region is far from the photocarriers generated region, the diffusion time can limit the bandwidth. The diffusion time is given by [] (2.33) where is the diffusion distance and is the minority carrier diffusion coefficient. The x Dc diffusion time limited bandwidth is described by (2.34) Avalanche limited bandwidth Avalanche limited bandwidth is the main limitation of an APD’s bandwidth at high gain due to feedback of carriers in building up the avalanche gain and the time required for the avalanche process to This will limit the response time in an APD. As studied by Emmons [], a model was presented to simulate the bandwidth versus multiplication with different values of ionisation coefficient ratio Assuming the photocarriers’ diffusion is β/α. negligible, the -3 dB bandwidth is mainly limited by the avalanche duration time. The -3 dB bandwidth is decreasing with avalanche gain due to time required for the avalanche duration. shows the calculated -3 dB bandwidth versus avalanche gain results presented by Emmons. It is indicated that as decreases, the avalanche gain is less effective in reducing the β/α frequency response. A curve of = is superimposed on those curves. When the M M>β/α, β/α multiplication has little effect on the bandwidth as the bandwidth is largely determined by the transit time and is less dependent on gain. While when the bandwidth is decreasing M<β/α, with avalanche multiplication. The avalanche duration time is dependent on the value of τa ionisation coefficient ratio and is given by [] k= β/α, (2.35) is the absorption layer thickness, is the avalanche gain value, is the ionisation wa M k coefficient ratio, is the avalanche region thickness and is the saturated carrier velocity. It w vs is important to note that at very large is a constant so that the gain bandwidth M, M/τa product has a constant value at very large gain.
region is far from the photocarriers generated region, the diffusion time can limit the bandwidth. The diffusion time is given by [] (2.33) where x is the diffusion distance and Dc is the minority carrier diffusion coefficient. The diffusion time limited bandwidth is described by (2.34) Avalanche limited bandwidth Avalanche limited bandwidth is the main limitation of an APD’s bandwidth at high gain due to feedback of carriers in building up the avalanche gain and the time required for the avalanche process to This will limit the response time in an APD. As studied by Emmons [], a model was presented to simulate the bandwidth versus multiplication with different values of ionisation coefficient ratio β/α. Assuming the photocarriers’ diffusion is negligible, the -3 dB bandwidth is mainly limited by the avalanche duration time. The -3 dB bandwidth is decreasing with avalanche gain due to time required for the avalanche duration. shows the calculated -3 dB bandwidth versus avalanche gain results presented by Emmons. It is indicated that as β/α decreases, the avalanche gain is less effective in reducing the frequency response. A curve of M = β/α is superimposed on those curves. When M>β/α, the multiplication has little effect on the bandwidth as the bandwidth is largely determined by the transit time and is less dependent on gain. While when M<β/α, the bandwidth is decreasing with avalanche multiplication. The avalanche duration time τa is dependent on the value of ionisation coefficient ratio k= β/α, and is given by [] (2.35) wa is the absorption layer thickness, M is the avalanche gain value, k is the ionisation coefficient ratio, w is the avalanche region thickness and vs is the saturated carrier velocity. It is important to note that at very large M, M/τa is a constant so that the gain bandwidth product has a constant value at very large gain.
Thesis-Jingjing%2020130924%20final%20version.docx