1 Introduction

Terahertz (THz) wave lies between the microwave and infrared in the electromagnetic wave spectrum. Due to the safety, penetrability, fingerprint property, and its wide distribution, THz wave possesses substantial application values in the areas of electronics, information, biology, national defense, and aerospace technology. Therefore, THz technology (Siegel 2004; Song and Nagatsuma 2011) has become one of the most important technologies so many countries and governments are willing to support and develop. For example, the US has identified THz technology as one of the most important ten technologies which can change the future of the world in 2004; Japan has established THz technology as the top priority of national key technologies in 2005.

Nowadays, THz technology research primarily focuses on THz source and THz detector. Among them, THz detector consists of Schottky diode (Liu et al. 2010), bolometer (Cherednlchenko et al. 2011), HEB (Semenov et al. 2007), SIS mixer (Shan et al. 2010), STJ detector (Ariyoshi et al. 2006), TES (Rogalski and Sizov 2011), QWIP (Liu et al. 2004), and BIB detector (Wang et al. 2016a), and the different detector corresponds to the different detection principle. For example, Schottky diode can realize THz detection by increasing microwave frequency to THz frequency; Blocked-impurity-band (BIB) detector is a novel THz detector, and its detection principle is contrary to the case of Schottky diode, the THz wave can be detected by decreasing infrared frequency to THz frequency. BIB detector has the advantages including high sensitivity, large array size, and wide response spectrum, and thus has bright application prospects in the field of air monitoring, astronomical observation, and concealed contraband detection, etc. BIB detectors can be realized based on different material systems (i.e., Si, Ge, and GaAs). Among them, Si-based BIB detector with the frequency coverage of 7.5 THz is the most widely used due to the maturity of Si material; the response frequency of Ge-based BIB can be reduced to 1.4 THz because the bonding energy of shallow impurity level in the Ge is much lower than that in Si; GaAs-based BIB detector can further reduce the response frequency to as low as 0.6 THz, and thus has the potential application in the security check and drug detection.

The key functional structure of GaAs-based BIB detector consists of a highly doped absorbing layer and an intrinsic blocking layer. Among them, the role of the absorbing layer is to excite photo-generated carriers by absorbing incident THz radiation, while the role of the blocking layer is to suppress dark current by blocking hopping current path. At present, the research and development of GaAs-based BIB detector are still on the initial stage. No GaAs-based BIB focal plane array detector has been reported all over the world due to the large dark current. For example, Reichertz et al. (2005), from UC Berkeley investigated the dependence of dark current on the bias voltage at 2.2 K, and showed the phenomenon that dark current starts to increase tremendously when the bias voltage approaches 0.63 V. However, the physical mechanism behind the phenomenon has not been explored, and thus it is still not clear how to decrease dark current and increase the array format of GaAs-based BIB detector. Besides, operation temperature as a sensitive parameter can influence the dark current of GaAs-based BIB detector to a large extent, and the different operation temperature corresponds to the different physical mechanism. Therefore, in this work, the comprehensive analysis of temperature-dependent dark current characteristics has been made to provide a good insight into the dark current transport mechanism.

2 Device structure and physical models

Cross-sectional view of GaAs-based BIB detector is shown in Fig. 1, and all the functional structures are presented in the numerical order. They are: (1) GaAs conducting substrate with donor concentration of 5 × 1018 cm−3, (2) absorbing layer with donor concentration of 5 × 1015 cm−3, (3) blocking layer with donor concentration of 5 × 1013 cm−3, (4) contact layer with donor concentration of 3 × 1019 cm−3, (5) anode, and (6) cathode, respectively. From the device processing point of view, the absorbing layer (2) and the blocking layer (3) are sequentially grown on the GaAs conducting substrate (1) in MOCVD system; the contact layer (4) are formed on the blocking layer (3) by ion implantation; the anode (5) is formed upon the contact layer (4) by electron beam evaporation; the cathode (6) is formed upon the GaAs conducting substrate (1) after deep etching to remove the contact layer (4), the blocking layer (3), and the absorbing layer (2) in the etching zone. The THz wave is front-illuminated on the device.

