Compact Modeling of Physical Mechanisms Present in the Weak Breakdown Regime of Advanced Si and SiGe Bipolar Transistors

With the current increasing demand for faster and more reliable communication and computing electronic devices such as faster wireless communication networks, circuit designers are forced to carry out device optimization in order to achieve the maximum possible performance. To enable full circuit optimization, designers depend on compact models for the different circuit elements; this means that the compact models for the individual elements need to be accurate and reliable in order to achieve the best possible performance under different bias and temperature conditions. For present day RF bipolar transistors, there is a trade-off between device speed and breakdown voltage, i.e., faster devices have got a lower breakdown voltage; this imposes a great difficulty in devices such as power amplifiers, which require both high currents and voltages. For this, circuit designers are forced to explore device operation beyond certain breakdown voltages. Thus, the need for reliable compact models that can be used to accurately simulate the transistor characteristics in the breakdown regime under different operation conditions. This thesis addresses the physical mechanisms that are relevant and significant to breakdown characteristics of present day industrial Si BJT's and SiGe HBT's. As is demonstrated in the thesis, the standard Mextram model version 504.10, for example, actually is not capable of accurately simulating characteristics in the weak collector-base breakdown regime as a function of both bias and temperature, even though all appropriate temperature scaling rules, well established as they have been in the past for previous generations of semiconductor technology, appear to have been applied. This thesis analyses and resolves this inadequacy of Mextram. With respect to the physics involved, the key questions are: what are the mechanisms in this regime responsible for these misfits and how can they be addressed in order to achieve accurate model simulations? Addressing these questions formed the goal of this thesis. Between the introduction to the thesis provided in Chapter 1, and the overview of the conclusions and potential future prospects presented in Chapter 5, the thesis progresses as follows. In Chapter 2 an extraction method for base resistance (RB) and thermal resistance (RTH) of Si/SiGe bipolar transistors is presented. This method uses the measurements of the transistor characteristics in the weak collector-base breakdown regime, to accurately determine RB and RTH, by consistently accounting for the influence of self-heating and Early effect on the internal base-emitter voltage. Generally this method extends the category of the methods that utilizes the weak collector-base avalanche current to vary the base and collector currents independently of the emitter current, while eliminating voltage fluctuations across the emitter resistance by enforcing a fixed emitter current. The method was demonstrated on measured data taken on present day RF SiGe HBT's, and the corresponding results were compared with those from other earlier published extraction methods. By using the simulated data of the standard Mextram compact model as the input data of the method (instead of the measured data), we carried out a self-consistency check of the method; from the corresponding results, our extraction method yielded more accurate values for RTH than the earlier proposed methods. The RTH from this method is used later in Chapter 4 to take into account the influence of self-heating on the electrical characteristics in this weak collector-base breakdown regime. In Chapter 3, an extended review of the relevant and significant physical mechanisms that are responsible for the deviations between the measured family of weak breakdown characteristics and their simulated counterparts, as a function of both bias and temperature is carried out. Firstly, an extensive review of the physical mechanisms addressed by the Mextram compact model is undertaken. Secondly, a development of a physics-based compact model formulation of non-local avalanche effects in bipolar transistors and their temperature dependencies is carried out. The physical basis of this non-local avalanche model is the approximate energy balance equation and Chynoweth's empirical law for impact-ionization. The ionization coefficient as a function of the electron temperature, turned out to be a sharped peaked function about the maximum position. The approximate expression for the multiplication factor is attained by Taylor series expansion of the integral of ionization coefficient over epilayer width, in terms of the relative width of the function peak. With only two new model parameters, the final expression for the weak avalanche current turned out to be explicit in nature and in terms of elementary function, so it could easily be implemented in existing full compact bipolar transistor models. A compact formulation suitable for industrial applications of this non-local avalanche model was also derived and it accurately approximates the original formulation for low and intermediate collector currents, but it suppress the avalanche current for high collector currents. Using the existing Mextram model electric field distribution, the Mextram model was extended with the new non-local avalanche model; the resulting extended version of Mextram is physical in nature with only two new introduced model parameters, i.e., the relaxation length and its temperature coefficient. This extended model version is used to assess the relevant and significant physical mechanisms in the weak collector-base breakdown regime. Chapter 4 is devoted to an experimental assessment of the family of weak collector-base breakdown characteristics by employing the physical extended version of the Mextram model (with included the non-local avalanche compact model) derived in Chapter 3. Using the measurement data taken on present day Si/SiGe industrial bipolar transistors, we demonstrate that these observed breakdown characteristics are actually not just classical local/non-local avalanche characteristics as portrayed in most published literature, but other physical mechanisms are significant as well in this breakdown regime. We showed that these physical effects can actually be distinguished, and thus taken into account independently of avalanche effects. Here, we took advantage of the well developed physical basis of the Mextram compact model in addressing these effects, together with our extraction method for RTH developed in Chapter 2 to address self-heating effects on the measured electrical characteristics that significantly interfere in the weak collector-base breakdown regime. With these interfering physical effects well addressed, we demonstrated that the avalanche mechanism responsible for the deviations between the measured and simulated breakdown characteristics is non-local avalanche indeed, and with non-local effects adequately taken into account, accurate model fits to the measured characteristics taken on present day industrial Si/SiGe bipolar transistors are achieved as a function of both bias and temperature. Also with these physical effects adequately taken into account, the developed model (Mextram extended with our new non-local avalanche compact model) actually captures the presupposed underlying semiconductor device physics. Here, our extracted values for the electron energy relaxation length and its temperature coefficient, in actual industrial bipolar devices under normal forward bias conditions, are in agreement with earlier independent published values for these material coefficients. Though the relevant and significant physical mechanisms in the weak collector-base breakdown regime, each separately, have already been published in semiconductor device literature, and while most of them have been adopted in standard compact models for bipolar transistors, these effects cannot be used individually to address the deviations between the measured and simulated family of characteristics in this regime. All of them must be jointly taken into account in order to achieve accurate simulation of the characteristics in this breakdown regime; this is well demonstrated and verified in Chapter 4. Since the derived extended version of Mextram model is physical in nature, and the new model parameters are indeed material coefficients, with parameter values already available in published semiconductor device literature, the new compact model can be used to extract or verify model parameters representing other physical effects that interfere in the weak collector-base breakdown regime. Also the physical basis of the model can form a foundation for extension of the model to strong avalanche breakdown regime.