Abstract
In this paper, two component mode synthesis (CMS) approaches, namely, the fixed interface CMS approach and the free interface CMS approach, are presented and compared for an efficient solution of 2-D Schrödinger-Poisson equations for quantum-mechanical electrostatic analyses of nanostructures and devices with arbitrary geometries. In the CMS approaches, a nanostructure is divided into a set of substructures or components and the eigenvalues (energy levels) and eigenvectors (wave functions) are computed first for all the substructures. The computed wave functions are then combined with constraint or attachment modes to construct a transformation matrix. By using the transformation matrix, a reduced-order system of the Schrödinger equation is obtained for the entire nanostructure. The global energy levels and wave functions can be obtained with the reduced-order system. Through an iteration procedure between the Schrödinger and Poisson equations, a self-consistent solution for charge concentration and potential profile can be obtained. Numerical calculations show that both CMS approaches can largely reduce the computational cost. The free interface CMS approach can provide significantly more accurate results than the fixed interface CMS approach with the same number of retained wave functions in each component. However, the fixed interface CMS approach is more efficient than the free interface CMS approach when large degrees of freedom are included in the simulation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Wong, H., Frank, D.J., Solomon, P.M.: Device design considerations for double gate, ground plane, and single-gated ultra-thin SOI MOSFET’s at the 25 nm channel length generation. IEDM Tech. Dig., pp. 407-410 (1998)
Omura, Y., Kurihara, K., Takahashi, Y., Ishiyanma, T., Nakajima, Y., Izumi, K.: 50-nm channel nMOSFET/SIMOX with an ultrathin 2- or 6-nm thick silicon layer and their significant features of operations. IEEE Electron Device Lett. 18(5), 190–193 (1997)
Park, J., Colinge, J.: Multiple-gate SOI MOSFETs: device design guidelines. IEEE Trans. Electron Devices 49(12), 2222–2229 (2002)
Hason, S., Wang, J., Lundstrom, M.: Device design and manufacturing issues for 10 nm-scale MOSFETs: a computational study. Solid-State Electron. 48, 867–875 (2004)
Lopez-Villanueva, J.A., Melchor, I., Gamiz, F., Banqueri, J., Jimenez-Tejada, J.A.: A model for the quantized accumulation layer in metal-insulator-semiconductor structures. Solid-State Electron. 38(1), 203–210 (1995)
Ohkura, Y.: Quantum effects in Si n-MOS inversion layer at high substrate concentration. Solid-State Electron. 33(12), 1581–1585 (1990)
Janik, T., Majkusiak, B.: Analysis of the MOS transistor based on the self-consistent solution to the Schrödinger and Poisson equations and on the local mobility model. IEEE Trans. Electron Devices 45(6), 1263–1271 (1998)
Tang, Z., Xu, Y., Li, G., Aluru, N.R.: Physical models for coupled electromechanical analysis of silicon nanoelectromechanical systems. J. Appl. Phys. 97(11), 114304 (2005)
Ravaioli, U., Winstead, B., Wordelman, C., Kepkep, A.: Monte Carlo simulation for ultra-small MOS devices. Superlattices Microstruct. 27(3), 137–145 (2000)
Dattta, S.: Nanoscale device modeling: the Green’s function method. Superlattices Microstruct. 28(4), 253–278 (2000)
Ren, Z., Venugopal, R., Goasguen, S., Datta, S., Lundstrom, M.S.: nanoMOS 2.5: a two-dimensional simulator for quantum transport in double-gate MOSFETs. IEEE Trans. Electron Devices 50(9), 1914–1925 (2003)
Xu, Y., Aluru, N.R.: Multiscale electrostatic analysis of silicon nanoelectromechanical systems (NEMS) via heterogeneous quantum models. Phys. Rev. B 77(7), 075313 (2008)
Stern, F.: Self-consistent results for n-type Si inversion layers. Phys. Rev. B 5(12), 4891–4899 (1972)
Khan, H., Mamaluy, D., Vasileska, D.: Fully 3D self-consistent quantum transport simulation of double-gate and tri-gate 10 nm FinFETs. J. Comput. Electron. 7, 346–349 (2008)
Li, G., Aluru, N.R.: Hybrid techniques for electrostatic analysis of nanoelectromechanical systems. J. Appl. Phys. 96(4), 2221–2231 (2004)
Sune, J., Olivo, P., Ricco, B.: Self-consistent solution of the Poisson and Schrödinger in accumulated semiconductor-insulator interfaces. J. Appl. Phys. 70(1), 337–345 (1991)
