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EXAMPLE 5.13 PHOTORESPONSE TIME Sketch the hole concentration when a step illumination is applied to an n-type semiconductor at time t = 0 and switched off at time t = toff (>>> Th). SOLUTION We use Equation 5.27 with Gph = constant in 0 ≤ t ≤ toff. Since Equation 5.27 is a first-order differential equation, integrating it we simply find AP In G₁-P)+C₁ = Th Gph Th where C₁ is the integration constant. At t = 0, Ap = 0, so C₁ = In Gph. Therefore, the solution is Gph|1 (-)] Apn(t) = ThGph 1 - exp Apn(toff) We see that as soon as the illumination is turned on, the minority carrier concentration rises exponentially toward its steady-state value Ap(o) = TGph. This is reached after a time t > Th At the instant the illumination is switched off, we assume that toff » Th so that from Equation 5.28, dApn dt = TG ph = = Gph 0 ≤t < toff Apn Th [5.28] [5.27]

EXAMPLE 5.13 PHOTORESPONSE TIME Sketch the hole concentration when a step illumination is applied to an n-type semiconductor at time t = 0 and switched off at time t = toff (>>> Th). SOLUTION We use Equation 5.27 with Gph = constant in 0 ≤ t ≤ toff. Since Equation 5.27 is a first-order differential equation, integrating it we simply find AP In G₁-P)+C₁ = Th Gph Th where C₁ is the integration constant. At t = 0, Ap = 0, so C₁ = In Gph. Therefore, the solution is Gph|1 (-)] Apn(t) = ThGph 1 - exp Apn(toff) We see that as soon as the illumination is turned on, the minority carrier concentration rises exponentially toward its steady-state value Ap(o) = TGph. This is reached after a time t > Th At the instant the illumination is switched off, we assume that toff » Th so that from Equation 5.28, dApn dt = TG ph = = Gph 0 ≤t < toff Apn Th [5.28] [5.27]

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How we got the expression marked by green ? show the integration process

EXAMPLE 5.13 PHOTORESPONSE TIME Sketch the hole concentration when a step illumination is applied to an n-type semiconductor at time t = 0 and switched off at time t = toff (>> Th). SOLUTION We use Equation 5.27 with Gph = constant in 0 ≤ t ≤ toff. Since Equation 5.27 is a first-order differential equation, integrating it we simply find t In G₁4 - (AR) - - - - + C₁ Gph 1 Th Th where C₁ is the integration constant. At t = 0, Apn solution is Apn(toff) = ThGph d▲pn dt = = Apn(t) = ThGph - TAG₂h [1 - exp(-2)] We see that as soon as the illumination is turned on, the minority carrier concentration rises exponentially toward its steady-state value Apn(∞) = tħGph. This is reached after a time t > Th. At the instant the illumination is switched off, we assume that toff » Th so that from Equation 5.28, Gph 0, so C₁ Apn Th - In Gph. Therefore, the 0 ≤ t < toff [5.28] [5.27]
Transcribed Image Text:EXAMPLE 5.13 PHOTORESPONSE TIME Sketch the hole concentration when a step illumination is applied to an n-type semiconductor at time t = 0 and switched off at time t = toff (>> Th). SOLUTION We use Equation 5.27 with Gph = constant in 0 ≤ t ≤ toff. Since Equation 5.27 is a first-order differential equation, integrating it we simply find t In G₁4 - (AR) - - - - + C₁ Gph 1 Th Th where C₁ is the integration constant. At t = 0, Apn solution is Apn(toff) = ThGph d▲pn dt = = Apn(t) = ThGph - TAG₂h [1 - exp(-2)] We see that as soon as the illumination is turned on, the minority carrier concentration rises exponentially toward its steady-state value Apn(∞) = tħGph. This is reached after a time t > Th. At the instant the illumination is switched off, we assume that toff » Th so that from Equation 5.28, Gph 0, so C₁ Apn Th - In Gph. Therefore, the 0 ≤ t < toff [5.28] [5.27]
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