Equation

Definition

$I_{ph}=I_{ds}\left(\text{illumination}\right)-I_{ds}\left(\text{dark}\right)$

Photocurrent

It is the difference in the drain-to-source currents under illumination and dark condition (no illumination).

$R=I_{ph}/P$

$P=A\Phi h\nu /\left(\text{1}-r_s\right)\left(\text{1}-r_m\right)$

Responsivity

Photocurrent generated per incident optical power.

A being the illuminated device area, h is the Planck’s constant, ν is the frequency of radiation, r_s is the reflection coefficient at the metal-semiconductor interface, and r_m is the reflection coefficient at the metal entrance. It is a complete parameter considering all the internal and external factors.

$EQE\left(\%\right)=\left(Rh\nu /q\right)\times 100\%$

External Quantum Efficiency (EQE)

It is the number of electron-hole pairs generated per incident photon of energy hν.

Thus, it depends only on the photocurrent, the incident photon flux, and the illuminated device area and is independent of the photon energy or the wavelength of radiation.

$M=I_{ph}/I_L$

$I_L=Aq\Phi \left(1-\exp \left(-\alpha d\right)\right)$

Photocurrent Gain

Ratio of the photocurrent and the primary photocurrent. Primary photocurrent is the photocurrent resulting from power absorption in the device. It describes whether or not the device will exhibit amplification.

d being the surface to substrate thickness.

$\begin{array}{l}Sen\left({\Phi }_{high}\right)\%\\ =\frac{I_{ds}\left({\Phi }_{high}\right)-I_{ds}\left({\Phi }_{low}\right)}{I_{ds}\left({\Phi }_{high}\right)}\times 100\%\end{array}$

Sensitivity (Sen)

Sensitivity at a particular flux density is the ratio of difference between the drain to source currents at two different flux densities to the value of the drain to source current at the higher flux density. It depicts the sensitivity of the device to slight or large variations in the optical power.

$\tau =Q_{deptsc}/I_{ds}$

Switching time

It is the ratio of the gate depletion region and the sidewall space charge to the total drain to source current and is the average of the rise and fall times of the pulse response. This corresponds to how fast the device responds to transition between light off to light on and vice versa.

3 dB Bandwidth

Bandwidth (Bw)

Frequency at which the photocurrent reduces to 0.707 times its DC response. It is the frequency upto which the device can detect without errors.

$D={\left(ABw\right)}^{1/2}/NEP$

$NEP={\langle i_n^2\rangle }^{1/2}/R$

$\begin{array}{l}{i}_n=4kTBw[1/R_L+1/R_{gg}+1/R_d\\ +1/R_{s1}+1/R_{d1}+1/R_{ds}+1/R_i]\end{array}$

Detectivity

Describes the smallest detectable signal or the ability to detect weak signals.

NEP being the noise equivalent power, i_n is the noise current wherein R_L is the load resistance, R_gg is the gate bias resistance, R_d is the drain resistance, R_s1 is the source series resistance, R_d1 is the drain series resistance, R_ds is the drain to source resistance, and R_i is the input resistance;

R_ds is the change is the reciprocal of the change in the drain to source current with respect to the change in the drain to source voltage at constant gate to source voltage. The output channel conductance, g_d is the reciprocal of R_ds.

$LDR=\text{2}0\text{ln}\left(J_{ph}/J_d\right)\text{dB}$

Linear and Dynamic Range (LDR)

It depicts the linearity between the photocurrent and the optical power over a certain dynamic range expressed in dB. It is required to detect both weak and strong light. LDR gives the extent of high resolution imaging and sensing. J_ph is the photocurrent density measured at an optical power density of 1 mW/cm² and J_d is the dark current density.

$f_T=g_m/2\pi C_{gs}$

$g_m=\partial I_{ds}/\partial v_{gs}\backslash V_{DS}=\text{const}$

$C_{gs}=\partial Q_{deptsc}/\partial v_{gs}\backslash V_{DS}=\text{const}$

Unity-gain cut-off frequency

It is the highest frequency below which the device exhibits amplification and is given by the ratio of the transconductance and 2π times the gate to source capacitance. Transconductance is the variation in the drain to source current with the change in the gate-to-source voltage and is the amplification parameter. Gate to source capacitance is the variation in the gate depletion region and sidewall space charge with the change in the gate to source voltage and is the switching parameter. In both the cases, the drain to source voltage is maintained constant. Thus, unity-gain cut-off frequency denotes the amplification bandwidth of the device.