ErAs:In(Al)GaAs photoconductors have proven to be outstanding devices for photonic terahertz (0.1–10 THz) generation and detection with previously reported sub-0.5 ps carrier lifetimes. We present the so far most detailed material characterization of these superlattices composed of ErAs, InGaAs, and InAlAs layers grown by molecular beam epitaxy. The variation of the material properties as a function of the ErAs concentration and the superlattice structure is discussed with focus on source materials. Infrared spectroscopy shows an absorption coefficient in the range of 4700–6600 cm$\u22121$ at 1550 nm, with shallow absorption edges toward longer wavelengths caused by absorption of ErAs precipitates. IV characterization and Hall measurements show that samples with only 0.8 monolayers of electrically compensated ErAs precipitates (p-delta-doped at $5\xd71013$ cm$\u22122$) and aluminum-containing spacer layers enable high dark resistance ($\u223c10$–20 M$\Omega $) and high breakdown field strengths beyond 100 kV/cm, corresponding to $>500$ V for a 50 $\mu $m gap. With higher ErAs concentration of 1.6 ML (2.4 ML), the resistance decreases by a factor of $\u223c40$ (120) for an otherwise identical superlattice structure. We propose a theoretical model for calculation of the excess current generated due to heating and for the estimation of the photocurrent from the total illuminated current. The paper concludes with terahertz time-domain spectroscopy measurements demonstrating the strengths of the material system and validating the proposed model.

## I. INTRODUCTION

The advancement of modern terahertz (0.1–10 THz) systems relies on progress in materials research and development. While the terahertz domain was dominated for a long time by electronic systems composed of oscillators and multipliers, as well as SiGe and InP-based transistors,^{1,2} photonic systems become more and more popular, accelerated by an extreme improvement of system performance. Photonic systems use either a short-pulsed laser (pulse duration typically $<100$ fs) with a spectral width in excess of 7 THz or two continuous-wave lasers that are detuned by the desired terahertz frequency. Either a nonlinear optical process or a semiconductor device converts the optical signal to a terahertz signal by mixing its frequency components that is subsequently radiated. Though this process seems complicated at a first glance, it offers unique advantages, such as extreme frequency coverage of several terahertz ($\u223c$ 5–6 octaves) in one system. Over the past 20 years, the peak dynamic range (DNR) of photonic systems experienced dramatic improvement, reaching more than 100 dB and enabling several potential commercial applications. These include high resolution thickness measurements,^{3,4} photonic vector network analysis (VNA),^{5,6} photonic spectrum analyzers,^{7} and many more. In many modern photonic systems, the conversion of the optical signal to the terahertz wave is performed by semiconductors called photoconductors. They are composed of a special, highly resistive material that absorbs the optical signal resulting in the generation of electron-hole pairs, making the material conductive. The conductance is modulated at terahertz frequencies due to the spectral shape of the optical signal. With the help of a DC bias, the device generates a terahertz current that is subsequently fed into an antenna for emission of the terahertz waves. The process can also be reversed to form a terahertz detector by biasing the photoconductor with a received terahertz wave instead of a DC bias, while the same laser signal used for terahertz generation is incident on the device. The photoconductor mixes the terahertz and the laser signal, resulting in a DC component that is proportional to the received terahertz field strength. The photoconductive material must fulfill several requirements for efficient terahertz generation,^{8}

An absorption coefficient ($>5000$ cm$\u22121$) to generate high currents at considerably low laser powers.

A high dark resistivity ($>500$ $\Omega $ cm). Otherwise, the application of the DC bias will lead to a large dark current flow that thermally destroys the semiconductor.

A high carrier mobility ($>400$ cm$2$/V s) enabling high AC current generation at low DC bias.

For emitters, a large breakdown field strength ($>100$ kV/cm) enables the application of a large DC bias in order to generate high currents at the relatively low laser power of table-top (fiber-coupled) lasers (few 10 mW).

A low carrier lifetime ($<1$ ps) allows for recovery of the highly resistive state after optical illumination and enables the device to follow the fast terahertz modulation. This is particularly relevant for receivers and continuous-wave operation, not so much for pulsed sources, though helpful to shift the spectral emission peak to frequencies beyond 1 THz.

