Very High In‐Plane Magnetic Field Sensitivity in Ion‐Implanted 4H‐SiC PIN Diodes

In this study ion‐implanted lateral 4H‐SiC pin diodes are reported, which show an unexpectedly high room temperature in‐plane magnetic field sensitivity approaching 100 % at 0.5 Tesla. Using dedicated TCAD simulations the underlying transduction mechanism is studied, and the effect of implantation‐induced carrier traps on the observed high sensitivity is unraveled. The study shows how such traps can greatly control the injection conditions at the highly doped implant regions providing a plausible explanation for an observed portion in the IV‐characteristics of the pin diodes exhibiting the aforementioned high magnetic field sensitivity.


Introduction
In the last two decades a huge progress has been made in the fabrication technology of silicon carbide (SiC), which resulted in the realization of a variety of SiC based power devices with superior performance compared to their silicon counterparts. [1]14] A key point in the aforementioned progress has been the extensive study of various electrically active defect types [15][16][17][18][19] and DOI: 10.1002/aelm.202300531[22] Such defects can show up as lifetime limiting defects in the epilayer, [15] which are especially of interest for bipolar devices or as mobility limiting defects at the SiC oxide interface [19] mainly relevant for MOS devices.35][36] In this paper we investigate the magnetic response of ionimplanted 4H-SiC lateral pin diodes realized in a wafer-scale 4H-SiC technology provided by Fraunhofer IISB. [10][39] We measure the bias dependence of the magnetic field-induced current change and reveal the underlying transduction mechanism using TCAD simulations.Hereby we take implantation-induced carrier traps at the implant junctions into account.We show that these traps provide a plausible explanation for the measured high magnetic field sensitivity.

Device Structure and Fabrication
Figure 1a illustrates the structure of the investigated lateral pin diodes.The pin diodes are fabricated on an n-type 4H-SiC 4°offaxis substrate with a doping level of n = 5e18cm −3 .An p-type epilayer having a thickness of 10 μm and doping level p = 8e14cm −3 is separated by a p+ doped buffer layer of thickness 2 μm from the substrate.The epilayer serves as the i-region of the pin diode.The electron and hole injecting regions, i.e., the cathode and anode, are formed by 7°tilted nitrogen and aluminum ion implant steps at room temperature and are subsequently annealed at 1700 °C for 30 min using a carbon cap based on photoresist.The implant dose and energies are depicted in Figure 1b.Finally, NiAl based ohmic contacts are formed.The surface is passivated by an NO-annealed silicon dioxide.The device die is bonded to a ceramic board for magnetic field-dependent characterization.In this study the cathode is kept at 0 V and the voltage of the anode is swept from 0 to 20 V. The substrate is kept floating.We note that measurements with the substrate reverse-biased resulted in almost the same characteristics.The magnetic field is applied inplane with respect to the diode's surface (Figure 1a).
The basic operation principle relies on a Lorentz deflectioninduced conductivity modulation of the low-doped i-region.The magnetic field leads to a deflection of the charge carriers both in the bulk epilayer and in the vicinity of the injecting regions.In the first case being the dominating transduction mechanism, a magnetic field polarity deflecting the charge carriers toward the bulk enlarges the current path and would hence reduce the current, which is however the opposite to what we observe in the measurements.In the latter case injection modulation can prevail, which modulates the current.Depending on the direction of the applied field injection is consequently enhanced or weakened and the mean carrier density is increased or decreased.The resulting conductivity modulation leads to a reduction or increase in the diode current.Using TCAD simulations we show that indeed a Lorentz deflection-induced modulation of trap-limited injection can explain the experimentally observed response both in terms of the magnetic field polarity-dependent sign of the current change in addition to the unexpected large magnitude of this change.

