Diffused resistors

Fig. 7.3.1 shows the principle of the piezoresistive sensor. Diffused resistors (gages) are formed on the thin-walled section called the diaphragm. An applied pressure is detected via the piezoresistive effect, which is the change in electrical resistance when a stress is applied to the diaphragm. The sensitivity is determined by the material, diameter, and thickness of the diaphragm. The thin-film piezoresistive sensor offers low sensitivity because the piezoresistive coefficient of thin-film silicon is less than one-third of that of single-crystal silicon. 

The silicon piezoresistive sensor detects distortion. Therefore diffused resistor (gage) layout and diaphragm geometry design have a profound effect on the sensor characteristics. We utilize simulation technology for pressure-sensing element design. 

The sensitivity of a piezoresistive pressure sensor depends on the piezoresistive coefficient. Silicon crystal face selection and gage layout on the crystal face are important because of the anisotropy of the piezoresistive effect. Silicon (100) and (110) are often used with P-type diffused resistors to achieve a desired sensitivity. The next consideration is the thermal stress effect originating from the silicon crystal face. Fig. 7.3.5 shows the stress-distribution maps for silicon (100) and silicon (110) by the finite element method (FEM). 

The test structures used were iridium - silicon dioxide-silicon capacitors with rather large area. Available commercial hydrogen and ammonia sensors consist, e.g., of a sensing element in the form of a transistor, a heater (a diffused resistor) and a temperature sensors (a pn-junction) on the same chip with dimensions smaller than about 1x1 mm. Research and development work is, however, in several cases most easily done on metal-insulator semiconductor capacitors mounted on a thermostatted sample holder. The description of the test structures, their fabrication and physics, given below is, however, very short. More details can be found in several of the references, e.g., ref. [1 — 3,8]. 

There has been long-standing difficulty in producing fully integrated MOS RC-op amp circuits with precise characteristics. This is because the MOS fabrication process does not result in sufficiently precise control over the absolute values of resistance and capacitance (and, hence, the RC product). In addition, MOS integrated (diffused) resistors have poor temperature and linearity characteristics, as well as requiring a large silicon area. Ordinarily the RC values cannot be controlled to better than 20%. This limitation was soon overcome by the development of circuit techniques wherein the resistor is simulated by a capacitor... 

Electrically Functional. Refractory coatings are used in semiconductor devices, capacitors, resistors, magnetic tape, disk memories, superconductors, solar ceUs, and diffusion barriers to impurity contamination from the substrate to the active layer. 

The start of the solid-state electronic industry is generally recognized as 1947 when Bardeen, Brattain, and Shockley of Bell Telephone Laboratories demonstrated the transistor function with alloyed germanium. The first silicon transistor was introduced in 1954 by Texas Instruments and, in 1956, Bell Laboratories produced the first diffused junction obtained by doping. The first-solid state transistor diodes and resistors had a single electrical function and were (and still are) known as discrete devices. 

The percutaneous absorption picture can be qualitatively clarified by considering Fig. 3, where the schematic skin cross section is placed side by side with a simple model for percutaneous absorption patterned after an electrical circuit. In the case of absorption across a membrane, the current or flux is in terms of matter or molecules rather than electrons, and the driving force is a concentration gradient (technically, a chemical potential gradient) rather than a voltage drop [38]. Each layer of a membrane acts as a diffusional resistor. The resistance of a layer is proportional to its thickness (h), inversely proportional to the diffusive mobility of a substance within it as reflected in a... 

One of the most widely used materials for the fabrication of modern VLSI circuits is polycrystalline silicon, commonly referred to as polysilicon. It is used for the gate electrode in metal oxide semiconductor (MOS) devices, for the fabrication of high value resistors, for diffusion sources to form shallow junctions, for conduction lines, and for ensuring ohmic contact between crystalline silicon substrates and overlying metallization structures. 

An explanation of the observed relaxation transition of the permittivity in carbon black filled composites above the percolation threshold is again provided by percolation theory. Two different polarization mechanisms can be considered (i) polarization of the filler clusters that are assumed to be located in a non polar medium, and (ii) polarization of the polymer matrix between conducting filler clusters. Both concepts predict a critical behavior of the characteristic frequency R similar to Eq. (18). In case (i) it holds that R= , since both transitions are related to the diffusion behavior of the charge carriers on fractal clusters and are controlled by the correlation length of the clusters. Hence, R corresponds to the anomalous diffusion transition, i.e., the cross-over frequency of the conductivity as observed in Fig. 30a. In case (ii), also referred to as random resistor-capacitor model, the polarization transition is affected by the polarization behavior of the polymer matrix and it holds that [128, 136,137]... 

The simplest model is the connection of resistor and capacitor in either series or parallel. Figure 4.2a shows the connection of a resistor and a capacitor in series. This equivalent circuit is the simplest model for an ideal polarizable electrode, with the assumption that neither the charge transfer on the electrode surface nor the diffusion limitations are present. 

If a resistor is added in series with the parallel RC circuit, the overall circuit becomes the well-known Randles cell, as shown in Figure 4.11a. This is a model representing a polarizable electrode (or an irreversible electrode process), based on the assumptions that a diffusion limitation does not exist, and that a simple single-step electrochemical reaction takes place on the electrode surface. Thus, the Faradaic impedance can be simplified to a resistance, called the charge-transfer resistance. The single-step electrochemical reaction is described as... 

A different analyser method based upon the same effect (deviating thermal conductivities of gaseous components) is shown in Fig. 6.127. The gas to be analysed diffuses into the measuring cell. Here, a thermal conductivity sensor made of three superimposed silicon chips shows a balanced (zero) output of two thin film resistors fitted on a membrane on the chip in the middle of this stack. One of these thin film resistors is exposed to the gas to be measured. Due to its thermal conductivity, the pair of thin film resistors show an unbalanced signal output. 

Example 11.5 Diffusion Impedances in Series If, as is shown in eqmtion (4.23), the impedance corresponding to two resistors in series is equal to the sum of the resistances, why is it incorrect to treat diffusion through two layers by adding two diffusion impedances ... 

Differential capacitance measurements were used to determine the extent that DMSA adsorbsonto the metal surface as a function of its concentration in solution. In this approach the metal-solution interface is modelled as a resistor and capacitor in series and if the diffuse part of the double layer is neglected, the measured capacitance can be expressed as ... 

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