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Photoconductive antennas (PCAs) for terahertz (THz) time-domain spectroscopy (TDS) require high carrier mobility and ultrashort carrier lifetime, a contradiction that represents a fundamental limitation. Quantum photoconductive antennas (QPCAs) aim to overcome this limitation by spatially separating carrier transport and trapping. However, their use has been limited to THz receivers only due to the low resistivity of their undoped, high-mobility InGaAs layers. Here, we present for the first time Rh-doped quantum photoconductors co-doped with Ru, with up to eight times higher resistivity. Ru acts as a highly electrically active deep-level acceptor, facilitating carrier compensation at low doping concentrations. In this way, a sixfold reduction in free electron concentration down to 1.4 × 1012 cm−3 is achieved, providing a very high resistivity of 1309 Ωcm, while maintaining an excellent carrier mobility of 3330 cm2/Vs. In addition, optical pump-probe measurements show a negligible effect of Ru-doping on the carrier lifetime, demonstrating that the QPCA principle of distinct charge carrier transport and trapping is maintained. These results represent an important milestone toward applying QPCAs as THz emitters in THz TDS.
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1 Introduction
Photoconductive antennas (PCAs) excited at 1550 nm wavelength are the key components in state-of-the-art, fiber-coupled terahertz (THz) time-domain spectroscopy (TDS) systems, serving as both THz emitters and receivers [1]. Their widespread use has been made possible by the advent of low-cost, off-the-shelf fiber-optic components, in particular ultrafast fiber lasers at 1550 nm, and continuous optimization of the photoconductive material, which has led to significant improvements in THz power and dynamic range over the past decade [2‐5].
However, the main challenge in the optimization of THz PCAs has remained the same: Obtain high carrier mobility combined with ultrashort carrier lifetime and high material resistivity at the same time, which has proven to be beneficial for the THz emitter and receiver alike. To achieve this, many different material systems have been investigated, including ion-implanted InGaAs [6, 7], low-temperature grown (LTG) InGaAs [8, 9], LTG Beryllium-doped InGaAs/InAlAs superlattices [10‐13], InGaAs:ErAs superlattices [4, 14] as well as transition metal-doped InGaAs [5, 15‐17]. Despite these numerous efforts, the trade-off between carrier mobility on the one side and carrier lifetime on the other is difficult to prevent and thus remains a critical limitation for further improving the performance of PCAs for THz time-domain spectroscopy.
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Recently, we have presented Rh-doped quantum photoconductive antennas (QPCAs) that can overcome this limitation [18]. In QPCAs, carrier generation and transport occur mainly in the nominally undoped In0.53Ga0.47As absorber layer that provides high carrier mobility, while ultrafast carrier trapping is facilitated by deep acceptor states in a highly Rh-doped In0.75Ga0.25As quantum-well layer located between two absorber layers (Fig. 1a). In this way, carrier transport and trapping and, thus, the associated material requirements are spatially separated from each other, allowing for their independent optimization. Based on this approach, we have demonstrated a sub-picosecond carrier lifetime of 0.75 ps combined with a very high carrier mobility of 3397 cm2/Vs, representing a significant improvement compared to the wide range of previously tested material systems. However, undoped as-grown InGaAs naturally shows a strong n-type background, i.e., a very high concentration of free electrons. This results in very low material resistivity for QPCAs, typically below 400 Ωcm so far, which limits their use as THz emitters, as these require a high electrical field breakdown threshold, i.e., high material resistivity. Therefore, a remaining challenge is to compensate for the n-type background in the high-mobility In0.53Ga0.47As layers of QPCAs in order to increase their resistivity.
