Photoconductors for THz generation
Photoconductive switches are most widely used for the detection and generation of THz waves, in this domain they are also frequently called photoconductive antennas (PCA), as they are directly radiating the THz signal. In the generation process, the electrodes are electrically biased and the gap between them is illuminated by a laser. There are two options possible : the use of ultrashort laser pulses emitted from a femtosecond mode-locked laser (Figure 1-7/a), or simultaneous illumination of two continuous wave (CW) laser with a frequency difference (Figure 1-7/b). In the first case, the ultrashort pulses are generating THz pulses. The rise time of these pulses corresponds to the laser pulse rise time while the pulse width and shape depends on the carrier lifetime of the material. In the frequency domain the generated ultrashort pulses have an extremely wide bandwidth up to the THz domain. In this setup the photoconductive antenna is frequently called photoconductive switch. For the second case the two CW lasers wavelength (frequency) difference is in the range of THz and the photoconductor will emit a continuous Terahertz signal with a frequency corresponding to the frequency difference of the CW lasers, in this case the device is frequently called photomixer.
Before and during the ‘90s, very few researches were addressing the THz domain, mainly because of the lack of efficient and convenient THz sources. Since the exploitation of photoconductive switches and lasers for THz generation, the number of scientific papers concerning the THz domain is exponentially increasing from the years 2000s . Terahertz waves can be used for many applications , starting from spectroscopy, imaging, sensing, biomedical applications and telecommunication. Many materials have unique spectral signatures at THz frequencies, which makes it useful for material characterization and identification. Also, many optically opaque materials are transparent for THz waves. In the telecommunications field the unused wireless frequencies above 100 GHz and in the unregulated spectrum above 300 GHz motivates the research to develop telecommunication systems using the THz waves . However, several passive services exist above 300 GHz for radio-astronomy and earth observation, which needs to be protected from the possible interferences by THz communications. Figure 1-8 shows the free-space loss and resonance peaks up to 3 THz . Suggested bands chosen for long-and medium distance, and indoor applications are marked in the figure.
The THz range also has the advantage of frequent frequency reuse due to the high free-space loss and the several water absorption peaks at higher frequencies , as we can see the numerous peaks in the figure corresponding to this. The high losses can also be seen as a disadvantage for the restriction of high-distance communication. Recent researches have already demonstrated high bandwidth and high data-rate wireless communication at 300 GHz  or even at 600 GHz .
The first devices by Auston were made of silicon (Si) ( and ), later gallium-arsenide (GaAs) was used thanks to its good carrier mobility and direct bandgap. In particular, GaAs deposited with molecular beam epitaxy (MBE) at low temperatures (LT-GaAs), proved to have very good properties with sub picosecond carrier lifetime (1.6 ps in  and 0.27 ps in ). Many of the devices are used for THz generation as photoconductive antennas. In the following state of art review, we are looking at photoconductive antennas and switch designs. An excellent review of PCAs by Burford and El-Shenawee was done in 2017 , the following review is partly based on their work.
The bandgap of 1.42 eV in GaAs requires the illumination with 800 nm wavelengths or below, which allows the use of the popular titanium-sapphire mode-locked lasers. Nowadays the best performing photoconductors for THz generation and detection are made of LT-GaAs. The benefits of the low temperature growth around 200°C – 250°C, are the rather higher carrier mobility due to the high level of crystallinity and the excess arsenide within the crystal to create point defects. These defects are helping the recombination and reduces the carrier lifetime. It also has a high resistivity due to the small number of free carriers. An example from 1991 for LT-GaAs was published by Gupta et al. from the United States with 0.4 ps carrier lifetime grown at 200°C . The result showed a moderate electron mobility of 120-150 cm2/Vs and high resistivity.
