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As an engineer you are asked to design LEDS for traffic light signals. Specifically, you are asked to design LEDS for yellow light at wavelength A, = 590 nm and red light at wavelength A, = 625 nm. You are provided gallium arsenide and gallium phosphide material systems to reach these designs.

Consider the plot on the left. Here T refers to T valley in the transition of electron in the band structure of GaAs1-x Px. T-branch in the plot refers to direct band gap transition leading to radiative recombination. L branch refers to indirect bandgap radiative recombination. Finally, X refers to indirect band gap transition but in this branch, the momentum recombination which is not a conservation during recombination is sufficient enough for a photon emission (refer notes for details). That is, X branch is indirect recombination but still produces radiative recombination, and therefore can be used for LED material.

Find out the formula for the ternary semiconductor material GaAs1-xPx, by finding the value of x for(a) Yellow LED (b) Red LED of t

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Consider a MOS capacitor, in which the thickness of the oxide layer is d=2nm and dielectric constant of the oxide made from SiO2 is eox = 3.9. The body of the MOS capacitor is made from a p-type substrate.The gate metal is chosen in such a way that the flat band voltage of the device turns out to be VFB-0.5 V. The doping density in the p-body region is given by Na = 1017 cm³. The intrinsic carrier density in Si at room temperature is given by n; = 1.45 × 1010 cm³. KT at room temperature is 0.026 eV.

1) When the applied gate voltage is V, = -1.3 V, find

regime of operation in which the MOS CAP is currently operating (accumulation,depletion or inversion).а.

b. the type of carriers (p-type or n-type) at the metal-oxide interface,

c. carrier density of the carriers at the metal-oxide interface.

2) When the applied gate voltage is V, = 1.3 V, (it given that the threshold voltage is V; = 0.376,but you can also confirm this by doing the calculations using the formula for Vt ) find

a. regime of operation in which the MOS CAP is currently operating (accumulation,depletion or inversion).

b. the type of carriers (p-type or n-type) at the metal-oxide interface,

c. carrier density of the carriers at the metal-oxide interface.

3) Mark the two points identifying the above two voltage points in the following chart

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Problems-a) Consider a Si-solar cell with square cross-section with dimensions 2 cm x 2 cm, with thermal current Ith= 32 nA (here thermal current is same as leakage current) with an optical generation rate of 1018 EHP cm³s within Lp=Ln=2 µm of the junction. If the depletion width is 1 µm, calculate the short-circuit current and the open-circuit voltage for this cell. Also calculate the power expected from the single cell of the fill factor is known to be 0.7. (EHP means electron hole pairs)

b) Because Si-bandgap is 1.1 eV, what is the cut-off wavelength for the photo current to be produced due to an incidence of light.

c) Can sunlight in the visible region produce a photo current for this solar cell? (compare the calculated wavelength from (b) with the sunlight wavelength).

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We know that the PN junctions, diodes, photodiodes (LEDS and photodetectors) have similar physical structure. But +ve and -ve terminals and direction of currents depends on how the device is being operated.Consider following PN junctions with light shining on it, such that hv > Eg. Here E,is the band gap of the semiconductor material of the PN junction.

We are considering three cases of using the PN-junction, as shown in the first column of the table. Fill in the table based on your understanding of rectifier diodes, photodetectors and solar-cells.

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Write the general equation governing the photo generation phenomenon in a PN junction diode. In the equation you should have the current-term due to the voltage biasing and the photo generated current term due to an incident light. Mark the terms in your provided equation.

(1) Draw the I-V current relation (I versus V plot) for changing gop (rate of optical generation).

(2) Which quadrant of this I-V relation is utilized for solar-cell applications. (mark in your I-Vcurve)?

(3) Which quadrant of the I-V relation is utilized for photo-detector application (mark in your I-Vcurve)?

Now consider the photogeneration current term. What will be the effect on photo generated current, if the P and N sides are highly doped in comparison to light doped. (hint: how depletion region width changes? How does depletion width change the current?)

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