These features are difficult to fulfill simultaneously as they partially compete with each other. The most successful versions of photoconductors are grown by molecular beam epitaxy (MBE). Defect engineering is the answer to the aforementioned requirements. For 800 nm operation, specially engineered materials include LTG-GaAs^{9} and ErAs:GaAs,^{10–12} where midgap trap states or quasimetallic clusters with a Fermi energy close to the bandgap center enable fast carrier trapping and, hence, carrier lifetimes below 500 fs as well as high resistance (typically 10s of G$\Omega $ cm). At the same time, mobilities in the range of 1000–2000 cm$2$/V s have been reported.^{13} The breakdown field strength lies beyond 500 kV/cm.^{14}

Due to the rapid development of the telecom sector, 1550 nm compatible photoconductors are highly useful for compact, affordable, and versatile systems. Material engineering to achieve desirable values for all the above mentioned properties under telecom excitation faces challenges. Several material engineering approaches have been implemented so far where the most promising ones can be broadly divided into four categories: (i) alloying GaAs with larger amounts of Er to form a miniband within the bandgap of GaAs.^{15,16} Absorption takes place in a two step process via the trap states. These structures, grown by MBE at 600 $\xb0$C and codoped with $8.8\xd71020$ cm$\u22123$ Er, were reported to feature a resistivity of 6800 $\Omega $ cm and mobility of 2350 cm$2$/V s. (ii) The second approach includes periodic incorporation of the higher bandgap material InAlAs in InGaAs, forming a superlattice (SL) structure. When these structures are grown by MBE at 400 $\xb0$C, an alloy clustering effect with InAs- and AlAs-like precipitates results in a resistivity of 2500 $\Omega $ cm and 2700 cm$2$/V s mobility.^{17} However, the lifetime of these materials were very long ($>10$ ps). Another approach includes low temperature growth (LTG)-InGaAs/InAlAs SL, locally doped with $2.5\xd71019$ cm$\u22123$ Be, which also showed high material quality (500 $\Omega $ cm resistivity and 340 cm$2$/V s mobility).^{18} (iii) The third approach is based on doping InGaAs with transition metals leading to substitutional defects. MBE growth at 400 $\xb0$C with an optimized iron doping concentration of $5\xd71019$ cm$\u22123$ featured 2000 $\Omega $ cm resistivity and 900 cm$2$/V s mobility.^{19} The best results achieved so far with this method were obtained using rhodium (Rh) doped material ($8\xd71019$ cm$\u22123$), featuring 3190 $\Omega $ cm resistivity and 1010 cm$2$/V s mobility.^{20,21} (iv) The fourth promising approach implements localized ErAs precipitates in an InGaAs/InAsAs SL structure. Previous publications report a resistivity of $>600$ $\Omega $ cm and a mobility of 1100 cm$2$/V s.^{22}

This paper presents detailed material characterization of several ErAs:InGaAs/InAsAs SL structures. We discuss Hall measurements, infrared (IR) absorption characteristics, and DC characterization. An insight into the dependence of the material properties on several growth parameters such as doping concentration and SL structure is also discussed, concluding with terahertz spectra generated with the investigated materials.

## II. SAMPLE GROWTH

The ErAs:In(Al)GaAs photoconductors are grown by MBE at standard growth temperatures of InGaAs (490 $\xb0$C), lattice-matched to InP. ErAs precipitates self-align by growing a thin layer, corresponding to 0.8–2.4 monolayers (ML) of ErAs, on top of InGaAs.^{23} Due to a mismatch of the lattice structure (Zinc blende for InGaAs and rock salt for ErAs), ErAs does not wet the InGaAs surface and clusters to form semimetallic precipitates with a Fermi energy close to the conduction band edge of InGaAs.^{24} P-type codoping with beryllium or carbon shifts the Fermi energy close to the bandgap center in order to enable efficient carrier trapping and high resistance. Table I shows a series of ErAs:In(Al)GaAs photoconductors employed for terahertz generation and detection. Figure 1 depicts the layer structure of the investigated ErAs:InGaAs/InAlAs SL.

