Noise Analysis of Photoconductive Terahertz Detectors

Abstract

The noise performance of photoconductive terahertz detectors is analyzed and the tradeoff between low-noise and high-responsivity operation of photoconductive detectors is investigated as a function of device parameters and operational settings. The analysis is conducted on two general photoconductive detector architectures, symmetrically pumped and asymmetrically pumped photoconductive detector architectures. The results indicate that the highest signal-to-noise ratios are offered by the symmetrically pumped and asymmetrically pumped detector architectures for the photoconductive detectors based on short-carrier lifetime and long-carrier lifetime semiconductors, respectively.

APPENDIX A: Derivation of the diffusion photocurrent in asymmetrically pumped photoconductive detectors

The average diffusion photocurrent induced in the absence of the incident terahertz radiation as the result of the asymmetric optical pumping is calculated using the continuity equations. For this derivation, we assume an ohmic contact between the photoconductor contact electrodes and the photo-absorbing semiconductor. The continuity equations determine the dependence of the photo-generated carrier density as a function of distance from the interface between the semiconductor and contact electrodes, x, in steady state conditions:

$$ \frac{ dn}{ dt}=\frac{\eta_e\alpha }{ hv.{d}_i{w}_e}{P}_{opt}-\frac{n}{\tau_n}+{D}_n\frac{d^2n}{d{x}^2}=0 $$

(A-1)

$$ \frac{ dp}{ dt}=\frac{\eta_e\alpha }{ hv.{d}_i{w}_e}{P}_{opt}-\frac{p}{\tau_p}+{D}_p\frac{d^2p}{d{x}^2}=0 $$

(A-2)

where D _n (= μ _n kT/q) and D _P (= μ _p kT/q) are electron and hole diffusion constants in the photo-absorbing semiconductor, respectively. Assuming the carrier density at the interface between the semiconductor and contact electrodes approaches its thermal equilibrium value, the steady state photo-generated carrier density as a function of distance from the interface between the semiconductor and contact electrodes is calculated as

$$ n(x)=\frac{\eta_e\alpha {\tau}_n}{ hv.{d}_i{w}_e}{P}_0\left[1-{e}^{-\frac{x}{\sqrt{\tau_n{D}_n\;}}}\right] $$

(A-3)

$$ p(x)=\frac{\eta_e\alpha {\tau}_p}{ hv.{d}_i{w}_e}{P}_0\left[1-{e}^{-\frac{x}{\sqrt{\tau_p{D}_p}}}\right] $$

(A-4)

Therefore, the induced average diffusion photocurrent at the semiconductor contact interface can be calculated accordingly:

$$ {I}_{diff}=\frac{{ w}_e}{\alpha}\left(q{D}_n\frac{ dn}{ dx}\left|x=0-q{D}_p\frac{ dp}{ dx}\right|x=0\right)=\frac{q{\eta}_e}{ hv.{d}_i}{P}_0\left(\sqrt{\tau_n{D}_n}-\sqrt{\tau_p{D}_p}\right) $$

(A-5)