A popular method of reducing the carrier lifetime is by performing ion-implantation. An example was proposed by the team of A. Krotkus from Lithuania and C. Jagadish from Australia , in which they were implanting As ions into the GaAs semiconductor to create defects. An ultra-fast lifetime of 0.2 ps was achieved, however the mobility become very low and it also resulted in a low resistance. An annealing process at 600°C was required to increase the mobility to 2000 cm2/Vs and to increase also the resistance, which also resulted in a carrier lifetime increase to 1 ps. Further annealing at 800 °C increased the lifetime up to 10 ps. This shows the difficulty of achieving good values in all the parameters needed for ultrafast operation.
It is possible to reduce the lifetime of GaAs with carbon irradiation too . Semi Insulating (SI) GaAs without irradiation is showing lifetimes in the range of 70 ps, after carbon irradiation 0.55 ps was achieved. The device was used for THz detection in a 1.5 THz bandwidth.
In IMEP-LAHC laboratory, LT-GaAs samples with beryllium doping was used in 2005 , (at that time it was LAHC laboratory in Le-Bourget-du-Lac), and studied in a collaboration with the team of A. Krotkus in 2002 . Beryllium doping is another method to control the optoelectronic properties and to reduce the lifetime, the samples had a mobility of 540 cm2/Vs and a carrier lifetime of 0.5 ps.
As we saw, there are several methods to improve the GaAs properties with various degrees. At the end of the ‘90s, the interest started to increase towards materials working with 1550 nm illumination. At this wavelength smaller size and simpler laser are available. There were researches using the GaAs with 1550 nm, but the efficiency was much lower than in case of 800 nm illumination. A two-step absorption process makes it possible to work at this sub-bandgap wavelength and it requires interband transition of electrons with midgap states or non-linear two-photon absorption. In  with LT-GaAs, an efficiency of 10% was obtained compared to 800 nm excitation.
Another alternative to LT-GaAs has been introduced by the group of A. Gossard in the United States, they proposed a structure composed of self-assembled layers of erbium-arsenide (ErAs) islands in GaAs semiconductor . The advantage of the structure is the possibility to control the response time and resistance by precise engineering of the layers. A carrier lifetime of 0.12 ps was measured with a low electron mobility of 100 cm2/Vs. The layered GaAs:ErAs structure can be used with 1550 nm wavelengths too.
There are also techniques to increase this low efficiency with complex designs of the electrodes, as it will be shown in section I/2.3. Nonetheless, a compound material of InGaAs turned out to be an efficient alternative for the longer wavelengths.
Compared to GaAs devices, InGaAs is not yet that well established technology, significant improvements were achieved only in the past 10-20 years. The bandgap of 0.8 eV allows the InGaAs material to work with 1550 nm wavelength sources. This wavelength also has the advantage of using the well-established fibre-technology in the systems.
Some researches were investigating the low temperature growth InGaAs similarly to GaAs. A Be doped bulk LT-InGaAs was fabricated in , it showed a relatively low resistance of 700 Ω and low carrier mobility of 100 cm2/Vs, however with a good lifetime of 0.35 ps.
Similarly to GaAs, ErAs island embedding can also enhance the InGaAs properties. The method is improving the crystal quality and carrier mobility . As the result of ErAs, the Fermi level is slightly modified in the structure, resulting in an unwanted free carrier concentration. To overcome this problem, beryllium was added as a p-type donor. A 0.3 ps lifetime and 200 cm2/Vs carrier mobility was achieved with this technique.
Ion-irradiation is also possible to improve the material properties, however this results in a low resistance. In  brome irradiation of InGaAs showed a carrier lifetime of 0.2 ps and a good mobility.
Another method for improved properties is to construct a superlattice structure of InGaAs and InAlAs layers . The InAlAs layers are transparent to 1550 nm wavelengths, their role is to add a high concentration of deep-electron traps, acting as a recombination layer via tunnelling process. The InGaAs layer is beryllium doped to reduce the free electron concentration. A mobility of 1900 cm2/Vs was achieved with a very good resistance of 0.12 MΩ. The detected THz pulse width were measured to be 0.75 ps. Recently, this technological approach has gained in performances and has allowed the development of very sensitive components for THz time domain spectroscopy (TDS) setups, the group of B. Globisch in Germany demonstrated a TDS system with a Signal-to-Noise ratio of 55 dB at 4 THz  achieved with beryllium doped InGaAs/InAlAs superlattice.