Sample . | Layer structure . |
---|---|

A1 | 90×(InGaAs|C:InAlAs| δ_{C}-0.8 ML ErAs||C:InAlAs) |

A2 | 90×(InGaAs|C:InAlAs| δ_{C}-1.6 ML ErAs||C:InAlAs) |

A3 | 90×(InGaAs|C:InAlAs| δ_{C}-2.4 ML ErAs||C:InAlAs) |

B1 | 90×(InGaAs|δ_{C}-1.6 ML ErAs||C:InAlAs) |

B2 | 70×(InGaAs|δ_{Be}-0.8 ML ErAs||Be:InAlAs) |

C1 | 100×(InGaAs|δ_{C}-0.8 ML ErAs|) |

C2 | 100×(InGaAs|δ_{Be}-0.8 ML ErAs|) |

Sample . | Layer structure . |
---|---|

A1 | 90×(InGaAs|C:InAlAs| δ_{C}-0.8 ML ErAs||C:InAlAs) |

A2 | 90×(InGaAs|C:InAlAs| δ_{C}-1.6 ML ErAs||C:InAlAs) |

A3 | 90×(InGaAs|C:InAlAs| δ_{C}-2.4 ML ErAs||C:InAlAs) |

B1 | 90×(InGaAs|δ_{C}-1.6 ML ErAs||C:InAlAs) |

B2 | 70×(InGaAs|δ_{Be}-0.8 ML ErAs||Be:InAlAs) |

C1 | 100×(InGaAs|δ_{C}-0.8 ML ErAs|) |

C2 | 100×(InGaAs|δ_{Be}-0.8 ML ErAs|) |

Three different SL structures have been grown: SL consisting of ErAs precipitates sandwiched between (a) two InAlAs layers (denoted as $A$), (b) one InAlAs layer (denoted as $B$), and (c) no InAlAs layer (denoted as $C$). Incorporation of the higher bandgap InAlAs layer in the SL increases the resistivity and the breakdown field strength of the material. Additional p-doping of $5\xd71018$ cm$\u22123$ (Be or C) was incorporated in the InAlAs layers for all samples (except B2: $1.3\xd71019$ cm$\u22123$ C-doping) to compensate the n-type conductivity of ErAs.^{25,26} A drawback of InAlAs barriers is that they increase the overall carrier lifetime of the material.^{27} Hence, InAlAs layers are omitted for the dedicated receiver materials C1 and C2. The localized ErAs nanoislands act as trap centers for charge carriers reducing the carrier lifetime of the material. Localized ErAs precipitates allow use of otherwise unmodified, undoped InGaAs absorber layers with high mobility and high absorption coefficient. The A-structures feature different ErAs ML concentrations (0.8–2.4 ML) at a constant p-type delta doping concentration of $5\xd71013$ cm$\u22122$ allowing for the study of the material properties as a function of the ErAs ML concentration. The details of the material structure such as the layer thickness and ML concentration are mentioned in the caption of Fig. 1.

## III. MATERIAL CHARACTERIZATION

### A. Infrared spectroscopy

IR spectroscopy of the structures was performed using a commercial spectrometer from Agilent Technologies (Cary7000). The sample was placed at an incidence angle of 6 $\xb0$C. Two receivers record the reflected and transmitted signal at angles of 12 $\xb0$C and 180 $\xb0$C with respect to the incident signal, respectively. The coherence length of the source was greater than 2 $\mu $m, hence showing Fabry–Pérot interferences caused by the photoconductive film, however, not by the substrate. The reflectance measurements have been used to estimate the refractive index, $n$, of the active region by evaluating the free spectral range (FSR) $\Delta \upsilon =c0/(2n\xd7d)$, where $c0$ is the speed of light and $d$ is the thickness of the active SL structure. The latter was measured using a Dektak profilometer (10s of nanometer resolution) after locally removing the photoconductive layer. Figure 2 shows the refractive index of the samples as a function of wavelength with a standard deviation of $\xb10.15$. At wavelengths greater than 1700 nm, the calculated refractive index is in agreement with the expected refractive index ($n\u22483.4$), excluding B1 which could probably be due to different buffer layer thickness. At lower wavelength, the calculated refractive index value is higher due to the presence of the bandgap and absorption (Kramers–Kronig relations). The sharp increase of the refractive index around 1580 nm (close to the band edge of InGaAs) is probably associated with the absorption edge of the active material. However, further investigation is required for a conclusive argument.

The IR spectroscopic measurements have also been used to calculate the absorption coefficient, $\alpha (\lambda )$. As the substrates are much thicker than the coherence length of the spectrometer’s light, no Fabry–Pérot interference takes place. The (multiple) reflections within the sample sum up incoherently for both transmission and reflection data. The very minor reflection at the InGaAs/InP interface was neglected. The measured nonabsorbed fraction of the light, $X(\lambda )=T(\lambda )$+$R(\lambda )$, allows one to calculate the absorption coefficient, $\alpha (\lambda )$, by solving the quadratic equation for $e\u2212\alpha (\lambda )d$,

where $Ri=(1\u2212ni1+ni)2$ and $Ti=1\u2212Ri$ ($i=1,2$). $Ri$ and $Ti$ are the power reflection coefficient and power transmission coefficient, with subscript denoting air-active material interface ($i=1$, $nInGaAs\u22483.4$) and air-substrate interface ($i=2nInP\u22483.1$). Figure 3 shows the calculated absorption coefficient vs wavelength. In order to validate the calculated absorption coefficient, a reference measurement using only the InP substrate was employed. Analysis confirmed that the substrate had no influence on $\alpha (\lambda )$ for the wavelength range of interest.

