ZnS宽禁带半导体毕业设计 (10)

哈尔滨理工大学学士学位论文 with the experimental values, as shown in Table 1.

Table.1. Equilibrium lattice constant a, structural parameters c/a, internal parameter u,volume V by atom, bulk modulus B, and pressure derivative of B(B')

for the different phases analyzed for AlN.

Hence, the local environment of each atom is very much the same as in the case of the zinc-blende phase and thus the resulting semi-conducting structure is very close in energy to the zinc-blende one as shown in Figures 1 and 2. This is consistent with the results of Serrano et al. [19]. Both approximations, namely

- 38 -

哈尔滨理工大学学士学位论文 LDA and GGA give almost the same values for u and c/a. The bulk modulus for AlN in the wurtzite structure as illustrated by our LDA calculation agrees very well with the experimental value reported in reference [19] within the experimental uncertainties, while our GGA obtained value is somewhat lower. So far, to the best of our knowledge, no experimental data have been reported for B for AlN in the zinc-blende structure. However, as compared with other published theoretical values, our results agree reasonably well with those reported in references [19, 25]. For the rocksalt structure, our LDA result is in good agreement with the experimental value reported in reference [29] within the experimental uncertainties, whereas the GGA value lies between the experimental values reported in references [28,29]. Moreover, our LDA value is consistent with the LDA results of previous calculations. The numerically calculated results for B obtained from LDA seem to be better than those obtained from GGA for both wurtzite and rocksalt structures. The B' for the wurtzite and zinc blende phases has almost the same value as illustrated by either LDA or GGA. These values compare well with the theoretical results reported in references [19, 22, 27]. For the rocksalt structure our both LDA and GGA results are in good agreement with the X-ray diffraction data reported in reference [29] within the experimental uncertainties. It is worth noting that the lattice constants obtained from LDA are smaller than those calculated from GGA,however the reverse is seen for the bulk moduli. This is a well-known trend. As a matter of fact, on the basis of Figures 1 and 2 where the LDA and GGA curves are almost similar (the difference in energy is too small) and are ?t to the Murnaghan’s equation of state, and giving the fact that the lattice constant is overestimated by the GGA and underestimated by the LDA, one may expect an underestimation of the bulk moduli by the GGA and an overestimation by the LDA The transition pressure (Pt) between wurtzite to rocksalt and zinc-blende to rocksalt of AlN were determined directly from the information contained in Figures 1 and 2. We have determined the common tangent between the stable

- 39 -

哈尔滨理工大学学士学位论文 Table 2. Transition pressures and relative volume changes for the wurtzite to

rocksalt and zincblende to rocksalt structures.

structures as pressure is increased (or volume is decreased). The slope of the common tangent, corresponds to minus the coexistence pressure for the low-and high pressure phases, and the volume of each phase at the transition (the transition volume Vt) corresponds to that at the tangent point. In Table 2, our calculated Pt and relative volume changes (?Vt/V0) are presented and compared with experiment where possible as well as with other available theoretical results. According to our LDA calculation, a structural phase transformation from the wurtzite phase to a six fold coordinated rocksalt phase occurs at 20.91 Gpa with a relative volume change of 20.67%. However, our GGA value is somewhat larger as regards Pt. Experimentally, the wurtzite to rocksalt transition in AlN has been reported to start at 22.9 Gpa by Ueno et al. [30], at 14 Gpa by Xia et al. [28], and more recently at 20.0 Gpa by Uehara et al. [29]. Our LDA value is in good agreement with the experimental one reported more recently by

- 40 -

哈尔滨理工大学学士学位论文 Uehara et al. [29], whereas the GGA value is larger than those reported in references [28–30]. In contrast, our ?Vt/V0 obtained from both LDA and GGA calculations are close to each other and are somewhat larger than theexperimentally reported ones in references [28, 30]. Comparing to theoretical data published previously, our results regarding Pt are larger than those reported by Christensen and Gorczyca [27] using the self-consistent linear-muffn-tin orbitals (LMTO) band-structure calculations, and signi?cantly different from those reported recently by Serrano et al.[19] performed within the framework of the density-functional theory (DFT) with the local-density approximation (LDA). We are more con?dent to our results since they are closer to the experiment than those of references [19, 27]. The transition pressure for AlN from the zincblende phase to the rocksalt phase is found to occur at Pt =19.69 and 25.75 Gpa with ?Vt/V0 of 20.99 and 20.56% within the LDA and GGA, respectively. Our results in both approaches are once again very different from that reported in reference [19] as regards Pt. However, our ?Vt/V0 obtained from both LDA and GGA are close to each other and agree very well with that of reference [19]. In the absence of the experimental data regarding the Pt from zinc-blende to rocksalt, to the best of our knowledge, no comments could be ascribed to the accuracy of our results. In addition, one can note that the use of a GGA in dealing with the exchange-correlation energy functional, instead of the LDA adopted in the present work, enlarges the value of Pt in both transition cases: Wurtzite→ Rock-salt and zinc-blende→Rocksalt. However, this does not result in any clear difference as regards ?Vt/V0. According to Uehara et al. [29] the maximum pressure achieved in high-pressure experiments on AlN was 132 Gpa and up to this pressure the rocksalt structure does not undergo any further transitions. The local dynamical stability of the high-pressure rocksalt phase in the group-III nitrides has been explained by Serrano et al. [19] to be due particularly to the large ionicity in group-III nitrides as compared to the rest of the III–V compounds.

- 41 -

哈尔滨理工大学学士学位论文 4 Conclusion

In conclusion, we have presented structural parameters of wurtzite, zinc-blende and rocksalt AlN as calculated using the DFT with both the LDA and GGA. The transition pressures and their corresponding relative volume changes for both transformations from the wurtzite to rocksalt and from the zincblende to rocksalt structures have also been determined. The results are in good agreement with available experimental data and showed signi?cant improvement as compared to the previous published theoretical calculations yielding thus a consistent theoretical description of the material of interest that belongs to a class of technologically important semiconductor compounds.

One of us S.S. would like to thank Dr. M. Cote from the University of Montreal (Canada) for providing numerical support. References

1. H. Morkoc, S.N. Mohammad, Science 267, 51 (1995)

2. J.W. Orton, C.T. Foxon, Rep. Prog. Phys. 61, 1 (1998) and references cited therein

3. S.C. Jain, M. Willander, J. Narayan, R. Van Overstraeten, J. Appl. Phys. 87, 965 (2000) and references cited therein

4. I. Vurgaftman, J.R. Meyer, L.-R. Ram-Mohan, J. Appl. Phys. 89, 5815 (2001) and references cited therein

5. I. Vurgaftman, J.R. Meyer, J. Appl. Phys. 94, 3675 (2003) and references cited therein

6. Y.F. Wu, B.P. Keller, S. Keller, D. Kapolnek, P. Kozodoy, S.P. Denbaars, U.K. Mishra, Appl. Phys. Lett. 69, 1438 (1996)

7. A. Rubio, J.L. Corkill, M.L. Cohen, E.L. Shirley, S.G. Louie, Phys. Rev. B 48, 11810 (1993)

8. K. Lawniczak-Jablonska, T. Suski, I. Gorczyca, N.E. Christensen, K.E. Attenkofer, R.C.C. Perera, E.M. Gullikson, J.H. Underwood, D.L. Ederer,

- 42 -

搜索“diyifanwen.net”或“第一范文网”即可找到本站免费阅读全部范文。收藏本站方便下次阅读，第一范文网，提供最新小学教育ZnS宽禁带半导体毕业设计 (10)全文阅读和word下载服务。