In a conventional p-i-n structure, assume the light is fully absorbed in p+ cladding layer, dark carriers are uniformly generated in i region for simplicity. In the local model, the position dependent multiplication for primary carriers generated within is given by w So that the gain of pure injection as carriers injected at position = 0 is given by x The mean gain from the multiplied dark carriers and photo carriers is denoted as the Mt, parameters used to calculate is explained in the following Mt total photo generated carriers injected at = 0 Np: x dark carriers generated in the region at position, since dark carriers are uniformly Gi: i x generated in i region so that is independent of position, the total dark carriers generated in Gi the region would be i the ratio of the total primary dark carriers over the photo generated carriers, z: ionisation coefficients ratio, k: k=β/α The mean gain concerning multiplied dark carriers and photo carriers, which is namely the gain measured under DC condition, is given by Here is the gain of pure electron injection, which is namely the gain measured under AC M(0) condition. If is very small, which means, , will not be deviated a lot from if cannot be z Mt M(0), z ignored, here we consider two cases, and k=0 k=1 i) k=1 if k=1, α= β, M(x)=M(0), it suggests that when the dark carriers and photo carriers will have similar gain values k=1, and the gain measurement will not be affected either under DC or AC condition. ii) k=0 so that the mean gain can be expressed as β=0,M(0)=exp(αw),
In a conventional p-i-n structure, assume the light is fully absorbed in p+ cladding layer, dark carriers are uniformly generated in i region for simplicity. In the local model, the position dependent multiplication for primary carriers generated within w is given by So that the gain of pure injection as carriers injected at position x = 0 is given by The mean gain from the multiplied dark carriers and photo carriers is denoted as Mt, the parameters used to calculate Mt is explained in the following Np: total photo generated carriers injected at x = 0 Gi: dark carriers generated in the i region at x position, since dark carriers are uniformly generated in i region so that Gi is independent of position, the total dark carriers generated in the i region would be z: the ratio of the total primary dark carriers over the photo generated carriers, k: ionisation coefficients ratio, k=β/α The mean gain concerning multiplied dark carriers and photo carriers, which is namely the gain measured under DC condition, is given by Here M(0) is the gain of pure electron injection, which is namely the gain measured under AC condition. If z is very small, which means, , Mt will not be deviated a lot from M(0), if z cannot be ignored, here we consider two cases, k=0 and k=1 i) k=1 if k=1, α= β, M(x)=M(0), it suggests that when k=1, the dark carriers and photo carriers will have similar gain values and the gain measurement will not be affected either under DC or AC condition. ii) k=0 so that β=0,M(0)=exp(αw), the mean gain can be expressed as
Thesis-Jingjing%2020130924%20final%20version.docx