All samples feature a shallow absorption edge occurring at wavelengths longer than 1600 nm; however, the material is not becoming completely transparent as compared to a reference InP wafer. After the absorption edge, there is even a gradual increase in $\alpha (\lambda )$ at longer wavelengths for all the samples. Figure 3 (a) shows that an increasing Er content (0.8 ML, 1.6 ML, and 2.4 ML for A1, A2, and A3, respectively) results in larger absorption at the long wavelength end. This allows us to conclude that the absorption below the bandgap arises from the ErAs nanoislands in the In(Al)GaAs SL structure. The absorption of low energy IR radiation occurs through photoionization of ErAs nanoparticles. This may enable the employment of ErAs:InGaAs also for operation with lasers emitting at wavelengths beyond 1600 nm. A similar process has been employed earlier to operate GaAs photoconductors at 1550 nm.^{28}

Figure 3(b) presents a comparison of $\alpha (\lambda )$ for different SL structures maintaining a constant ErAs content of 0.8 ML. Similar to sample series A, below 1600 nm the absorption coefficients are very similar, yet with sample C1 being slightly more absorptive. This is due to the absence of InAlAs layers that cause an increase of the effective bandgap due to quantization effects (similar to a quantum well). A higher bandgap decreases the probability of extrinsic photoconductivity by the ErAs precipitates. An InAlAs layer thickness of 2.5 nm (B2) and placing the ErAs precipitates at the InGaAs-InAlAs interface in the SL decreases slightly the long wavelength absorption. For sample A1, where the ErAs precipitates are encapsulated between two 1.5 nm thick InAlAs layers, the absorption further decreases $\alpha (\lambda )$. In conclusion, a sharper absorption edge with lower absorption coefficient, $\alpha (\lambda )$, at longer wavelength is seen for samples with thicker InAlAs barriers and lower ErAs ML.

### B. Hall measurements

The Hall measurement results for all samples are presented in Table II. All samples are n-type conductive with a carrier concentration, $nc$, in the range of $1012$–$1015$ cm$\u22123$. Sample A1 and B2 with 0.8 ML ErAs concentration show the lowest carrier concentration of $nc\u223c$ 3.6$\xd7$10$12$ cm$\u22123$ and $8.6\xd71012$ cm$\u22123$, respectively, almost reaching the intrinsic carrier concentration of InGaAs of $ni=6.3\xd71011$ cm$\u22123$. A higher ErAs content of 1.6 ML (2.4 ML) for sample A2 (A3) leads to approximately two (three) orders of magnitude increase in the electron concentration in the conduction band [$\u223c1.3\xd71014$ cm$\u22123$ (A2) and $\u223c1.5\xd71015$ cm$\u22123$ (A3)]. This indicates only a partial compensation of the n-doping caused by the ErAs ML for samples A2 and A3. The resistivity of the samples follows a similar behavior for A1 ($\u223c3.9$ k$\Omega $ cm) and B2 ($\u223c4.7$ k$\Omega $ cm); however, the measurement error of such highly resistive samples is large. We later present IV characteristics of the samples which imply that A1 features a higher resistance. Samples C1 and C2 that are dedicated receiver materials show reasonably high mobility ($>750$ cm$2$/V s).

Sample . | ρ (Ω cm)
. | μ (cm^{2}/V s)
. | n_{s} (cm^{−2})
. | n_{c} (cm^{−3})
. | Carrier type . |
---|---|---|---|---|---|

A1 | 3900±400 | 450±40 | 5.85±0.5 ×10^{8} | 3.60±0.4 ×10^{12} | N |

A2 | 60±7 | 800±70 | 2.05±0.3 ×10^{10} | 1.25±0.2 ×10^{14} | N |

A3 | 15±3 | 300±25 | 2.50±0.2 ×10^{11} | 1.50±0.2 ×10^{15} | N |

B1 | 100±10 | 890±80 | 1.15±0.2×10^{10} | 7.05±0.8 ×10^{13} | N |

B2 | 4700±500 | 190±20 | 8.65±0.9 ×10^{8} | 8.60±0.9 ×10^{12} | N |

C1 | 290±30 | 775±70 | 3.45±0.3 ×10^{9} | 3.40±0.3 ×10^{13} | N |

C2 | 60±6 | 2080±200 | 6.55±0.6 ×10^{9} | 5.30±0.5 ×10^{13} | N |

Sample . | ρ (Ω cm)
. | μ (cm^{2}/V s)
. | n_{s} (cm^{−2})
. | n_{c} (cm^{−3})
. | Carrier type . |
---|---|---|---|---|---|

