maximum at around 2.2×1013cm-2 when nfix varies from 4×1012 to 3.5×1013cm-2 (the corresponding range of ns is from 1.18×1013 to 1.6×1013 cm-2 and was given by Eq. (3)). It is clear that the mobility will show the same variation as ns increases because ns is proportional to nfix according to Eq. [3]. The inset in Fig. 8 shows the experimental results of the same structure in Ref. [44] for ns from 1011 to 1013 cm2.
It can be seen that the theoretical values are consistent with the experimental ones from the
general trend. And a similar result was given for a SiN/AlGaN/AlN/GaN structure [46]. The values of mobility for
some given fixed charge are given in Table 1.
4. Conclusions In summary, the influence of optical phonons on 2DEG’s mobility has been investigated in details in Al2O3/AlxGa1-xN/AlN/GaN structures by the transfer matrix and finite difference methods. The results show that increasing temperature and the thickness of Al2O3 or AlN layer reduces the electronic mobility. The mobility almost drops by one order of magnitude when Al component in AlGaN increases from 0.2 to 1, so the effect of ternary mixed crystals should not be ignored. It is also found that bigger density of fixed charge will increase the mobility, with the most appreciate value being about 2.2×1013cm-2 for a 4nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure. Meanwhile, a comparison is conducted between the structures with and without AlN interlayer. The results show that introducing an interlayer improves the mobility not only because of the reduction of alloy disorder scattering, but also because the scattering from IF phonons is significantly weakened when the interlayer is thin enough, usually being 1nm. The paper helps deepening the understanding of optical phonons and electronic mobility in HEMTs with these structures. Acknowledgements The work was supported by the National Natural Science Foundations of China (Grant Nos. 61274098 and 11304142) and the Natural Science Foundation of Inner Mongolia Autonomous Region (Grant No. 2016MS0619). The authors also would like to thank Z. Gu and Y. H. Zan for helpful discussions.
References 13
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ACCEPTED MANUSCRIPT LIST OF FIGURE AND TABLE CAPTIONS Fig. 1. Structure diagram of an Al2O3/AlGaN/AlN/GaN MOS HEMT. Fig. 2. Sheet densities ns of 2DEG vs (a) Al2O3 thickness d1, Al0.3Ga0.7N thickness d2, AlN thickness d3 and (b) Al component x for different thicknesses of passivation Al2O3. The asterisk in (a) represents the experimental value of ns for a 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure [41]. Fig. 3. Band diagrams and wave functions vs (a) Al2O3 thickness d1, (b) Al0.3Ga0.7N thickness d2, (c) AlN thickness d3, and (d) Al component x. Fig. 4(a) Dispersion relations of HS phonons oscillating in GaN channel, (b) potentials of eight branches of highfrequency phonon modes and (c)low-frequency phonon modes, (d) potentials of one branch of lowfrequency phonon modes for different thicknesses d2 of Al0.3Ga0.7N , (e) d3 of AlN and (f) Al component x. Fig. 5. 2DEG’s mobility μ vs Al component x for
a 16nm Al2O3/13nm AlxGa1-xN/AlN/GaN structure.
Fig. 6. 2DEG’s mobility μ vs thickness d1 of Al2O3 layer for different structures. Triangles represent the experimental results of the mobility for 4nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN [44], 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN [41], 16nm Al2O3/13nm Al0.25Ga0.75N/1nm AlN/GaN [22] and 20nm Al2O3/17.6nm Al0.25Ga0.75N/2nm AlN/GaN [23] structures, respectively. Fig. 7. 2DEG’s mobility μ vs thickness d3 of AlN layer at different temperatures. Fig. 8. 2DEG’s mobility μ as a function of the fixed charge density nfix in comparison with the experimental values [44]. Table 1. The calculated and experimental values of fixed charge and 2DEG sheet densities and mobility at different tempratures in some structures.
17
ACCEPTED MANUSCRIPT Highlights
The effects of optical phonon modes on electronic mobility were studied in Al2O3/AlGaN/AlN/GaN heterojunctions.
The two-mode of property of TO phonons in AlxGa1-xN material was included.
The effect of ternary mixed crystals was considered in this structure.
