1. Introduction

2. Development of CZT material

2.2. Preparation of CZT materials

2.2.1. The evolution of the way CZT grows

The preparation methods for CZT can be broadly categorized into three main types: the melt method, the solvent method, and the vapor-phase transport method [12]. In order to produce CZT crystals with excellent properties and high uniformity, the commonly employed crystal growth methods include the Bridgman method (BV) and the Traveling Heater Method (THM) [13].

The Bridgman method is a practical technique characterized by a simple furnace structure and convenient operation. Essentially, it involves melting all CZT raw materials or polycrystalline materials and gradually solidifying the molten material from the head to the tail end by slowly moving the crucible or furnace. Moreover, based on variations in growth apparatus and growth conditions, it can be categorized into several methods including the High-Pressure Bridgman method (HPB), Modified Vertical Bridgman method (MVB), Horizontal Bridgman method (HB), and the Vertical Gradient Freeze method (VGF) [14].

The HPB method as one of the earliest fabrication techniques. During the growth process, inert gas, typically argon, is used to compress the vapor pressure of the molten material into a small area, preventing element evaporation and safeguarding against atmospheric influences like water and oxygen. As early as 1992, Doty et al. [15] first utilized the HPB method and reported the viability of CZT as a γ-ray detector. Subsequent optimizations by the Szeles team and the introduction of the High-Pressure Gradient Freeze technique (HPGF) moderately improved the monocrystalline rate of crystal production but still encountered crystal cracking issues. The HPGF method incorporated multi-segment temperature control and furnace temperature field improvements, successfully eliminating cracks. However, crystals grown by this method still exhibited polycrystalline and twinning phenomena, resulting in lower utilization [16,17,18,19].

The MVB method introduces several improved techniques based on the traditional Bridgman method, such as crucible rotation, additional Cd compensation, or the use of seed crystals for CZT crystal growth. In the MVB method, the introduction of seed crystals during CZT crystal growth resulted in Yinnel Tech, led by Li et al. [20], achieving 3-inch diameter CZT crystals, where a single crystal with a volume of approximately 100 cm³ accounted for roughly 80% of the entire crystal ingot volume. However, twinning and grain boundaries persisted within the crystal ingot. In 2007, Xu Yadong et al. [21] investigated CZT crystals grown via the Modified Vertical Bridgman method. Testing CZT ingots doped with indium, the infrared transmittance remained relatively high and constant within the wave numbers of 2000cm^-1 to 4000cm^-1. However, the transmittance rapidly decreased to zero between 2000cm^-1 and 500cm^-1. These CZT crystals exhibited low dislocation density and high crystalline quality.

Jie Wanqi et al. [22,23,24] initiated studies on CdTe/CZT crystals using the Bridgman method as early as 1993. In 2010, Wang Tao and Jie Wanqi, among others, utilized an improved Vertical Bridgman method to fabricate CZT crystals. With this method, crystals of over 60mm in diameter achieved a utilization rate of over 70%. The crystal exhibited low tellurium precipitation and impurity density, measuring less than 1×10³cm^-2, while displaying a resistivity of 4×10¹⁰Ω·cm. Detectors produced using these crystals exhibited excellent resolution for both low and high-energy radiation, with a spectral resolution of 4.2% for ¹³⁷Cs and 4.7% for ²⁴¹Am γ spectra. In 2020, through the introduction of seed crystals and Cd compensation, along with crucible acceleration rotation and a series of technical optimizations, the team successfully achieved the Bridgman method's full single-crystal growth of 2 inch CZT crystals for the first time internationally. This advancement has paved the way for industrial-scale implementation of the technology.

HB method positions the ampoule horizontally during crystal growth, ensuring that the growth interface remains unaffected by the molten material's weight. This growth technique offers a uniform matrix, enhances yield, and reduces production costs. However, a downside to this method, in comparison to the more traditional High-Pressure Bridgman (HPB) method, is that its volume resistivity is lower by an order of magnitude, approximately 10⁹Ω·cm. This lower resistivity leads to higher leakage current, ultimately reducing the detector's energy resolution at lower energies (<100 keV) [25].

The Traveling Heater Method (THM) involves a preparation technique where, from bottom to top, a seed crystal, a tellurium-rich melt, and CZT polycrystalline material are sequentially placed in the crucible. During crystal growth, the temperature field comprises a high-temperature zone in the melt region and low-temperature zones at both ends. Ideally, the melt region is thoroughly and uniformly mixed, ensuring the same composition and melting point at both the growth and dissolution interfaces. As the heater moves upward at a consistent rate, the lower growth interface's temperature shifts towards the cooler direction, leading to supercooling and solute precipitation, while the upper dissolution interface's temperature shifts towards the hotter direction, resulting in overheating and solute dissolution. With the slow movement of the heater, CZT solute continually dissolves from the dissolution interface into the tellurium-rich melt and is transported to the lower growth interface, where it precipitates, allowing for the continuous growth of CZT crystals [26].

