Electrical Engineering ( material and device ) assignment

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HW 4: Plotting carrier concentrations in forward biased diode and deriving circuit quantities For this exercise, we will use a one-sided p-n diode, with p-side Na=2×1018cm-3, and n-side Nd=2×1016cm3 . For the carrier lifetimes, use 1ns, and the included electron mobility (1000cm2/Vs) and the included hole mobility (400cm2/Vs). 1. 2. 3. 4. 5. 6. 7. 8. 9. Calculate the EQUILIBRIUM minority carrier concentrations on the 2 sides, i.e. pn0 and np0. Calculate the fermi level positions on the 2 sides in the quasi-neutral regions Draw the full band diagram under EQUILIBRIUM Assuming the quasi-neutral regions on the 2 sides are 10x the diffusion length, estimate the series resistances in Ωcm2 on the 2 sides. Draw the band diagram under 0.2V forward bias. Where does this voltage drop? Make sure to indicate the quasi-fermi levels, i.e. how they split under application of voltage. Where is the peak electric field? Plot the carrier distributions and current densities on the 2 sides using the attached Scilab code. At V=-.2V, calculate the DEPLETION region width, and the associated capacitance in F/cm2. Diffusion capacitance extraction) a. Now, calculate the total excess charge in the diffusion induced minority carriers at 0.2V in #/cm2 and C/cm2. Remember to do this for both pn and np. b. Calculate the total excess charge in the diffusion induced minority carriers at 0.26V forward bias in #/cm2 and C/cm2. Remember to do this independently on the 2 sides. c. From the expressions (in the notes) −𝒊𝒏𝒇 ∆𝒏𝒑 (𝒙)𝒅𝒙]/𝒅𝑽 𝑪𝒅𝒊𝒇𝒇𝒖𝒔𝒊𝒐𝒏,𝒑−𝒔𝒊𝒅𝒆 = 𝒒𝒅[∫ −𝒙𝒑 +𝒊𝒏𝒇 𝑪𝒅𝒊𝒇𝒇𝒖𝒔𝒊𝒐𝒏,𝒏−𝒔𝒊𝒅𝒆 = 𝒒𝒅[∫ ∆𝒑𝒏 (𝒙)𝒅𝒙]/𝒅𝑽 +𝒙𝒏 Calculate the diffusion capacitances on the 2 sides in F/cm2. d. Which side has larger diffusion capacitance? e. How does this diffusion capacitance compare with your depletion capacitance? 10. Sketch the equivalent circuit diagram (remember from the notes)? Include Rn, Rp¸Cdepletion, Cdiffusion,n-side and Cdiffusion,pside. 11. Now, perform the integration analytically using the following equations for the carrier distributions we derived in class: 𝑛𝑖2 𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑 𝑥 − 𝑥𝑛 ∆𝑝𝑛 (𝑥) = ( ) (exp ( ) − 1) exp⁡(− ) 𝑁𝐷 𝑉𝑡ℎ 𝐿𝑛 𝑥 + 𝑥𝑝 𝑛𝑖2 𝑉𝑎𝑝𝑝𝑙𝑖𝑒𝑑 ∆𝑛𝑝 (𝑥) = ( ) (exp ( ) − 1) exp⁡( ) 𝑁𝐴 𝑉𝑡ℎ 𝐿𝑛 This is actually not so hard. Integral of exponential is exponential, and when exp(-x)0 as xinf.
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