Electronic mobility is improved by introducing AlN interlayer.
X.J. Zhou, Y. Qu, S.L. Ban, Z.P. Wang PII:
S0749-6036(17)31207-7
DOI:
10.1016/j.spmi.2017.08.042
Reference:
YSPMI 5217
To appear in:
Superlattices and Microstructures
Received Date:
17 May 2017
Revised Date:
16 August 2017
Accepted Date:
23 August 2017
Please cite this article as: X.J. Zhou, Y. Qu, S.L. Ban, Z.P. Wang, Optical phonon scattering on electronic mobility in Al2O3/AlGaN/AlN/GaN heterostructures, Superlattices and Microstructures (2017), doi: 10.1016/j.spmi.2017.08.042
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ACCEPTED MANUSCRIPT Optical phonon scattering on electronic mobility in Al2O3/AlGaN/AlN/GaN heterostructures X. J. Zhou,1,2 Y. Qu,1 S. L. Ban,1 and Z. P. Wang1, a) 1
Department of Physics, School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China
2
Ordos Institute of Technology, Ordos 017000, Inner Mongolia, China
Abstract: Considering the built-in electric fields and the two-mode property of transverse optical phonons in AlGaN material, the electronic eigen-energies and wave functions are obtained by solving Schrödinger equation with the finite difference method. The dispersion relations and potentials of the optical phonons are given by the transfer matrix method. The mobility of the two dimensional electron gas influenced by the optical phonons in Al2O3/AlGaN/AlN/GaN heterostructures is investigated based on the theory of Lei-Ting force balance equation. It is found that the scattering from the half-space phonons is the main factor affecting the electronic mobility, and the influence of the other phonons can be ignored. The results show that the mobility decreases with increasing the thicknesses of Al2O3 and AlN layers, but there is no definite relationship between the mobility and the thickness of AlGaN barrier. The mobility is obviously reduced by increasing Al component in AlGaN crystal to show that the effect of ternary mixed crystals is important. It is also found that the mobility increases first and then decreases as the increment of the fixed charges, but decreases always with increasing temperature. The heterostructures constructed here can be good candidates as metal-oxide-semiconductor highelectron-mobility-transistors since they have higher electronic mobility due to the influence from interface phonons weakened by the AlN interlayer. Keywords:
Electronic
mobility;
Optical
phonon
scattering;
Al2O3/AlGaN/AlN/GaN
heterostructure 1. Introduction At present, III-N compound heterojunctions are basic elements for manufacturing various types of high-end electronic and optoelectronic devices. The key for these devices working with high power, high frequency and high speed is to improve the density and mobility of the two dimensional electron gas (2DEG). In recent twenty years, it has been reported that a high density of 2DEG with high mobility can be achieved in the AlGaN/GaN heterostructures even without a)Author
to whom correspondence should be addressed. Electronic mail: [email protected] 1
ACCEPTED MANUSCRIPT being doped due to the large band gap and the strong polarization [1-3]. As a result, the high electronic mobility transistors (HEMTs) based on these heterostructures have a good prospect of application. However, it is found that the traditional HEMTs even those consisting of AlGaN/GaN have the problems of a large leakage current and a small breakdown voltage. These problems not only reduce the device performance [4,5], but also lead to leakage current collapse [6]. Another defect of these structures is that the scatterings from alloy disorder and interface roughness greatly affect the mobility and the sheet density of 2DEG [7,8]. In order to improve the performance of the devices, a lot of efforts have been made to design AlGaN/GaN heterostructures [9-11]. Firstly, an oxide material is usually cultivated as a passivation layer on the surface of AlGaN barrier to form the so-called metal-oxide-semiconductor (MOS) HEMTs, which can not only reduce the leakage current [12-14], but also can