In InGaAs-based optoelectronic devices, carrier compensation can be achieved by doping with iron (Fe), since it is incorporated as a deep-level acceptor in the center of the InGaAs bandgap and in this way can facilitate near intrinsic carrier concentration [19, 20]. However, Fe shows strong diffusivity, especially in the presence of p-dopants [21], so that its compensation effect as a deep acceptor is hindered. Therefore, the use of Fe as a compensator requires high doping concentrations, resulting in compromised crystal quality and hence carrier mobility, a critical parameter that the QPCA structure seeks to preserve. Another prominent compensator is rhodium (Rh), which provides much higher thermal stability due its lower diffusion coefficient of DRh(800 °C) = 1 \(\times\) 10−14 cm2/s compared to Fe (DFe(750 °C) 1 \(\times\) 10−11 cm2/s) [22]. However, the relative concentration of electrically active Rh in Rh-doped InP has been shown to be only 1% when grown with hydrogen as carrier gas [23], which is typically the case in MOCVD and gas-source MBE growth. Therefore, comprehensive electron compensation again requires high doping concentration. In contrast to Fe and Rh, ruthenium (Ru) is a more exotic dopant, but has been shown to act as a compensator for electrons and holes alike [24]. In addition, the concentration of electrically active Ru atoms is three times higher [23] and Ru has even an order of magnitude lower diffusion coefficient (DRu(800 °C) = 1 \(\times\) 10−15 cm2/s) [25] than Rh. Therefore, Ru has the potential to facilitate a higher concentration of deep acceptors at lower doping concentrations, making it a promising candidate for compensating the n-type background in InGaAs while maintaining a high crystal quality and hence carrier mobility.
In this article, we present for the first time high-mobility, Rh-doped InGaAs-based QPCs co-doped with Ru for electron compensation and increased material resistivity. In the first section, the grown QPC sample structure will be introduced. Then, the effect of Ru as an electron compensator in QPCs is demonstrated by Hall-effect measurements for a sample series with increasing Ru concentration. Lastly, we analyze the carrier and photoconductivity dynamics in these samples by optical-pump optical-probe (OPOP) and optical-pump THz-probe (OPTP) measurements.
2 Sample Structure and Growth
The investigated QPC sample structures are modifications of the structure described in Ref. [18]. A stepped quantum well unit is formed by a trapping, well and barrier layer, referred to as T-, W-, and B-layers, as depicted in Fig. 1a, which is repeated 33 times to form a multi-quantum-well heterostructure. The T-layer is a 3-nm thick Rh-doped In0.75Ga0.25As quantum well that is located between two 18-nm thick high-mobility Ru-doped In0.53Ga0.47As layers (W-layers). The quantum well unit is then terminated on each side by an 8-nm InAlAs barrier (B-layer) and separated from the next unit by a 1.5 nm thick strain compensating AlAs layer. For a comprehensive description of the QPC working principle, the reader is referred to Ref. [26].
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The samples were grown on quarters of 2″ Fe-doped InP substrates using a gas-source molecular beam epitaxy (MBE) RIBER compact 21 system. For all samples, the growth temperature TG was set to approximately 400—410 °C, as measured with a thermocouple, and the Rh cell temperature was adjusted to 1600 °C to achieve the high Rh concentration needed for ultrafast carrier trapping in the T-layer. To investigate the effect of Ru as an electron compensator in the high-mobility W-layer, a sample series of four samples was grown with differing Ru-cell temperatures, ranging from 1500 °C to 1650 °C. These temperatures result in Ru vapor pressures between 7 × 10−9 Torr and 2 × 10−7 Torr, based on the relation between cell temperature and vapor pressure [27] (Fig. 1b). For comparison, in Rh-doped bulk InGaAs PCAs, a two orders of magnitude higher Rh vapor pressure of > 1 × 10−5 Torr was required for effective electron compensation, illustrating the low degree of Ru doping used in the QPC samples presented in this work. Table 1 summarizes the growth conditions as well as the Hall effect, OPOP, and OPTP measurement results for all grown samples, including a reference sample without Ru doping from our previous work [18].