Experimental Results
In Figure 2a the room temperature IV-characteristic of a sample pin diode is shown in a semilogarithmic scale.One can observe a hump starting ≈15 V.By plotting  = d log(I)/d log(V) we see that the characteristic follows a power law I ∼ V  in the range ≈10-13 V with an exponent close to 3, which is a typical characteristic of double injection into a near intrinsic region. [40]With increasing bias, a hump with accompanied large current increase sets in, which is reflected in an increase in the exponent .Such behavior is indicative of a trap-induced effect.In Figure 2b the IV-characteristic is plotted on a linear scale for the cases of no magnetic field and for 0.5 T for both magnetic field polarities.In the aforementioned hump region, a pronounced large magnetic field response is clearly visible, which is also reflected in Figure 3, where the extracted absolute as well as the relative current change are plotted.The sensitivity increases almost linearly up to ≈14 V.At ≈15 V, where the high current increase sets in, there is also a strong increase in the magnetic field sensitivity, which achieves a maximum of ≈100% at ≈17 V for a magnetic field of 0.5 T (Figure 3b).
In Figure 4 the temperature dependency of the magnetic field dependent characteristics is depicted.As the temperature rises the sharpness of the IV hump as well as the magnetic field sensitivity are reduced.
In general, the shape of the IV-characteristics resembles that of a radiation-treated diode, where traps govern the electrical characteristics of the diode. [41,42]Being produced by ion implantation of the p+ and n+ regions, it is reasonable to  expect that this effect is originating from traps produced by the ion implant process.Particularly SiC is known to be rich of ion implant-induced defects, which are not fully removed by annealing.
To drive further conclusions on the origin of the observed behavior different diode variants produced on the same wafer were investigated as depicted in Figure 5.When the n+ injecting region is embedded inside an implanted n-well and the p+ injecting region directly in the p-epilayer the hump in the IV characteristics and the pronounced magnetic response are preserved.However, when the p+ region is also embedded in the n-well the IV hump disappears, and the magnetic sensitivity is significantly lowered.Furthermore, the hump is observed in the vertical diode configuration, where the n+ substrate acts as the diode's cathode, however, the in-plane magnetic field sensitivity is diminished.This strongly favors the hump and accompanied high magnetic sensitivity in the lateral diode arising from implant-induced compensating trapping defects at and in the vicinity of the p+ region controlling the lateral current flow to the laterally positioned n+ cathode.This coincides with experimental observations of a high density of annealing persisting defects originating from aluminum implants in SiC. [44,45]Another effect is the large dependency of the observed hump and sensitivity on the overlap length of the oxide with the p+ region.The smaller the overlap, the smaller the hump and sensitivity (Figure 6).Interestingly, the strength of the hump and sensitivity also depends on whether the p+ implant is located to the left or to the right side of the n+ implant as reflected in Figure 6.
As aluminum implants in 4H-SiC are known for a pronounced straggling effect, [46] the implant lateral extension left and right are asymmetrical, resulting in a different overlap length on the left and right side and in turn in this pronounced asymmetrical behavior.The origin of this overlap dependency is studied later in the TCAD section.