Fig. 1
figure 1

Device structure of GaAs-based BIB detector

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To analyze the temperature-dependent dark current characteristics of GaAs-based BIB detector, the drift–diffusion package (Wang et al. 2012) is used, which consists of the Poission equation, the carriers’ continuity equations, and the current transport equations. Besides, the key physical models utilized by the package include generation–recombination model (Wang et al. 2014), high-field saturation model (Wang et al. 2016b), and incomplete ionization model (Wang et al. 2016c), and the above three models are all temperature dependent. Therefore, it is necessary to find a simplified way for analyzing the dark current transport mechanism. In this work, the diffusion current and the generation–recombination current as two dominating components of dark current in the absorbing layer is equivalent to the electron drift current in the blocking layer, and thus the analysis of dark current transport mechanism can be greatly simplified by electron drift current related discussion.

3 Results and discussion

Figure 2 presents dark current as a function of anode bias with operation temperature (TO) increasing from 4 K to 30 K in 2 K steps. It is found that for a fixed TO the relationship between dark current and anode bias can be classified into three phases: (1) dark current is independent of anode bias; (2) dark current increases rapidly with anode bias; (3) dark current increases slowly with anode bias. For phase (1), dark current fluctuates around a relatively low level corresponding to the turn-off status of dark current. For phase (2), dark current turns on and approaches a relatively high level rapidly. For phase (3), the slope of dark current versus anode bias decreases gradually and eventually approaches a certain value. Moreover, for a fixed anode bias dark current is a monotonically increasing function of TO. For better understanding the relationship between dark current and TO, the lowest anode bias inducing turn-on of dark current is defined as the threshold voltage (VT), and the linear dependence of VT on TO is obtained as shown in the inset of Fig. 2.

Fig. 2
figure 2

Dark current as a function of anode bias for different TO. Inset shows the relationship between VT and TO

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In order to explain the temperature-dependent dark current characteristics shown in Fig. 2, the dark current transport mechanism of GaAs-based BIB detector must be clarified. In our previous work (Wang et al. 2017), it has been demonstrated that the dark current in the absorbing layer is dominated by diffusion current (Hu et al. 2013, 2014) and generation–recombination current (Qiu et al. 2015, 2016). These two current components contribute dark current by providing extra carriers in both conduction band and impurity band. Specifically, the transport of extra electrons in the conduction band can give rise to the electron current, while the transport of extra vacancies in the impurity band can give rise to the hopping current. For the blocking layer, the situation is completely different. Ionized impurity and generation–recombination center can hardly be found in the blocking layer due to its high-purity property, and thus the dark current in the blocking layer is only dominated by electron drift current. Based on the principle of current continuity, the analysis of diffusion current (IdiffAbs) and generation–recombination current (Ig-rAbs) in the absorbing layer can therefore be equivalent to the discussion of electron drift current (InDriftBlo) in the blocking layer. As a result, the dark current of GaAs-based BIB detector (Idark) can be expressed as:

$$I_{\text{dark}} = I_{\text{diffAbs}} + I_{\text{g-rAbs}} = I_{\text{nDriftBlo}} = Aq\mu_{\text{n}} En = Aqv_{\text{n}} n$$
(1)

where A is the photosensitive area; q is the unit electronic charge; μn is the electron mobility; E is electric-field intensity; vn is electron velocity; and n is electron density. Our following discussion will focus on drift related electron behaviors in the blocking layer.

Figure 3 presents the conduction band diagrams at 1.5 V with TO increasing from 4 K to 10 K in 1 K steps. It is found that the degree of conduction band bending become higher and the region of conduction band bending become narrower with the increased temperature, and it is noticed that the bent conduction band is completely localized in the blocking layer when TO ≥ 10 K. According to the Poisson equation:

$$\frac{{d^{2}\uppsi_{\text{i}} }}{{dx^{2} }} = - \frac{\rho }{{\varepsilon_{\text{s}} }}$$
(2)

the following two equations about the electric field can be derived:

$$E = \frac{1}{q} \cdot \frac{{dE_{\text{C}} }}{dx}$$
(3)
$$\frac{dE}{dx} = - \frac{nq}{{\varepsilon_{\text{s}} }}$$
(4)

where ψi is the electrostatic potential; EC is the bottom of the conduction band; εs is the dielectric constant; and x is the position along the vertical direction. The vertical distributions of electric field at 1.5 V for different TO is presented in Fig. 4.

