Photoresponse characteristics from computationally efficient dynamic model of uni-traveling carrier photodiode

Abstract

A time domain model of bulk InGaAs/InP uni-traveling carrier photodiode is developed in terms of coupled differential equations of incident photon flux and photo generated carrier density rates. For fast computation of model parameters linear approximation of material absorption coefficient is made with carrier density. Wavelength and bias voltage dependent responsivity is well demonstrated by the model and their values at different absorption layer widths agree well with the experimental results. Optical power induced output photocurrent saturation is also explained. Furthermore, from the temporal variation of output photocurrent, estimation of device bandwidth is shown.

Appendix 1

Integrating both side of Eq. (1), we get

$$\mathop \int \limits_{{Q_{in} \left( t \right)}}^{{Q_{out} \left( t \right)}} \frac{dQ(x,t)}{Q(x,t)} = - \mathop \int \limits_{0}^{{W_{A} }} \left[ {\alpha (N,\lambda ) + \beta (N)} \right]dx$$

and employing the material loss coefficient expression of β(N) from Eq. (2) and linearised approximation of absorption coefficient α(N, λ) from Eq. (4), the above expression can be solved as

$$Q_{out} (t) = Q_{in} (t) \cdot \exp \left[ { - (m + \beta_{1} )\mathop \int \limits_{0}^{{W_{A} }} N(x,t)dx + (mN_{0} - \beta_{0} )]\mathop \int \limits_{0}^{{W_{A} }} dx} \right].$$

Now integrating the first term of Eq. (6) with respect to x from 0 to W _A , we get

$$\begin{aligned}&- \mathop \int \limits_{0}^{{W_{A} }} \left[ {\alpha (N,\lambda ) + \beta (N)} \right]Q(x,t)dx=Q_{out} (t) - Q_{in} (t) \hfill \\&\quad =Q_{in} (t)\left[ {\exp \left\{ { - (m + \beta_{1} )\int\limits_{0}^{{W_{A} }} {N(x,t)dx + (mN_{0} - \beta_{0} )} \int\limits_{0}^{{W_{A} }} {dx} } \right\}} \right] - Q_{in} \left( t \right) \hfill \\&\quad=Q_{in} (t)\left[ {\exp \left\{ { - (m + \beta_{1} )\frac{h(t)}{A} + (mN_{0} - \beta_{0} )W_{A} } \right\} - 1} \right] \hfill \\ \end{aligned}$$

by using Eq. (7).