TCAD Model and Main Physical Effects
Using the nonisothermal galvanomagnetic carrier transport model implemented in the TCAD device simulator Sentaurus Device, [63] we study the origin of the hump observed in the diode's electrical characteristics as well as the high magnetic field sensitivity mechanism.Therefore, the minority carrier lifetime in the p-epilayer, was first estimated from current gain measurements on a lateral bipolar transistor.Hereby the pin diode's p+ implant together with the p-epilayer served as the base and the pin diode's n+ implant as the collector region.A third n+ implant located 8 μm to the pin diode's n+ implant served as an emitter.A minority carrier lifetime value of 50 ns was obtained.
Driven by the previous discussion of the measured IVcharacteristics, especially in Figure 5, indicating the presence of implant-induced traps at the p+ implanted region as the root cause of the diode's electrical hump and magnetic sensitivity, different implant-induced traps scenarios at the p+ implant region on the diode's electrical characteristics and magnetic sensitivity were studied.We show that a hole trap density in the range of 1 % of the p+ implant doping density of 5e19 cm −3 and exceeding the junction by just ≈200-250 nm laterally and vertically (Figure 7) is sufficient to result in the observed behavior.][44][45] We note that although traps are known to be generated by both aluminum and nitrogen implants, their density can be considerably higher for aluminum implants due to the higher atomic mass of aluminum, thus creating more defects. [45]ue to their high thermal stability, implant-induced intrinsic defects can survive the high annealing temperatures, which annihilates many other extrinsic defects.[26] A potential hole trap candidate is the pseudodonor D I , which is supported by the investigations in refs.[24,44,45].However regardless of the trap atomical origin, the underlying physics are expected to be similar.Other traprelated scenarios such as bulk or oxide interface traps solely were not sufficient to produce the observed behavior on their own when taking plausible concentrations into account.
Due to defect diffusion, formation, and annihilation processes during the post-implant anneal, the trap distribution is expectedly non-uniform.Also, during post-metallization anneal, as the oxide covers only the non-metallized implant regions, a nonuniformity between the trap distribution in the implanted p+ region beneath the oxide and the implanted p+ region beneath the metallization might be induced.The hypothesis of a lower trap density beneath the oxide was found to better match the experimental results as explored later.The justification of this hypothesis is further discussed in Section 4.4 along with a discussion on potential physical mechanisms causing such an anisotropic trap distribution.
To narrow down the parameter space covering trap parameters and its spatial distribution, we restricted the TCAD model to a simplified stepwise homogenous abrupt box model.The p+ implant is considered homogenous with a junction depth of 0.25 μm, whereas for the traps a two-stepwise homogenous profile or homogenous profile were considered extending 0.25 μm beyond the p+ implant's depth and extending laterally 0.2 μm beyond the p+ implant's lateral extensions as depicted in Figure 7.
Different trap parameters and distributions were found to cause significantly differing magnetic field responses, which is in addition considerably affected by the strength of surface recombination.In the following we investigate two scenarios.One scenario in which the sign of the magnetic field response matches the experiment and another one which exhibits an opposing magnetic response.The trap concentrations and the hole capture cross-section of the hole traps were hereby used as tunable model parameters.
A fixed series contact resistance of 10 Ω at the anode side was taken into account, which models the contact resistance of the NiAl/p+ ohmic junction.It has shown to numerically improve convergence and physically to lower the magnetic field sensitivity.Also, a major difference between scenario A and B is the surface recombination velocity, where for the latter it was set to 1 and is hence negligible.The additional parameters N ox and  rad are the epilayer/oxide interface charge density and radiative recombination coefficient and are neglected at this stage.For electron hole scattering the Brooks Herring model is used with the default simulator parameters set to silicon default parameters due to the absence of calibrated values for SiC.
