Numerical simulation analysis of carbon defects in the buffer on vertical leakage and breakdown of GaN on silicon epitaxial layers

Carbon doping in GaN-on-Silicon (Si) epitaxial layers is an essential way to reduce leakage current and improve breakdown voltage. However, complicated occupy forms caused by carbon lead to hard analysis leakage/breakdown mechanisms of GaN-on-Si epitaxial layers. In this paper, we demonstrate the space charge distribution and intensity in GaN-on-Si epitaxial layers from 0 to 448 V by simulation. Depending on further monitoring of the trapped charge density of CN and CGa in carbon-doped GaN at 0.1 μm, 0.2 μm, 1.8 μm and 1.9 μm from unintentionally doped GaN/carbon-doped GaN interface, we discuss the relationship between space charge and plateau, breakdown at CN concentrations from 6 × 1016 cm−3 to 6 × 1018 cm−3. The results show that CN in different positions of carbon-doped GaN exhibits significantly different capture and release behaviors. By utilizing the capture and release behavior differences of CN at different positions in carbon-doped GaN, the blocking effect of space charge at unintentionally doped GaN/carbon-doped GaN interface on electron conduction was demonstrated. The study would help to understand the behavior of CN and CGa in GaN-on-Si epitaxial layers and more accurate control of CN and CGa concentration at different positions in carbon-doped GaN to improve GaN-on-Si device performance.


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 ratios 8 , 2 µm carbon-doped GaN (GaN:C) layer, 200 nm unintentionally doped GaN (UID-GaN) layer, and 25 nm Al 0.25 Ga 0.75 N barrier layer.The common carbon doping concentration of 1 × 10 19 cm −3 was set in the GaN:C layer 4 .Except for the Al 0.25 Ga 0.75 N barrier layer, background carbon doping of 1 × 10 15 cm −3 was considered for all nitride layers 11 .
Based on the measured results, E V + 0.9 eV was chosen as the energy level of C N defects and E C -0.11 eV was chosen as the energy level of C Ga defects 11 1 × 10 -15 cm 2 was selected as the electron and hole capture crosssection size for C N and C Ga . 17Referring to the results of Refs. 18,19, the C N concentration 6 × 10 16 cm −3 , 4 × 10 17 cm −3 , 6 × 10 17 cm −3 and 6 × 10 18 cm −3 were introduced in 1 × 10 19 cm −3 carbon concentration GaN:C layer, and the C Ga concentration has been set as 50% of the corresponding C N defect concentration 11,12 .The following descriptions of C N were carried out under a fixed 50% ratio of C Ga .
Concerning dislocations and impurities, the defect energy level of 0.6 eV and 1.3 eV with a concentration of 5 × 10 16 cm −3 are introduced in the AlN layer and SRL 20,21 .
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 region 16,22 .The band-to-band model 23 , thermionic emission mechanism 18,24 , and trap-assisted tunneling (TAT) model are introduced to simulate the current conduction process 18,25 .Impact ionization based on Chynoweth's law is taken into account in the simulation, which a (electrons) is 2.32 × 10 6 cm −1 , b (electrons) is 1.4 × 10 7 V/cm, a (holes) is 5.41 × 10 6 cm −1 and b (holes) is 1.89 × 10 7 V/cm 11 .www.nature.com/scientificreports/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 here 26 .