improve the on-state drain current performance [15]. Despite the result of remote charge scattering [16-17], it can increase the 2DEG’s density and mobility [18]. Many materials can be used as a passivation layer, but Al2O3 is considered to be one of the most suitable for AlGaN material because of its thermal and chemical stabilities with a high breakdown field and a large band-gap [19]. Secondly, some results showed that two kinds of scattering from alloy disorder and interface roughness are the main factors affecting the mobility with the increase of Al component [20]. Fortunately, the effect of the disorder scattering can be well reduced if a thin AlN layer is introduced between the AlGaN and GaN layers [21]. Thus, Al2O3/AlxGa1-xN/AlN/GaN heterostructures were fabricated and investigated. For example, a high threshold voltage was achieved in Al2O3/Al0.25Ga0.75N/AlN/GaN MOS HEMTs by the combination of the fluorine-based treatment technique and an Al2O3 film as the gate oxide layer, the 2DEG’s mobility and density were reached to 1900cm2/Vs and 8.8×1012cm-2, respectively [22]. Subsequently, it was reported that these structures had a lower gate leakage current and a better small signal radio frequency (RF) performance compared with the structure of SiN passivation [23], and the electronic mobility was demonstrated up to 2361cm2/Vs. Although some studies have shown that there are many factors affecting the electronic mobility in these structures such as interface roughness, acoustic and optical phonons, alloy disorder, and remote interface charge scatterings, it is the optical phonon scattering at high temperature and high electronic density that plays the most important part [24,25]. Unfortunately, the study on optical 2
ACCEPTED MANUSCRIPT phonon scattering in Al2O3/AlxGa1-xN/AlN/GaN heterostructures is still lack. In our previous work, electronic mobility affected by optical phonons in Al2O3/AlGaN/GaN structure was investigated, it is found that the influence from interface (IF) phonons is great in any case, even replaces the half space (HS) phonon modes as a main factor when Al component is smaller than 0.3 [26]. This conclusion motivates us to think of improving electronic mobility by decreasing the scattering from IF phonons. It was known that the introduction of an AlN interlayer not only changes the built-in electric field and the strain between materials, but also modulates the fine structure of optical phonons [27]，so the optical phonons in an Al2O3/AlGaN/AlN/GaN structure may be completely different from those in an Al2O3/AlGaN/GaN structure. This also implies that introducing an AlN interlayer between AlGaN and GaN materials may modulate the mobility in HEMTs. In this paper, the optical phonons and electronic states are analyzed in details by means of the transfer matrix method and the finite difference method considering the two-mode property of transverse optical phonons in AlGaN material [28]. Electronic mobility determined by the electron-phonon interaction is calculated numerically for Al2O3/AlxGa1-xN/AlN/GaN multilayers to show how to optimize the properties of HEMTs based on these kinds of heterostructures. 2. Model and theory Figure 1 shows a schematic diagram of the Al2O3/AlxGa1-xN/AlN/GaN MOS HEMT considered in this paper. The growth direction is considered to be the z axis, and the x-y plane of the AlxGa1xN/GaN
interface perpendicular to the z direction is denoted as ⊥. For convenience, materials
Al2O3, AlxGa1-xN, AlN and GaN are labeled as 1, 2, 3 and 4, respectively.
Fig. 1. Structure diagram of an Al2O3/AlGaN/AlN/GaN MOS HEMT. 3
ACCEPTED MANUSCRIPT 2.1. Electronic states Considering the band offsets and built-in electric fields induced by the polarization, the Schrödinger equation of a single electron in the heterostructure can be expressed as 2 1 VC z eF z z z E z , 2 z m j z z
(1)
where ħ is Planck’s constant, m j z is the position-dependent effective mass of the electron in material j along the z axis. VC (z), which can be expressed as VC12 at Al2O3/AlxGa1-xN interface,
