## Abstract

We investigate the influence of Beryllium (Be) doping on the performance of photoconductive THz detectors based on molecular beam epitaxy (MBE) of low temperature (LT) grown In_{0.53}Ga_{0.47}As/In_{0.52}Al_{0.48}As multilayer heterostructures (MLHS). We show how the optical excitation power affects carrier lifetime, detector signal, dynamic range and bandwidth in THz time domain spectroscopy (TDS) in dependence on Be-doping concentration. For optimal doping we measured a THz bandwidth in excess of 6 THz and a dynamic range of up to 90 dB.

© 2014 Optical Society of America

## 1. Introduction

Over the past decade, terahertz time domain spectroscopy (THz TDS) has matured from pure
scientific research and expensive laboratory sized setups to industrial applications and
compact, portable THz-TDS systems [1]. Therefore, many
future applications for terahertz technology have come into close reach [2]. A great portion of this development originates from the utilization of
readily available Er-doped femtosecond fiber lasers at 1550 nm wavelength, of-the-shelf telecom
components, and the design of suitable photoconductive antennas (PCAs) [3–7]. More recently, progress has
been made concerning photoconductive THz emitters based on InGaAs/InAlAs multi-layer
heterostructures (MLHS) [8]. Here, MBE growth at substrate
temperatures of approx. 375-400 °C together with an adjusted heterostructure design led
to good optical-to-THz conversion efficiencies with output powers up to 64 µW [9]. However, the results of principal physical models of THz
generation and detection predict that material development for emitters and receivers has to be
done separately, since the main requirements are different [10–12]. The goal of this paper is the
careful investigation of how the interplay of carrier lifetime and carrier mobility in PCA
detectors influences THz bandwidth, dynamic range and detector noise. Therefore, we investigated
four different samples of low temperature (LT) grown Beryllium (Be)-doped InGaAs/InAlAs MLHS
with different nominal Be-doping concentrations of 0.3 × 10^{18}
cm^{−3}, 0.9 × 10^{18} cm^{−3}, 2.0 ×
10^{18} cm^{−3} and 4.0 × 10^{18} cm^{−3}
(cf. Table 1).To obtain a detailed picture of the carrier trapping, carrier recombination and
trap saturation dynamics, the samples were probed via differential transmission (DT)
measurements at different pump pulse powers. A detailed presentation of the results on the DT
measurements performed with these samples and their theoretical interpretation has been
published in [13]. After giving a brief overview on these
DT results for illustration, this paper focuses on the influence of carrier dynamics and carrier
lifetime on PCA detector performance in a THz-TDS system made from the exact same samples.

## 2. Influence of beryllium doping on the carrier lifetime

The dominating mechanism of electron relaxation from the conduction band (CB) in LT-grown Be-doped InGaAs/InAlAs MLHS is phonon-assisted electron capture into arsenic anti-site defects (As_{Ga}) and subsequent recombination with a hole. More precisely, electron capture is dominated by the part of the arsenic antisite defects that has been positively ionized (As_{Ga}^{+}) due to doping with Be-acceptors and hence lowering the Fermi level. Since, to a good approximation, every Be-dopant ionizes one As_{Ga} defect, the density of fast traps is equal to the Be-doping concentration [13, 14]. The time constants for the electron capture process are typically on the order of a few hundred femtoseconds (fs) to picoseconds (ps) depending on the As_{Ga}^{+} density. The time constant for the recombination process of electrons captured in As_{Ga} defects with holes is on the order of a few tens of ps to hundreds of ps. As pointed out in [13], there is strong evidence that the recombination occurs with holes captured by Be-dopants rather than with free holes in the valence band (VB) and hence is also dependent on the Be-doping concentration. However, even for high doping concentrations the recombination time remains on the order of several tens of picoseconds. The excitation source for all DT and THz-TDS measurements was a mode-locked fiber ring laser with a center wavelength of 1550 nm, a pulse width of approx. 90 fs and 100 MHz repetition rate. The excitation spot size was approx. 12 µm for both DT and THz TDS measurements in order to obtain similar excitation conditions for a quantitative comparison between both measurements. Additionally, all the samples were structured with mesa-type dipole antennas with a 10 µm × 10 µm photoconductive gap. Hence, the optically excited photoconductive region was precisely defined for both measurement methods.

The results obtained from DT measurements at 1550 nm pump and probe wavelength are given in Fig. 1(a), Fig. 1(b)
and Fig. 1(c) for a low (0.25 mW), intermediate (2 mW)
and a high pump power (16 mW), respectively. These excitation powers correspond to carrier densities in the CB directly after
fs-excitation of approx. 1 × 10^{17} cm^{−3}, 6.5 ×
10^{17} cm^{−3} and 1.28 × 10^{18}
cm^{−3}, respectively. For the calculation of these carrier densities, the
absorption saturation due to the limited density of states in the CB over the photon energies
covered by the excitation laser pulse was taken into account.

