Z.-W. Hsue1, T.-H. Shieh2, H.-W. Ting1, K.-M. Hung1,a) and B.-Y. Hou1, J.-L. Li1, C.-H. Nin1, Y.-C. Tsai1
1Dept. of Electronics Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan
2Dept. of Electronics Engineering, Kun Shan University, Tainan Hsien, Taiwan
Introduction
GaAs is of great interest as one of candidate channel material in complementary metal oxide semiconductor (CMOS) devices due to its high electron and hole mobility [1]. There are many difficulties in realizing GaAs CMOS devices according to different physical and chemical properties of GaAs in comparison with Si. The most challenging issues that have been widely studied include the structural evolution (SE) of HfO2 during post-dielectric processes with a large thermal budget [2], the interface instability and valence band offset (VBO) between HfO2 and GaAs [3], especially, for the HfO2 film being smaller than 2nm, which has been widely used in modern CMOS technology with the channel length smaller than 45nm [4]. However, the most studies are focused on the film greater than 2nm. The knowledge on the properties of ultra-thin HfO2 film on GaAs is poor.
In this letter, the density functional theory (DFT) is applied to study the properties of ultra-thin HfO2 film on GaAs. The oxygen-rich cubic-HfO2 (c-HfO2) and monoclinic-HfO2 (m-HfO2) are studied. The partial density of states (PDOS) and valence band offset (VBO) are calculated.
Theory and Structure Model
In this work, the DFT as implemented in the CASTEP code is applied to calculate the formation energy, partial density of states (PDOS) and VBO of ultra-thin HfO2 film on GaAs. The interaction between core and valence electrons is included by an effective (ultra-soft) pseudo-potential. The generalized gradient approximation of Perdew and Wang [5] is used for the exchange-correlation functional. A Monkhorst-Pack k-point sampling mesh 4x4x1 is used, and the cutoff energy for the basis functions is 300eV. The structure of HfO2/GaAs is modeled as a supercell which includes (i) a fifteen-monolayer (100) GaAs with fixed atomic positions and with Ga rich surfaces, (ii) a seven-monolayer (100) c(m)-HfO2 with O-rich surfaces being stacked on the GaAs, as plotted in Fig. 1(a) (Fig. 1(b)).
The fully-relaxed structure (large atoms) shows that the hafnia layer is strongly deformed to relax the highly tensile strain that is forced by GaAs substrate according to a large lattice mismatch. The dilation of hafnia layer breaks a part of Hf-O bonds to absorb the stress, and results in: (i) the 8-coordinated Hf atom in c-HfO2
collapses into 6-coordinated, and the 7-coordinated Hf atoms in m-HfO2 collapse into 5-, 6- and 7-coordinated;
(ii) the 4-coordinated O atoms in c-HfO2 relax into 3-coordinated, and the 3- and 4-coordinated O atoms in m-HfO2 relax into 2-, 3- and 4-coordinated. (iii) Since the lattice constants of m-HfO2 (a=5.18 Å, b=5.185 Å and c=5.284 Å) is more close to GaAs (5.65 Å) than c-HfO2 (5.115 Å), the structure deformation of m-HfO2 is weaker than c-HfO2 as shown in Fig. 1. Such a weaker deformation in m-HfO2, however, results in a superstoichiometric HfOy (y=2.2), but the stronger deformation in c-HfOy retains y=2. In addition, the m-HfO2
has different surfaces along (100) and (100), where a two-oxygen surface presents in (100) plane but a three-oxygen surface in (100) plane.
Fig. 1 The relaxed (large atoms) and unrelaxed (small atoms) structures of (a) c-HfO2/GaAs and (b) m-HfO2/GaAs.
Results and Discussions
The structure instability during structural evolution is studied by measuring the variation of formation energy.
The formation energy is calculated using the equation
As As O O GaAs GaAs HfO
HfO tot
f E n E n E n n E
E
2
2 , (1)
where Etot is the energy for the supercell containing nHfO2 bulk c-HfO2 molecules, nO excess O atoms, nGaAs bulk GaAs molecules, and nAs bulk As atoms. EHfO2 is the energy per molecule of bulk c-HfO2. EGaAs is the energy per molecule of bulk GaAs, EAs is the energy per atom of bulk As, and O is one half of O2 chemical potential.
The calculated results, as shown in Table-I, show that the c-HfO2 is more stable than m-HfOy. Table-I
Ef (eV) VBO (eV)
c-HfO2
unrelaxed -1.0971 2.2125 relaxed -11.446 1.2175 m-HfO2
unrelaxed 3.2097 0.7576 relaxed -3.0927 1.8894
The VBO of the structure is directly measured from PDOS [6]. In Figure 2, the calculated PDOSs for the centered GaAs and HfO2 layers are plotted. The valence band maximum (VBM) of GaAs is the average of Ga and As layers, and the VBM of HfO2 is the average of Hf and O layers.
-3 -2 -1 0 1 2
The VBO is read to be the difference of VBMs of GaAs and HfO2. The calculated results for c-HfO2/GaAs and m-HfO2/GaAs with/without relaxation, as shown in Table-I, indicate that the VBO is significantly affected by structural relaxation. The strain-induced bond breaking in hafnia layer gives rise to an additional charge transfer between HfO2 and GaAs, and results in VBO variation. For c-HfO2, the VBO decreases after relaxation according to the charge transfer from c-HfO2 to GaAs, contrarily, increases for m-HfO2 due to a backward charge transfer from GaAs. The backward charge transfer is mainly resulted from the excess O atoms in superstoichiometric HfOy, because the large electro-negativity of O atom attracts the valence electrons in GaAs into O sites.
Conclusions
The VBO of ultra-thin c-HfO2 and m-HfO2 films on GaAs substrate is studied using DFT theory. The heavy stress in hafnia layer significantly causes the structure deformation and results in a charge transfer and superstoichiometric m-HfOy. The calculated formation energy shows that the c-HfO2 is more stable than m-HfO2, which is well agreement with experiment. The VBO of the structure c-HfO2/GaAs is increased, while that of m-HfO2/GaAs is decreased after structure relaxation, according to the charge transfer between HfO2 and GaAs. These characteristics of ultra-thin HfO2 film should be observed in CMOS devices made from an ultra-thin HfO2 dielectric film stacked on GaAs channel.
Acknowledgement
This work is supported by the Science Council of the Republic of China, Taiwan, under Contract No.
References
a) To whom all correspondence to be sent: kmhung@cc.kuas.edu.tw.
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