Competition between subbandgap linear detection and degenerate twophoton absorption in gallium arsenide photodiodes
 Benjamin Vest^{1},
 Baptiste Fix^{2}Email author,
 Julien Jaeck^{2} and
 Riad Haïdar^{2}
https://doi.org/10.1186/s4147601600228
© The Author(s) 2016
Received: 10 May 2016
Accepted: 21 October 2016
Published: 13 December 2016
Abstract
This letter is on the response of gallium arsenide pin diodes to subbandgap photons (1.55 μm). We investigate the various regimes of subbandgap operation by using different light sources delivering pulses ranging from nanosecond to microsecond durations. We evidence two regimes : a regime of degenerate twophoton absorption, with a clear quadratic dependence with respect to the incident flux, and a subbandgap, temperature dependant linear regime, that drives photocurrent generation at lower power densities. Both processes are associated to a very low quantum efficiency, around 10–8. We then determine absorption coefficients as well as trap densities, thanks to a model involving a photoassisted Shockley Read Hall effect.
Keywords
Background
Semiconductors materials with high nonlinear coefficients, such as GaAs or InP are good materials for numerous optical devices, such as optical switches [1], logic gates [2], and quantum detectors [3]. Twophoton absorption is a third order optical process describing the quasi simultaneous absorption of a pair of photons in a material, with a quadratic dependence relatively to light intensity.
Inside semiconductors, two photon absorption using subbandgap photons can be described by a twostep process: those photons of energy E<E _{ g } can promote an electron from the valence band to a virtual state (meaning a non stationary state) in the gap. During the lifetime of this state, given by the second Heisenberg principle \(\Delta \tau \ge \frac {\hbar }{2 \left (E_{g}  E \right)}\), a second photon with enough energy can complete the transition, hence creating an electronhole pair and generating a photocurrent, named twophoton current (TPC). As the lifetime of this intermediate state is very short in visible gap material (in the fs range), this process is particularly well suited for ultra fast correlation measurements [3–6]. However, the very short lifetime of the virtual state is also responsible for the intrinsically low efficiency of this process, as it requires the quasi simultaneous occurrence of two photons in this time interval. As a consequence, common twophoton absorption applications in semiconductors are, so far, essentially limited to the study of very fast processes, more generally to high peak intensity regimes, only reached by pulsed light sources.
Yet, TPC can also be considered as an interesting solution to detect infrared light in wide gap semiconductor. Those materials are less sensitive to thermally generated carriers and, if associated with TPC, they would open new applications in the field of roomtemperature infrared detection. However, such configuration implies the detection of low optical power delivered by CW light sources which signifies lower levels of generated TPC.
The quadratic behavior of TPC with the optical power has already been checked over several decades by many authors in highly crystalline detectors such as GaAs photocathodes and PMTs [7]. It has also been observed in GaN photodiodes at high peak power using pico and femtosecond pulsed lasers [8]. In complement to these previous results, our study of subband gap absorption in GaAs photodiodes at lower temporal regimes (from nano to microsecond pulses) reveals a linear detection process, which appears in competition with TPC.
Such a process might be attributed either to photoassisted tunneling (PAT) or to photoassisted ShockleyReadHall mechanism (PASRH). Indeed, these two mechanisms involve traps in the energy bandgap and are thus dependant to the quality of the detector in terms of defects.
In this Letter, we investigate the detection of subbandgap photons in a series of commercial GaAs pin photodiode at 1.55 μm at very low flux. Our study evidences the existence of subbandgap absorptions composed of two competitive processes : a linear, temperature dependant, subbandgap contribution attributed to PASRH and a quadratic twophoton absorption regime. We also investigate the competition between the two processes in various temporal regimes from ns to μ s allowing to determine the twophoton absorption coefficient and the trap densities in the photodiode material.
Methods
Competition between two transition processes
Summary of the different parameters associated to each experiment
Setup  OPO1  OPO2  AOM 