Ion-implantation of the InGaAs material can also improve the performances. Iron (Fe) implantation reduced the emitted THz pulsewidth from 0.68 ps to 0.57 ps compared to the unimplanted case, the calculated mobility was 1500 cm2/Vs for the ion-implanted InGaAs . While this mobility is lower compared the unimplanted InGaAs, an increase was observed in the THz radiation amplitude.
The InGaAs photoconductive switch used in this thesis is implanted with nitrogen ions . The mobility was reported to be around 6900 cm2/Vs with a relatively good dark resistance of 6 kΩ, and as we will show in Chapter II, the lifetime is in the picosecond range.
As a summary, the sensitivity to 1.5 μm wavelengths is an important advantage of InGaAs devices, however their dark resistance compared to GaAs is lower and their low breakdown voltage is also amongst the disadvantages. Despite these, good properties and performances can be achieved with some of the variously manipulated InGaAs photoconductors. Comparing to GaAs materials, the reported THz field amplitude for these devices is still lower .
In the next section (I/2.3) we review the widely used techniques to improve the photoconductor efficiencies. This includes fabrication of the electrode structures at nano-scale level, which is a technology that became available widespread only in the past decade.
Techniques to improve the quantum efficiency
One main limitation of the efficiency is originating from the geometry of the electrodes on the photoconductor. While an ultrafast photoconductor is illuminated, only the carriers generated in a few hundred nanometres distance from the electrodes can considerably contribute to the generated THz signal, as it is explained by N. T. Yardimici and M. Jarrahi in . The quantum efficiency is defined as the ratio of carriers collected by the electrodes and the number of photons illuminating the photoconductor. To increase the area where the carriers can reach the conductor, interdigitated structures are used where thin “fingers” connected to the electrodes were fabricated with a width in the μm range with a gap between them also in the μm range. An illustration of this interdigitated structure is shown in Figure 1-9.
The neighbouring arms are connected to opposite electrodes, creating an interweaving structure. The fingers are increasing the area where the carriers can be collected but on the other hand the illuminated area is decreasing by the shadowing effect of the metal electrodes.
One of the first photoconductor example with interdigitated structure was demonstrated by Chen et al. in 1991 . They observed that a reduction in electrode spacing by 100 times from 20 μm to 0.2 μm by using the interdigitated structure is improving the responsivity 100 fold. This small gap is in the range of the carrier transit time for a carrier lifetime of 1 ps. Brown et. al.  showed with theoretical calculations that the quantum efficiency is dependent on the electrode length and gap width. There is a trade-off between high quantum efficiency and ultrafast operation of the semiconductors: the faster the semiconductor (shorter the lifetime) the shorter the carrier travel distance before recombination or trapping, therefore less carriers can be collected. The interdigitated structure therefore significantly improved the photoconductor switch’s and antenna’s efficiency by increasing the effective area.
Efficient resonant structures
Another way to increase the efficiency is by increasing the absorption rate of the illuminating light. The fabrication of resonant structures in the semiconductor can significantly improve the absorption efficiency. A solution proposed at IEMN laboratory (Institut d’électronique de microélectronique et de nanotechnologie) by Peytavit et al.  based on a Fabry-Pérot resonant cavity constructed between two gold layers. Figure 1-10/a (Source: ) illustrates the light path with several reflections between the gold layers. Figure 1-10/b shows the enhancement of quantum efficiency when the LT-GaAs thickness corresponds to a multiple of the quarter-wavelength (λ/4).
The Au layers are serving as the electrodes and the mirrors for the cavity and the sub-micron distance between them also increases the electrical DC field in the GaAs layer. With these devices, a microwave signal conversion loss of 22 dB was achieved at 100 GHz (with 780 nm wavelength illumination), which is an improvement of 40 dB compared to other photoconductors .