VC23 at AlxGa1-xN/AlN interface and VC34 at AlN/GaN interface, is the potential caused by conduction-band offset given by Ref. [29]. Electronic wave function z and corresponding energy level E can be obtained using the finite difference method to solve Eq. (1). The built-in electric field F (z) was given by Refs. [30,31]. 2.2. Potentials of optical phonons Because the Al2O3 layer is far away from the 2DEG, the influence of optical phonons in this layer can be ignored, this is equivalent to considering phonon modes in AlxGa1-xN /AlN/GaN structure, in which the optical phonons are mainly IF, HS, and local modes. The previous results showed that the IF and HS phonons in GaN channel play a major role in the mobility [26], therefore only these two factors are considered here. Based on the continuum dielectric model and Loudon’s uniaxial model, the potential of optical phonons with frequency ω in material j along the z direction is obtained by [32]
j q, z c j e
ik j z
c je
ik j z
,
(2)
here q is the component of wave vector q along the x-y plane, and cj+ and cj- are the normalization constants. kjω is given by k j j / jz q (j = 2, 3, and 4), the frequency-dependent dielectric function εjk of material j in directions k (k = z or ⊥) can be calculated by
jk jk 2 2jkL / 2 2jkT [33], in which jk ， jkL and jkT represent the highfrequency dielectric constant，frequencies of the longitudinal and transverse optical phonons, respectively, they were given by Refs. [34,35] for AlN and GaN materials. Considering the twomode property of transverse optical phonons, these parameters related to AlxGa1-xN material can 4
ACCEPTED MANUSCRIPT be calculated using the weight model [28]. The dispersion relation of each phonon mode can be obtained by the transfer matrix method using boundary condition according to the continuum dielectric model, and the frequency ω of optical phonons can be derived by solving the equation of dispersion relation [32,36]. 2.3. Sheet density and mobility of 2DEG Charges with a high sheet density will gather at the AlN/GaN interface due to the piezoelectric and spontaneous polarizations in an Al2O3/AlxGa1-xN/AlN/GaN heterostructure. Considering the fixed charges at Al2O3/ AlxGa1-xN interface, the sheet density ns of 2DEG can be written as [21]
ns nfix
net e
1 2
e d1
VC12
2z 2
e d2
VC23
3z 2
e d3
VC34
1 2 z 2 z 3 z
e d1 d 2 d3 2
e B EF ,
(3)
where nfix is the sheet density of the fixed charge. σnet represents the total induced net polarization density [37]. And e is the absolute value of the electron charge. The dielectric constant ε1 of Al2O3 can be obtained by Ref. [38]. dj is the thickness of material j (j = 1, 2, 3 or 4). The Schottky-barrier of a gate contact e B was also given by Ref. [38]. EF is the Fermi energy [39]. According to the force-balance equation [40], the electronic mobility of 2DEG influenced by optical phonons with the frequency of ω can be expressed as
1
2 ns ekBT
q
2 x
M q , 02 q , 2
q
exp / kBT 1 exp / kBT
2
,
(4)
where kB is the Boltzmann’s constant, and variable T represents temperature. qx is the component of wave vector q along the x axis. Π02 is the imaginary part of the zero-order two-dimensional density-density correlation function whose specific form was depicted by Ref. [40] in detail. And the Fröhlich interaction matrix M q , can be given by
M q , e † z j (q , z ) z dz .
(5)
3. Results and discussion Eq. (4) shows that the mobility of 2DEG is directly related to the electronic density, wave function, fixed charge and phonon’s potential. Therefore, it is necessary to analyze the influence 5
ACCEPTED MANUSCRIPT of size and ternary mixed crystals (TMCs) effects on these parameters for investigating the mobility. 3.1. Effects of size and TMCs 3.1.1. Sheet density of 2DEG
Fig. 2. Sheet densities ns of 2DEG vs (a) Al2O3 thickness d1, Al0.3Ga0.7N thickness d2, AlN thickness d3 and (b) Al component x for different thicknesses of passivation Al2O3. The asterisk in (a) represents the experimental value of ns for a 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure [41].