Pulse duration Δ t  10 ns  10 ns  1 μs 
Repetition rate f  150 kHz  15 kHz  150 kHz 
Wavelength  1.55 μm  1.55 μm  1.55 μm 
Accessible average power (W)  10^{−7}−10^{−2}  10^{−4}−10^{−1}  10^{−4}−10^{−2} 
Such a linear regime could be explained by two mechanisms, either the PAT or the PASRH. The PAT is based on the curvature of the energy bands and hence depends on the applied bias. However, our experiments did not show such a dependence for biases ranging from 1V to 0V, and we thus neglect this contribution. On the other hand, as it has been observed and described in silicon [10], PASRH is based on the ionization of traps from deep levels in the bandgap to the conduction band. This generationrecombination process is driven by the thermal agitation, meaning that PASRH is strongly temperature dependent.
At 80 K, the IP characteristic is quadratic over the two decades of measurement. We can notice that the TPC regime is independent of the temperature. But more importantly, no parasitic linear regime is observable at cryogenic temperature due to the freezing of defects and trap levels contribution to this process.
where e is the electron charge, h ν the photon energy, Δ t the pulse duration,f the repetition rate, R _{ c }=Δ t f the duty cycle and assuming a focal spot of area S=π∗(40 μm)^{2} and an active medium thickness of L=10 μm (determined from capacitancevoltage data).
It is well known that beta depends on the polarisation of the light source with respect to the semiconductor crystallographic orientation [11]. Indeed, the twophoton absorption coefficient in GaAs varies with the direction of polarisation as sin2(2θ) for [100] crystal, as (1+3 cos2(θ)) sin2(θ) for [110] crystal or with the ellipticity of the polarisation for a [111] crystal. We achieved a set of complementary measurements and found that the GaAs is oriented along its [100] axis in our commercial photodiode, for which \(\beta ^{max}_{[100]} = 45.4 \pm 7.5 \, \mathrm {cm/GW} \).
On the other hand, estimation of the quantum yield of the linear process is made difficult because of important uncertainties on the photocurrent due to the very weak signal to noise ratio associated to the determination of the incident power at low flux, as well as predominance of TPC at higher fluxes.
Results and discussion
Improving the measurement precision on the quantum efficiency of the PASRH by changing the temporal regime
The setup uses now a 1.55 μm CW fiber laser source, and an acoustooptic modulator (AOM). This component chop the continuous wave to define a 1 μs wide laser pulse, with a similar 150 kHz repetition rate. The light is then collimated at the output of the fiber and refocused onto the detector (see Table 1).
Figure 3 shows the IP characteristic obtained with this setup. The preliminary Zscan alignment step does not display a lorentzian shape anymore, meaning that the nonlinear contribution is not predominant. The IP characteristic is coherent with this first observation, as the linear behaviour of the detector is mainly observed in the intensity range under study. Principles leading the modelization step are nevertheless the same, and we must take into account both contributions. Our modelization leads to values of η=[6.1±0.6].10^{−8}. Now that the incident power is known with a much better precision than previously, the derived value for η can be considered as reliable. Yet, due to the microsecond regim, this experiment is not adapted to measure the twophoton absorption coefficient with precision.
The PASRH requires the existence of real electronic states inside the bandgap which are mostly due to defects in the semiconductor [10]. Thus, it is possible to retrieve the density of defects from our experiment. By assuming an optical cross section typically in the 10^{−15}cm^{−2} range we find a volumic density of defects in the 10^{14} cm^{−3} range.
Finally, TPC can be compared to PASRH through the introduction of an effective quantum yield. This quantum yield generally describes a probability for a photon to be absorbed in the medium. The quadratic dependance of TPC leads to an intensitydependent yield, as this probability increases with the number of available photons in the active medium. The inset of Fig. 3 shows a representation of the TPC with respect to the average incident power. It depicts the predominance of absorption of photon pairs in the nanosecond regime, whereas PASRH remains predominant in the microsecond regime. Indeed, the PASRH is proportional to the number of available photons, whereas TPC is sensitive to the photon concentration both in space and time.
Conclusion

A significant decrease of the PASRH level, by either cooling the detector [10], or thanks to fewer interactions with trap levels in more controlled active medium and smaller interaction volumes.

A significant increase of the TPC by enhancing the nonlinear process in adequate devices, such as resonant nanostructures [12], quantum wells [13] or photonic crystals [14].
Declarations
Acknowledgements
This work is partially supported by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (Labex NanoSaclay, reference: ANR10LABX0035) and by a DGAMRIS scholarship. The authors wish to thank Pr. Jacob Khurgin from Johns Hopkins University for fruitful discussions and Pr. Emmanuel Rosencher for his considerable contribution to this work.
Authors’ contributions
BV and BF have led the experiments and have equally contributed to the work. JJ has established the experimental protocol. RH has supervised the work. All have contributed to data analysis. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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