Fig. 3
figure 3

Conduction band diagrams at 1.5 V for different TO

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Fig. 4
figure 4

Vertical distributions of electric field at 1.5 V for different TO

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It is noticed that numerical simulation is completely consistent with the analytical result by comparing Fig. 4 and Eq. (3). According to Fig. 4 and Eq. (4), it can be found that a certain amount of negative charges accumulated in both the blocking layer and the absorbing layer. However, negative charges in the blocking layer are originated from the extra electrons transporting from the absorbing layer, while negative charges in the absorbing layer are originated from the ionized acceptors unintentionally introduced during the epitaxy process.

Figure 5 shows the vertical profiles of electron mobility at 1.5 V for different TO. It is interesting to note that the electron mobility at x = 0 is a monotonically decreasing function of TO due to electron velocity saturation at such position, which can be confirmed by Fig. 6. Specifically, electron mobility (μn), electric field (E) and electron velocity (vn) at x = 0 exhibit the following relationship:

$$\mu_{\text{n}} E = v_{\text{n}} = v_{\text{nSat}} = {\text{constant}}$$
(5)

and thus Eq. (5) reduces to:

$$\mu_{\text{n}} \propto 1 /E$$
(6)
Fig. 5
figure 5

Vertical profiles of electron mobility at 1.5 V for different TO

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Fig. 6
figure 6

Vertical profiles of electron velocity at 1.5 V for different TO

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According to Fig. 4, electric field at x = 0 is a monotonically increasing function of TO, and thus effect of TO on μn at x = 0 is completely opposite to that on E.

Figure 7 shows the vertical distributions of electron density at 1.5 V for different TO. It is demonstrated that a higher TO will result in a larger electron density for both blocking and absorbing layers. Additionally, a nearly uniform distribution of electron density in the blocking layer can be observed indicating that neither diffusion nor generation–recombination process occurs; instead drift process dominates in the blocking layer, which further confirms the assumption put forward at the beginning of our discussion.

Fig. 7
figure 7

Vertical distributions of electron density at 1.5 V for different TO

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Figures 8, 9, and 10 show the vertical profiles of electron current density, hopping current density, and total current density, respectively. Comparing Figs. 8 and 9, it is interesting to note that electron current density is a monotonically increasing function of TO, while hopping current density in the blocking layer is near zero regardless of TO, confirming dark current in the blocking layer is dominated by electron current, instead of hopping current. On the contrary, dark current in the absorbing layer is simultaneously dominated by electron current and hopping current and the importance of hoping current become more and more prominent with increasing TO. Figure 10 shows the vertical profiles of total current density at 1.5 V for different TO. According to Fig. 10, the total current density keeps constant in either blocking layer or absorbing layer for a fixed TO, which confirms that the analysis of electron current and hopping current in the absorbing layer can be equivalent to the discussion of electron current in the blocking layer.

Fig. 8
figure 8

Vertical profiles of electron current density at 1.5 V for different TO

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Fig. 9
figure 9

Vertical profiles of hopping current density at 1.5 V for different TO

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Fig. 10
figure 10

Vertical profiles of total current density at 1.5 V for different TO

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Based on the above discussion, it can be concluded that the dark current in the blocking layer is dominated by electron drift current. With the increased operation temperature electron drift velocity keeps constant, while electron density monotonically increases, which can well explain why dark current is a monotonically increasing function of TO for a fixed anode bias. The results imply that from dark current suppression point of view, low donor doping level and low operation temperature are preferred.

4 Conclusion

In this work, temperature-dependent dark current transport mechanism has been analyzed for GaAs-based blocked-impurity-band (BIB) detectors. The analysis of dark current transport mechanism can be greatly simplified by electron drift current related discussion based on the assumption that the diffusion current and the generation–recombination current as two dominating components of dark current in the absorbing layer is equivalent to the electron drift current in the blocking layer. The reason why dark current is a monotonically increasing function of operation temperature for a fixed anode bias is because electron drift velocity keeps constant, while electron density monotonically increases with the increased operation temperature. Our results reveal that from dark current suppression point of view, low donor doping level and low operation temperature are preferred.