Table 1
Sample overview of Rh-doped QPCs co-doped with Ru including growth conditions, measured Hall mobility μ, carrier concentration N, and material resistivity R, as well as carrier and conductivity lifetime (τOPOP and τOPTP) measured at pump fluences of 16 µJ/cm2 and 13 µJ/cm2, respectively
(a) Schematic band diagram of a QPC quantum well, consisting of an Rh-doped trapping layer (T), Ru-doped well layers (W), and nominally undoped barrier layers (B). (b) Vapor pressures for the elements Fe, Rh, and Ru as a function of MBE cell temperature based on the work presented in Ref. [27]. The Ru-cell temperatures used in this work range from 1500 °C to 1650 °C, as indicated by the orange area, which results in relatively low Ru vapor pressures between 7 × 10−9 Torr and 2 × 10−7 Torr. For comparison, the typical temperature ranges of Fe and Rh cells used for the growth of photoconductors are indicated by the gray and blue areas, respectively
We performed room temperature Hall effect measurements in van-der-Pauw geometry on all fabricated samples to investigate the effect of Ru as electron compensator in the high-mobility W-layer of the QPC structure. Ohmic contacts were realized by soldering indium onto the sample surface. Figure 2a shows the Hall resistivity (black squares) and free carrier concentration (orange squares) as a function of the Ru-cell temperature. The reference sample without Ru-doped W-layer has a high free electron concentration of N = 8.5 × 1012 cm−3, which together with its very high carrier mobility of 4515 cm2/Vs results in a very low resistivity of only 163 Ωcm. Introducing Ru to the W-layer at a Ru-cell temperature of 1500 °C, provides a strong compensation effect of the n-type background, as the free electron concentration is reduced by a factor of 2 to 4.1 × 10−12 cm−3, which increases the resistivity to 438 Ωcm. A further increase in the Ru-cell temperature to 1530 °C (1550 °C) reduces N by an additional factor of 3 (2), resulting in an eightfold (sevenfold) increase in resistivity to 1309 Ωcm (1110 Ωcm) compared to the reference sample. Thus, Ru-doping of the W-layer at low Ru-cell temperatures ≤ 1550 °C, provides a significant improvement of the QPC resistivity by compensating the prominent n-type background in the high-mobility InGaAs layers. At the same time, the carrier mobility in these samples remains very high at 3450 cm2/Vs, 3330 cm2/Vs, and 2866 cm2/Vs for Ru-cell temperatures of TRu = 1500 °C, 1530 °C, and 1550 °C, respectively (Fig. 2b). This indicates that the crystalline quality, i.e., the electronic transport in the W-layer, is only slightly degraded by the Ru-doping at these Ru-cell temperatures. The combination of very high resistivity of 1309 Ωcm and carrier mobility of 3330 cm2/Vs represents a significant improvement for the application of QPCs as THz emitters.
Fig. 2
Hall effect measurement data of QPC samples co-doped with Rh and Ru as a function of Ru-cell temperature, showing the (a) Hall resistivity (black squares) and carrier density (orange squares) and (b) Hall mobility. Filled squares indicate n-type conductivity, and open squares p-type conductivity. A high resistivity > 1000 Ωcm and a very low free electron concentration ≤ 2.0 × 1012 cm−3 are achieved for Ru-cell temperatures of 1530 °C and 1550 °C. An excellent carrier mobility > 2800 cm2/Vs is maintained for Ru-cell temperatures up to 1550 °C
However, a reverse trend for the resistivity and free carrier concentration can be observed upon further increasing the Ru-cell temperature > 1550 °C. For TRu = 1650 °C, a transition from n-type to p-type conductivity can be observed, indicating a significant overcompensation of electrons due to the higher Ru-doping concentration at this Ru-cell temperature. As a result, a large hole concentration of 3.5 × 1015 cm−3 is measured, which reduces the material resistivity to 22 Ωcm. At the same time, the carrier mobility drops to 81 cm2/Vs, which can be attributed to the higher effective mass of holes compared to electrons in InGaAs (me = 0.041 m0 and mh = 0.363 m0 [28]).
4 Dynamic Properties
We have conducted optical-pump optical-probe (OPOP) measurements to investigate the impact of Ru-doping on the dynamic properties of carriers in the QPC structure during pulsed photoexcitation. A femtosecond laser pulse with a duration of 90 fs and a central wavelength of 1550 nm was used to excite charge carriers, predominantly in the W-layer of the QPC structure. The depopulation of excited states in the W-layer was then determined by measuring the transmission of a probe pulse, likewise centered at 1550 nm, at different times Δt after photoexcitation. Further details of the measurement setup are given in Ref. [15].