One of the most promising technology for photoswitch improvement is the fabrication of nanoplasmonic structures. Nanostructured metals can enhance the optical response due to the interaction of metal surface plasmons with the incident light . Surface plasmons are electron-plasma oscillations existing at the metal-dielectric interface . Due to this effect, near the plasmonic structures, the photo absorption is enhanced, increasing the carrier generation in the close proximity of the electrodes. This leads to an increased number of photocarriers reaching the electrodes before recombination , suggesting higher achievable radiation power for emitters and higher sensitivity for detectors. In  a comparison was performed with an LT-GaAs photoconductive antenna with a gap of 20 μm without plasmonic contact electrodes, and with plasmonic contact electrodes composed of 200 nm wide arms with 100 nm gaps. An illustration of the plasmonic contacts is shown in Figure 1-11, with the electrons, electric field, electrode and gap sizes, and the needed orientation of the incident optical field.
While illuminated, the plasmonic electrodes are exciting surface plasmon waves along the grating interface. These waves are allowing the transmission of a large portion of the optical signal into the photo-absorbing substrate. These devices were dedicated to THz wave radiation and the reported improvement of radiation power thanks to the plasmonic surface is 50 fold higher than the conventional case, and for detection, a 30 fold improvement in photocurrent was observed , as compared to a non-plasmonic device.
Other plasmonic techniques includes plasmonic light concentrators, large area nanoantenna arrays or plasmonic nanocavities . These solutions are aiming to enhance the absorption of the photoconductor and reduce the carrier transport length. As a result, they are reducing the trade-off between high quantum efficiency and ultrafast operation. The fabrication of plasmonic structures, a very precise, advanced technology is required.
Plasmonic and resonant structures
M. Billet et al.  used LT-GaAs with a Fabry-Pérot (FP) cavity and a plasmonic diffraction grating to enhance the absorption efficiency of 1550 nm wavelength illumination. The FP cavity is similar as we mentioned previously, however instead of an Au plate, a grating is constructed at the top of the structure as shown in Figure 1-12.
It was shown, that the grating is allowing the excitation of waveguide modes in the structure and increased the efficiency by 3 times. Microwave signal conversion losses of 65 dB was also observed .
These listed techniques details only the most promising methods of improving the photoconductor by designing the appropriate structures, which would also improve the performances of the applications detailed in this thesis. The photoconductor devices presented in Chapter II has an interdigitated switch geometry with gap and arm width of 3-5 μm. The improvement of this structure with these techniques are not the topic of the thesis and the necessary resources were not available at that time.
Photoswitch as a frequency mixer
In this thesis, we are focusing on the semiconductor performance at lower frequencies in the microwave and the millimetre wave range and not in the THz range. One application is the use as a frequency mixer, the fundamentals of mixing is introduced in this section. Other application is the use as a sampler in Analog to digital converters (ADCs), the fundamentals are detailed in the following section I/4, while some ADC properties already introduced in this section.
Fundamentals of mixing
Mixing of signals is a fundamental process for radiofrequency applications. The up- or downconversion of signals in the frequency domain is one of the most important function in signal processing. Usually, a frequency mixer has two input ports with incoming signals at different frequencies, they are called the radiofrequency signal (RF) and local oscillator signal (LO). At the output port the mixed products can be measured at the intermediate frequencies (IF). A basic mixing scheme is illustrated in Figure 1-13.
The frequency mixing can be deduced from time domain signals with the following equations (18) and (19). We define the RF signal as XRF(t) and the LO as XLO(t), the mixing output signal is XIF(t).
Where fRF and fLO are the RF and LO frequencies respectively. The terms a(t) and θ(t) are possible amplitude and phase modulations of the RF signal. The IF signal at the output can be calculated by multiplying the RF and LO.
As the result of the mixing we will have two components at the frequencies (fRF – fLO) and (fRF + fLO). In case of the lower frequency we talk about downconversion, if the output has a higher frequency than fRF we talk about upconversion of signals. In practical systems the frequency components not under treatment are filtered out to reduce possible interferences. There are numerous applications of mixing, for example in a telecommunication transmission system it can be used for signal downconversion for data-processing, or upconversion for transmission or signal frequency re-positioning to avoid interference in a dense communication channel.