A1 | 3900±400 | 450±40 | 5.85±0.5 ×10^{8} | 3.60±0.4 ×10^{12} | N |

A2 | 60±7 | 800±70 | 2.05±0.3 ×10^{10} | 1.25±0.2 ×10^{14} | N |

A3 | 15±3 | 300±25 | 2.50±0.2 ×10^{11} | 1.50±0.2 ×10^{15} | N |

B1 | 100±10 | 890±80 | 1.15±0.2×10^{10} | 7.05±0.8 ×10^{13} | N |

B2 | 4700±500 | 190±20 | 8.65±0.9 ×10^{8} | 8.60±0.9 ×10^{12} | N |

C1 | 290±30 | 775±70 | 3.45±0.3 ×10^{9} | 3.40±0.3 ×10^{13} | N |

C2 | 60±6 | 2080±200 | 6.55±0.6 ×10^{9} | 5.30±0.5 ×10^{13} | N |

### C. IV Characteristics

Next, we present both dark and illuminated IV characteristics of structures that are potentially well suited for implementation in emitters. These include samples A1, A2, A3, and B2. Since these samples have the same p-doping concentrations and similar SL structure, the IV characteristics are predominantly influenced by the ML concentration of ErAs and the thickness of the InAlAs layers (B2 vs A-series). In order to emulate realistic operation conditions, we have waited at each bias until the current is stabilized in order to take into account increased dark- and photocurrents due to a temperature rise of the sample. Such IV characteristics are a direct measure of the quality of the fabricated devices. A high quality device features (i) dark IV curves which are predominantly linear (ohmic resistance), (ii) low dark current (high dark resistance), (iii) high photocurrent (low illuminated resistance), and (iv) high breakdown field strength (dark/illuminated).

The test structures consisted of three different electrode gap sizes of 25, 35, and 50 $\mu $m in a square geometry with two identical copies of each kind. One set of these was used to determine dark IV characteristics. The second set was used to record illuminated IV characteristics, implementing 42 mW average laser power at 1550 nm using a pulsed laser system with $\u223c90$ fs pulse width and a 100 MHz repetition rate similar to the one in Ref. 8. All samples were destroyed during operation in order to determine the point of breakdown.

The IV characteristics of the four different emitter structures A1, A2, A3, and B2 are shown in Fig. 4. Due to the square shape of the biased area, the currents are almost identical for all investigated gap sizes at low and intermediate biases, proving high reproducibility. A1 and B2 with 0.8 ML ErAs show the lowest dark current (highest dark resistance). This is in agreement with previously reported results where incorporation of 0.8 ML ErAs with $5\xd71013$ cm$\u22122$ Be compensation featured high quality material^{23,29,30} and in line with the Hall results. Comparing Figs. 4(a) and 4(d) one can observe that structure A1 with ErAs sandwiched between the two InAlAs layers shows less dark current ($\u223c5.9$ $\mu $A at 100 V) as compared to B2 with one InAlAs layer in the SL structure ($\u223c18\mu $A at 100 V). The lower dark current is due to two reasons: (i) the requirement of tunneling of charges into the recombination centers through InAlAs from either side in structure A1, whereas in B2 the absorbing InGaAs layer touches on one side the ErAs recombination centers. (ii) The two InAlAs layers are 0.5 nm thicker than the single InAlAs layer of sample B2. InAlAs features a large bandgap (1.46 eV), thus orders of magnitude lowering the intrinsic carrier density. Furthermore, the Fermi level of the ErAs inclusions is close to the bandgap center of InAlAs.

The current under illumination, $Iill$, with 42 mW incident power for samples A1 and B2 at 100 V bias (25 $\mu $m electrode spacing) was 162 $\mu $A (27.5 times higher than $Idark$) and 316 $\mu $A (17.8 times higher than $Idark$), respectively. All four structures withstood at least 450 $\mu $A for all gap sizes without thermal failure or electrical breakdown under illumination. Samples A2 and A3 with twice and three times higher Er content but otherwise identical sample structure as A1 show 30 times (130 $\mu $A at 40 V) and 110 times (460 $\mu $A at 40 V) higher dark current, respectively, pointing out imperfect charge compensation by p-doping. This is in excellent agreement with the lower resistance found in the Hall measurements. The illuminated current is also considerably larger than that of structure A1, with 260 $\mu $A ($720\xb1120$ $\mu $A) at 40 V for structure A2 (A3). This gives the impression that the photocurrent, $Iph=Iill\u2212Idark$, of samples A2 and A3 was larger than those of samples A1 and B2. However, the large current flow under illumination, combined with high bias, considerably heats up the samples. The measured dark currents are, therefore, not representative and cannot be used to calculate the photocurrent, $Iph$.

