Metal–organic Chemical Vapor Deposition (MOCVD) has become the most common growth method for gallium nitride (GaN) owing to its advantages of easy control, high crystal quality, and relatively simple equipment, which is conducive to large-scale industrialization1,2. However, MOCVD will inevitably introduce carbon impurities leading to undesired leakage paths in the growth of GaN-based epitaxial layers3. Carbon is also often intentionally doped in GaN to obtain the high resistance GaN region, which is important for high frequency, high power and high mobility transistors with semi-insulating or insulating properties4. Nevertheless, carbon can occupy the N site to form CN defect, the Ga site to form CGa defect, or compounds such as CN–ON, CN–Hi, and other forms in GaN epitaxial layers5, which would lead to complex defect formation problems. In addition, carbon defects would bring issues such as current collapse, which lead to excessive power loss and device efficiency reduced6,7.

Many studies have been done on carbon-doped GaN to solve the above problems4,8. Researches have shown that CN is the predominant defect type that results in deep traps with an energy level of EV + (0.86–0.9) eV5,9, and no associated compound impurities are formed at low carbon doping concentrations10. However, CGa always accompanied by CN causes the self-compensation effect occurs, which makes the CN concentration much lower than the doping concentration and thus reduces the device performance11. Studies have revealed that the ratio of concomitant donor defects to acceptor defects is roughly 0.5 in carbon-doped GaN12. The sum of the acceptor concentration and the donor concentration determines the breakdown voltage, and the effective defect concentration determines the current-collapse magnitude11. The reduction of leakage current and the increase of breakdown voltage by the introduction of carbon doping are dependent on the charging/discharging process of the carbon defects.

However, the concentration and dynamic behavior of the carbon defects vary significantly with the total carbon doping concentration and growth conditions10. Even at the same carbon doping concentration significant variations in CN and CGa concentration can occur3,13. Therefore, the possible effects of variations in the concentration of carbon defects need to be analyzed under precise control of other carbon defects concentration. Furthermore, due to the complicated carbon occupy forms, the discussion of carbon defects is usually based on the total carbon doping concentrations or simple one-dimensional analysis14,15, rather than the specific defect concentration or directly observing the trap state, which has resulted in other possible effects caused by carbon defects not being taken into account. It also needs to be further clarified whether the space charge formed by carbon defects through charging/discharging affects the leakage16.

In this work, we use Sentaurus TCAD simulation to discuss the role of the specific energy level of CN and CGa defects to analyze their influence on vertical leakage/breakdown at different concentrations in GaN-on-Si epitaxial layers. The relationship between space charge and leakage/breakdown is analyzed intuitively with the advantage of simulation. The roles of CN and CGa in the whole leakage process were elucidated by monitoring the trapped charge density. Understanding the complex dynamic mechanisms of acceptor and donor traps in carbon-doped GaN is great significance for guiding the improvement of GaN device performance14.

This paper is organized as follows, Section Modeling details the relevant settings for the simulation of GaN-on-Si epitaxial layers. Section Result and Discussion shows vertical leakage characteristics at different CN concentrations at first. Followed by a discussion of the variation of space charge with different voltage, and the variation of CN and CGa trapping in GaN:C. Section Result and Discussion-Plateau discusses the effect of CN and CGa on the plateau in vertical leakage characteristics by space charge, and Section Result and Discussion-Breakdown discuss the effect of CN and CGa on breakdown via space charge. Finally, the breakdown mechanism of the additional introduction of CN on top of GaN:C to increase the breakdown voltage was confirmed. In the log J-V diagram of leakage characterization, the region of current-limiting growth is called the plateau region, the point of sudden rapid current growth is called the kink, and the current of 1 A/cm2 is defined as breakdown.

Modeling

In this paper, Sentaurus TCAD was used for 2D simulation of electrical properties of GaN-on-Si epitaxial layers. The structure is shown in Fig. 1. From bottom to top, consists of silicon substrate, 300 nm AlN layer, 1.2 μm step-graded AlGaN stress relief layers (SRL), common ratio combinations of 75%, 50% and 25% have been chosen for the SRL component ratios8, 2 µm carbon-doped GaN (GaN:C) layer, 200 nm unintentionally doped GaN (UID-GaN) layer, and 25 nm Al0.25Ga0.75N barrier layer. The common carbon doping concentration of 1 × 1019 cm−3 was set in the GaN:C layer4. Except for the Al0.25Ga0.75N barrier layer, background carbon doping of 1 × 1015 cm−3 was considered for all nitride layers11.

Figure 1
figure 1

Structure of the GaN-on-Si constructed by simulation.