For 0.25 mW pump power none of the samples shows significant trap filling as the induced carrier density in the CB is a least a factor of three smaller than the As_{Ga}^{+} density of every sample. Thus the absorption relaxation, i.e. the DT signal, can be fitted by assuming a mono exponentially declining carrier density within the CB. The respective fit results for the electron lifetime from the DT data are given in Table 1, the corresponding capture cross section according to Shockley-Read-Hall theory for the As_{Ga}^{+} defects was determined to σ_{e}^{As+}≈2 × 10^{−14} cm^{2} [13].

For the intermediate pump power of 2 mW MLHS 1 already shows a very slow absorption recovery. This is because the induced carrier density in the CB is on the same order as the available As_{Ga}^{+} trap density, i.e. ≈0.3 × 10^{18} cm^{−3}. Hence, the DT signal is dominated by the recombination time of electrons in As_{Ga} defects with holes captured by Be-dopants, since this process forms a bottleneck for the carrier relaxation. MLHS 2 shows a slightly increased absorption recovery time which is caused by partial filling of the available As_{Ga}^{+} traps.

MLHS 3 and 4 show no significant increase of absorption recovery time due to the high amount of As_{Ga}^{+} that still exceeds the density of electrons in CB at this excitation power.

For 16 mW pump power [Fig. 1(c)], the samples MLHS 1 and 2 both show strong As_{Ga}^{+} trap saturation and thus very long relaxation times in the DT signal, again governed by the electron-hole recombination time. The DT signal of MLHS 3 shows a slight deviation from a mono-exponential decay and an increased carrier lifetime due to partial trap filling. MLHS 4 still shows almost no change in the DT signal since the density of As_{Ga}^{+} traps, i.e. n_{t} ≈4 × 10^{18} cm^{−3}, is still significantly higher than the excited carrier density in the CB of n_{e} ≈1.28 × 10^{18} cm^{−3}.

## 3. Influence of the optical power on the detected THz signal and bandwidth

For further investigation of the influence of the Be-doping concentration and the resulting carrier dynamics on the THz detection properties, we performed THz-TDS measurements in dependence of the optical power at the detector. The photoconductive THz emitter used for the measurements in this chapter was a strip-line mesa-antenna with 25 µm gap made from the 4.0 × 10^{18} cm^{−3} Be-doped sample MLHS 4. For all measurements the applied bias was 50 V at an optical excitation power of 25 mW. For an efficient out-coupling of the THz radiation, the emitter and the respective detectors were attached to hyper-hemispherical HRFZ silicon substrate lenses. Furthermore, two off-axis parabolic mirrors for THz collimation and focusing were used.

The peak-to-peak signals obtained from THz-TDS measurements for the case of low excitation power (0.25 mW) are given in Fig. 2.In this low carrier density regime, the potential influence of THz field screening by free carriers in the CB and VB can be safely neglected leaving only two main influences to the current signal. One is the carrier scattering time (cf. Table 1) which limits carrier velocity and hence the detector current. The other influence is the carrier capture time which limits the integrated detector current, i.e. the value of the convolution integral in TDS detection Eq. (1). The scattering time extracted from Hall mobility data and the unsaturated carrier capture time from DT measurements at 0.25 mW are also shown in Fig. 2. It should be noted that the carrier capture time enters the carrier scattering time via Matthiessens rule since carrier capture is inelastic scattering.

However, because scattering mechanisms such as phonon scattering and more importantly elastic ionized impurity scattering due to the Be-doping are dominant in our case, the contribution of carrier capture to the carrier scattering time can be safely neglected.

For an understanding of the influence of carrier capture time on the frequency behavior of a PCA detector, it is instructive to consider two simplified limiting cases:

- 1. An infinitely
*short*carrier lifetime, i.e. a Dirac delta function like carrier density in the CB: $n(t)=\delta (t)$. - 2. An infinitely
*long*carrier lifetime, i.e. a theta function like carrier density in the CB:$n(t)=\theta (t)$.

The TDS current of the detector for a linear response with respect to the electric field, i.e. neglecting influences such as THz field screening by charged carriers, can be described by the convolution:

which in Fourier space is given byHere $\sigma $is the conductivity, ${E}_{THz}$is the incident THz field, $n$is the carrier density, $\mu $is the mobility, $\ast $ denotes the convolution operation and $e$ is the elementary charge.For the first case Eq. (2) yields

In case of the 0.25 mW, i.e. without trap saturation, MLHS 1 shows the highest THz peak-to-peak amplitude (cf. Figure 2). When compared with the other samples it is obvious that the amplitude increase is mostly due to an increase of lower frequency components, i.e. < 2 THz. At higher frequencies, e.g. 2-4 THz, the detected amplitudes are smaller as compared to the other MLHS. We attribute this to the slow trapping time (cf. Table 1). A closer investigation of the results in Fig. 2 reveals that, in general, longer carrier lifetimes in the detector shift the center frequency towards lower frequencies and enhance the frequency roll-off, as expected from Eq. (3) and Eq. (4). Furthermore, it agrees with predictions from more sophisticated Monte Carlo calculations in [12].