In 2011, Wilson et al. [27]conducted research on CZT crystals grown using the THM for X-ray detection. They tested crystals sized at 80×80mm, with an array of 11×11 and a spacing of 250μm. Their study validated that the combination of large area and low-density arrays can provide higher energy resolution, facilitating conditions for spectroscopic imaging of high-energy X-rays. In 2013, Chen Xi et al. [28] utilized electron probe and photoluminescence spectroscopy to test the radial composition and defect distribution of crystals prepared using the THM. They conducted a comparative analysis with CZT crystals grown using the Vertical Bridgman method. Their findings suggested that CZT crystals produced using the THM method exhibited greater uniformity, lower defect density, and better uniformity in defect distribution, especially in the case of large-volume CZT crystals. The uniformity of tellurium inclusions within the crystal significantly affects charge collection and charge transport [29].However, challenges within the THM process involve slow growth rates and demanding temperature gradients. The high temperature gradients induce vigorous liquid-phase convection, potentially leading to temperature fluctuations or uneven solute distribution, resulting in unstable growth interfaces and the potential for defect formation [30,31].

Table 2. Advantages and disadvantages of different CZT crystal growth methods.

Table 2. Advantages and disadvantages of different CZT crystal growth methods.

Preparation Method	Advantages	Disadvantages
BV	Simple structure and ease of operation for producing uniform CZT crystals; various Bridgman method variations available as per requirement.	Potential issues of crystal cracking and occurrences of polycrystalline and twinning phenomena.
HPB	Provides a high crystal growth rate by using high-pressure inert gas to prevent element evaporation	May still encounter crystal cracking and potential polycrystalline and twinning issues.
MVB	Enhanced CZT crystal quality using improved techniques; production of relatively large CZT crystals	Possibility of twinning and grain boundary problems.
HB	Achieves a uniform matrix during growth, improving yield and cost-effectiveness	might result in lower volume resistivity, potentially affecting energy resolution; not suitable for detecting lower energy radiation.
THM	Enables continuous crystal growth, resulting in CZT crystals with higher uniformity and lower defect density.	Slower crystal growth rates, significant temperature gradients during preparation, which can lead to temperature fluctuations and uneven solute distribution.

Different preparation methods for CZT crystal synthesis have their respective advantages and drawbacks, necessitating the selection of an appropriate manufacturing technique based on specific requirements and applications. Continuous technological improvements and optimizations further enhance the quality of CZT crystals, improving their responsiveness to radiation and advancing the application of CZT detectors in various fields.

2.2.2. Doping and performance changes of CZT

Altering the component content within the crystal and introducing doping elements can modify the crystal's performance. In 2003, Mu Renchu et al. [32] researched the resistivity of CZT crystals grown under different excessive tellurium conditions. The study found that the most efficient detector was produced from CZT crystals containing a 1.5% excess of tellurium. This CdTe was adequate to fix the Fermi level in the middle of the bandgap without an excessive number of defects to capture charge carriers. Additionally, empirical research has shown that besides altering the ratio of Cd to Zn in CZT materials, minute elements introduced via other doping can also enhance crystal properties.

In 2012, researchers such as Nan Ruihua et al. [33] conducted a study on crystals doped with indium elements, achieving resistivity as high as 1×10¹²Ω·cm. They utilized thermal stimulated current spectroscopy to measure the trap levels within CZT:In, determining that the high resistivity was due to changes in the crystal traps caused by indium doping, anchoring the Fermi level near the middle of the bandgap.

Researchers from Roy's team at Brookhaven National Laboratory [34] investigated the impact of selenium addition to cadmium zinc telluride (CZT) matrix on radiation detector performance. Given that Zn segregation in CZT crystals can generate sub-grain networks, in 2015, the Roy team initially utilized the MVB to prepare selenium-doped, which effectively guaranteed solid solution hardening in the CdTe matrix, avoiding sub-grain boundary networks in CdTexSe1−x crystals. They studied its properties and found that the etch-pit density in the crystals was one order of magnitude smaller than the commonly used CZT crystals, demonstrating improved charge collection efficiency in CTS compared to CZT.

In 2019, Utpal N. Roy et al. [35] synthesized a novel quaternary compound Cd_0.9Zn_0.1Te_0.98Se_0.02 using the THM and discovered that this crystal exhibited remarkable compositional uniformity, with fewer extended defects such as second phases and sub-grain boundary networks. The virtual Frisch grid detector produced using this method displayed an energy resolution for 662 keV γ rays in the range of 0.87–1.5%. The study concluded that it possesses excellent material quality, extremely low defect density, and highly uniform composition, thereby presenting a promising prospect as an outstanding room-temperature detection material.

The Roy team subsequently evaluated the CZTS detector for various γ ray energies [36]. At room temperature, the prepared CZTS detector crystal sized 4.5 × 4.5 × 10.8mm³ exhibited extremely low leakage current, approximately 0.63nA at a bias of 500V. The Te resistivity of the detector was about 2.9×10¹⁰Ω·cm, meeting the requirements for high resistivity detector-grade materials. Under irradiation by 662 keV γ rays, the detector achieved an exceptionally high resolution of about 1.07% at a bias of 3000V. At 662 keV conditions, the shaping time was 2μs, the energy resolution was within 1.2%, the peak-to-valley ratio was 28, and the peak Compton ratio was 5.6, demonstrating excellent detector performance. The energy resolution of this CZTS detector remained remarkably stable throughout its operation. For other γ ray energies such as 511keV and 1.275MeV irradiation, the energy resolution of the detector was about 1.34% and approximately 1%, respectively. Additionally, the detector successfully identified all γ ray lines from the 133Ba source, including the 31keV X-ray line, with an energy resolution of approximately 9%. For high-energy γ lines at 1.17MeV and 1.33MeV, the energy resolution of the CZTS detector was about 1.1% and 1.0%, respectively.