In Figure 8a, the IV characteristics and electron density distribution are shown for the case of no traps.With the electron density exceeding the epi layer's hole density, high injection conditions with p ≈ n prevail.Hence the depicted electron density reveals the distribution of the hole injection as well.We see that the injection extends over the whole p+ junction area and in turn a magnetic field-induced injection modulation effect, despite of being present, is only minute.The IV characteristics resemble that of a conventional pin diode as expected, with the current being limited by the series resistance.On the other hand, in the trap-laden cases in scenario A and B the injection is considerably limited to a confined portion of the p+ implant area as visible in Figure 8b,c.In either scenario the hole traps create an injection barrier for hole injection from the p+ implant into the epilayer.For scenario A the IV-characteristics as well as the resulting mag-netic response show a good qualitative match to the measurement results (Figure 2b) when considering the simplified box profile and one trap specie assumption of the simulation model shown in Figure 7.We show later that by further adapting other parameters, the qualitive behavior of this simplified box profile trap model comes even closer to the experiment.Nevertheless, the simplified model already shows good qualitive agreement and can well reflect the IV hump region, the large magnetic response as well as the sign of the response.In contrast, scenario B shows a magnetic response opposing to the experiment.
In Figure 9 showing the absolute current density at the p+ implant region and its near surrounding, the origin of the magnetic field sensitivity in the trap-laden cases as well as the differing signs for scenarios A and B can be well observed.In either scenario, the implant-induced traps result in confined injection, creating one or two distinctive injection channels.
Depending on the trap distribution, the trap cross sections and applied bias, injection can be pronounced either at the first injection channel at the p+ implant's corner side adjacent to the surface, at the second injection channel at the bottom side of the p+ implant region beneath the ohmic contact's corner or distributed among both channels.The first injection channel is characterized by a lateral injection, whereas for the second injection channel injection is predominantly tilted vertically.In scenario B, where only the first injection channel is considerably active an in-plane field deflects the laterally moving electrons either toward or away from the lateral injection source.In the former case injection is enhanced, whereas in the latter case injection is reduced.In scenario A injection from this lateral injection channel is weakened or strengthened for down and up deflection similarly to the case of scenario B. However, in scenario A injection is additionally pronounced through the vertical injection channel.An in-plane field results additionally in deflection of the focused vertical current of this second injection channel toward or away from the confined vertical injection source.The vertical injection channel shows opposing behavior to the lateral one, i.e., whereas the lateral injection channel is weakened for positive field polarity, the vertical injection channel is significantly strengthened.As the vertical injection channel enhancement is more pronounced than lateral injection channel's decrease, current increases for positive field polarity, which is in accordance with the experimental observations.
In Figure 10 the induced electron density is shown in the case of a positive magnetic field polarity.We see for scenario A that the carrier density is largely increased for an applied in-plane magnetic field of positive polarity originating from the enhanced injection from the dominating vertical injection channel.Although injection from the lateral injection channel is decreased, its effect is lower as the strength of this injection channel or in other words its contribution to the total current is lower.The result is an increased conductivity modulation and consequently an increase in the current for a given forward voltage.For reversed magnetic field, reversed conditions prevail.In scenario B with only the lateral injection channel prevailing, hole injection is diminished as electrons are pushed downward away from the confined lateral injection source.As such also less electrons are injected, reducing the conductivity modulation and in turn the current.The great contrast to scenario A is clearly seen.