There are some important properties of mixing, which are defining the performances of a frequency mixer.
The ratio between the signal to be down (or up) converted and the mixed signal power is called the conversion loss (CL) or in some occasions, when there is a gain during the process, the conversion gain. This value, expressed in decibels, shows the efficiency of the conversion and usually has a dependence on the local oscillator power. As there can be several mixed products, we calculate the CL considering only one IF signal we are interested in. The calculation is written in Equation (21).
Bandwidth and frequency range
The mixer frequency range is defining the frequencies where the mixer has the same performance. The difference between the lower and upper frequency is the mixer bandwidth. There could be different ranges for the RF and LO inputs. It is also possible that the mixer has a wider operating frequency range than its bandwidth, which means that it works only for low bandwidth input RF signals.
In an ideal mixer the IF output contains only the mixed products, however in many real life cases the LO and RF signals can be seen at the output with various degrees. If the isolation is low the feedthrough signals of RF and LO can cause problems for the devices following a mixer, for example saturating an IF amplifier. The isolation between the LO and RF signals is also important to prevent backward propagation of signals in a system, for example if the RF signal is a received signal by an antenna, the LO signal could radiate through this antenna due to the low isolation. Optoelectronic mixers have particularly good isolation between the RF and LO signal because one signal is in the optical domain and the other is in the electrical domain.
Mixers are using a non-linear element or a time-varying element for frequency conversion . One of the most important non-linear property is the third order intercept point (IP3) which is the theoretical power of the fundamental output IF signal when the third order intermodulation product has the same power level. In practice, this point cannot be measured directly because it is usually at a higher power level than the 1 dB compression point of the system.
Spurious free dynamic range in mixers
The spurious free dynamic range (SFDR) can show the operating range where the devices can perform with good characteristics. The non-linear mixing process is creating intermodulation products. The SFDR is the range between the maximum fundamental signal level where the third order intermodulation product has the same level as the noise floor and the noise floor . Third order intermodulation products can be the following: 2*fRF±fLO, 2*fLO±fRF. SFDR is given in decibel scale and for mixers it is usually measured with a dual tone experiment, when two signals are set as an input with a minimal frequency difference.
The SFDR in Analog to Digital Converts (ADCs), which is another application we will detail in section I/4, is defined differently. It is usually measured as a ratio of the signal level to the highest spurious signal level which falls in the frequency range of DC to fs/2, where fs is the sampling frequency. It can be given in dBc, where the reference is the signal level (c refers to the carrier) or dBFS where the reference is the full-scale (FS) level of the ADC .
Mixing with pulsed LO
Using a pulsed signal and a continuous signal as the LO, we can also perform mixing which can be also seen as the sampling of the signal. Sampling is one of the essential functions of an ADC. The digital signals containing the data are modulated in an analog carrier signal and are transferred to the receiver through a channel, the receiver needs to convert the analog signal to digital for signal processing. The conversion is done with sampling and digitization in an ADC.
The local oscillator input in this case is a pulse train (p(t)) with a repetition rate of fs = 1/T, where T is the pulse period. A schematic of the mixing is illustrated in Figure 1-14. We mark the sampled output signal with s(t).
According to the Shannon criteria (equation (22)), the sampling frequency should be at least twice as the maximum frequency of the input RF signal in order to be able to reconstruct all the information.
Where fmax is the maximum frequency of the RF input signal. We mark the minimum frequency as fmin, and the bandwidth BW as the difference of the maximum and minimum frequency: BW = fmax – fmin. Figure 1-15 is illustrating a 10 MHz sinusoidal signal sampled with 100 MHz repetition rate pulses. The left column shows the time domain signals and the right column shows the corresponding signals in the frequency domain. The pure sinusoidal signal only has a single peak at 10 MHz in the frequency domain, while the periodic sampling signal has several peaks at 100 MHz and its harmonics. If we mix these two signals, which means the sampling of the sinusoidal with the pulses, in the time domain we will see the periodic samples of the signal, in the frequency domain it contains several copies of the original signal replicated around the sampling peaks. Around one harmonic of the sampling signal we have two copies of the RF.
