A working single-level trap model and a resistivity scaling law for the proton-induced high-resistivity silicon

A particle-enhanced isolation technology had previously been proposed to direct energetic proton flux on VLSI-processed mixed-mode IC wafers before packaging for the prevention of undesirable substrate coupling [C.P. Liao, D. Tang, H.C. Lu, Creation of local semi-insulating regions on semiconductor substrates, US Patent 6,046,109, April 4, 2000]. Results of an improvement of 25-30 dB in noise coupling suppression and a great enhancement of two to three folds on Q values of on-chip inductors had also been reported [C.P. Liao, M.N. Liu, K.C. Juang, Cross-talk suppression in mixed-mode IC's by the π technology and the future with a SOC integration platform: particle-beam stand (PBS), IEEE Trans. Electron Dev. 50 (3) (2003) 764 (special issue on RF and SOC); C.P. Liao, T.H. Huang, C.Y. Lee, D. Tang, S.M. Lan, T.N. Yang, L.F. Lin, Method of creating local semi-insulating regions on silicon wafers for device isolation and realization of high Q inductors, IEEE Electron Dev. Lett. 19 (12) (1998) 461-462; C.P. Liao, C.W. Liu, Y.M. Hsu, Observation of explosive spectral behaviors in proton-enhanced high-Q inductors and their explanations, IEEE Trans. Electron. Dev. 50 (3) (2003) 758 (special issue on RF and SOC)]. Today, continued improvement of this technology has led to a new VLSI back-end facility: the particle-beam stand (PBS), which may ultimately become the general SOC (system-on-a-chip) integration platform. However, so far the mechanism and TCAD model behind such an approach have yet to be quantitatively determined. In this work, the establishment of an effective, self-consistent, 1-level trap model is attempted through fitting the existing single-trap-level theory [J.L. Moll, Physics of Semiconductors, McGraw-Hill, New York, 1964 (Chapter 6)] with experimentally obtained parameters and the assistance from numerical simulations of the SRIM (The Stopping and Range of Ions in Matter) code [SRIM-The Stopping and Range of Ions in Matter, a computer code constantly updated by J.F. Ziegler, J.P. Biersack. Available from: 〈http://www.srim.org/〉. A full description of the calculation is found in The Stopping and Range of Ions in Solids, by J.F. Ziegler, J.P. Biersack, U. Littmark, Pergamon Press, New York, 2003] (a charged-particle stopping-power calculation program). It is revealed that, more than merely simple traps of charge carriers, those proton-created defects are also intrinsically charged (carrying +e or −e) and thus all are participating in the Rutherford-like scattering of the remaining free charge carriers escaping the defect trapping. The found effective single trap levels (ET) are about +0.24 eV in n-Si and −0.34 eV in p-Si, measuring from the middle of the energy bandgap. Finally, a scaling law for such proton-rendered resistivity enhancement is given.