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Based on the measured results, EV + 0.9 eV was chosen as the energy level of CN defects and EC—0.11 eV was chosen as the energy level of CGa defects11 1 × 10–15 cm2 was selected as the electron and hole capture cross-section size for CN and CGa.17 Referring to the results of Refs.18,19, the CN concentration 6 × 1016 cm−3, 4 × 1017 cm−3, 6 × 1017 cm−3 and 6 × 1018 cm−3 were introduced in 1 × 1019 cm−3 carbon concentration GaN:C layer, and the CGa concentration has been set as 50% of the corresponding CN defect concentration11,12. The following descriptions of CN were carried out under a fixed 50% ratio of CGa.

Concerning dislocations and impurities, the defect energy level of 0.6 eV and 1.3 eV with a concentration of 5 × 1016 cm−3 are introduced in the AlN layer and SRL20,21.

To simulate trap effect on GaN-on-Si epitaxial layers, both Shockley–Read–Hall (SRH) and Poole Frankel (PF) conduction mechanisms are introduced in the defect-containing region16,22. The band-to-band model23, thermionic emission mechanism18,24, and trap-assisted tunneling (TAT) model are introduced to simulate the current conduction process18,25. Impact ionization based on Chynoweth's law is taken into account in the simulation, which a (electrons) is 2.32 × 106 cm−1, b (electrons) is 1.4 × 107 V/cm, a (holes) is 5.41 × 106 cm−1 and b (holes) is 1.89 × 107 V/cm11.

For the accuracy of the simulation, the mesh within the AlN layer and at the AlN/Si interface has been specifically refined to accurately simulate the complexities of the electron channels here26.

Results and discussion

To investigate the effect of CN concentration on the leakage characteristics of GaN-on-Si epitaxial layers, the log J–V characteristic for CN concentration from 6 × 1016 cm−3 to 6 × 1018 cm−3 is shown in Fig. 2. As CN increases from 6 × 1016 cm−3 to 6 × 1018 cm−3, the breakdown voltage increases from 378 to 448 V. Kinks at about 120 V changed a little with the increase of CN concentration. The result of the leakage characteristics here is consistent with the actual situation compared with the results of Refs.11,27. Since CN and CGa through the charging/discharging process will result the change of space charge14. Therefore, it is a good choice to analyze the total effect of CN and CGa charging/discharging process by observing the change in space charge.

Figure 2
figure 2

The log J-V curve with the concentration of CN from 6 × 1016 cm−3, 4 × 1017 cm−3, 6 × 1017 cm−3 and 6 × 1018 cm−3, the concentration of CGa is 50% of each CN above in GaN:C layer.

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To further investigate the influence of space charge on the electron conduction process and how CN and CGa increase breakdown voltage in GaN-on-Si epitaxial layers. The space charge for GaN:C at 50 V, 150 V, 350 V and 448 V for CN 6 × 1018 cm−3 are shown in Fig. 3, which were derived by intercepting the space charge simulated data at middle positions of GaN-on-Si epitaxial layers. UID-GaN/GaN:C interface was set at 0 μm and at 2 μm was set as GaN:C/SRL interface. The simulation results are consistent with Refs.14,19. As shown in Fig. 3, it was found the following:

  1. (i)

    High density of space charge appears at 0 μm and 2 μm. This is due to the difference in conductivity between the different layers13.

  2. (ii)

    Alternating positive and negative space charges appear within GaN:C at 150 V, 350 V and 448 V. By the condition of electrical neutrality, space charges of opposite electrical properties are bound to appear on either side of the space charge at the interface, and this opposite space charge further induces space charge in the adjacent region. Therefore, the GaN:C layer, by virtue of it’s larger thickness, appears to have alternating low-density space charges.

  3. (iii)

    At 448 V, contiguous positive space charge appears in the middle of GaN:C and stronger negative space charge appears at 0 μm. At higher voltages, the high electric field increases the number of carriers captured by CN and CGa.

Figure 3
figure 3

Space charge diagram at voltages 50 V, 150 V, 350 V, 448 V with CN 6 × 1018 cm−3 in GaN:C layer.

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However, positive space charge appears in GaN:C layer, which is not consistent with the trap state after CN capture electrons captures suggests that the CN in GaN:C layer may not always capture electrons, but release electrons to make the appearance of positive space charge. If so, the release of electrons by CN cannot explain the decrease in plateau current caused by the increase in CN concentration in Fig. 2, suggesting that the CN and CGa trapping process is needed to discuss further.