In order to estimate the photocurrent ($Iph$) from the recorded total illuminated current ($Iill$), we present a theoretical model to calculate the photocurrent considering the temperature rise of the sample. The excess current due to heating of the material is proportional to the amount of thermal carriers in the conduction (valence) band. As the samples are all n-type, the mass action law dictates that the hole concentration in the sample is much smaller than the electron concentration. We, thus, simplify the subsequent calculations by restricting to electrons in the conduction band only. The electron density is given by

where $kB$ is the Boltzmann constant, $Nc=2.1\xd71017$ cm$\u22123$ is the effective density of states in the conduction band, and $Ea\u2248Ec\u2212EF$ is the activation energy. From the carrier concentration obtained by the Hall measurements presented in Table II at 300 K, Eq. (2) yields an activation energy of 0.271 eV (A1), 0.192 eV (A2), 0.127 eV (A3), and 0.266 eV (B2). When subject to heat, the dark current increases as

where $Id(T)$ is the excess dark current under laser illumination and $T0=300$ K is the initial temperature under dark condition where $Id300K$ is measured. Here, we neglect that the Fermi energy and the bandgap energy are a weak function of temperature. We note that $Id300K$ is approximately the dark current shown in Fig. 4 because without the laser signal, the only heat source is Joule heat. The total current, however, is at least an order of magnitude less, and so is the heat deposition. The thermal load of the active area under illumination is given by

where $PL$ = 42 mW is the average laser power and the second term is Joule heat. $Iill$ is current under illumination that can be obtained from Fig. 4. The maximum thermal load given by a heat conduction out of a hot disk on a heat sink (the InP substrate) follows:^{31}

where $\lambda =0.68$ W/(cm K) is the heat conductivity of the InP substrate and $A$ is the cross-sectional area of the device, where we assume homogeneous illumination with a temperature rise of an average temperature of $\Delta T$ for simplicity. For samples with 25 $\mu $m gaps, considering a focal spot size of the laser in the range of $22.5\xb12.5$ $\mu $m, we can estimate a temperature rise of the active structure. At the maximum biases where currents started increasing superlinearly, the temperature rise is $\Delta TA1=69\xb18$ K at 270 V, $\Delta TA2=41\xb15$ K at 86 V, $\Delta TA3=43\xb15$ K at 45 V, and $\Delta TB2=46\xb15$ K at 145 V. One can observe the rise in temperature for all samples are almost the same, except A1. Substituting these values into Eq. (3), the excess dark current $Id(T0+\Delta T)$ and the photocurrent, $Iph=Iill\u2212Id(T0+\Delta T)$ can be calculated. The values are summarized in Table III.

Samples . | ΔT (°C)
. | (I_{d}(T)μA)
. | (I_{Ph}μA)
. |
---|---|---|---|

A1 (270V) | 69±8 | 108±22 | 349±22 |

A2 (86 V) | 41±5 | 565±61 | 82±61 |

A3 (45 V) | 43±5 | 1215±100 | 153±100 |

B2 (145 V) | 46±5 | 100±16 | 367±16 |

Samples . | ΔT (°C)
. | (I_{d}(T)μA)
. | (I_{Ph}μA)
. |
---|---|---|---|

A1 (270V) | 69±8 | 108±22 | 349±22 |

A2 (86 V) | 41±5 | 565±61 | 82±61 |

A3 (45 V) | 43±5 | 1215±100 | 153±100 |

B2 (145 V) | 46±5 | 100±16 | 367±16 |

Table III shows that the actual photocurrent of structures A1 and B2 is superior to structures A2 and A3, indicating that samples A1 and B2 will be best suited for sources. This will be proven by their superior terahertz performance shown in Sec. III D. We note that the values in Table III underestimate the excess dark current as we assumed a large laser spot size of the order of 20–25 $\mu $m, which may not be the case in the experiment. The diffraction-limited spot size, if the sample is mounted perfectly in the center of the focal spot, can be as low as 10 $\mu $m for the used optics. However, the samples are usually a bit defocused. The actual spot size can also show some variation for each measurement leading to some change in the illuminated IV curves.