Without losing generality, the fixed charge nfix in 2DEG’s density ns calculated by Eq. (3) is taken as 1.0×1013 cm-2, and the dependences of ns on the size of each layer and Al component x are shown in Figs. 2(a) and (b). The three curves in Fig. 2(a) represent the variation of density with thicknesses of Al2O3, Al0.3Ga0.7N and AlN layers for 2~20nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN, 2nm Al2O3/ 2~20nm Al0.3Ga0.7N/1nm AlN/GaN and 5nm Al2O3/20nm Al0.3Ga0.7N/ 2~20nm AlN/GaN heterostructures, respectively. It can be clearly seen from the figure that electronic density increases with increasing the thickness of barrier Al0.3Ga0.7N, while decreases with passivation layer Al2O3 and interlayer AlN. This conclusion is in accord with Refs. [21,42], especially with Ref. [43]. The asterisk in Fig. 2(a) denotes the experimental value which is 1.4×1013 cm-2 for 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure given by Ref. [41], the corresponding theoretical value calculated by Eq. (1) is 1.48×1013 cm-2, which is very close to the experimental one. The dependence of ns on x is given in Fig. 2(b) for Al2O3/10nm AlxGa1-xN/1nm AlN/GaN structures with different thicknesses of Al2O3 layer. As depicted in the figure, the rise of x will lead to a decrease of ns, but a slower pace of decline appears when the Al2O3 thickness d1 increases gradually. This result can be attributed to the changes of the frequency-dependent dielectric functions and the polarization, as shown in Eq. (3). 6
ACCEPTED MANUSCRIPT 3.1.2. Conduction bands and electronic wave functions
Fig. 3. Band diagrams and wave functions vs (a) Al2O3 thickness d1, (b) Al0.3Ga0.7N thickness d2, (c) AlN thickness d3, and (d) Al component x.
Figure 3 displays the conduction band profiles and electronic wave functions varying with the size of each layer and Al component x, obtained using the finite difference method to solve Eq. (1). As seen in Fig. 3(a), a pure translation of the ground state wave functions is observed for Al2O3/13nm Al0.3Ga0.7N/1nm AlN/GaN structures as d1 increases from 2 to 6nm, which originates from the ignorance of passivation layer’s influence on the built-in electronic field. However, the effective barrier height increases obviously with increasing the thicknesses of d2 (in 16nm Al2O3/6~10nm Al0.3Ga0.7N/1nm AlN/GaN structures), d3 (in 16nm Al2O3/13nm Al0.3Ga0.7N/ 1~3nm AlN/GaN structures) and x (in 16nm Al2O3/13nm AlxGa1-xN/1nm AlN/GaN structures with x = 0.1, 0.3, 0.5, 0.7 and 0.9), as shown in Figs. 3(b), (c), and (d), especially in the last two figures. This will undoubtedly lead to a larger localization degree of 2DEG and a stronger interaction between an electron and phonons, and hence reduced electronic mobility as discussed later. 3.1.3. Potentials of HS phonons
7
ACCEPTED MANUSCRIPT
Fig. 4(a) Dispersion relations of HS phonons oscillating in GaN channel, (b) potentials of eight branches of highfrequency phonon modes and (c)low-frequency phonon modes, (d) potentials of one branch of low-frequency phonon modes for different thicknesses d2 of Al0.3Ga0.7N , (e) d3 of AlN and (f) Al component x.
It is found that the influence from the HS phonons oscillating in GaN channel is higher than that from the IF phonons by at least one order of magnitude under the same condition. Thus, only HS phonon modes are considered here. In theory, there are countless HS phonon modes satisfying the required dispersion relations, which can be divided into two kinds by the transfer matrix method as shown in Fig. 4(a): high- and low-frequency phonon modes. The dispersion relations of the first eight branches of low-frequency phonon modes and the last eight branches of high-frequency
8
ACCEPTED MANUSCRIPT phonon modes are displayed in Fig. 4(a). It can be seen that when wave vector q increases, the two kinds of phonon modes tend to display the maximum and minimum frequencies, respectively, which are same as the results of Ref. [25]. Figures 4(b) and (c) show the potentials of eight branches of the high- and low-frequency phonon modes depicted in Fig. 4(a) when wave vector q is taken as 0.0529nm-1. It can be found that the curves in the two figures are similar in trend, but the potentials of low-frequency phonons (Fig. 4(c)) are higher than those of high-frequency ones (Fig. 4(b)) near AlN/GaN interface, so their influences on the mobility is comparatively larger. It also can be seen from Fig. 4(b) that the potential reduces obviously with decreasing the frequency of high-frequency phonons (or increasing the low-frequency phonons shown in Fig. 4(c)), hence their influences of scattering on electrons become weaker and weaker so that they can be neglected when their frequencies are less (or greater for the low-frequency phonons) than a certain value. Figs. 4(d), (e) and (f) show the size and TMCs effects on the potential of one branch of low-frequency phonon modes given in Fig. 4(c). As shown in Figs. 4(e) and (f), the potential increases with increasing d3 and x. However, it shows a regular fluctuation with increasing d2 as shown in Fig. 4(f) where d2 varies from 1to 5nm, and the interval is 0.1nm. 3.1.4. Mobility of 2DEG
Fig. 5. 2DEG’s mobility μ vs Al component x for
a 16nm Al2O3/13nm AlxGa1-xN/AlN/GaN
structure.
