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6  Bias Temperature Instability

The Bias Temperature Instability (BTI) is a time, temperature and electric field dependent effect encountered in metal-oxide-semiconductor (MOS) field effect devices, leading to a drift in the threshold voltage Vth  [112, 113, 29] (cf. Figure 6.1). The drift in threshold voltage is usually measured as a drift in drain Id or source Is current over time. Depending on the gate voltage Vg, it is either referred to as negative BTI (NBTI), if Vg ≤ 0, or as positive BTI (PBTI), if Vg > 0. It has been established that BTI is due to the formation of chargeable defects inside the gate insulator or directly at the interface of the gate insulator in MOS devices, especially MOSFETs  [114, 115, 29]. The exact influence of temperature, oxide field and stress time on the time evolution of ΔVth has been established by carefully designed experiments, which will be briefly introduced in Section 6.1. Any diffrences in the setup lead to a misinterpration of the measurement data and unreproducability (by other researchers) of the experiment  [116]. A typical BTI experiment (cf. Figure 6.2) involves a temperature-controlled environment, fast voltage and if possible temperature transients as well as fast and highly accurate measurement equipment  [117]. For simulation of BTI, it is important to design the simulation such that the input (voltages, temperature, stress time, etc.) over time is as close as possible to the design of the experiment in order to avoid any errors.

PIC

Figure 6.1: Threshold voltage drifts at elevated temperatures depending on the oxide field. The plot shows the result of a measure-stress-measure experiment (symbols) at 150°C for various stress gate voltages. During recovery the gate voltage was kept at the nominal threshold voltage. Between the end of stress and the first measurement point in recovery is a delay of 1ms. For comparison a fit of the Two-Stage model to the data (lines) is also shown. Most evident is the asymmetry in time between stress and recovery. Data are taken from  [118].

In this chapter the intricacies involved in numerically assessing BTI and numerically reproducing measurement results will be laid out. The origins and physical descriptions for BTI available so far will be briefly summarized in Section 6.2. For an exhaustive discussion of the physical background, historic BTI models and mathematical modelling the reader is referred to  [112, 113, 29]. Historically the role of hydrogen in the gate oxide is of high importance. Nevertheless, this work will not cover the influence of hydrogen in the gate oxide on the degradation. Details on the influence of the hydrogen concentration in the oxide on BTI is for example given in  [119, 120].

 6.1  Measurement Techniques
  6.1.1  Measure Stress Measure Technique
  6.1.2  On-the-Fly Technique
  6.1.3  Direct Current Current Voltage
  6.1.4  Time Dependent Defect Spectroscopy
 6.2  Models for the Bias Temperature Instability
  6.2.1  Phenomenological Models
  6.2.2  Non-radiative Multiphonon Transitions
  6.2.3  Structural Relaxation
  6.2.4  The four State NMP Model
 6.3  Implementation and Requirements
  6.3.1  Self-Consistent Solutions
  6.3.2  Parameter Dispersion
  6.3.3  Suitable Transport Models
 6.4  Model Evaluation on pMOSFETs using the Direct Current Current Voltage Method
  6.4.1  Experimental Setup
  6.4.2  Comparison of SRH and the four State NMP Model
 6.5  Results on Trap-Assisted Tunneling

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