In 2017, Ruihua Nan et al. [37] used an improved vertical Bridgman method to prepare Cd_0.9Zn_0.1Te crystals doped with aluminum under cadmium-rich conditions. The researchers observed the distribution of microscopic defects. The CZT:Al sample's volume resistivity was measured to be 10⁸Ω·cm. However, the resistivity of the material was not ideal, exhibiting relatively high leakage currents. The introduction of aluminum as a dopant led to an increase in crystal defects, consequently resulting in reduced detection performance.

Compared to other primary melt-growth methods, such as Bridgman-based techniques, the Traveling Heater Method (THM) is the most commonly utilized method for commercial CZT crystal growth. CZTS detectors fabricated using this method exhibit quality comparable to high-quality commercial CZT detectors. Additionally, doping with trace elements such as indium and selenium can enhance the crystal's performance.

2.2.3. Semiconductor surface treatment technology

To enhance the performance of CZT detectors, the primary approaches involve establishing material selection standards, such as controlling lattice mismatch, and improving material surface defects. Additionally, refining the material preparation methods, including CZT annealing and MCT pre-growth preparation, can play a crucial role in these enhancements [38]. Since the development of CZT crystals for detector applications, researchers have extensively investigated the influence of surface treatments on the crystal's performance. In 1999, H. Chen and colleagues from the University of Alabama [39] conducted a study on the passivation of CZT surfaces by low-energy atomic oxygen. They discovered that CZT samples exposed to low-energy oxygen atoms generated smoother and more uniform surfaces, thereby enhancing their performance and reducing leakage currents.

In 2006, Dongmin Zhang and colleagues [40] treated mechanically polished CZT crystals with an H₂O₂ and N₂H₄ solution for different durations to passivate the surfaces. They observed that the surfaces became notably smoother and denser after passivation. The resistivity of the CZT increased, indicating that the surface passivation process significantly affected the performance of the CZT detector chips. Characteristic curve analysis and SEM surface morphology observations revealed that passivation with an H₂O₂ solution for 20 minutes showed better results. Additionally, passivation using an NH₄F/H₂O₂ solution for 30 minutes notably reduced surface leakage currents, resulting in an increase in resistivity by 1-2 orders of magnitude to 10^9-10 Ω·cm, demonstrating considerable improvement in reducing leakage current.

In 2010, Sun Yubao et al. [41] conducted research on the surface etching process during crystal preparation to reduce surface leakage current of detectors. Testing revealed that oxidative etching at a certain power level not only removed the compositional segregation on the CZT surface between the electrodes but also generated a dense TeO oxide layer on the CZT surface, causing passivation of the electrode surface of the CZT pixel detector. Radiofrequency power was identified as a critical factor in the oxygen ion etching process; using high power caused severe damage to the CZT surface, resulting in a substantial increase in surface leakage current. Conversely, when etching was performed at low power, chemical action dominated, leading to a sharp decrease in surface leakage current.

In 2014, A. Hossain et al. [42] improved the surface etching process. They experimented with two types of reagents: a low-concentration bromine-based etchant mixture combined with a surface passivation reagent and a non-bromine-based etchant to treat the crystal surface. Ultimately, their developed new non-bromine-based etchant generated a non-conductive surface, reducing defects.

In the preparation process of CZT crystals, the impurities and micro-defects brought by the etching step are the main drawbacks of the CZT crystal, and they cannot be completely eliminated. These flaws affect the optoelectronic properties of CZT and the quality of the surface. Several techniques are used to suppress or eliminate the defects in CZT materials, and one of them is surface coating treatment [43].

Lezhen Zhang et al. [44] conducted research on the Chemical Mechanical Polishing (CMP) process of CZT crystals. From 2021 to 2022, the team aimed to obtain a high-precision CZT crystal surface by proposing a dual modification method for Stöber synthesis through improved technology. They carried out orthogonal experiments on the CMP process parameters and polishing liquid ratios of CZT crystals. The study explored the impact of factors such as abrasive quality fraction, H₂O₂ volume content, pH value, polishing pressure, polishing disc speed, and polishing liquid flow rate on the surface processing performance of CZT crystals. The results indicated that the abrasive quality fraction and polishing liquid pH value significantly influenced the polishing accuracy and processing efficiency of the CZT crystal surface. Peili Gao [45] conducted comparative experiments based on the proposed new technology and new polishing liquid. They concluded that the super-precision surface processing performance of mesoporous structured abrasives was superior to that of solid abrasives. Also, the performance of the morphology and structure dually-modified RmSiO2 abrasives was better than that of single-modified abrasive grains.