Results and discussion
To investigate the effect of C N concentration on the leakage characteristics of GaN-on-Si epitaxial layers, the log J-V characteristic for C N concentration from 6 × 10 16 cm −3 to 6 × 10 18 cm −3 is shown in Fig. 2. As C N increases from 6 × 10 16 cm −3 to 6 × 10 18 cm −3 , the breakdown voltage increases from 378 to 448 V. Kinks at about 120 V changed a little with the increase of C N concentration.The result of the leakage characteristics here is consistent with the actual situation compared with the results of Refs. 11,27.Since C N and C Ga through the charging/discharging process will result the change of space charge 14 .Therefore, it is a good choice to analyze the total effect of C N and C Ga charging/discharging process by observing the change in space charge.
To further investigate the influence of space charge on the electron conduction process and how C N and C Ga 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 C N 6 × 10 18 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: (i) High density of space charge appears at 0 μm and 2 μm.This is due to the difference in conductivity between the different layers 13 .(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  www.nature.com/scientificreports/ 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.(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 C N and C Ga .
However, positive space charge appears in GaN:C layer, which is not consistent with the trap state after C N capture electrons captures suggests that the C N 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 C N cannot explain the decrease in plateau current caused by the increase in C N concentration in Fig. 2, suggesting that the C N and C Ga trapping process is needed to discuss further.
To further investigate the trap states behavior of C N and C Ga at different voltages, we monitored the trap states of C N and C Ga 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 C N in Fig. 4, it was found that: (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 expand 18 .To satisfy the electrically neutral condition, the neighboring locations of the interface keep releasing charge.(ii) The trapped charge of C N 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.(iii) The trapped charge of C N at 1.8 μm and 0.2 μm from the GaN:C/UID-GaN interface increase then decrease after 150 V.For C N at 0.1 μm from the GaN:C/UID-GaN interface, trapped charge decline and then grow after 150 V.For C N 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.
For C Ga shown in Fig. 4, the trapped charge of C Ga decline from 0 to 50 V, then increase from 50 to 100 V. To satisfy electrically neutral conditions, C Ga 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 C Ga is essentially constant.For the C Ga shallow energy level, it always maintains complete ionization 11 .Therefore, C Ga 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 voltages 18 .Even if few electrons tunnel through the barrier 24 , 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 emission 18 .The kink in the log J-V curve would appear until the defects in the GaN:C layer were full filled 27 .www.nature.com/scientificreports/ In brief, in the plateau region, C N plays a major role in forming space charge by charging/discharging, whereas the C Ga capture charge remains essentially constant.The increase of C N helps to capture more electrons, thus causing the plateau current drop.Since the reduction of the plateau current requires C N to capture electrons, the study on the capture and release behavior of C N at different positions indicates that the plateau current can be better reduced by introducing more C N at the C N capture position.

Breakdown
To further discuss the effect of C N and C Ga 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 C N 6 × 10 16 cm −3 -6 × 10 17 cm −3 at about 330 V.When C N increases to 6 × 10 18 cm −3 , the slope decreases at about 310 V, and the breakdown voltage rises from 378 to 448 V with the increase in C N 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 C N 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 C N concentration 13 .High C N concentrations cause sufficiently narrow negative space charge region within GaN:C, while lower C N 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 C N leads to a further increase in negative space charge density.The increase in voltage allows for a large ionization of C N producing a high negative space charge density reduce the current.
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 × 10 18 cm −3 of C N within the top 0.4 μm of GaN:C layer with C N 6 × 10 17 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 × 10 13 cm −2 fixed charge at the Al 0.25 Ga 0.75 N 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 Al 0.25 Ga 0.75 N 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: 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 C N concentration, the value of space charge is about five times higher than without additional defects.www.nature.com/scientificreports/(iii) The electric field will be more concentrated in regions with a high number of space charges.Therefore, the introduction of additional C N 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 C N is introduced.(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 conduction 4,14 .Würflfl et al. achieved a balance between breakdown voltage and dynamic resistance by additional doping of the top of GaN:C 28 .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.
Briefly, for breakdown, the ionization of C N with C Ga 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 C N concentration contributes to the increase in breakdown voltage.

Conclusion
In this paper, the variation of space charge and the C N and C Ga charging/discharging process from 0 to 448 V in GaN-on-Si epitaxial layers have been investigated.The results indicate that C N in GaN:C layer not only captures electrons but also releases electrons in response to the formation of adjacent space charges.By introducing 1 × 10 13 cm −2 fixed charge at Al 0.25 Ga 0.75 N barrier/UID-GaN interface and additional 6 × 10 18 cm −3 C N 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 C N 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 C N and C Ga 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 C N at different positions in GaN:C layer.Studying the charging/discharging process of C N and C Ga at different concentrations will help us guide better control of the leakage/breakdown in GaN-on-Si device.

Figure 1 .
Figure 1.Structure of the GaN-on-Si constructed by simulation.
(i) In Fig. 6a, the additional introduction of C N increases the breakdown voltage from 388 to 433 V.For Fig. 6b, the additional introduction of C N 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 C N region.No significant change in space charge in other regions.(ii) In Fig. 6a, the introduction of fixed charge causes the breakdown voltage to drop from 410 to 388 V and

Figure 6 .
Figure 6.(a) Log J-V curve at C N 6 × 10 17 cm −3 without any change (Normal), with the fixed charge at Al 0.25 Ga 0.75 N barrier/UID-GaN interface (Fixed Charge) and with more carbon defects concentration at the top of GaN: C layer (Addition C N Concentration).(b) Space charge diagram at breakdown voltages at C N 6 × 10 17 cm −3 without any change (Normal), with the fixed charge at Al 0.25 Ga 0.75 N barrier/UID-GaN interface (Fixed Charge) and with more carbon defects concentration at the top of GaN: C layer (Addition C N Concentration).