Bipolar Transistor and MOSFET Device Models

We discuss some basic properties of semiconductors which are crystals and consist of many atoms with periodic fashion. The energy band formation of the crystal is qualitatively presented, which leads to a concept of effective mass. We can treat electrons in conduction band as free ones using this effective mass concept. The motion of electrons in non-filled valence band can be expressed with holes with positive charge. We then evaluate intrinsic carrier concentration in crystalline silicon and energy density using semi-classical quantum theory and Fermi level is defined. The carrier concentration is controlled by donors or acceptors over a wide range. The free carries are scattered by fluctuation of periodic potential in the crystal structure. The main scattering mechanism is lattice vibration and doped impurities. This scattering is related to carrier mobility. The current and continuity equations are then derived. All these above are basic concepts used in this book.

pn junction is a basic component of other devices such as bipolar transistors and MOSFETs. Therefore, the analysis in this chapter is indispensable for understanding the devices treated in entire of this book. The prominent feature of pn junction is that it rectifies the current flow, where it allows current flow in one direction but not in opposite direction. We study the potential distribution, current voltage characteristics, and breakdown of the pn junction.

Cancer consists of a wide range of diseases that are mainly driven by the continuous unregulated proliferation of cancer cells. Current treatment options include the use of chemotherapies, radiotherapy, and surgery. Recently, there was an increased interest in applying nanoparticles (NPs) in cancer diagnosis and treatment. NPs are materials in the size range 1 to 100 nm and can be classified based on their properties, shape, or size. They have attracted wide attention because of their versatile physicochemical properties, nanoscale sizes, high surface-to-volume ratios, favourable drug release profiles, and targeting modifications. Nanotechnology can be used to improve the personalisation of cancer diagnosis and treatment by enhancing the detection of cancer-specific biomarkers, imaging of tumours and their metastases, specific drug delivery to target cells, and real-time observation of treatment progression. This chapter will highlight the main types of lipid NPs with their preparation methods. The clinical applications of these lipid NPs in cancer diagnosis and treatment will be presented along with the currently approved drugs based on these NPs.

We show the bipolar transistor models in low injection region, where the injected minority carrier concentration is much smaller than doping concentration. We describe the emitter, base, and collector current models, and related circuit parameters. The transit times in emitter, base, and collector regions are also important for circuit performance, and corresponding models are described. We first treat models for uniformly doped device, and extend them to the ones for non-uniform doped devices. Polycrystalline Si (poly-Si) is used for diffusion source to form emitter region in bulk Si. This poly-Si also plays a role as an emitter, and the related models are described. Further, we analyze the optimum base doping profile to minimize base transit time. We also cover the models for base width modulation and base resistance related to the lateral current flow beneath emitter region. Finally, we describe small signal, and large signal circuit model.

Electric field and collector depletion region are modulated by injected electrons when collector current density increases. Using a perturbation approximation, the collector current and base transit time models were derived in any injection region. The models were derived assuming the uniformly doped transistors, and then they were extended to the arbitrary doped transistors. The modulated electric field improves the base transit time for uniformly doped base while it degrades for Gaussian doped one. The collector depletion region is vanished when the collector current density increases, and neutral base region widening occurs. This is called Kirk effect and the related model is presented. It is also noted that the lateral voltage drop along the emitter-base junction cannot be neglected in high injection region. This induces the emitter current crowding at the emitter edge, which is also treated in this chapter.

Metal-oxide-semiconductor field-effect transistor (MOSFET) is the most important device in VLSI (very-large-scale integrated circuit). The fundamental part of MOSFET is MOS diode, and we analyze the surface potential model of the diode, which emerges threshold voltage. We then analyze the drain current model considering carrier velocity saturation at the drain edge. We further analyze channel length modulation, velocity overshoot, and source-drain series resistance. We finally show the scaling theory of the device, which shows a guide line to minimize the device ensuring device operation.

Non uniform channel doping profile enables us to control threshold voltage suppressing short channel effects. We showed how threshold voltage V_th is controlled for various channel doping profiles such as epi-channel, and counter doped channel. V_th is controlled by the thickness of epi-layer in epi-channel MOSFETs and it is controlled widely with centroid and dose in counter doped channel MOSFETs. The models were verified by comparing with numerical data. The feasibility of counter doped channel is also studied.

Short channel MOSFET model was presented. The difficulty for the model exists in that depletion width changes along the channel. A universal channel depletion width parameter was proposed, which effectively expresses the channel depletion width variation for various device parameters and bias conditions. Using this parameter, a two-dimensional potential distribution was solved and a corresponding threshold voltage model was derived, which reproduces the numerical data of sub-0.1-m gate length devices. We further extend the model to non-uniform channel doping devices of epi-MOSFETs.

Single-gate SOI MOSFET has been proposed to alleviate scaling limit of bulk MOSFETs. We show an analytical model for threshold voltage for the device considering two-dimensional effects in both SOI and buried oxide layers. The model explains the dependence of short channel effects on the device parameters of channel-doping concentration, gate oxide, SOI, and buried oxide thicknesses, which agree well with numerical data.

Double-gate SOI MOSFET is proposed to overcome the scaling limit of bulk MOSFETs. The device structure and corresponding device characteristics are quite different from those of bulk MOSFETs. The potential distribution of the device is investigated. The models for long channel and short channel devices are derived. The results show that remarkable attention should be paid to the threshold voltage adjustment of the double-gate SOI MOSFETs. n+-p+ polycrystalline Si gate double-gate SOI MOSFETs are also proposed to adjust the threshold voltage without introducing new gate materials, and their superb device characteristics are demonstrated.

Parasitic capacitance and resistance associated with source/drain silicide contacts are not scaled down, and they have a large influence on the device characteristics considering the scaling effect. The fringe capacitance and source/drain resistance are investigated in this chapter. Futher, the impact of B penetration through gate oxide on threshold voltage is analyzed. As the device is scaled down, the impurities in polycrystalline Si gate tend to penetrate the substrate through the thin gate oxide, and the influence of the penetrated impurity to the shift of threshold voltage becomes significant.