Fig. 6. 2DEG’s mobility μ vs thickness d1 of Al2O3 layer for
different
structures.
Triangles
represent
the
experimental results of the mobility for 4nm Al2O3/20nm Al0.3Ga0.7N/1nm
AlN/GaN
[44],
5nm
Al2O3/20nm
Al0.3Ga0.7N/1nm
AlN/GaN
[41],
16nm
Al2O3/13nm
Al0.25Ga0.75N/1nm AlN/GaN [22] and 20nm Al2O3/17.6nm Al0.25Ga0.75N/2nm AlN/GaN [23] structures, respectively. 9
ACCEPTED MANUSCRIPT From the preceding discussion, it is clear that the sheet density, wave function and phonon’s potentials are greatly affected by the size and TMCs effects, so the mobility must be also affected according to Eq. (4). Fig. 5 shows the electronic mobility versus x for 16nm Al2O3/13nm AlxGa1xN
/1nm AlN/GaN structures. The blue and red curves represent the individual contribution from
high- and low-frequency phonon modes in GaN channel. The black curve denotes the total mobility. As described in the picture, the mobility is mainly determined by the low-frequency phonons due to their larger potentials near the interface shown in Fig. 4(c), and the influences from the two kinds of modes become larger and larger when x increases. This is because the confinement of 2DEG and the potentials of phonons have been obviously enhanced with increasing x (as illustrated in Figs. 3(d) and 4(f)), so that the total mobility declines gradually when x increases according to Eqs. (4) and (5). This downward trend is similar to the result given in Ref. [27] for AlxGa1-xN/AlN/GaN heterostructures. The numerical results show that the mobility declines from 2781 cm2/Vs to 392 cm2/Vs when x varies from 0.2 to 1, so a smaller component is better for fabricating the device with high electronic mobility. In fact, the experimental values of Al component are typically 0.25 and 0.3. Table 1. The calculated and experimental values of fixed charge and 2DEG sheet densities and mobility at different tempratures in some structures. Structure
Temprature
d1/d2 (x) /d3 (nm)
T (K)
nfix (cm-2)
ns (cm-2)
μ ( cm2/Vs)
ns (cm-2)
μ ( cm2/Vs)
5/20 (0.3) /1
300
1.0×1013
1.19×1013
2450
1.4×1013
1500 [41]
16/13 (0.25) /1
200
1.0×1013
1.12×1013
12134
300
1.0×1013
1.12×1013
2496
8.8×1012
1900 [22]
400
1.0×1013
1.12×1013
1091
500
1.0×1013
1.12×1013
700
600
1.0×1013
1.12×1013
522
200
1.0×1013
6.03×1012
1556
300
1.0×1013
6.03×1012
954
400
1.0×1013
6.03×1012
566
500
1.0×1013
6.03×1012
408
16/13 (0.25) /2
Calculation
10
Experiment
ACCEPTED MANUSCRIPT 600
1.0×1013
6.03×1012
321
20/17.6 (0.25) /2
300
1.0×1013
5.99×1012
2388
4/20 (0.3) /1
300
4.0×1012
1.18×1013
2403
3.0×1012
2000 [44]
300
1.0×1013
1.23×1013
2717
7.5×1012
2210 [44]
300
2.0×1013
1.3×1013
3294
1.0×1013
742 [44]
2361 [23]
Figure 6 illustrates the electronic mobility as a function of d1 for the Al2O3/17.6nm Al0.25Ga0.75N/2nm AlN/GaN, Al2O3/13nm Al0.25Ga0.75N/1nm AlN/GaN, Al2O3/20nm Al0.3Ga0.7N/ 1nm AlN/GaN and Al2O3/13nm Al0.25Ga0.75N/GaN heterostrutures at 300K when nfix is taken as 1.0×1013 cm-2. As shown in the figure, the mobility decreases with increasing d1, but varies irregularly with d2. This is because that increasing d1, though not changing electronic wave functions (shown in Fig. 3(a)) and phonon’s potentials, will reduce ns (see Fig. 2(a)). And this reduction leads to a decrease of mobility according Eq. (4). However, although a wave function increases slightly (seeing Fig. 3(b)), the change of mobility is irregular with raising d2 due to the fluctuation of potential shown in Fig. 4(d). In addition, the 2DEG’s mobility was calculated for an Al2O3/13nm Al0.25Ga0.75N/GaN structure without AlN interlayer for comparison. The results show that the mobility will be steeply improved if an AlN interlayer is introduced. The reason is that the impact of IF phonons is comparable to that of HS phonons in