The result of measuring “the best die” is shown in Fig. 2‐7, in which curves are more smooth compared to those interfered by parasitic leakages. And then, activation energy is estimated based on Arrhenius equation (Eq. 2‐6) by fitting data with exponential function in the plotting of measured dark current at a given reverse bias versus 1/T (not shown), and extracting the exponent to calculate activation energy Ea at each reverse bias point.
Fig. 2‐7 Temperature dependence of I‐V characteristics.
Activation energy is the energy needed for electrons to overcome process barrier.
The activation energy for diffusion process is germanium bandgap 0.66 eV, and for SRH process with deep traps Ea should be close to half bandgap, 0.33 eV. Activation energy versus reverse bias is shown in Fig. 2‐8.
k Ae / Eq. 2‐6
Fig. 2‐8 Activation energy versus reverse bias from experimental data.
Dark current is initially dominated by diffusion mechanism near zero volts, and continually Shockley‐Read‐Hall generation takes place in higher reverse bias.
Ea of five samples as a function of reverse bias are shown in Fig. 2‐8.Only the top curve (red solid triangles) maintains above Ge half bandgap (0.33 eV) until ‐2V, which is regarded behaving as intrinsic semiconductor leakage. Other four curves (small dots) reveal that these samples are more affected by leakages from parasitic conducting path.
Activation energy is dropping as reverse bias increases (goes to negative/left direction as arrowed). For the top curve, it starts with Ea ≈ 0.6 eV, which means that the average dark current over ‐10°C to 125°C is dominated by diffusion of minority carriers in small bias. As reverse bias gets higher, Ea gradually drops close to 0.3 eV, which means that at higher reverse bias, average dark current is subjected to SRH recombination process.
Another analysis shows this trend similarly. In Fig. 2‐9, the logarithm of the measured leakage current (curves with blue solid symbols) at different applied voltages are plotted versus 1000/T together with ni and ni² dependencies (straight lines with open symbols). The inset of Fig. 2‐9 is again Eq. 2‐5, with first term related to diffusion current and second term related to SRH generation current as indicated.
ni dependency on temperature is shown more clearly in Eq. 2‐7. Bandgap correction with respect to temperature is taken into account when plotting of ni and ni² dependencies.
2 2 2 ∗
2 2 ∗
2 Eq. 2‐7
In Fig. 2‐9, it shows that SRH generation leakage has a stronger dependence on reverse bias compared to diffusion current. It is because with higher reverse bias, the diode is more depleted (depletion region gets wider), which means more traps are exposed out as generation sites, resulting in higher generation current. Sets of curves show a trend that dark current of measured GePD is in a combination behavior of diffusion and SRH generation. Judged from the slope and tangent line, SRH generation is the main component in dark current at room temperature 25°C, while the GePD is at its operation point ‐0.5V. Above 87°C, diffusion current plays a role.
Fig. 2‐10demonstrates this more clearly, which is the zoom in version of Fig. 2‐9, while Y‐axis is replaced as the amount of measured current subtracted by calculated diffusion current (first term of Eq. 2‐5), which should give SRH generation behavior.
A neat fitting with SRH equation lines (five parallel yellow lines) could be seen in temperature below 25°C. Deviations in higher temperature and higher reverse voltage regime are supposed to attribute to extra current from diode edge, which is randomly distributed as shown before.
Fig. 2‐9 Reverse Currents (A/µm) versus 1000/T(K‐1).
Measured current (solid symbols) at different temperature as a function of 1000/T. Two straight lines with open symbols are plotted from Eq. 2‐5 as in the inset, with first term related to diffusion current and second term related to SRH generation current as indicated.
Fig. 2‐10 Total reverse current subtracted by diffusion current.
Solid symbols are measured total current subtracted by pure calibrated diffusion current from Eq. 2‐5, and empty symbols are pure calibrated Shockley‐Read‐Hall current from equation.
Lifetimes of electrons are also roughly calculated to be 0.06 µs. Based on literature[18], the defect density of the best die is estimated around 1e19/cm3 from Fig. 2‐11. In Chapter 3, defect density would be estimated by TCAD simulator.
Fig. 2‐11 Variation of recombination lifetime versus effective dopant concentration[18].
2.4 Conclusion
At the beginning of this chapter, we overviewed physical mechanisms behind dark current in a germanium photodiode. Section 2.2 describes the structure of germanium photodiode used in this thesis, and the temperature dependence measurement method. Severe parasitic leakage was observed on many devices. Due to this yield issue, a meaningful analysis could only be performed on well‐chosen devices.
Subsequently, in section 2.3, we show the investigation of dark current in germanium photodiode via experimental data.
Firstly, from the analysis of activation energy, when the bias is small, the average dark current over ‐10°C to 125°C is diffusion current; as bias gets more reversed, it would subject to SRH process. Secondly, it can be verified that dark current is in the combination behavior of diffusion current and SRH generation current. At room temperature, and at the bias ‐0.5V, SRH generation is the main component in dark current. There is a good qualitative agreement between formula trend and measured data. Thirdly, from a rough estimate of carrier lifetime, equivalent trap densities of our best samples are estimated to be around 1E19/cm3.This will be more precisely estimated in Chap 3.