Most of the illuminated IV characteristics of structures A2 and A3, as well as all dark IV characteristics show an exponential increase of the current at the highest biases in Fig. 4, indicating either thermal breakdown by current runaway due to excessive intrinsic carrier generation at high temperatures or electrical breakdown. In all cases, the dark breakdown field strength is much higher than the illuminated one. Figure 5 summarizes the break down field strengths. Materials A1 and B2 feature a high breakdown field strength of $153\xb15$ kV/cm and $138\xb15$ kV/cm, respectively, for 25 $\mu $m gaps and decrease with an increase in the gap size. As the thermal load of these samples is low under dark conditions, A1 and B2 breakdown electrically. For higher ErAs ML concentrations, the breakdown field strengths decrease drastically: $56\xb12$ kV/cm and $21\xb11$ kV/cm for samples A2 and A3, respectively, for 25 $\mu $m gap. For the illuminated case, empirical data in Ref. 32 suggest thermal breakdown for LT-GaAs-based samples occurring at a temperature rise of about 120 K. We expect similar values for InGaAs on InP as the thermal conductivity of InP ($\lambda =0.68$ W/cm K) is slightly higher than that of GaAs ($\lambda =0.55$ W/cm K), but the thermal conductance of the thin InGaAs layer is about 12 times worse. The 25 $\mu $m samples were destroyed at biases above 270 V (A1), 85 V (A2), 45 V (A3), and 145 V (B2), respectively. The estimated temperature rise assuming homogeneous illumination is summarized in Table III. These temperatures are about a factor of 2–3 smaller than the empirical value of 120 K despite, but, nevertheless, the samples were destroyed. This may have two causes: (i) the devices were thermally destroyed due to nonhomogeneous illumination causing much higher local temperatures or (ii) devices broke down electrically caused by charging up of the structures due to charge separation and trapping at high optical fluence combined with high bias, locally exceeding the breakdown field strength.^{33} For case (i), the approximately Gaussian shape with an optical spot size that is smaller than the area of the devices indeed causes nonhomogeneous distribution of the optical power. Thus, the center of the optical spot may get too hot causing thermal failure. However, inhomogeneous illumination is indeed advantageous to a certain degree. Poorly illuminated areas of the gap between the electrodes remain fairly resistive, the resistance is solely reduced by charge carriers drifting into these regions from adjacent illuminated areas. These regions act as current limiters that keep the temperature rise in the optical spot manageable, preventing early breakdown of the sample. For case (ii), separation of optically generated charges by the applied bias leads to an excess of holes close to the negative electrode and an excess of electrons at the positive electrode. These charge clouds screen the externally applied bias, leading to an inhomogeneous potential landscape with a large potential drop in the vicinity of the electrodes while the center of the gap experiences a lower field. The effect is intensified by charge trapping in the low lifetime material as trapped charges unlikely to find an oppositely charged recombination partner for charge neutralization. This leads to early breakdown as the local field strength in the vicinity of the electrodes may exceed the breakdown field strength. Excessive charge trapping, however, is mitigated if a large dark current flows through the sample in addition to the photocurrent while the thermal load increases. The interplay of both cases is most likely the cause of the destruction of the samples. Interestingly, the breakdown field strength is higher for smaller gap sizes. For smaller gaps, the field is less uniform along the growth direction. The trend in the breakdown field strength for sample A1 in Fig. 5 also confirms the earlier reported breakdown field strength of $170\xb140$ kV/cm for a 10 $\mu $m gap.^{8}

Figure 6 plots the dark resistance as a function of the applied voltage for test structures with dimensions of $35\xd735$ $\mu $m$2$. Structure A1 with 0.8 ML ErAs exhibits the highest resistance. As opposed to an ideal resistor, the resistance increases from 6 to 25 M$\Omega $ with increasing bias voltage. Several factors could lead to such an effect. These include nonlinearities in mobility at high bias field strength and saturation of drift velocity of the material (intrinsic InGaAs $\u223c4$ kV/cm). However, a sublinear increase in the photocurrent and linear increase in the emitted terahertz p-p signal with bias voltage as reported in Ref. 8 indicates that material parameters like mobility and drift velocity may show some laser power dependence. Higher bias increases the efficiency of tunneling of the carriers through InAlAs layers, providing easier access to the ErAs trap centers. This could also have a significant contribution to the decrease in the received current. Further investigation is, therefore, required. After a fourfold increase in the device resistance with bias, a decrease in the resistance is observed ($>400$ V) caused by the onset of breakdown. Finally, current runaway and breakdown leads to the demise of the device. A similar trend in the resistance can be observed for B2 and A2. For B2 with a single InAlAs barrier, the resistance is approximately five times lower than that of A1 (1 M$\Omega $ at low bias voltage and $\u223c7$ M$\Omega $ at 350 V). The resistance of A3 is monotonically falling with increasing bias due to the high currents eventually causing thermal failure.

From the IV characteristics, we conclude that samples A1 and B2 are best suited as sources as they show the highest breakdown field strengths at considerably large photocurrents. In Sec. III D, we will show that they indeed outperform the other samples as terahertz sources.