In summary, domestic and foreign improvements in semiconductor material surface treatment processes primarily focus on the enhancement of surface treatment technology and surface coating optimization.

2.3. Research on the properties of CZT materials

2.3.1. Reaction of γ rays with CZT material

The working principle of CZT as a detector material involves the interaction of high energy radiation such as X-rays or γ-rays with the CZT crystal within a biased detector. When irradiated, the detector absorbs a portion or the entire energy of the incoming radiation. This absorption leads to the generation of electron-hole pairs within the crystal, proportional to the incident high-energy radiation. These pairs drift under the influence of an electric field towards different electrodes within the crystal. Eventually, they are collected on the electrodes [46]. Electric pulses are formed on the electrodes, and after passing through charge-sensitive preamplifier analog circuits, voltage pulses proportional to the energy of the incident radiation are output [47].

When high-energy radiation enters the CZT crystal and generates electron-hole pairs, use V_B represents the bias voltage applied to the crystal and d indicates the thickness of the crystal, the electric field within the crystal can be expressed by the formula：

$$E=\frac{V_B}{d}$$

(1)

The charge drift velocity is as：

$$V=\mu E=\mu \frac{V_B}{d}$$

(2)

The induced current i can be obtained from Shockley-Ramo theorem using Formula：

$$i=E_{Q}qv=\frac{1}{d}q\mu E=\frac{1}{d}q\mu E\frac{V_b}{d}=q\mu \frac{V_b}{d^2}$$

(3)

If the electron-hole pairs generated by the radiation in the CZT crystal reach opposite electrodes, the distance of charge drift equals the entire thickness of the crystal, denoted as d. Thus, the time for charge drift to reach the electrode, the charge collection time can be expressed by formula [48]：

$$t=\frac{d}{v}=\frac{d^2}{V_B{\mu }_e}$$

(4)

The induced charge Q of the detector is as：

$$Q=it=q\mu \frac{V_B}{d^2}\frac{d^2}{V_B\mu }=q$$

(5)

If the electron-hole pairs produced by the rays in the CZT crystal are at a distance of x from the anode, then the collection time of the electrons t_e：

$$t_e=\frac{x}{v_e}=\frac{xd}{V_B{\mu }_e}$$

(6)

The time of collection of holes is t_h：

$$t_h=\frac{d-x}{v_h}=\frac{(d-x)d}{V_B{\mu }_h}$$

(7)

The induced charges Q_e and Q_h generated by the two are respectively：

$$Q_e=i_e{t}_e=q{\mu }_e\frac{V_B}{d^2}\frac{xd}{V_B{\mu }_e}=q\frac{x}{d}$$

(8)

$$Q_h=i_h{t}_h=q{\mu }_h\frac{V_B}{d^2}\frac{(d-x)d}{V_B{\mu }_e}=q\frac{d-x}{d}$$

(9)

If the generation of electron-hole pairs occurs at the midpoint of the CZT crystal, then at the moment when the charges are fully collected:

$$Q_e=Q_h=\frac{q}{2}$$

(10)

Due to the migration efficiency of electrons being approximately three times that of holes μ_e≈3μ_h, the charges collected on the electrode are not entirely complete when the electrons have fully arrived. This incomplete charge collection is due to the extended collection time of holes, resulting in tailing effects in the final output signal. The collection time of the detector is correlated with the detector's thickness. Based on the specific thickness of the detector, an appropriate collection time can be calculated to facilitate the determination of specific subsequent circuit parameters. In 2009, L. Abbene et al. [49] conducted a study on the hard X-ray response of pixelated CZT detectors. Comparing detectors made in the same manner with identical materials but with CZT crystals of 1mm and 2mm thickness, the thicker detector exhibited better performance. This suggests that increasing the detector thickness improves both detection efficiency and charge collection, consistent with the small-pixel effect. To maximize the complete collection of generated charges within the lifetime of the hole, the charge collection time should be at least several times the electron collection time when the electron-hole pairs are at the midpoint of the detector. Determining the collection time provides a reference for establishing the pole-zero cancellation time and Gaussian shaping time, as these times must not be less than the charge collection time. Otherwise, it significantly affects the energy resolution of the detector system [50,51,52].

2.3.2. Research on the energy resolution of CZT materials

The energy resolution of a detector is a critically important performance indicator. As semiconductor materials form a crucial component of detectors, extensive research has been conducted on the energy resolution performance of CZT crystals.

In 2011, Kristen Wangerin et al. [53] studied three different geometries of CZT anodes and compared the energy resolution and absolute peak efficiency before and after data corrections. Following the correction of the test data, both the energy resolution and efficiency showed improvement. It was observed that detectors with a pixel pitch of 1.3mm, exhibiting the best small-pixel effect, presented superior energy resolution, with an optimal resolution of 5.1 keV [54] Beginning in 2008, A.E. Bolotnikov et al. from the Brookhaven National Laboratory [55] conducted research on extended defects in CZT crystals for γ-ray detectors. CZT material contains a high concentration of extended defects, especially tellurium inclusions, dislocation networks, grain boundaries, and subgrain boundaries affecting the device's energy resolution and efficiency. In 2014, Xu Huichao et al. [56] from Shanghai Jiao Tong University investigated the noise performance of CZT crystals. They studied the detector's geometric shape, detector voltage, and time constants. The incomplete charge collection within the detector crystal is the main factor affecting detector performance. The primary reason is that the product of the mobility and lifetime of holes in the material is one to two orders of magnitude smaller than that of electrons. A.E. Bolotnikov group from BNL [57] conducted research on charge loss under normal circumstances, as shown in the formula：

$$Q=Q_0\mathrm{e}\mathrm{x}\mathrm{p}(-\frac{t_{drighft}}{{\tau }_{bulk}})$$

(11)