The 2.0 × 10^{18} cm^{−3} doped MLHS 3 shows the highest signal in the frequency range of 2-4 THz at this low excitation power, indicating a trade-off between fast trapping and high mobility. The dynamic range for all detectors under this excitation condition was limited by the noise of the detection system itself and not the respective MLHS. The system noise amplitude measured with an open circuit, i.e. without an antenna, is depicted as a grey line in Fig. 3.For medium optical excitation power of 2 mW, the frequency roll-off for MLHS 2-4 remains almost equal to the roll-off at 0.25 mW. For MLHS 1, a minor shift of the center frequency towards lower frequencies and a slightly steeper roll-off is visible. Considering the prolonged carrier lifetime of MHLS 1 at this excitation condition (cf. Fig. 1(b)) the change of the frequency roll-off is weaker than what would be expected from Eq. (4). The relative increase of the THz signal amplitude as compared to the other samples is small indicating the onset of a saturation behavior, as will be discussed later in more detail.

At 16 mW MLHS 1 shows a further red shift of the center frequency as expected for this long carrier lifetime and hence a mostly integrating antenna behavior. The peak in the frequency components around 5-30 GHz originates from resonances in the contact metallization. The damping of these resonances is reduced for long carrier lifetimes. MLHS 2 also shows a steeper frequency roll-off due to the prolonged carrier lifetime at 16 mW. However the effect is not as pronounced as for the MLHS 1. MLHS 3-4 show almost no difference in the roll-off behavior and MLHS 3 shows only a slight shift of the center frequency and thus a superior bandwidth. These results indicate that the benefit of a short carrier capture time outweigh the lower detector signals due to the simultaneous increase of the carrier scattering time for higher Be doping concentrations. Furthermore, in case of MLHS 1 we observed a strong saturation and even reduction of the detector peak-to-peak pulse amplitude for higher excitation powers which can be seen in Fig. 4.We assume that the decrease is due to screening of the incident THz field by free and trapped carriers which in case for MLHS 1 gets relevant due to the long carrier capture and recombination lifetimes. In this case the detector response is not linear in the electric field since the carrier acceleration becomes dependent on the CB carrier density and Eq. (1) loses its validity. A model describing carrier screening effects in the semiconductor response of a PCA has been proposed by Jepsen et al. [10].

The peak-to-peak amplitudes of MLHS 2 to 4 do not show such a saturation behavior even at higher optical excitation powers suggesting a linear response. The slight sub-linear behavior of the peak-to-peak amplitude with respect to the optical power is assumed to be due to absorption saturation. The amplitudes of MLHS 2-4 are therefore determined by the carrier scattering time and the carrier capture lifetime which enters via the convolution integral [Eq. (1)] as explained before.

## 4. Noise and bandwidth

Another important characteristic of THz detectors is the electronic detector noise which potentially limits the dynamic range and thus the detectable bandwidth. Duvillaret et al. [15] and Jepsen et al. [16] have analyzed how noise limits the extractable data in THz-TDS spectroscopy. Even though, the authors of [15] show that emitter noise dominates the noise in TDS measurements they find that detector noise contributions are not negligible. Grischkowsky and Van Exter [17] as well as Castro-Camus et al. [18] have shown that the major detector noise contribution arises from thermal Nyquist noise. Shot noise and generation-recombination (GR) noise are found to have only minor influence as they scale with the square root of the THz field induced detector current which is generally relatively small. The Nyquist noise current is given by:

where${K}_{B}$, $T$ and $\Delta f$ are Boltzmann constant, absolute temperature and measurement bandwidth, respectively. $R$ is the detector resistance. Since the measurement of the signal in TDS detection is essentially a DC or very low frequency current measurement, the time average resistance of the detector is sufficient for analysis.We measured the average root-mean-square (rms) noise current in the detector, without an incident THz field, in dependence of the optical power at the detector. Additionally, we calculated the Nyquist noise currents from PCA resistances by numerically solving the carrier density equations given in [13]. Both results are given in Fig. 5.For MLHS 1 and 2 there is a strong increase (~factor 7) in the measured and calculated Nyquist noise current for higher excitation powers, which is due to the long carrier lifetimes in the saturation regimes and hence a low average resistivity. For MLHS 1 and 2 the general behavior of the Nyquist noise as a function of optical excitation power, is covered quite well by the simulation results. However, the absolute values differ by a factor of approx. 2. Here, it should be noted that thermal re-excitation of carriers from trap states into to the CB and the VB was not included in the calculation. After the optical excitation and until electrons and holes in trap states have recombined, only Quasi Fermi levels are defined.