an Al2O3/AlGaN/GaN structure which has been proved in our previous work [26]. However, it can be ignored when AlN layer is inserted between AlGaN barrier and GaN channel. This means that the rise of mobility is not only due to the decreases of interface roughness and alloy disorder scatterings considered by other authors, but also because the effect of IF phonons is weakened after introducing the interlayer. It is believed that the latter is the main reason at high temperatures. The asterisks in Fig. 6 represent the experimental values of mobility which are 2210 cm2/Vs for 4nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN [44], 1500 cm2/Vs for 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN [41], 1900 cm2/Vs for 16nm Al2O3/13nm Al0.25Ga0.75N/1nm AlN/GaN [22] and 2361cm2/Vs for 20nm Al2O3/17.6nm Al0.25Ga0.75N/2nm AlN/GaN structures [23], the corresponding values calculated in this paper are 2715, 2450, 2496 and 2388 cm2/Vs, respectively. For clarity, these values of mobility and the corresponding charge densities are also listed in Table 1. 11
ACCEPTED MANUSCRIPT
Fig. 8. 2DEG’s mobility μ as a function of the Fig. 7. 2DEG’s mobility μ vs thickness d3 of AlN layer at different temperatures.
fixed charge density nfix in comparison with the experimental values [44].
Figure 7 describes the mobility as a function of d3 for a 16nm Al2O3/13nm Al0.25Ga0.75N/1~2.3nm AlN/GaN structure at temperatures of 200, 300, 400, 500 and 600K. Similar to the effect of d1, the mobility declines obviously when d3 varies from 1nm to 2.3nm. The reason of this result can be found from the above three figures. It can be seen from Figs. 3(c) and 4(e) that as d3 increases, both electronic wave functions and phonon’s potentials are strengthened to induce an intensive interaction between electrons and phonons. Meanwhile, a decrease of ns with increasing d3 is shown in Fig. 2(a). According to Eq. (4), all these changes result in a downward trend of the mobility, and the same trend was reported in Refs. [27] and [45] for AlGaN/AlN/GaN and AlInN/AlN/GaN structures. In combination with the previous comparison between the two cases with and without the interlayer in Fig. 6, this result reveals that an AlN interlayer helps to increase the mobility when its thickness is thin enough. This is the reason why the 1 or 2nm wide interlayer is commonly used in previous studies [22,23,41,44]. It is also found from Fig. 7 that the mobility is significantly reduced as increasing temperature due to the enhancement of thermal vibration amplitude of atoms [21,44]. The calculated mobilities are also given by Table 1 for 16nm Al2O3/13nm Al0.25Ga0.75N/1 or 2 nm AlN/GaN structures at different temperatures. 3.2. Influence of fixed charges on the mobility Many studies suggest that the fixed charges at the interface between passivation layer Al2O3 and barrier AlGaN affect the mobility of 2DEG in MOS HEMTs due to the remote charge scattering. But their influence on the mobility of Al2O3/AlxGa1-xN/AlN/GaN heterostructures has not been investigated, so it is necessary to study it for deeply understanding of properties in these 12
ACCEPTED MANUSCRIPT structures. The mobility as a function of nfix is given in Fig. 8 for 4nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure. It can be seen that the mobility reaches a maximum at around 2.2×1013cm-2 when nfix varies from 4×1012 to 3.5×1013cm-2 (the corresponding range of ns is from 1.18×1013 to 1.6×1013 cm-2 and was given by Eq. (3)). It is clear that the mobility will show the same variation as ns increases because ns is proportional to nfix according to Eq. [3]. The inset in Fig. 8 shows the experimental results of the same structure in Ref. [44] for ns from 1011 to 1013 cm2.