Tan, I.-H., Snider, G.L., Chang, L.D., Hu, E.L.: A self-consistent solution of Schrödinger-Poisson equations using a nonuniform mesh. J. Appl. Phys. 68(8), 4071–4076 (1990)
Kerkhoven, T., Galick, A.T., Ravaioli, U., Arends, J.H., Saad, Y.: Efficient numerical simulation of electron states in quantum wires. J. Appl. Phys. 68(7), 3461–3469 (1990)
Trellakis, A., Galick, A.T., Pacelli, A., Ravaioli, U.: Iteration scheme for the solution of the two-dimensional Schrödinger-Poisson equations in quantum structures. J. Appl. Phys. 81(12), 7880–7884 (1997)
Trellakis, A., Ravaioli, U.: Computational issues in the simulation of semiconductor quantum wires. Comput. Methods Appl. Mech. Eng. 181, 437–449 (2000)
Godoy, A., Ruiz-Gallardo, A., Sampedro, C., Gamiz, F.: Quantum-mechanical effects in multiple-gate MOSFETs. J. Comput. Electron. 6, 145–148 (2007)
Garcia Ruiz, F.J., Godoy, A., Gamiz, F., Samperdro, C., Donetti, L.: A comprehensive study of the corner effects in pi-gate MOSFETs including quantum effects. IEEE Trans. Electron Devices 54(12), 3369–3377 (2007)
Colinge, J.P.: Quantum-wire effects in trigate SOI MOSFETs. Solid-State Electron. 51, 1153–1160 (2007)
Garcia Ruiz, F.J., Tienda-Luna, I.M., Godoy, A., Donetti, L., Gamiz, F.: Equivalent oxide thickness of trigate SOI MOSFETs with high-k insulators. IEEE Trans. Electron Devices 56(11), 2711–2719 (2009)
Tang, X., Baie, X., Colinge, J.P., Gustin, C., Bayot, V.: Two-dimensional self-consistent simulation of a triangular P-channel SOI nano-flash memory device. IEEE Trans. Electron Devices 49(8), 1420–1426 (2002)
Colinge, J.P., Alderman, J.C., Xiong, W., Cleavelin, C.R.: Quantum-mechanical effects in trigate SOI MOSFETs. IEEE Trans. Electron Devices 53(5), 1131–1135 (2006)
Wang, J., Polizzi, E., Lundstrom, M.: A three dimensional quantum simulation of silicon nanowire transistors with the effective-mass approximation. J. Appl. Phys. 96(4), 2192 (2004)
Shin, M.: Three-dimensional quantum simulation of multigate nanowire field effect transistors. Math. Comput. Simul. 79, 1060–1070 (2008)
Craig, R., Bampton, M.: Coupling of substructures for dynamic analysis. AIAA J. 6, 1313 (1968)
Min, K.-W., Igusa, T., Achenbach, J.D.: Frequency window method for forced vibration of structures with connected substructures. J. Acoust. Soc. Am. 92(5), 2726–2733 (1992)
Shyu, W.H., Gu, J., Hulbert, G.M., Ma, Z.D.: On the use of multiple quasi-static mode compensation sets for component mode synthesis of complex structures. Finite Elem. Anal. Des. 35, 119–140 (2000)
Shyu, W.H., Ma, Z.D., Hulbert, G.M.: A new component mode synthesis method: quasi-static mode compensation. Finite Elem. Anal. Des. 24, 271–281 (1997)
Markovic, D., Park, K.C., Ibrahimbegovic, A.: Reduction of substructural interface degrees of freedom in flexibility-based component mode synthesis. Int. J. Numer. Methods Eng. 70, 163–180 (2007)
Craig, R.R., Chang, C.J.: Free-interface methods of substructure coupling for dynamic analysis. AIAA J. 14(11), 1633–1635 (1976)
Tournour, M.A., Atalla, N., Chiello, O., Sgard, F.: Validation, performance, convergence and application of free interface component mode synthesis. Comput. Struct. 79, 1861–1876 (2001)
Koutsovasilis, P., Beitelschmidt, M.: Model order reduction of finite element models: improved component mode synthesis. Math. Comput. Model. Dyn. Syst. 16(1), 57–73 (2010)
Craig, R.R., Kurdila, A.J.: Fundamentals of Structural Dynamics. Wiley, New York (2006)
Craig, R.R.: Coupling of substructures for dynamic analysis: an overview. In: Structures, Structural Dynamics and Material Conference (2000). AIAA-2000-1573
Rixen, D.J.: A dual Craig-Bampton method for dynamic substructuring. J. Comput. Appl. Math. 168, 383–391 (2004)
Li, G.: A multilevel component mode synthesis approach for the calculation of the phonon density of states of nanocomposite structures. Comput. Mech. 42(4), 593–606 (2008)
Aluru, N., Li, G.: Finite cloud method: a true meshless technique based on a fixed reproducing kernel approximation. Int. J. Numer. Methods Eng. 50(10), 2373–2410 (2001)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, H., Li, G. Component mode synthesis approaches for quantum mechanical electrostatic analysis of nanoscale devices. J Comput Electron 10, 300–313 (2011). https://doi.org/10.1007/s10825-011-0366-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10825-011-0366-7