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## An ideal photo-diode of unit quantum efficiency, at room temperature, is illuminated with 8 mW of radiation at 0.65 µm wavelength. Calculate

Question

An ideal photo-diode of unit quantum efficiency, at room temperature, is illuminated with 8 mW of radiation at 0.65 µm wavelength. Calculate the current and voltage output when the detector is used in the photo-conductive and photovoltaic modes respectively. The reverse saturation current (Is) is 9 nA.

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Physics
5 months
2021-09-01T03:12:33+00:00
2021-09-01T03:12:33+00:00 1 Answers
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## Answers ( )

Answer:I = 4.189 mA V = 0.338 V

Explanation:In order to do this, we need to apply the following expression:

I = Is[exp^(qV/kT) – 1] (1)However, as the junction of the diode is illuminated, the above expression changes to:

I = Iopt + Is[exp^(qV/kT) – 1] (2)Now, as the shunt resistance becomes infinite while the current becomes zero, we can say that the leakage current is small, and so:

I ≅ Iopt

Therefore:

I ≅ I₀Aλq / hc (3)Where:

I₀A = Area of diode (radiation)

λ: wavelength

q: electron charge (1.6×10⁻¹⁹ C)

h: Planck constant (6.62×10⁻³⁴ m² kg/s)

c: speed of light (3×10⁸ m/s)

Replacing all these values, we can get the current:

I = (8×10⁻³) * (0.65×10⁻⁶) * (1.6×10⁻¹⁹) / (6.62×10⁻³⁴) * (3×10⁸)

I = 4.189×10⁻³ A or 4.189 mANow that we have the current, we just need to replace this value into the expression (2) and solve for the voltage:

I = Is[exp^(qV/kT) – 1]

k: boltzman constant (1.38×10⁻²³ J/K)

4.189×10⁻³ = 9×10⁻⁹ [exp(1.6×10⁻¹⁹ V / 1.38×10⁻²³ * 300) – 1]

4.189×10⁻³ / 9×10⁻⁹ = [exp(38.65V) – 1]

465,444.44 + 1 = exp(38.65V)

ln(465,445.44) = 38.65V

13.0508 = 38.65V

V = 0.338 V