In addition, the impact of Ru-doping on the conductivity lifetime was investigated by optical-pump THz-probe (OPTP) measurements. Here, a commercially available free-space laser (Toptica Photonics FemtoFiber Ultra 1550) with a pulse duration of 170 fs and a central wavelength of 1550 nm was used for photoexcitation. The decay of photoconductivity was then determined by measuring the transmission of a THz-probe pulse as a function of the pump-probe delay time Δt using a commercial THz TDS system (Toptica Photonics TeraFlash pro) with fiber-coupled photoconductive THz emitter and receiver modules [3, 5]. To ensure accurate synchronization and linear scanning of the pump–probe delay time, both the free-space laser and the fiber-coupled THz modules were pumped by the same seed laser operating at an 80 MHz repetition rate.
Figure 3 shows the 1/e carrier lifetimes τOPOP and conductivity lifetimes τOPTP of all samples as a function of the Ru-cell temperature. For a direct comparison, the measurements were performed at similar pump fluences of 16 µJ/cm2 and 13 µJ/cm2, respectively, which are low enough to avoid significant saturation effects such as the filling of Rh-related trapping states in the T-layer by photoexcited charge carriers. As seen in the figure, Ru-doping reduces the carrier lifetime τOPOP relative to the reference sample without Ru-doping. However, this reduction is negligible for the samples grown at TRu = 1500 °C, 1530 °C, and 1550 °C, for which τOPOP decreases by less than 26%, from 1.73 to 1.34, 1.37, and 1.29 ps, respectively. This indicates a low incorporation of Ru-related deep-level acceptor states, i.e., minimal defect formation at these growth temperatures, consistent with the high carrier mobilities observed in these samples. In contrast, the effect of Ru-doping becomes substantial at TRu = 1650 °C, where the carrier lifetime drops by 55%, down to 0.77 ps. This significant reduction in carrier lifetime, together with the high hole concentration observed in the Hall measurements, points to a high level of Ru-related defects at this Ru-cell temperature.
Fig. 3
Comparison of the 1/e carrier and conductivity lifetimes, τOPOP and τOPTP, of QPC samples co-doped with Rh and Ru as a function of Ru-cell temperature. The measurements were taken at pump fluences of 16 µJ/cm2 and 13 µJ/cm2, respectively. The carrier and conductivity lifetimes are reduced relative to the reference sample (TRu = 0 °C) by up to 26% and 32%, respectively, for the samples with Ru-cell temperatures ≤ 1550 °C, and more substantially, by 55%, for the sample with TRu = 1650 °C
The conductivity lifetime τOPTP exhibits a similar trend, decreasing from 4.70 to 4.27, 3.42, and 3.27 ps, i.e., by a maximum of 32% for the samples grown at TRu ≤ 1550 °C, and more significantly to 2.13 ps, i.e., by 55% for the sample grown at TRu = 1650 °C. Thus, although the conductivity lifetime is considerably longer (by an average factor of 2.7 at this pump fluence), it is clearly correlated with the carrier lifetime.
To investigate the difference in carrier and conductivity lifetime as well as their dependency on the level of Ru-doping further, we have performed pump fluence dependent OPOP and OPTP measurements for the samples with no Ru-doping (TRu = 0 °C), maximum Ru-doping (TRu = 1650 °C), as well as intermediate Ru-doping (TRu = 1530 °C), which is representative for the remaining two samples with TRu = 1500 °C and 1550 °C.
4.1 Investigation of Carrier Dynamics by OPOP Measurements
Figure 4a–c show the measured OPOP transmission decay curves as a function of the pump-probe delay time for different pump fluences in the range of 4 to 130 µJ/cm2. The measurements were fitted using a bi-exponential function with fast and slow time constants, τ1 and τ2. The insets of each figure show the contribution of the fast time constant A1 to the bi-exponential decay as a function of the pump fluence. For the reference sample with TRu = 0 °C, the decay of transmission is almost fluence-independent, which can also be seen by the small change of A1 within the pump fluence range, ranging from 0.38 at 4 µJ/cm2 to 0.22 at 130 µJ/cm2. Therefore, the depopulation of excited states in this sample is due to carrier thermalization, described by τ1, and subsequent carrier relaxation from the W-layer into the T-layer, described by τ2. The latter process is facilitated by longitudinal optical (LO) phonon emission and, thus, is independent from the pump fluence, i.e., photoexcited carrier density, as intended by the QPC structure [26].