Temperature Behavior
In Figure 11 the effect of temperature on the IV-characteristics and magnetic response is compared between the experimental measurements and the simulated scenario A. Similar qualitive behavior is obtained.The hump's region slope decreases, and the magnetic sensitivity gets reduced.At low to moderate bias the reduced trap occupancy due to enhanced thermal emission results in a smaller injection barrier.In turn the diode's current increases.This contrasts the high bias regime ≈18 V, where the carrier mobility decrease prevails resulting in a lower current.Both effects, i.e the reduced trap occupancy and lower carrier mobility, result in a decreased magnetic field sensitivity.

Effect of Oxide/p+ Implant Overlap Length
In Figure 12 the effect of the reduced oxide/p+ implant overlap length on diminishing the sensitivity is investigated.Hereby same parameters of scenario A are assumed with the reduced trap density N c2 being restricted to the area beneath the oxide.The reduced p+ implant extension beyond the ohmic contact corner results in a smaller barrier for injection through the p+ implant corner side and as such the injection strength of both the lateral as well as vertical injection channels are pronounced.As both channels show opposing magnetic field response, their magnetic field modulation effect compensates each other, and the sensitivity is reduced in accordance with the experimental observations shown in Figure 6.

Effect of Anisotropic Trap Distribution
Figure 13 reflects the essence of vertical channel injection confinement for a large magnetic response particularly for positive field direction.The higher trap density N c1 under the contacted area in scenario A was stepwise reduced till a homogenous trap distribution is obtained.As one can see the vertical injection channel gets less confined and blurred with decreasing trap anisotropy compared to scenario A, resulting in a diminishing sensitivity for positive magnetic field polarity as the vertical injection path shows minute modulation, which is compensated by the opposing lateral injection modulation.When the trap density N c1 is reduced even more, the confinement is further reduced, in-turn further reducing the magnetic field sensitivity.In contrast, the trap distribution with higher density under the contact results in a focused or confined injection path as shown in the previous figures, which majorly results in the high magnetic field sensitivity.This hence favors the assumption that the trap density is lowered beneath the oxide region compared to the region beneath the ohmic contact as considered in scenario A. Although this assumption remains speculative, we note that in a cathodoluminescence study in ref. [24] a supporting spectroscopic contrast was observed, where the photoluminescence in the implanted area beneath the contacted implanted area exhibited considerably higher cathodoluminescence signal indicating higher D I pseudodonor defects compared to the non-contacted implanted region covered by oxide.As it was suggested in ref. [24]  the D I pseudodonor defects are not formed directly by the ionimplant process but rather during the sequent annealing steps, where vacancy and interstitials diffuse and react.As during the implant activation anneal the surface is covered by a carbon cap, it is not plausible that a considerable trap anisotropy results during this step.However, during ohmic contact anneal, the noncontacted implanted areas are covered by oxide, while the contacted area is covered by NiAl.Two effects can hereby cause an anisotropic trap distribution.][52] Considering the crystallographic direction dependency, as the oxidation process is known to introduce new traps or annihilate existing traps by carbon injection into SiC, [53] one can argue that an anisotropic annihilation of the hole traps takes place triggered by a vertically favored diffusion, hence affecting the area beneath the oxide.Considering the mechanical strain dependency, as ion implanted regions in 4H-SiC are found to cause considerable strain, [54] we can expect this strain distribution to become anisotropic within the implanted region after contact opening and metal deposition.Indeed in ref. [55] the stress distribution in 4H-SiC power devices was determined using a combination of FEM analysis and micro-Raman spectroscopy revealing a sharp stress variation between metallized and oxide covered p-implanted area, which coincides to that encountered in our current case.Given that mechanical strain is found to alter the defect diffusivity [50,51] and diffusion barrier for defects in crystals including 4H-SiC, [52] we expect such a sharp stress variation to favor an anisotropic defect diffusion, formation, or annihilation during the annealing process, resulting in a considerable final trap anisotropic distribution as assumed.

Effect of Conduction Losses on High Bias Region
Next, we devote our attention to the significant reduction in the magnetic response at high bias for the case of positive field polarity at room temperature, which contrasts the experiment.A variety of phenomena become important at high bias.With increasing bias, injection from the vertical injection channel increases.The traps get hereby saturated and further injection enhancement due to deflection gets also saturated as visible in Figure 14 explaining the merge of the IV-characteristic at high bias.This contrasts to the experiment, which however exhibits lower current at 20 V. Apparently, this regime of trap saturation is not reached in the experiment.Due to the confined nature of both injection channels, the strength of electron hole scattering,    radiative recombination, and surface recombination can considerably affect the current level at high bias as these effects affect the bias dependent strength of both injection channels and in turn the magnetic response and the onset of saturation of the magnetic response.Indeed, considering further tuning of these effects' physical parameters results in a response closer to the experimental observations as depicted in Figure 14.The surface recombination velocity was increased by a factor of four to 4e5 cm −1 s, which fits to the findings in ref. [56] for similar oxide annealing conditions.The radiative recombination parameter was set to 4e-11 cm 3 s −1 based on the study in ref. [57] for undoped and n-type 4H-SiC epilayers.Finally, the electron-hole scattering was heuristically reduced to 75% of the default value for silicon, which is motivated by the investigation in ref. [58] revealing considerably higher electron-hole scattering in 4H-SiC compared to silicon.
The combined effects of enhanced surface recombination, activated radiative recombination, and increased electron-hole scattering increase the conduction losses, which in turn delay the onset of trap saturation for the vertical channel.However as explored in Section 4.7, in contrast to surface recombination enhancing the magnetic sensitivity, both radiative recombination and electron-hole scattering have a detrimental effect on it.Overall, considering these effects reproduces better the experimental results limited to a bias of 20 V. We note however that at intermediate bias ≈5-12 V the magnetic responses of both scenario A as well as its refined version A* do not match the experimental results and cannot be reproduced unless neglected oxide charge or a smaller trap lateral extension are considered, which will be discussed in next Section 4.6.