To further investigate the trap states behavior of CN and CGa at different voltages, we monitored the trap states of CN and CGa at 0 V to 448 V at the distance 0.1 μm, 0.2 μm, 1.8 μm, 1.9 μm from UID-GaN/ GaN:C interface to GaN:C layer, which shown in Fig. 4. For CN in Fig. 4, it was found that:

  1. (i)

    The trapped charge in GaN:C at 0.1 μm, 0.2 μm, 1.8 μm and 1.9 μm from the GaN:C/UID-GaN interface decrease from 0 to 50 V. Because the plateau region has been entered at 50 V, the defects within the GaN:C continue to capture electrons and the region of space charge caused by polarization begins to expand18. To satisfy the electrically neutral condition, the neighboring locations of the interface keep releasing charge.

  2. (ii)

    The trapped charge of CN at 0.1 μm, 0.2 μm, 1.8 μm and 1.9 μm from the UID-GaN/ GaN:C interface tends to increase from 50 to150V. As the voltage increases, the number of electrons entering the GaN increases making the number of captures increase.

  3. (iii)

    The trapped charge of CN at 1.8 μm and 0.2 μm from the GaN:C/UID-GaN interface increase then decrease after 150 V. For CN at 0.1 μm from the GaN:C/UID-GaN interface, trapped charge decline and then grow after 150 V. For CN at 1.9 μm, trapped charge decreased from 150 to 448 V. The reason for the difference between the different locations is that electrical properties space charge on both sides is disparate.

Figure 4
figure 4

Trapped charge density–Voltage plot of (left) CN, (right) CGa at 0.1 μm, 0.2 μm, 1.8 μm and 1.9 μm in GaN:C layer from UID-GaN/GaN: C interface.

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For CGa shown in Fig. 4, the trapped charge of CGa decline from 0 to 50 V, then increase from 50 to 100 V. To satisfy electrically neutral conditions, CGa releasing charge in response the captured electrons at the interface of GaN:C and the expansion of space charge regions. Between 100 and 400 V, the trapped charge of CGa is essentially constant. For the CGa shallow energy level, it always maintains complete ionization11. Therefore, CGa trapped charge is essentially constant. Finally, under the further expansion of the space charge region, decreases significantly between 400 and 448 V.

Plateau

Since the existence of the barrier at AlN/Si interface, many electrons are confined near the AlN/Si interface at low voltages18. Even if few electrons tunnel through the barrier24, they are trapped by defects in the AlN layer, SRL, or GaN:C layer, causing the current to increase slowly and then forming a plateau. When the applied voltage is high enough, lots of electrons at the AlN/Si interface would pass through the barrier by thermionic emission18. The kink in the log J-V curve would appear until the defects in the GaN:C layer were full filled27.

In brief, in the plateau region, CN plays a major role in forming space charge by charging/discharging, whereas the CGa capture charge remains essentially constant. The increase of CN helps to capture more electrons, thus causing the plateau current drop. Since the reduction of the plateau current requires CN to capture electrons, the study on the capture and release behavior of CN at different positions indicates that the plateau current can be better reduced by introducing more CN at the CN capture position.

Breakdown

To further discuss the effect of CN and CGa on breakdown, we investigate the change near breakdown in Fig. 2 and explain the reasons for the change in conjunction with the results in Figs. 3 and 4. Firstly, in Fig. 2, the slope of log J–V starts to decrease at CN 6 × 1016 cm−3–6 × 1017 cm−3 at about 330 V. When CN increases to 6 × 1018 cm−3, the slope decreases at about 310 V, and the breakdown voltage rises from 378 to 448 V with the increase in CN concentration. Secondly, in Fig. 3, it is found that when the voltage reaches 350 V, a contiguous region of positive space charge appears in GaN:C layer, while a stronger negative space charge appears in UID-GaN layer. Finally, Fig. 4 shows that the CN trapped charge at 400 V, it starts to decrease at 0.1 μm, 0.2 μm, 1.8 μm and 1.9 μm in GaN:C from the GaN:C/UID-GaN interface.

Due to the Maxwell–Wagner effect, there is a negative space charge region at the UID-GaN/GaN:C interface that increases with CN concentration13. High CN concentrations cause sufficiently narrow negative space charge region within GaN:C, while lower CN causes this space charge region expand into GaN:C. This is reflected in the energy band as a bending of the energy band (Fig. 5). As the electrical stress increases, the ionization of CN leads to a further increase in negative space charge density. The increase in voltage allows for a large ionization of CN producing a high negative space charge density reduce the current.

Figure 5
figure 5

Energy band of the GaN-on-Si constructed at CN concentration of 6 × 1016 cm−3, 4 × 1017 cm−3, 6 × 1017 cm−3 and 6 × 1018 cm−3.