Q and Q₀ are charged and initial charges collected by the incident particle or photon, t_drigft is the drift time of the electron cloud from the interaction point to the anode, τ_bulk is the lifetime of the electrons in the CZT body. When a defect occurs inside the crystal, the charge is lost as：

$$Q=Q_i\{1-{\eta }_i\left[1-\exp \left(-\frac{t_i}{{\tau }_i}\right)\right]\}$$

(12)

t_i and τ_i represent the electron drift distance and lifetime, they are averaged over the i geometric region. ${\eta }_i$ is a portion of the charge of the electron cloud passing through the encompassed geometric area. The integrated charge left behind in the electron cloud after encountering it is shown as：

$$\mathrm{Q}=Q_i\{1-{\eta }_i\left[1-\exp \left(-\frac{D_i}{E_i{\mu }_i{\tau }_i}\right)\right]\}$$

(13)

E_i is the local electric field strength, μ_iτ_i represents the attenuation distance, i denotes the average distance.

It has been observed through testing that the decrease in collected charge signal amplitudes due to tellurium inclusions is proportional to the electron cloud's drift distance.

Based on this, in 2015, the domestic team led by Wang Chuang [58] characterized the prepared CZT pixel detectors. They analyzed the impact of tellurium inclusions and other defects within the crystal on the electronic properties, such as detector leakage current and spectral response characteristics. The comparison revealed that enrichment of tellurium inclusions increased detector leakage current, reduced charge collection efficiency, and deteriorated the detector's energy resolution. In 2019, Fan Lei et al. [59], in an effort to enhance CZT's discrimination capability, introduced an improved method using ¹⁰B as a conversion layer for thermal neutron detection. The reaction of neutrons with ¹⁰B primarily generates energies of 2.792 MeV and 2.31 MeV:

n+¹⁰B→α+⁷Li+2.792 MeV( 6.1%)

(14)

n+¹⁰B→α+⁷Li^* +2.31 MeV( 93.9%)

(15)

To achieve a higher energy resolution in CZT crystals, it is necessary to reduce the crystal's leakage current. This can be accomplished through surface treatments, optimized electrode designs, minimizing grain boundaries and defects, controlling impurity levels within the crystal, selecting appropriate sizes, and using high-quality crystals. These optimization methods are effective in enhancing the energy resolution of CZT crystals, making them more suitable for high-precision detector applications [60].

The thickness of the CZT itself also has an effect on the energy resolution of the detection system. In 2014, Shen Min et al. [61] conducted experiments and simulations on CZT crystals of different thicknesses using various radiation sources. They found a high level of consistency between theoretical and experimental values of energy spectra and peak efficiencies for CZT detectors of different thicknesses under different γ photon energy conditions. They noted that thicker CZT detectors achieved higher energy resolution and peak efficiency at higher energies, whereas thinner detectors exhibited relatively better characteristics at lower energies. Thin CZT crystals at 662 keV, using ¹³⁷Cs as a radiation source, showed low photon attenuation characteristics. The conclusion drawn was that for detecting high-energy radiation, CZT crystals must have sufficient thickness to provide better accumulation of high-energy photons and improved detection efficiency. In 2021, Yu Hui et al. [62] from Northwestern Polytechnical University studied the impact of crystal thickness on the spectrum of CZT detectors. They found that as the CZT thickness increased, the peak height of the final image increased, the full width at half maximum (FWHM) decreased, the peak address decreased, and the total charge collection efficiency reduced.

In summary, to improve the energy resolution of detectors by enhancing CZT crystals, key methods include optimizing the geometric shape of the array to achieve the best small-pixel effect. Additionally, improving crystal performance and enhancing energy resolution can be achieved by changing semiconductor crystal thickness and optimizing manufacturing processes.

2.3.3. Research on the energy bands of CZT crystals

For the semiconductor crystal, when the energy of incident photons is greater than the bandgap width, electrons in the valence band are excited into the conduction band. Interaction between electrons and the crystal lattice causes electron transitions into the conduction band. The vacancies left by the departing electrons, known as holes, then transition back to the valence band. When the exciting photons are removed, the excess electrons and holes cannot maintain a thermal equilibrium state within the crystal. Consequently, they recombine. Electrons transition from the conduction band back to the valence band. As the scattering of photons must adhere to the conservation of energy and momentum, the scattered energy equals the difference in energy between the conduction and valence bands [63].