### D. Time domain spectroscopy results

The performance of the emitter structures was tested using a fiber-based 1550 nm TeraFlash Pro TDS system. It provides laser pulse widths of $\u223c90$ fs at a 100 MHz repetition rate.^{34} The laser power coupled into the device was 15 mW both for the emitter and receiver. For emitters, a 25 $\mu $m slotline antenna was employed (see, e.g., Ref. 35), and each sample was biased to have similar amount of illuminated current ($Iill\u223c200\xb120$ $\mu $ A). The receiver consisted of a 25 $\mu $m H-dipole antenna with 5 $\mu $m gap using material C1. Figure 7(a) shows the receiver current which is proportional to the transient terahertz field. Material A1 with the highest resistivity shows the best performance with a received terahertz p-p signal of 0.925 $\mu $A. This is followed by the single InAlAs barrier structure B2 (0.690 $\mu $A p-p terahertz pulse). The spectra show a peak DNR of $\u223c100$ dB with a bandwidth beyond 5 THz for sample A1. While sample B2 shows slightly lower DNR, the high frequency performance of the sample is similar to that of sample A1 [Fig. 7(b)]. Increasing the ErAs ML concentration drastically reduces the TDS performance with terahertz p-p signals of 225 nA and 37 nA for samples A2 and A3, respectively.

The transient pulse in Fig. 7(a) can be used to estimate the actual photocurrent, $Iph$, from the total observed illuminated current, $Iill$. The increase in the temperature of the material is estimated using Eqs. (4) and (5). For sample A1, the temperature increases by $\u2248$ 35 K for a laser power of 15 mW where we assumed a close to diffraction-limited spot size of $\u223c13\xb13$ $\mu $m. The photocurrent $Iph$ for sample A1 is estimated to be $\u223c157\mu $A using Eq. 3 and $Iill$ mentioned in the caption of Fig. 7. Since $Iph\u221dETHz$, the photocurrent of samples A2, A3, and B2 can be estimated from Fig. 7. (a) referenced to the estimated photocurrent of sample A1. The calculated photocurrent $Iph$ for the samples are $\u223c40$ (A2), $\u223c7$ (A3), and $\u223c120$ $\mu $A (B2). These are approximately 85% (A1), 18% (A2), 3% (A3), and 63% (B2) of the total illuminated current, $Iill$. With minor variations, the fraction of the $Iph$ is in the same range of those shown in Table III [namely, $86\xb15$% (A1), $12.6\xb19.4$% (A2), $11\xb17$% (A3), and $79\xb14$% (B2)]. The deviations are due to strong dependence on the actual laser spot size, which can just be estimated as well as the neglected influence of the carrier lifetimes that differ for all samples.

## IV. CONCLUSION

We have characterized ErAs:In(Al)GaAs SL structures for suitability as terahertz sources. The absorption coefficient, $\alpha $, calculated from IR spectroscopic data shows a shallow absorption edge with nonzero absorption below the bandgap (of the order of 600–4000 cm$\u22121$) due to absorption through mid-bandgap states provided by the ErAs precipitates. Increase in the ErAs concentration or decrease in the thickness of the InAlAs layers leads to a higher absorption coefficient at frequencies $>1700$ nm. The absorption coefficients at 1550 nm for all investigated samples are in the range of 4700–6600 cm$\u22121$, well suitable for operation at this wavelength.

Hall measurements show that the materials feature an n-type conductivity with more than two orders of magnitude increase in the carrier concentration for an increase of the ErAs deposition from 0.8 ML to 1.6 ML (2.4 ML) for otherwise identical SL structures. Four different samples have been investigated as terahertz emitters. A theoretical model has been developed to estimate the actual photocurrent from the total illuminated current, taking heating of the samples into account. Samples containing 0.8 ML ErAs per SL period feature high dark resistance of several M$\Omega $ per square at biases of the order of 200 V. An increase of the ErAs concentration causes orders of magnitude decrease of the resistance. For 1.6 ML ErAs, the resistance decreases by a factor of $\u224840$ and for 2.4 ML ErAs, the resistance decreases by a factor of $\u2248120$. Samples with 0.8 ML ErAs feature a high breakdown field strength of $150\xb110$ and $140\xb110$ kV/cm, respectively (A1 and B2 with 25 $\mu $m electrode gaps) with decreasing breakdown field strength for larger gaps.

Terahertz time-domain measurements with a peak DNR of 100 dB were used to quantify the actual photocurrent responsible for terahertz generation. The photocurrents were estimated at 85% (A1), 18% (A2), 3% (A3), and 63% (B2) of the total observed illuminated current. These measured results show a good match with the theoretical predictions for all the samples.

## ACKNOWLEDGMENTS

The authors would like to thank Katja Dutzi, Anselm Deninger and Nico Vieweg from Toptica Photonics for collaboration and providing us the TeraFlash Pro TDS system. The authors further acknowledge the Deutsche Forschungsgemeinschaft (DFG) for funding within Project No. PR1413/3-2 (REPHCON).

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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