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To further verify the blocking effect of negative space charge on electron conduction near breakdown at UID-GaN/GaN:C interface, two ways below are used as follow: (1) By introducing an additional 6 × 1018 cm−3 of CN within the top 0.4 μm of GaN:C layer with CN 6 × 1017 cm−3 in GaN:C layer to form a stronger positive space charge region in the top of GaN:C layer, thus inducing a stronger negative space charge at UID-GaN/GaN:C interface to enhancing the blocking of electron injection. (2) By introducing 1 × 1013 cm−2 fixed charge at the Al0.25Ga0.75N barrier/UID-GaN interface, thereby reducing the negative space charge at UID-GaN/GaN:C interface, thus weakening the blocking of electron injection. The fixed charge value was chosen because it need be greater than the polarized charge at the Al0.25Ga0.75N barrier/UID-GaN interface for a more significant effect to be possible. The results are shown in Fig. 6. As a result of Fig. 6, the reasons that the negative space charge at the UID-GaN/GaN:C interface block electron conduction and plays an important role in increasing the breakdown voltage, based on the following:

  1. (i)

    In Fig. 6a, the additional introduction of CN increases the breakdown voltage from 388 to 433 V. For Fig. 6b, the additional introduction of CN in GaN:C significantly increases the negative space charge intensity at the UID-GaN/GaN:C interface. Except for the UID-GaN/GaN:C interface and the additional introduction of CN region. No significant change in space charge in other regions.

  2. (ii)

    In Fig. 6a, the introduction of fixed charge causes the breakdown voltage to drop from 410 to 388 V and no drop in slope of log J-V at 330 V. There is no significant change in the log J-V curve from 0 to 350 V. In Fig. 6b, comparing normal with fixed charge, the negative space charge intensity at the UID-GaN/GaN:C interface is reduced. For the space charge at UID-GaN/GaN:C interface with the additional CN concentration, the value of space charge is about five times higher than without additional defects.

  3. (iii)

    The electric field will be more concentrated in regions with a high number of space charges. Therefore, the introduction of additional CN in GaN:C led to much higher space charge, which cause more the electric field to be concentrated in and adjacent to the region where the additional CN is introduced.

  4. (iv)

    Studies have shown that there is an accumulation of negative space charge at the top of GaN:C and discuss the possibilities for blocking conduction4, 14. Würflfl et al. achieved a balance between breakdown voltage and dynamic resistance by additional doping of the top of GaN:C28. Our simulations confirm the presence of a strong negative space charge at UID-GaN/GaN:C interface and explain the reason for the additional doping to increase the breakdown voltage in terms of space charge. This shows that our results consistent with reality.

Figure 6
figure 6

(a) Log J-V curve at CN 6 × 1017 cm−3 without any change (Normal), with the fixed charge at Al0.25Ga0.75N barrier/UID-GaN interface (Fixed Charge) and with more carbon defects concentration at the top of GaN: C layer (Addition CN Concentration). (b) Space charge diagram at breakdown voltages at CN 6 × 1017 cm−3 without any change (Normal), with the fixed charge at Al0.25Ga0.75N barrier/UID-GaN interface (Fixed Charge) and with more carbon defects concentration at the top of GaN: C layer (Addition CN Concentration).

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Briefly, for breakdown, the ionization of CN with CGa at higher electrical stresses results in high negative space charge density at the UID-GaN/GaN:C interface. The negative space charge at the UID-GaN/GaN:C interface blocks the conduction of electrons. Therefore, the increase in CN concentration contributes to the increase in breakdown voltage.

Conclusion

In this paper, the variation of space charge and the CN and CGa charging/discharging process from 0 to 448 V in GaN-on-Si epitaxial layers have been investigated. The results indicate that CN in GaN:C layer not only captures electrons but also releases electrons in response to the formation of adjacent space charges. By introducing 1 × 1013 cm−2 fixed charge at Al0.25Ga0.75N barrier/UID-GaN interface and additional 6 × 1018 cm−3 CN concentration in the top 0.4 μm of GaN:C layer, it is confirmed that the blocking of electron injection by negative space charge at UID-GaN/GaN:C interface is the reason for the increase of breakdown voltage. The additional introduction of CN defects can bring the space charge at the UID-GaN/GaN:C interface up to about five times higher than normal case. In the whole process, positive and negative space charges are formed at different positions in GaN: C layer by CN and CGa charging/discharging process. The study shows that the plateau current and the breakdown voltage can be regulated by utilizing the capture and release behavior of CN at different positions in GaN:C layer. Studying the charging/discharging process of CN and CGa at different concentrations will help us guide better control of the leakage/breakdown in GaN-on-Si device.