PLEASE ANSWER THE QUESTION IN FULL DETAIL. PLEASE DO NOT SKIP STEPS. Answer all

Question

PLEASE ANSWER THE QUESTION IN FULL DETAIL. PLEASE DO NOT SKIP STEPS.

Answer all questions in detail.

1) Determine the reverse saturation current for the BC PN junction

2) Assuming Vce (sat) = 0.3 volts, calculate Ic?

3) Using ideal diode equation, calculate the forward diffusion current in the BC junction diode.

4) Finally, discuss and compare the values to Ic -- What do you conclude from these results?

Explanation / Answer

In electronics, a diode is a two-terminal electronic component with an asymmetric transfer characteristic, with low (ideally zero) resistance to current flow in one direction, and high (ideally infinite) resistance in the other. A semiconductor diode, the most common type today, is a crystalline piece of semiconductor material with a p-n junction connected to two electrical terminals.[1] A vacuum tube diode is a vacuum tube with two electrodes, a plate (anode) and heated cathode. The most common function of a diode is to allow an electric current to pass in one direction (called the diode's forward direction), while blocking current in the opposite direction (the reverse direction). Thus, the diode can be viewed as an electronic version of a check valve. This unidirectional behavior is called rectification, and is used to convert alternating current to direct current, including extraction of modulation from radio signals in radio receivers—these diodes are forms of rectifiers. However, diodes can have more complicated behavior than this simple on–off action. Semiconductor diodes begin conducting electricity only if a certain threshold voltage or cut-in voltage is present in the forward direction (a state in which the diode is said to be forward-biased). The voltage drop across a forward-biased diode varies only a little with the current, and is a function of temperature; this effect can be used as a temperature sensor or voltage reference. Semiconductor diodes' nonlinear current–voltage characteristic can be tailored by varying the semiconductor materials and doping, introducing impurities into the materials. These are exploited in special-purpose diodes that perform many different functions. For example, diodes are used to regulate voltage (Zener diodes), to protect circuits from high voltage surges (avalanche diodes), to electronically tune radio and TV receivers (varactor diodes), to generate radio frequency oscillations (tunnel diodes, Gunn diodes, IMPATT diodes), and to produce light (light emitting diodes). Tunnel diodes exhibit negative resistance, which makes them useful in some types of circuits. Diodes were the first semiconductor electronic devices. The discovery of crystals' rectifying abilities was made by German physicist Ferdinand Braun in 1874. The first semiconductor diodes, called cat's whisker diodes, developed around 1906, were made of mineral crystals such as galena. Today most diodes are made of silicon, but other semiconductors such as germanium are sometimes used When the BJT is in the saturation, the Vce(sat) means the voltage difference between the Collector and Emitter at the spec. "Ic" current value. The value of Vce(sat) have relation to Ic(sat) and the collector resistance "rc" Assumptions and boundary conditions The electric field and potential are obtained by using the full depletion approximation. Assuming that the quasi-Fermi energies are constant throughout the depletion region, one obtains the minority carrier densities at the edges of the depletion region, yielding: (4.4.1) and (4.4.2) These equations can be verified to yield the thermal-equilibrium carrier density for zero applied voltage. In addition, an increase of the applied voltage will increase the separation between the two quasi-Fermi energies by the applied voltage multiplied with the electronic charge. The carrier density at the metal contacts is assumed to equal the thermal-equilibrium carrier density. This assumption implies that excess carriers immediately recombine when reaching either of the two metal-semiconductor contacts. As recombination is typically higher at a semiconductor surface and is further enhanced by the presence of the metal, this is found to be a reasonable assumption. This results in the following set of boundary conditions: (4.4.3) and (4.4.4) 4.4.2.3. General current expression The general expression for the ideal diode current is obtained by applying the boundary conditions to the general solution of the diffusion equation for each of the quasi-neutral regions, as described by equation (2.9.13) and (2.9.14): (2.9.13) (2.9.14) The boundary conditions at the edge of the depletion regions are described by (4.4.1), (4.4.2), (4.4.3) and (4.4.4). Before applying the boundary conditions, it is convenient to rewrite the general solution in terms of hyperbolic functions: (4.4.5) (4.4.6) where A*, B*, C* and D* are constants whose value remains to be determined. Applying the boundary conditions then yields: (4.4.7) (4.4.8) Where the quasi-neutral region widths, wn' and wp', are defined as: (4.4.9) and (4.4.10) The current density in each region is obtained by calculating the diffusion current density using equations (2.7.24) and (2.7.25): (4.4.11) (4.4.12) The total current must be constant throughout the structure since a steady state case is assumed. No charge can accumulate or disappear somewhere in the structure so that the charge flow must be constant throughout the diode. The total current then equals the sum of the maximum electron current in the p-type region, the maximum hole current in the n-type regions and the current due to recombination within the depletion region. The maximum currents in the quasi-neutral regions occur at either side of the depletion region and can therefore be calculated from equations (4.4.11) and (4.4.12). Since we do not know the current due to recombination in the depletion region we will simply assume that it can be ignored. Later, we will more closely examine this assumption. The total current is then given by: (4.4.13) where Is can be written in the following form: (4.4.14) 4.4.2.4. The p-n diode with a "long" quasi-neutral region A diode with a "long" quasi-neutral region has a quasi-neutral region, which is much larger than the minority-carrier diffusion length in that region, or wn' > Lp and wp' > Ln. The general solution can be simplified under those conditions using: (4.4.15) yielding the following carrier densities, current densities and saturation currents: (4.4.16) (4.4.17) (4.4.18) (4.4.19) (4.4.20) We now come back to our assumption that the current due to recombination in the depletion region can be simply ignored. Given that there is recombination in the quasi-neutral region, it would be unreasonable to suggest that the recombination rate would simply drop to zero in the depletion region. Instead, we assume that the recombination rate is constant in the depletion region. To further simplify the analysis we will consider a p+-n junction so that we only need to consider the recombination in the n-type region. The current due to recombination in the depletion region is then given by: (4.4.21) so that Ir can be ignored if: (4.4.22) A necessary, but not sufficient requirement is therefore that the depletion region width is much smaller than the diffusion length for the ideal diode assumption to be valid. Silicon and germanium p-n diodes usually satisfy this requirement, while gallium arsenide p-n diodes rarely do because of the short carrier lifetime and diffusion length.

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