Effect of Lateral Traps Extension and Oxide Charge on Moderate Bias Region
Before the onset of the hump region, the experimentally measured diodes show considerable sensitivity to magnetic fields reaching 20% at 10 V, which can be utilized for magnetic field sensing at reduced power consumption.Figure 15a,b show the measured and simulated response (scenario A) at low and moderate bias before onset of the hump region.In contrast to the experiment, where the sign of the magnetic response is found not to change over the whole bias range, the simulated voltage current curves intersect at moderate bias, resulting in a change in the sign of the magnetic response.This is visualized in Figure 15b, where the magnetic sensitivity exhibits reversed sign at the bias range 5-10 V compared to 10-20 V.This contrasts however the experiment, which shows scenario A like behavior down to the diode's threshold bias.
The lateral and vertical injection paths resemble two diodes in parallel with differing threshold voltages.The magnetic response is consequently composed of the summed response of the lateral and vertical injection paths.At low bias modulation of the lateral injection path prevails for the simulated scenario A, resulting in a Scenario B like behavior shown previously in Figure 9b.Tuning the lateral traps' extension is found to significantly affect the behavior of the low and moderate bias response, with a reduced extension diminishing the scenario B like response as shown in Figure 15c.Similarly, the consideration of negative interface charge is found to cause similar effect.Both a reduced lateral extension as well as negative interface charge result in a dominating modulation of the vertical injection path in response to a magnetic field compared to the lateral injection path.These results hence favor a lateral trap extension below 200 nm or the existence of significant negative charge in the oxide or at the interface with SiC, in particular at the interface with the trap-laden region.
In ref. [59] the effect of implant dose of different implants in SiC on the interface trap density was studied.A significant increase of negative effective oxide charge was observed with increasing aluminum implant dose.In addition, tensile stress was found in ref. [60] to considerably increase the interface trap density.We hypothesize that a considerable negative effective oxide charge, especially a high interface trap density, to be located at the oxide region overlapping the p+ implant region and its near vicinity, originating from the high aluminum implant dose and the tensile stress.

Effect of Various Parameters on Magnetic Sensitivity
The effect of trap-related model parameters for scenario A is depicted in Figure 16.At lower energy trap level, trap occupancy is reduced and in turn the injection confinement although still present is reduced.In turn the sensitivity is reduced (Figure 16a).Similarly, a reduction in the minority (electron) capture cross section for fixed hole capture cross section lowers the trap occupancy and the injection confinement (Figure 16b).In Figure 16c the effect of reduced oxide/p+ implant overlap on reducing the sensitivity as studied in Figure 12 is clearly visible, which reproduces the experimental behavior shown in Figure 6.In Figure 16d the essence of an anisotropic trap distribution for a high magnetic sensitivity is visualized.As the density N c1 beneath the NiAl contacted area is lowered toward N c2 the injection confinement is reduced and correspondingly the sensitivity.In Figure 16e,f the effect of lateral and vertical trap extension is shown.In either case, a reduced trap extension results in a lowered peak sensitivity.
Figure 17 visualizes the effect of other model parameters on the magnetic sensitivity.As surface recombination weakens the injection from the first injection path having opposing sensitivity and increases the lifetime gain or loss for a deflection away or toward the surface for the vertical injection channel, sensitivity increases with higher surface recombination 17a).
Whereas negative oxide charge was found to enhance the scenario A like sensitivity at moderate bias, it lowers the peak sensitivity (Figure 17b).This indicates that negative charge results in a surface barrier, which reduces the effective surface recombination velocity and in turn the magnetic sensitivity.
The reduction of series resistance (Figure 17c) significantly boosts the sensitivity, with an increase from 49% to 81% at zero external series resistance.As this value is closer to the experimental value, we conclude that the series resistance originating from the non-ideal ohmic contact to be lower at high bias.Increased electron hole scattering lowers the carrier mobility, which as expected from Lorentz deflection based magnetic field sensors lowers the sensitivity (Figure 17d).A decreased lifetime in the epi-layer, which originates either from radiative recombination or increased SRH recombination, lowers the sensitivity (Figure 17e,f).This is due to the increase in bulk losses, which compensates the effective lifetime increase gained from a carrier deflection away from the high recombination surface.
Apparently, the applied voltage bias, at which the maximum sensitivity is achieved as well as the maximum sensitivity value are dependent on a variety of injection strength and injection spatial distribution controlling parameters.