It has been found that Cd_1-xZn_xTe just like CdTe, is also a direct bandgap crystal. Because ZnTe (Eg=2.26 eV) has a larger band gap than CdTe (Eg=1.46 eV), so the inclusion of Zn elements will make the band gap of Cd_1-xZn_xTe larger than that of CdTe, and the band gap will change with the increase of zinc content. There are some differences in the results obtained by different researchers:

Table 3. Relationship between CZT band gap and Zn content and temperature [64,65,66,67,68,69,70,71].

Table 3. Relationship between CZT band gap and Zn content and temperature [64,65,66,67,68,69,70,71].

Empirical formula	Research Group	Temperature
Eg (eV)=1.604+0.42x+0.33x2	Taguchi	9K
Eg (eV)=1.5964+0.445x+0.33x2	Doty	12 K
Eg (eV)=1.586+0.5006x+0.29692x2		77 K
Eg (eV)=1.4637+0.496x+0.2289x2		300 K
Eg (eV)=1.598+0.614x-0.116x2	Polichar
Eg (eV)=1.5+0.5x+0.2x2	Toney
Eg (eV)=1.5045+0.631x+0.128x2	Tobin
Eg (eV)=1.606+0.332x+0.462x2	Hoschl
Eg (eV)=(1.494±0.005)+(0.606±0.010)x+(0.139±0.010)x2	Li

For different temperatures T, the bandgap width of CZT also varies. At x=0.5, the relationship between the bandgap width and temperature can be expressed by Formula [72]：

Eg (eV)=1.72-3.5×10^-4T-1.55×10^-7T²

(16)

When the energy of incident photons exceeds the bandgap width, electrons in the valence band are excited to the conduction band. The interaction between electrons and the crystal lattice induces electron transitions to the conduction band. Vacancies left behind by the departing electrons, known as holes, subsequently transition back to the valence band [73].

In 2015, Guo Rongrong et al. [74] investigated the impact of sub-bandgap light on CZT crystal. They discovered that under external sub-bandgap illumination, the crystal's defect density decreased, leading to a more uniform electric field distribution and a reduction in the concentration of active traps. Additionally, measurements of the ²⁴¹Am γ ray spectrum response by the detector confirmed that simultaneous illumination with sub-bandgap light significantly enhanced the energy resolution and charge collection efficiency of CZT detectors.

In 2022, Chen Xiang from the China Institute of Atomic Energy [75] conducted an optimization of the energy band structure of crystals, utilizing a CZT crystal with dimensions of 5mm×5mm×1mm provided by Shaanxi Detai Technology. Their study focused on the optimization of the γ sensitivity performance of CZT detectors, specifically addressing the issue of overshoot in the calibration current curves for CZT detector γ sensitivity. To address the trapping effect of deep-level traps on charge carriers within the crystal, the study employed sub-bandgap light to adjust the occupation of deep-level traps by charge carriers, thereby eliminating the overshoot in the calibration current curves of the detector. This approach increased the charge carrier collection efficiency, leading to the optimization of CZT detector performance. As a result, the particle sensitivity of the detector to γ rays with an energy of approximately 1.25 MeV reached1.18×10^-16C·cm^２.

Optimizing the detector sensitivity by enhancing the energy band structure of CZT crystals has been proven to hold practical value. Further research in this area holds potential for additional exploration and investigation.

3. Development of CZT array detectors

4. Application of CZT array detector in nuclear detection and imaging

4.2. Research on the application of Compton imaging and positioning

4.2.1. Principle of image formation

Now the application of CZT array detectors is currently focused on Compton imaging and localization. The concept of a Compton camera was initially proposed by Shenefeld in 1973 and subsequently tested in various applications, particularly in high-energy astrophysics and environmental radiation measurements, such as detecting radioactive elements in soil and open environments. The principle is that when γ rays undergo Compton scattering with extranuclear electrons, angle information regarding the source of the radiation can be inferred from the scattering signal, allowing for the estimation of the location of the radiation source [162].

The scattering angle range of Compton scattering is 0°-180°, and the probability of Compton scattering lines produced in different scattering angle directions is referred to as the differential cross-section, expressed by the following equation [163]：

$$\frac{d_{\sigma }}{d_{\Omega }}=\frac{r_e^2}{{2[1+\alpha (1-\cos \theta \left)\right]}^2}\{1-{cos}^2\theta +\frac{{\alpha }^2{(1-\cos \theta )}^2}{1+\alpha \left(1-\cos \theta \right)}\}$$

(20)

r_e represents the classical electron radius, αis a constant, dσ(θ) is the probability of one of the photons being scattered into a differential solid angle dΩ at an angle θ from the incident direction. dΩ is the differential solid angle in the direction of the scattering angle θ, r_e and α are respectively like [164]：

$$r_e=\frac{e^2}{m_0{c}^2}=2.818\times {10}^{-13}cm$$

(21)

$$\mathsf{\alpha }=\frac{E_0}{m_0{c}^2}$$

(22)

The formula mentioned is the Klein-Nishina formula [165], where e represents the charge of an electron, m₀ is the rest mass of an electron, and c denotes the speed of light. According to calculations, the higher the energy of incident photons, the lower the probability of Compton scattering. The ratio between events of high-angle Compton scattering to low-angle Compton scattering also decreases as the incident photon energy increases. This implies that higher-energy photons are less likely to undergo Compton scattering and are even less likely to undergo large angle Compton scattering.

