Hybrid functional versus quasiparticle calculations for the Schottky barrier and effective work function at TiN/HfO 2 interface
Hybrid functional versus quasiparticle calculations for the Schottky barrier and effective work function at TiN/HfO 2 interface
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DOI：
10.1103/physrevb.87.075325
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发表时间：
2013-02
影响因子：
3.7
通讯作者：
Y. Oh;A. Lee;H. Noh;K. Chang
中科院分区：
文献类型：
--
作者：
Y. Oh;A. Lee;H. Noh;K. Chang
通过密度泛函计算，研究了TiN/HfO界面上的Schottky势垒和有效功函数（EWF）。对于由Ti-O或N-Hf界面键组成的不同界面，本征金属诱导的间隙态几乎与界面结构无关，在氧化物中的衰变长度相似。由于弱的费米能级钉钉作用，EWF对界面键合的外在效应更为敏感。当富n键被富o键取代时，EWF降低了0.36 eV，这是由于形成了相反的界面偶极子。为了改善带隙和EWF，我们进行了混合泛函和准粒子（QP）计算。在$G{W}_{0}$近似中，仅通过更新QP能量自洽地计算格林函数并使用全频率相关的介电函数，大大提高了EWF与实验的一致性，而在${G}_{0}{W}_{0}$水平上计算QP或使用等离子体极介电函数容易高估EWF。在自洽$GW$方法中，QP能量和波函数都在迭代中更新，带隙被高估，导致EWF较低。另一方面，由于HfO${}_{2}$的价带边缘位移较大，杂化泛函严重低估了EWF。
We investigate the Schottky barrier and effective work function (EWF) at TiN/HfO${}_{2}$ interface through density functional calculations. For different interfaces that consist of either Ti-O or N-Hf interface bonds, the intrinsic metal-induced gap states are nearly independent of the interface structure, with similar decay lengths into the oxide. Due to the weak Fermi-level pinning, the EWF is more sensitive to the extrinsic effect of interface bonding. As N-rich interface bonds are replaced by O-rich bonds, the EWF decreases by up to 0.36 eV, which is attributed to the formation of opposing interface dipoles. To improve the band gap and EWF, we perform both hybrid functional and quasiparticle (QP) calculations. In the $G{W}_{0}$ approximation, in which the Green's function is self-consistently calculated by updating only QP energies and the full frequency-dependent dielectric function is used, the agreement of the EWF with experiment is greatly improved, while QP calculations at the ${G}_{0}{W}_{0}$ level or using the plasmon-pole dielectric function tend to overestimate the EWF. In the self-consistent $GW$ approach, in which both QP energies and wave functions are updated in iterations, the band gap is overestimated, resulting in the lower EWF. On the other hand, the EWF is severely underestimated with the hybrid functional because of the larger shift of the valence band edge level of HfO${}_{2}$.