Fig. 4
Optical-pump optical-probe- (OPOP) measurements at different pump fluences for the samples grown with Ru-cell temperatures (TRu) of (a) 0 °C, (b) 1530 °C, and (c) 1650 °C. The measurements show the logarithmic change of transmission normalized to the maximum transmission log(T/Tmax) and are fitted with a bi-exponential function that includes a fast and slow time constant, τ1 and τ2. The inset shows the amplitude of the fast time constant A1 as a function of the pump fluence. A significant change of A1 can only be observed for the sample grown with a Ru-cell temperature of 1650 °C
For the sample with TRu = 1530 °C (Fig. 4b), a fluence dependency of the OPOP signal can be observed, as the decay of transmission is slightly steeper for lower pump fluences. This is also represented by the larger change of A1, which now starts at 0.55 for 4 µJ/cm2 and decreases to 0.22 at 130 µJ/cm2. Thus, at smaller pump fluences < 20 µJ/cm2, carrier thermalization is supplemented by carrier trapping in Ru defect states in the W-layer, giving rise to a faster depopulation of excited states. At higher fluences, the photoexcited carrier density is much larger, resulting in a saturation of the Ru-related acceptor states, making carrier relaxation into the T-layer the dominant decay mechanism in this regime.
A similar trend is observed for the sample with TRu = 1650 °C. However, the increased Ru-doping concentration at this Ru-cell temperature leads to a much faster transmission decay throughout, which is evident from the very high A1 value at lower fluence (A1 = 0.91 at 4 µJ/cm2) and the increased A1 value at higher fluence (A1 = 0.31 at 130 µJ/cm2). This indicates increased filling of Ru-related traps with photoexcited carriers throughout the pump fluence range. Thus, in this sample, carrier trapping in Ru-related defect states in the W-layer, designated for carrier transport, is the dominant decay mechanism at smaller fluences < 30 µJ/cm2, a significant alteration of the QPC operational principle. This observation is consistent with the high hole concentration determined by the Hall measurements, which points to a very high concentration of Ru-related defects in this sample.
4.2 Investigation of the Photoconductivity Lifetime by OPTP Measurements
Figure 5a–c show the photoconductivity decay curves as measured by OPTP at different pump fluences of 6 to 33 µJ/cm2. The transients were fitted with a mono-exponential function to determine the photoconductivity lifetime τOPTP. Note that the fitting was limited to a pump-probe delay time of 7.5 ps after photoexcitation to avoid the secondary rise of photoconductivity caused by back-reflection of the pump pulse at the substrate backside.
Fig. 5
Optical-pump THz-probe- (OPTP) measurements at different pump fluences for the samples grown with Ru-cell temperatures (TRu) of (a) 0 °C, (b) 1530 °C, and (c) 1650 °C. The measurements show the logarithmic change of transmission normalized to the minimum transmitted amplitude for the THz-probe log(T/Tmin) and are fitted with a mono-exponential function
For all samples, a fluence dependence of the photoconductivity decay is observed, with τOPTP increasing as the pump fluence rises. The reference samples grown at TRu = 0 °C show the longest conductivity lifetimes—up to 12.8 ps at 33 µJ/cm2—as well as the strongest fluence dependence, with τOPTP varying by nearly an order of magnitude between the measurements at 6 and 33 µJ/cm2. In contrast, the sample grown at TRu = 1530 °C shows significantly shorter conductivity lifetimes, ranging from 2.3 to 5.7 ps, while the TRu = 1650 °C sample exhibits further reduced values of 1.3 ps and 4.7 ps at 6 µJ/cm2 and 33 µJ/cm2, respectively. These results demonstrate that Ru-doping of the W-layer substantially reduces τOPTP by introducing Ru-related acceptor states that trap a part of the photoexcited charge carriers, in addition to the relaxation channel into the T-layer. This observation is consistent with the results from the OPOP measurements that were presented in the last section.