When a γ ray from a radiation source undergoes Compton scattering once within the detector, depositing energy E₁ at a specific position x₁ in the detector, and the detector records the scattering position as x₁. The energy of the scattered photon produced by Compton scattering is detected a second time, depositing energy at position x₂. The total energy deposited by the γ ray in the detector is E₂. The positions x₁ and x₂ where the γ ray deposits energy twice, as well as the magnitudes E₁ and E₂ of the two energy deposits, can be obtained using position-sensitive cadmium zinc telluride detectors. E0 mean the energy of the γ ray, can be directly obtained by adding E₁ and E₂. With the information obtained from the position-sensitive detector regarding E₁ and E₂, combined with the Compton scattering formula, the scattering angle θ can be calculated as follows [166]：

$$E_c=\frac{E_0}{1+\frac{E_0}{m_0{c}^2(1-\cos \theta )}}$$

(23)

As the Compton scattering formula cannot deduce azimuthal information, the position of the radiation source must lie at a specific point on the surface of a conical section, where the vertex of the cone is at x₁, the axis is x₁x₂, and the half-angle is θ. After several occurrences of events that satisfy these conditions, many cones can be obtained. Theoretically, the position of the radiation source lies at the intersection of these cones. For instance, after detecting three valid events, three cones can be obtained. If the rays originate from an ideal point source, the three cones will inevitably converge at a unique focal point. This allows the determination of the radiation source's position, as illustrated in Figure 8:

However, in practical scenarios, both position and energy measurements are not entirely precise. To more accurately depict real-world conditions, cadmium zinc telluride detectors are typically divided into numerous grid units. When a γ ray deposits energy within one of these units, the position of the energy deposition can be approximately represented by the center position of the cadmium zinc telluride detector grid unit.

4.2.2. Developments in imaging technology

The data collected by the detector ultimately comprises countless discrete events, containing numerous invalid events, which cannot directly represent the position of the radiation source. To express information more intuitively, it is necessary to employ image reconstruction methods to process the data, transforming it into accurate visual representations. The primary methods used include: analytical reconstruction algorithms, iterative algorithms, and maximum likelihood estimation/expectation maximization methods (MLEM) [166].

In 2004, the Feng Zhang et al. [109,167] optimized the resolution and detection efficiency of the developed CZT3D detectors. They also conducted detailed research on the correction of time walk, concluding that to minimize time walk, the trigger threshold for the cathode should be set as low as possible, while the anode threshold should be set higher.

In 2007, the Gianluigi De Geronimo and Zhong He et al. [168,169] extended the maximum likelihood expectation maximization (MLEM) method to array systems in spatial and spatial-energy domains. By utilizing the interaction event system response function of a new computational model, they demonstrated the spatial domain maximum likelihood expectation maximization for interaction events. The MLEM method was employed using standard iterative MLEM equations to find the most probable source distribution in either spatial or combined spatial-energy domains, resulting in image formation. Multiple sets of restored images revealed that as the number of interaction events increased, the three-dimensional images obtained from detection became more realistic.

After data analysis, it was discovered that when performing MLEM deconvolution on two or more interacting events, it is possible to distinguish the energy peaks of different atomic numbers of substances irradiated by γ rays in the γ ray spectrum, achieving material discrimination.

In 2010, Li Miao et al. [170,171,172,173,174] established a γ ray pinhole imaging detection system using a 39 mm×39 mm CZT pixel array detector. They analyzed the response characteristics of the CZT detector to the 662 keV ¹³⁷Cs source, obtained the system's overall modulation transfer function through ¹³⁷Cs point source response imaging, and acquired and analyzed degraded images of the ¹³⁷Cs source at the center and edge positions of the CZT detector. The detection images were restored using bilinear interpolation and the Lucy Richardson algorithm. Through a discussion and analysis of the system's modulation transfer function and additional noise characteristics, it was determined that the pixel aperture transfer function and the diffusion effect of charge carrier signals in the detector were the primary factors limiting the spatial resolution of the CZT high energy imaging detection system. Therefore, it is possible to enhance the pixel aperture transfer function by improving the electrode fabrication process and further reducing the pixel electrode size. Additionally, by introducing protective gate electrodes between pixels, the goal of suppressing charge carrier signal diffusion can be achieved. In 2011, an imaging evaluation model based on the impact of trapped charge carrier induction was established for CZT pixel array detectors. The detector's modulation transfer function and pre-sampling modulation transfer function were derived. The study explored the influence of different key physical parameters on the imaging performance of CZT detectors under strong electric fields, with promising simulation results.

In 2017, the team led by Jianqiang Fu et al. [175] conducted research on aspects such as pixel electrodes and readout methods for the 3D CZT detection system. They carried out experimental studies aimed at acquiring information on interaction depths, intending to achieve three-dimensional position sensitivity, spectral reconstruction, and imaging technology. In response to the demands of the detection system, the Jianqian Fu team developed the data acquisition system from both hardware and software perspectives.

