Self-Heating of Annealed Ti/Al/Ni/Au Contacts to Two-Dimensional Electron Gas in AlGaN/GaN Heterostructures
, Justinas Jorudas 2, Artūr Šimukovič 1, Vitalij Kovalevskij 2 and Irmantas Kašalynas 2,*,†Round 1
Reviewer 1 Report
In this paper, the self-heating effect of annealed Ti/Al/Ni/Au ohmic contact and two-dimensional electron gas (2DEG) under the action of strong electric field and large current is studied. The dependence of Rc on the applied current is studied. It is explained theoretically and proved experimentally, which has a good research significance, but there are still some questions and suggestions.
1.According to the second part, the surface of the heterojunction structure has not been passivated, can you explain the impact of surface passivation on this study?
2.It is mentioned in the introduction that Rc is often regarded as a fixed value at low field, and the increase in total resistance associated with self-heating is usually regarded as an increase in Rch. Does this contradict the following conclusion that Rc is more sensitive to current changes by comparing the current related Rc with the channel resistance Rch?
3.The distances L between electrodes of TLM resistance samples are 6, 12.5, 25, 35, 45, 55 and 65μm, respectively. What is the theoretical basis for the value of L?
4. How does the internal resistance of the pulse voltage generator affect the results in Fig. 3?
5. Fig4(a) depicts the dependence of Rc and ∆Rc on current density for the three samples, how is this curve obtained? Is it measured by TLM?
6.In the discussion, it is expected that the properties of 2DEG channels of Rc2D and R2D are similar. Can the rationality of this hypothesis be explained？
Author Response
In this paper, the self-heating effect of annealed Ti/Al/Ni/Au ohmic contact and two-dimensional electron gas (2DEG) under the action of strong electric field and large current is studied. The dependence of Rc on the applied current is studied. It is explained theoretically and proved experimentally, which has a good research significance, but there are still some questions and suggestions.
Question 1: According to the second part, the surface of the heterojunction structure has not been passivated, can you explain the impact of surface passivation on this study?
Answer 1: The surface passivation has no influence on the results of this work. Selection of proper materials and the fabrication processes suitable for surface passivation is complex problem. Usually, GaN device fabrication is completed with deposition of dielectric layers to passivate the surface states minimizing their influence on the device/transistor performance [44]. However, the fabrication might introduce to up to three orders of magnitude higher gate leakage currents for passivated HEMTs in comparison to unpassivated ones due to introduction of surface related traps [45]. Low trap density in GaN/AlGaN field effect transistors without passivation was confirmed by low-frequency noise measurements [46]. Therefore, we prefer to use unpassivated GaN heterostructures in this work.
References:
[44] R. Vetury, N.Q. Zhang, S. Keller, and U.K. Mishra, The impact of surface states on the DC and RF characteristics of AlGaN/GaN HFETs, IEEE Trans. Electron Devices 48(3), 560–566 (2001), http://dx.doi.org/10.1109/16.906451
[45] S. Arulkumaran, T. Egawa, H. Ishikawa, and T. Jimbo, Surface passivation effects on AlGaN/GaN high-electron-mobility transistors with SiO2, Si3N4, and silicon oxynitride, Appl. Phys. Lett. 84, 613 (2004), http://dx.doi.org/10.1063/1.1642276
[46] P. Sai, J. Jorudas, M. Dub, M. Sakowicz, V. Jakstas, D. B. But, P. Prystawko, G. Cywinski, I. Kasalynas, W. Knap, and S. Rumyantsev, “Low frequency noise and trap density in GaN/AlGaN field effect transistors,” Appl. Phys. Lett. 115, 183501 (2019).
Question 2: It is mentioned in the introduction that Rc is often regarded as a fixed value at low field, and the increase in total resistance associated with self-heating is usually regarded as an increase in Rch. Does this contradict the following conclusion that Rc is more sensitive to current changes by comparing the current related Rc with the channel resistance Rch?