Table of contents :
Chapter I Photoconductive switches and its applications
I/1. Photoconductive devices
I/1.1. Photoswitch dynamics
I/1.2. Photoconductors for THz generation
I/2. Photoswitch evolution
I/2.1. GaAs devices
I/2.2. InxGax-1As devices
I/2.3. Techniques to improve the quantum efficiency
I/3. Photoswitch as a frequency mixer
I/3.1. Fundamentals of mixing
I/3.2. Mixing properties
I/3.3. Mixing with pulsed LO
I/3.4. Electronic mixers
I/3.5. Photonic aided mixers
I/3.5.a Photonic mixers
I/3.5.b Optoelectronic mixers
I/4. Photoswitch as a sampler
I/4.1. Sampling fundamentals
I/4.2. Analog-to-Digital converter challenges
I/4.3. Photonic Analog-to-Digital Converter types
I/5. Mode-locked lasers
I/6. Outline and Goals of the Thesis
Chapter II InGaAs photoconductive switch
II/1. The photoswitch samples
II/1.1. Switch fabrication
II/1.2. Characterisation setup
II/2. Electrical Characterization
II/2.1. Coplanar waveguide simulation
II/2.2. Photoswitch RF response in the dark state
II/2.3. Dark resistance in DC
II/2.4. Photoswitch equivalent circuit model
II/2.5. Improving the equivalent circuit model
II/2.6. U-I characterization
II/3. Optoelectronic characterization
II/3.1. Measurement setup
II/3.2. Dispersion of laser pulses
II/3.3. Photoswitch response with sampling oscilloscope
II/3.4. Measurement with opto-electronic autocorrelation
II/3.4.a Simulation of the autocorrelation curve
II/3.4.b Measurement setup
II/3.4.c Typical measurement result
II/3.4.d Measurement corrections
II/3.4.e Curve fitting
II/4. Conclusions on Chapter II
Chapter III Semiconductor mode-locked laser stabilization
III/1. Semiconductor mode-locked laser
III/1.1. MLL samples used in this work
III/1.2. Laser setup
III/1.3. Laser optical properties
III/1.4. Optical pulse characterization
III/1.5. MLL heterodyning on a photodiode
III/1.6. Phase noise of the electrical beating signal
III/1.7. Origins of phase noise
III/2. MLL stabilization
III/2.1. External direct modulation
III/2.2. All optical feedback – single loop setup
III/2.2.a Principles of stabilization
III/2.2.b Stabilization setup
III/2.2.c Stabilization results
III/2.3. All optical feedback – dual loop setup
III/3. Stabilization summary
III/4. Conclusions on Chapter III
Chapter IV Photoswitch as an optoelectronic mixer
IV/1. Heterodyne mixer of narrowband signals
IV/1.1. Setup design
IV/1.2. Conversion loss
IV/1.2.a Discussion about the high conversion losses
IV/1.3. Heterodyning of two DFB lasers
IV/1.3.a Conversion loss
IV/1.3.b Simulation of the conversion loss
IV/1.3.c System characterization
IV/1.3.d Heterodyne detection results
IV/2. Optoelectronic mixer for data-stream downconversion
IV/2.1. QPSK modulation format for the data-stream
IV/2.2. Data-stream demodulation – EVM and BER
IV/2.3. Optically provided local oscillator – MLL
IV/2.4. Optically provided local oscillator – DFB laser
IV/2.5. Electrically provided local oscillator
IV/3. Study of switch non-linearities
IV/4. Applications of the optoelectronic mixer schemes
IV/5. Conclusions of Chapter IV
APPENDIX A : Numerical model of the photoswitch
APPENDIX B : Chromatic dispersion in optical fibres
APPENDIX C : Chromatic dispersion measurement and compensation