The hardware design entailed creating a data acquisition board that fulfilled the following functions:

• Power Supply Output: Provision of DC power configuration to the ASIC module as required; Supply of the necessary high voltage power to the cadmium zinc telluride detector.
• Data Communication: Response to control and configuration commands from the PC; Transmission of the current system status and acquired data to the PC.
• ASIC Configuration: Configuration of 650 internal registers within the ASIC module based on configuration commands from the PC.
• Trigger Threshold Setting: Adjustment of the trigger voltage of the ASIC module according to configuration commands from the PC.
• Conditioning and Digitization of Energy and Time Signals: Energy information output by the ASIC module in the form of differential current signals necessitates analog conditioning to convert it into voltage signals before analog-to-digital conversion. Time information from the ASIC module is in the form of voltage signals, requiring initial driving before analog-to-digital conversion.
• Readout Timing Control: Control of the ASIC module for data readout according to the corresponding timing circuits.
• Self-Testing Functionality: Testing the status of the Ethernet connection.

The schematic diagram illustrating the principle design of the data acquisition board is depicted in Figure 9:

In the software domain, the team developed upper-level PC data acquisition software that corresponded to the hardware. This software was designed to facilitate system monitoring, data acquisition, and analysis for the 3D CZT detection system. The data acquisition software was required to possess the following functionalities:

• Configuration and monitoring of the current operational status of the data acquisition board;
• Real-time visualization of collected data for quick diagnosis of the detector's operational status;
• Capability to save the collected data.

Researchers developed 3D CZT detection system data acquisition software using LabVIEW software. This software featured three distinct panel interfaces, each corresponding to system configuration, real-time display, and file storage. The software underwent testing and adjustments to ensure its functionality and effectiveness.

In 2018, Young-su Kim et al. from the Korea Institute of Radiological and Medical Sciences [176] developed a Compton backscatter imaging detector to enhance the sensitivity of portable non-mechanical collimation detectors and achieve three-dimensional imaging. Using the ML-EM algorithm for Full Width at Half Maximum (FWHM) analysis of the reconstructed images, the detector demonstrated 3D imaging capabilities and the ability to penetrate several tens of centimeters deep into the object under examination.

In 2014, researchers led by Yufei Gu et al. [177,178] conducted research on Compton backscattering imaging (CBST) using an improved iterative reconstruction algorithm. Addressing the sensitivity of CBST image reconstruction to noise and error in measured values, they proposed a novel CBST reconstruction algorithm. This method involved the use of the augmented Lagrangian multiplier to decompose the optimization problem into two sub-problems with analytical solutions. By iteratively solving these sub-problems, the augmented Lagrangian function was minimized to achieve image reconstruction. Several iterations successfully implemented ray attenuation correction, resulting in high-quality images. The newly designed algorithm exhibits advantages in reconstruction quality and convergence speed, significantly reducing reconstruction time and memory usage without compromising image quality.

In 2018, Gao Ge et al. [179] constructed a physical model for a Compton γ camera based on a 3D position-sensitive cadmium zinc telluride detector using Geant4 software. Image reconstruction work was performed based on data obtained from Monte Carlo simulations. The researchers applied inversion reconstruction and the Maximum Likelihood Expectation Maximization (MLEM) algorithm for image reconstruction.

Additionally, in 2019, Wei Wang [180] simulated a dual-layer Compton imaging system composed of position-sensitive CZT crystals. Using a combined theoretical and simulation-based approach, they conducted theoretical research on several factors that cause scattering angle errors in this imaging system, affecting its angular resolution capabilities. The team calculated the range of scattering angle errors caused by various factors affecting angular resolution for photons of different energies, subsequently proposing an optimized design for the imaging system structure. They provided a rational estimation method for the scattering angle errors in Compton imaging systems.

Furthermore, in 2019, Zhangyong Song et al. [181], investigated a novel non-mechanical collimated Compton camera technology for cancer therapy devices. Their research confirmed that the spatial resolution of the detector is the primary factor influencing the quality of Compton camera imaging. They emphasized the need to select appropriate crystal unit sizes for the detector while balancing detection efficiency.

In 2021, Yu Zhang [182] developed a three-layer Compton camera with two distinct operational modes based on Maximum Likelihood Estimation (MLEM). These two modes leverage single and double Compton scatterings, thereby enhancing the system's detection efficiency while enabling simultaneous detection of γ sources of different energies. The system underwent simulation using Geant4 and Python software, culminating in the detection outcomes of single-point and multi-point sources for both single and double Compton scatterings, as illustrated in Figure 12:

Figure 10. (a) Single-point source imaging effect, (b) multi-point source imaging effect [182].

Figure 10. (a) Single-point source imaging effect, (b) multi-point source imaging effect [182].

The information provided suggests that by obtaining the position and deposited energy information of events in the detector, the simulated imaging system achieved an optimal angular resolution of approximately 6.5°. This system enables simultaneous imaging of sources with different energies through a single measurement. Compared to imaging methods relying solely on the principles of single scattering, the inherent detection efficiency of the system improved by 31.2% under similar conditions.

In summary, both domestic and international research in Compton detection and imaging techniques for CZT detectors primarily focus on algorithm optimization. The aim is to improve the accuracy of spatial reconstruction of radiation sources by iteratively combining and enhancing algorithms.

5. Conclusions

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