This trend is further illustrated in Fig. 6a–c, which shows τOPTP as a function of pump fluence next to the fast and slow time constant, τ1 and τ2, and the resulting carrier lifetime τOPOP which were extracted from the OPOP measurements. Here, the reference sample displays a quadratic dependence of τOPTP, whereas the samples grown at TRu = 1530 °C and TRu = 1650 °C show an almost linear increase. Even more significant, while τOPTP increases with the pump fluence for all samples, τ1, τ2 and the resulting carrier lifetime τOPOP remain nearly constant in this fluence range. The only exception is the sample grown at TRu = 1650 °C, where fitting the transient at the lowest fluence (4 µJ/cm2) yields a slightly elevated τ₂, though with negligible contribution (see Fig. 4c). This indicates that neither the charge carrier thermalization within the W-layer (described by τ1) nor the charge carrier relaxation from the W-layer to the T-layer (described by τ2) is affected by the increased charge carrier density at higher pump fluences. Consequently, the rise in photoconductivity lifetime must result from saturation of Rh-related acceptor states, i.e., saturation of carrier recombination, in the T-layer (for all samples) and additionally of Ru-related acceptor states in the W-layer (samples with TRu = 1530 °C and 1650 °C). This also implies that the offset between carrier and conductivity lifetime, as displayed in Fig. 3, increases with the pump fluence. This represents a significant deviation from the Rh-doped QPC samples from our previous work [18], which showed comparable, sub-picosecond carrier and conductivity lifetimes (τOPOP and τOPTP) even at much higher pump fluences of more than 90 µJ/cm2. For these samples, a lower growth temperature and higher Rh-doping likely facilitated a more efficient charge carrier trapping in the T-layer. Consequently, combining Ru-doping of the W-layers, as presented in this work, with optimized growth conditions for the T-layer, as presented in our previous work, can enable highly resistive QPC structures with sub-picosecond carrier and conductivity lifetime.
Fig. 6
Evolution of the conductivity and carrier lifetime, τOPTP and τOPOP, including the fast and slow time constant, τ1 and τ2, with pump fluence for the samples grown at Ru-cell temperatures (TRu) of (a) 0 °C, (b) 1530 °C, and (c) 1650 °C. The conductivity lifetime increases for all samples, while the OPOP time constants τ1 and τ2 as well as the carrier lifetime τOPOP remain nearly constant in this fluence range
In this work, we report for the first time on MBE-grown Rh-doped quantum photoconductors co-doped with Ru at different Ru-cell temperatures. Ru-doping of the high-mobility InGaAs layers in the QPC structure at cell temperatures ≤ 1550 °C is shown to reduce the effective free electron concentration by up to a factor of 6 compared to a reference sample without Ru-doping. This provides an eightfold increase in resistivity of up to 1309 Ωcm, thereby resolving the central limitation, a low resistivity, for the use of quantum photoconductors as THz emitters. At the same time, these co-doped QPCs maintain an excellent carrier mobility of > 2800 cm2/Vs, as required for efficient THz generation by carrier acceleration. In consistency with this, the effect of Ru-doping on the carrier lifetime was shown to be negligible for Ru-cell temperatures ≤ 1550 °C, indicating the low concentration of Ru-related defects incorporated into the high-mobility InGaAs layers of the QPC structure. Therefore, the optimization of Rh-doped quantum photoconductors by co-doping with Ru for high material resistivity represents a major milestone toward their application as THz emitters in fiber-coupled THz time-domain spectroscopy systems. In the future, these quantum photoconductors can be further optimized by reducing their conductivity lifetime through increased Rh-doping of the trapping layer, thereby mitigating the saturation effects observed in this study.
Declarations
Competing interests
The authors declare no competing interests.
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Rhodium-Doped Quantum Photoconductor with High Carrier Mobility > 3300 cm2/Vs and Eightfold Resistivity Enhancement via Co-Doping with Ruthenium
Verfasst von
Alexander Dohms
Mykhaylo P. Semtsiv
Manuel Claros
Tina Heßelmann
Stefan Mayerhofer
Steffen Breuer
Lars Liebermeister
Martin Schell
W. Ted Masselink
Robert B. Kohlhaas
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