During this time the probability for thermal re-excitation is increased, leading to a further reduction of the samples resistance. This effect could explain the discrepancy between measurement and simulation.

For MLHS 3 and 4 the measured noise currents seem to show a minor increase (~factor 1.5). However, since the measured noise currents are very close to the average system noise level (measured with an open circuit) the result is inconclusive. The prediction of the simulation for MLHS 3 is within the margin of the factor 2 discrepancy. The simulation of MLHS 4, however, is significantly lower than the measured one, suggesting that the system noise could be the limiting factor in this case.

To further examine the influence of the Be-doping level, we extracted the dynamic range and measureable bandwidth from all measured TDS spectra at different detector excitation powers for each of the MLHS samples. The noise floor for the dynamic range calculation was defined as the average value of the spectral amplitude between 6.5 and 10 THz. The detectable bandwidth was defined as the highest frequency component with an amplitude 6 dB above the noise floor in the respective THz power spectrum. The obtained results are given in Figs. 6(a) and 6(b). For MLHS 1, the dynamic range decreases for excitation powers in excess of 4 mW due to the amplitude saturation and the increase in Nyquist noise. In conjunction with the strong frequency roll-off, the detectable bandwidth is significantly limited at high excitation powers. Similarly, MLHS 2 shows a saturation behavior of the dynamic range for the highest excitation power due to an increased noise level (cf. Fig. 5) and a decrease of the detectable bandwidth for higher excitation. Both MLHS 3 and 4 show no saturation in the dynamic range or bandwidth as expected from their short carrier lifetime for all excitation levels. Interestingly, the highest measurable bandwidth is not obtained for MLHS 4 which features the shortest carrier lifetime. Instead, the slightly higher carrier lifetime and scattering time of MLHS 3 leads to an increase of the detected THz current. Since the noise level is defined by the system noise for these samples, the THz bandwidth increases for higher detector currents as long as the carrier lifetime is short enough. Considering the noise calculations shown in Fig. 5, MLHS 4 could potentially exceed the dynamic range of MLHS 3 if the system noise could be further reduced.

In an attempt to overcome the system noise limitation and increase the dynamic range, we employed a 100 µm strip-line emitter fabricated from a high mobility MLHS which has a significantly higher THz output than LT-grown Be-doped MLHS [8, 9]. The bias of the emitter was 100 V and the optical excitation was set to 25 mW. As detector we employed MLHS 4, which features the fastest trapping time. The average noise floor in the spectra wasextracted for different excitation powers at the detector for the high mobility emitter, the LT-grown emitter and without a THz field present, which is shown in Fig. 7.In accordance with our previous results the noise of the LT grown emitter is on the order of the system noise level. However, there is an increase of the noise floor for higher excitation levels if a THz field is present in case of the high mobility emitter. The square root like behavior strongly suggests that the increase is due to shot noise from the detector current which in turn, to a good approximation, is directly proportional to the optical excitation power at the detector and is given by:

Here ${I}_{THz}$ is the THz-field induced detector current, ${P}_{opt,\mathrm{det}}$is the optical power at the detector and $e$ is the elementary charge. Since for the high mobility emitter the detector currents have much higher values (approx. 285 nA for 16 mW excitation at the detector) the shoot noise contribution appears to become significant. However, since the shoot noise scales with the square root of the detector current were as the signal scales linear with the detector current the dynamic range is further increased as compared to the previous emitter.Finally we increased the emitter bias to 120 V and averaged over ten thousand trace taken at 16 Hz (approx. 10 min) resulting in a measureable bandwidth of over 6 THz and approx. 90 dB dynamic range as can be seen in Fig. 8.For this emitter and detector combination the spectrum of a single pulse trace with a measurement time of 62.5 ms still shows a dynamic range in excess of 65 dB and a bandwidth >4.5 THz (not shown).

## 5. Conclusion and outlook

We have shown that knowledge of the influence of Beryllium doping on carrier dynamics in LT-grown InGaAs/InAlAs MLHS is crucial for the design of THz-TDS detectors made from this material. We have found that trap saturation, i.e. long carrier lifetime, limits the detector dynamic range and bandwidth because of increased frequency roll-off and Nyquist noise. Furthermore, we have shown that in case of detectors with short carrier lifetimes and sufficiently strong THz fields the shot noise in the detector becomes a relevant noise source. Finally, it was demonstrated that for fast LT-grown InGaAs/InAlAs detectors, i.e. with appropriate Be doping concentration, together with highly efficient THz emitters it is possible to obtain PCA based THz-TDS measurement systems at 1550 nm excitation with 90 dB dynamic range and more than 6 THz bandwidth.

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