It can be seen that the theoretical values are consistent with the experimental ones from the
general trend. And a similar result was given for a SiN/AlGaN/AlN/GaN structure [46]. The values of mobility for
some given fixed charge are given in Table 1.
4. Conclusions In summary, the influence of optical phonons on 2DEG’s mobility has been investigated in details in Al2O3/AlxGa1-xN/AlN/GaN structures by the transfer matrix and finite difference methods. The results show that increasing temperature and the thickness of Al2O3 or AlN layer reduces the electronic mobility. The mobility almost drops by one order of magnitude when Al component in AlGaN increases from 0.2 to 1, so the effect of ternary mixed crystals should not be ignored. It is also found that bigger density of fixed charge will increase the mobility, with the most appreciate value being about 2.2×1013cm-2 for a 4nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure. Meanwhile, a comparison is conducted between the structures with and without AlN interlayer. The results show that introducing an interlayer improves the mobility not only because of the reduction of alloy disorder scattering, but also because the scattering from IF phonons is significantly weakened when the interlayer is thin enough, usually being 1nm. The paper helps deepening the understanding of optical phonons and electronic mobility in HEMTs with these structures. Acknowledgements The work was supported by the National Natural Science Foundations of China (Grant Nos. 61274098 and 11304142) and the Natural Science Foundation of Inner Mongolia Autonomous Region (Grant No. 2016MS0619). The authors also would like to thank Z. Gu and Y. H. Zan for helpful discussions.
References 13
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ACCEPTED MANUSCRIPT LIST OF FIGURE AND TABLE CAPTIONS Fig. 1. Structure diagram of an Al2O3/AlGaN/AlN/GaN MOS HEMT. Fig. 2. Sheet densities ns of 2DEG vs (a) Al2O3 thickness d1, Al0.3Ga0.7N thickness d2, AlN thickness d3 and (b) Al component x for different thicknesses of passivation Al2O3. The asterisk in (a) represents the experimental value of ns for a 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN structure [41]. Fig. 3. Band diagrams and wave functions vs (a) Al2O3 thickness d1, (b) Al0.3Ga0.7N thickness d2, (c) AlN thickness d3, and (d) Al component x. Fig. 4(a) Dispersion relations of HS phonons oscillating in GaN channel, (b) potentials of eight branches of highfrequency phonon modes and (c)low-frequency phonon modes, (d) potentials of one branch of lowfrequency phonon modes for different thicknesses d2 of Al0.3Ga0.7N , (e) d3 of AlN and (f) Al component x. Fig. 5. 2DEG’s mobility μ vs Al component x for
a 16nm Al2O3/13nm AlxGa1-xN/AlN/GaN structure.
Fig. 6. 2DEG’s mobility μ vs thickness d1 of Al2O3 layer for different structures. Triangles represent the experimental results of the mobility for 4nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN [44], 5nm Al2O3/20nm Al0.3Ga0.7N/1nm AlN/GaN [41], 16nm Al2O3/13nm Al0.25Ga0.75N/1nm AlN/GaN [22] and 20nm Al2O3/17.6nm Al0.25Ga0.75N/2nm AlN/GaN [23] structures, respectively. Fig. 7. 2DEG’s mobility μ vs thickness d3 of AlN layer at different temperatures. Fig. 8. 2DEG’s mobility μ as a function of the fixed charge density nfix in comparison with the experimental values [44]. Table 1. The calculated and experimental values of fixed charge and 2DEG sheet densities and mobility at different tempratures in some structures.
17
ACCEPTED MANUSCRIPT Highlights
The effects of optical phonon modes on electronic mobility were studied in Al2O3/AlGaN/AlN/GaN heterojunctions.
The two-mode of property of TO phonons in AlxGa1-xN material was included.
The effect of ternary mixed crystals was considered in this structure.
Electronic mobility is improved by introducing AlN interlayer.