# Transimpedance Amplifier for Noise Measurements in Low-Resistance IR Photodetectors
## 4 Results
The results of the noise measurements performed on the photodiode at 280 K and different bias levels are reported in Figure 8. The thermal noise corresponding to the resistance of the unbiased photodiode is also shown. From Figure 8, it is apparent that, except for the lowest biases at higher frequencies, the situation is one in which the flicker noise generated by the photodiode can be detected and estimated. Increasing the voltage causes a significant increase in flicker noise \(S(f)=1/f^{\alpha}\) in situations in which it is dominant in the overall examined frequency range, where the \(\alpha\) parameter has a value close to 1. The detailed behavior of the spectral noise in this type of photodetector has already been described in the literature [26], and it is outside the scope of this work. Figure 6: Current–voltage (I-V) characteristics of the tested photodiode at different temperatures. Figure 7: The determined differential resistance of the photodiode at a temperature of 280 K.  
It is, however, important to remark that the availability of effective instrumentation, such as that discussed in this paper, can be extremely useful. To show what can be obtained if effective and easy-to-use instrumentation is available, we can, for instance, discuss what can be inferred from the dependence of the current noise density at \(f\) = 10 Hz on the bias current, as reported in Figure 9.  
The line in the plot represents the trend for the proportionality of the flicker noise to the bias current squared. From the results reported in Figure 9, it can be observed that the proportionality of the flicker noise vs. the bias current squared can be assumed for low bias voltages (region A in the I-V characteristics reported in the inset); with increasing voltage (in reverse bias), region B in the I-V characteristics is explored, and, when region C is reached, the dependence of the noise on the bias current is differs significantly from the  
Figure 8: Current noise measurement results at different bias levels. Figure 5.0 Current noise at 10 Hz vs. bias current. The I-V characteristics of the device at 280 K from Figure 5 are reported in the inset. behavior at low voltages/currents. The shape of this noise characteristic results from the properties of the tested photodiode. The results of studies described in the literature show that the total \(1/f\) noise power spectral density is a complex function of a few noise currents. In [27], this function is presented by the model formula:  
Figure 5.1  
where \(I_{sh}\), \(I_{g-r}\), \(I_{diff}\) and \(I_{tun}\) are the shunt, generation-recombination, diffusion and tunneling dark current components, respectively, with the corresponding noise coefficients \(\alpha_{sh}\), \(\alpha_{g-r}\), \(\alpha_{diff}\) and \(\alpha_{tun}\). Depending on the photodiode construction and its operating point (temperature and bias voltage), each of the above noise sources will affect the total noise differently (i.e., the noise coefficients will take different values). Based on the results described in [26; 27; 28], the inset region in Figure 9 shows that the diffusion and \(g-r\) current components predominate in the detector's dark current in the low- and mid-voltage ranges (A,B). Meanwhile, at high voltage bias (C), the tunneling current components predominates. However, there is no correlation between the total dark current and the measured \(1/f\) noise PSD. This suggests that there are some current components other than diffusion that could have a higher influence on \(1/f\) noise at different levels of bias voltage. In the low-voltage range (A), the quadrature dependence is caused by the ohmic-like behavior of the tested device, and measured noise can be regarded as resistance fluctuation noise from detector shunt resistance. Along with increasing the voltage (B), the \(1/f\) noise components come from shunt, \(g-r\), and tunneling currents. At the highest voltages (C), the overall noise is dominated by tunneling current.