Charge Trapping and Variability in CMOS Technologiesat Cryogenic Temperatures

1.4 Scope and Outline of this Work

In this work, two approaches for developing a better understanding of MOSFET reliability at croygenic temperatures are followed. A theoretical, modeling approach presented in Part I Modeling and Simulation of Defects, in which an efficient charge trapping model for cryogenic temperatures is developed. In Part II Defect Characterization at Cryogenic Temperatures, various characterization, reliability and variability studies on multiple technologies are presented and analyzed with the models from Part I.

Part I \( - \) Modeling and Simulation of Defects

  • • Chapter 2 \( - \) Defect Candidates
    This chapter reviews specific defect candidates which have been found to play a major role in device degradation during operation. The defect candidates for SiO2 , SiON and HfO2  insulators have been studied in detail with theoretical tools such as density functional theory (DFT) or technology computer-aided design (TCAD), as well as experimentally. This allows the calculation and verification of various trap properties like densities, trap levels, relaxation energies or their typical spatial positions.

  • • Chapter 3 \( - \) Charge Transfer Models
    Charge trapping in oxides is a stochastic process which describes the exchange of charge carriers between a trap and a reservoir. A mathematical description of this trapping and detrapping process is essential for reliability studies. First models developed in the 1950s have been steadily improved for allowing precise simulations of measurements. In this work, the 2-state nonradiative multiphonon (NMP) models is used. This model is valid even in the limit of cryogenic temperatures, however, it is computationally expensive and thus not suitable for reliability simulations. Therefore, an efficient WKB-based charge transition model is derived in this work. This model is numerically superior and gives very precise results compared to the full model. An even more efficient model is presented, which is based on the assumption of non-deforming potential energy surfaces during charge transitions.

  • • Chapter 4 \( - \) Reliability Simulations
    The charge transition models presented in Chapter 3 are now used for reliability simulations. For this, the WKB-based approximation of the 2-state NMP model was implemented in the device reliability simulator Comphy. Comphy uses a surface potential based 1-dimensional electrostatics. By sampling thousands of defects in the oxide, the electrical response of these defects after applying a gate voltage allows to compute the caused threshold voltage shift. These simulations are used to compare the theoretical studies with measurements.

Part II \( - \) Defect Characterization at Cryogenic Temperatures

  • • Chapter 5 \( - \) Measurement Setup and Technologies
    Two different measurement setups have been used within this work to characterize various MOSFET technologies. On cryogenic probe stations, electrical measurements between 4.2 K and room temperature have been conducted using a Helium cooling system. Manual probe arms allowed the characterization of large-area planar high-κ-metal gate devices, planar SiON devices and planar MoS\( _2 \) devices. Since manual probing is a very time-consuming task and only a handful of devices can be characterized at once, a different approach was chosen to obtain statistical data representative for a certain technology. SmartArrays with thousands of transistors which can be addressed digitally have been characterized. This allows collecting large data sets and enables the study of different designs at cryogenic temperatures. In this work, time-zero variability and mismatch and their dependence on temperature and device geometry have been studied, which can be very critical especially for low-\( V_\mathrm {DD} \) applications.

  • • Chapter 6 \( - \) Time-Zero Characterization
    Time-zero studies form the foundation for every reliability study. The conduction of (math image)((math image)) curves allows the analysis of various MOSFET parameters such as threshold voltage, subthreshold swing or on-state current and their temperature dependence. The modeling of the temperature dependence of these parameters is extremely complex and must not only include the shifting Fermi level, the changing Fermi-Dirac statistics or bandgap widening but also interface and band-edge states. Time-zero characterization on SmartArrays allows studying the variability and the mismatch of the extracted parameters and their temperature dependence.

  • • Chapter 7 \( - \) Charge Noise Characterization
    Cryogenic environments are often used to minimize noise in the measurements. Thus, it is extremely important to understand the impact of low frequency noise (1/f noise) caused by traps at cryogenic temperatures. For this, the temperature and gate voltage dependence of RTN in various technologies has been studied. The findings have then be modeled with the quantum mechanical 2-state nonradiative multiphonon theory discussed in Chapter 3, which can correctly describe the temperature activation of charge trapping.

  • • Chapter 8 \( - \) Bias Temperature Instability
    In this chapter BTI studies on various technologies are presented. The different freeze-out behavior of large area SiON and high-κ metal-gate devices is discussed and modeled using the reliability simulator Comphy. For this, the quantum mechanical version of 2-state NMP theory has been used. Furthermore, BTI was studied on scaled MoS\( _2 \) devices using time-dependent defect spectroscopy (TDDS) measurements at cryogenic temperatures. Here, it is explicitly shown that single charge capture and emission events causing threshold voltage shifts are clearly visible at cryogenic temperatures.