Calibration and Model's Validity
We conclude with the results of an optimized parameter set calibrated to quantitively reproduce the IV-characteristics of one sample diode and discuss potential root causes for experiment model discrepancy.As shown in Figure 18 a very good fitting to the experimental measurements is reached before the onset of the hump region using the tuned model parameters listed in Figure 18.However, a tuning of the IV-characteristics at the hump region to quantitively match the experimental curve was not feasible in scope of the simplified trap model considered.
In general, we can distinguish between two categories of model uncertainties.The first one concerns the exact 2D implant and trap distributions as well as the trap physical parameters.The second concerns the validity of the physical model parameters Due to the simplified model considering an abrupt step-wise homogenous trap distribution, a fitting of both the diode's current level and the hump region's transition voltage were not attainable within the explored parameter space discussed in the previous subsection.For example, increasing the trap density to lower the simulated current toward the measured current simultaneously shifts the onset of the hump region to a higher voltage than observed in the experiment.As such a perfect tuning of the current level as well as the transition voltage level were not attainable using this simplified model.A tun-ing of both characteristics would require considering trap profile inhomogeneities.
Considering carrier mobility, only a majority carrier mobility model is available for SiC.However, the minority carrier mobility for electrons can differ from the assumed majority carrier mobility; e.g., in silicon, the electrons minority carrier mobility in ptype silicon is higher than the majority carrier mobility in n-type silicon of the same doping level at high doping levels. [61,62]Furthermore, the mobility in the simulations is considered isotropic due to the missing possibility of combining an anisotropic mobility model with the galvanomagnetic transport model in Sentaurus Device. [63]However, in reality the mobility in 4H-SiC parallel to the c-axis, i.e., in vertical direction, is higher by ≈20% percent than the mobility perpendicular to the c-axis, [18] i.e., the lateral mobility.Hence a stronger magnetic response would result.Also, the assumption of spatially constant electron and hole Hall scattering factors (r H,n = 1.15, r H,p = 0.7) is questionable, given that Coulomb scattering affecting the Hall scattering factors significantly differs in the trap-laden region and the epilayer.
Besides, the treatment of electron-hole scattering as an additional term in the carrier mobility is an approximation, and a more appropriate approach involves an extension of the driftdiffusion equations [64] beyond what is implemented in the device simulator.All in all, the region after the hump region is gov-erned by material parameters and physics, which are at the current stage barely researched for SiC.Nevertheless, the presented model provides fundamental insights for the origin of the experimental phenomenon along with the measured temperature and geometrical dependencies.

Conclusion
In this study, we have demonstrated highly magnetic fieldsensitive ion-implanted SiC pin diodes exhibiting a sensitivity approaching 100% for an in-plane magnetic field of 0.5 T at room temperature.Using TCAD simulations we have shown how implant-induced traps can explain the very high magnetic field response by strongly limiting carrier injection from the implant region into the low-doped epilayer and resulting in a focused carrier injection from distinctive injection channels.This focused injection in turn results in a high sensitivity to an applied magnetic field, opening the door to highly sensitive SiC based magnetic field sensors.Overall, the presented model provided good agreement with the experimental results concerning the magnetic response, temperature behavior, and geometrical variations.We studied the effect of a variety of physical and geometrical effects on the observed characteristics.The insights provided in this study on how implant-induced traps spatially limit the injection from implanted regions is expected to be also of interest for studying and understanding loss origins in implanted SiC based power devices as well as other wide-bandgap semiconductor devices.

Figure 1 .
Figure 1.a) Device structure and its orientation with respect to the applied in-plane magnetic field of positive or negative polarity.b) Cross section with depicted geometrical as well as p+ aluminum and n+ nitrogen implantation parameters.

Figure 2 .
Figure 2. a) Semi-logarithmic I-V characteristic at room temperature and power law exponent.b) Linear I-V characteristics with no magnetic field and for B = +/− 0.5 T.

Figure 3 .
Figure 3. Bias dependent a) absolute and b) relative diode current change for various magnetic field strengths.

Figure 4 .
Figure 4. Temperature dependency of the magnetic field dependent IV-characteristics.

Figure 5 .
Figure 5.Effect of different diode configurations on the IV-characteristics and the magnetic field sensitivity.

Figure 6 .
Figure 6.Effect of oxide overlap length l ov (left-right) and effect of p+ implant's location exchange (top-bottom) on the IV-characteristics and magnetic sensitivity.

Figure 7 .
Figure 7. Simulation model of the pin diode with implant-induced traps at the p+ region and parameter set of the traps for two different simulated scenarios.

Figure 8 .
Figure 8. Simulated IV-characteristic and electron density distribution with a) no traps and b,c) with implant induced traps (scenario A and B) considered.The scale is limited to 5e17 cm −3 to avoid obscuring the electron density in the epilayer from the maximum electron density peaking in the n+ implant region.

Figure 9 .
Figure 9.Total current density in A/cm at and in the vicinity of the p+ implant region for scenarios a) A at 17.2 V and b) B at 20 V. Scale maximum is limited to 1.5e5 A/cm to avoid obscuring of the current density in the epilayer from the maximum current density peaking in the p+ implant region.The same scale is used in Figures 12-14.

Figure 10 .
Figure 10.Induced electron density modulation in cm -3 by the presence of a 0.5 T in-plane magnetic field for a) scenarios A at 17.2 V and b) scenario B at 20 V.

Figure 11 .
Figure 11.a) Experimental and b) simulated (scenario A) temperature dependency of IV-characteristics.c) Simulated magnetic response at 50 °C and d) simulated magnetic response at 100 °C.

Figure 12 .
Figure 12.Effect of oxide/p+ implant overlap length on IV-characteristics, injection behavior, and magnetic field response.The current density distributions are shown at the bias voltage exhibiting the maximum sensitivity for positive field polarity.

Figure 13 .
Figure 13.Effect of trap density anisotropy degree on magnetic field dependent injection distribution.Less pronounced focused vertical injection is observed with decreasing anisotropy.

Figure 14 .
Figure 14.Effect of increased recombination losses and enhanced electron-hole scattering at 20 V (right).When absent (left) vertical injection path is saturated, with deflection having minute effect on injection strength.

Figure 15 .
Figure 15.a) Measured magnetic response and b) simulated magnetic response at low and intermediate bias.Effect of c) lateral traps extension and d) oxide interface fixed negative charge on magnetic sensitivity.

Figure 16 .
Figure 16.Effect of trap-related parameter variations on sensitivity for scenario A: a) Energy E, b) minority carrier capture cross-section c n , c) oxide/p + implant overlap l ov , d) density anisotropy degree N c1 /N c2 , e) lateral traps extension X ext , f) vertical traps extension Y ext .Scenario A values are shown in bold.

Figure 17 .
Figure 17.Effect of surface conditions and conduction losses variations on sensitivity for scenario A: a) surface recombination S r , b) interface charge N ox , c) series resistance R s , d) carrier-carrier scattering mobility contribution μ eh , e) radiative recombination  rad , f) SRH lifetime  SRH .Scenario A values are shown in bold.

Figure 18 .
Figure 18.Model experiment comparison for parameters calibrated to fit the measured current level of a sample diode in a) semi-logarithmic and b) linear scale.c) Corresponding calibrated model parameters.