Answer 2: In this work we investigated the change of the Rc and Rch due to self-heating effects. Our findings question previous assumptions that only Rch self-heating is important. Indeed, self-heating of both resistances should be taken into account for the interpretation of the total resistance R = Rc+Rch change at strong electric fields (charge current densities). Authors were surprised that Rc can increase and the rise of its value can be even faster than that of Rch. That is the main finding of this work. Lack of publications on the increase of Rc due to self-heating could be explained, at least in part, to the intricate analysis required, that R (of different L) should be compared at fixed currents I (but not voltages U).
Question 3: The distances L between electrodes of TLM resistance samples are 6, 12.5, 25, 35, 45, 55 and 65μm, respectively. What is the theoretical basis for the value of L?
Answer 3: Any distance between electrodes of TLM resistance samples can be used in theory. In our case, particular L values were selected in accordance to photo-lithography mask used for fabrication of the samples.
Question 4: How does the internal resistance of the pulse voltage generator affect the results in Fig. 3?
Answer 4: The internal resistance of the pulse voltage generator has no influence on the results. Voltage and current pulses of the sample were measured directly in order to exclude signal dependence on the internal resistance of the pulse source and coaxial lines.
Question 5: Fig4(a) depicts the dependence of Rc and ∆Rc on current density for the three samples, how is this curve obtained? Is it measured by TLM?
Answer 5: Yes, measurements were done on the TLM resistance samples. The value of Rc (closed symbols in Fig.4 (a)) were obtained from the Fig. 3(b) taking the interception point of the fit line of particular current data with the abscissa axis. Note, that position of the interception (i.e. Rc value) goes up with current as indicated by vertical arrow in Fig. 3(b). The ΔRc value was found from all Rc values subtracting the low-field value Rc0 which was observed at low current density. We modified caption of Figure 4:
"Figure 4. The dependence of the contact resistance Rc (closed symbols) on the current density I/W (a) and on the dissipated electric power density Pc in contacts (b) for different samples; AlGaN/GaN (squares), AlGaN/AlN/GaN (triangles and circles). The dependence of the contact resistance change DRc =Rc - Rc0 relatively to its low-field value is also presented by open symbols (right-side axis).. "
Question 6: In the discussion, it is expected that the properties of 2DEG channels of Rc2D and R2D are similar. Can the rationality of this hypothesis be explained?
Answer 6: We thank Reviewer for very important question. We agree that we do not prove this hypothesis experimentally and do not give strong arguments regarding its correctness. However, this statement is redundant for the discussion and for the formulation of the conclusions. We modified this section in the revised manuscript (text from line 335):
"Let’s first discuss the option that the self-heating of Rc is caused by the self-heating of Rc2D (see Eq. 7), while ρc self-heating is negligible. The current density in Rc2D is smaller than in R2D, therefore, the stronger self-heating of Rc2D compared to R2D, might seem surprising. The current profile is illustrated in Fig. 1 (b), where the horizontal current vector magnitude gradually decreases as the current branches toward the electrodes. A detailed description of the current dependence on the distance can be found elsewhere [22]. We could suppose, that Rc2D > R2D due to lower electron mobility or lower sheet electron density under the electrodes. In this case dissipated power per unit area P2D at given current density j will be higher because P2D ~ Rc2D j2. Higher dissipated power in the contact resistance result in higher self-heating of Rc2D. The next option is the self-heating of rc… "
Reviewer 2 Report
The following points need to be addressed.
1- The authors describe the material structure of the DUT in the 1st paragraph of section 2, lines 86 to 96. In the text, there are layers that are not shown in the figure. For example, there is a mention of high resistivity GaN and UID GaN, in the text. But only one GaN layer is shown in the figure. Is this GaN layer the high resistivity layer, UID layer, or a doped layer? It is not clear.
2- Also, there is a mention of a GaN cap, but it is not shown in the figure. Is this GaN cap grown on top of the GaAlN to form a good ohmic contact?
3- What is the doping of the UID GaN? Would it affect the channel resistance?
4- The device structure explained in the text should be illustrated in the graph and their physical parameters (doping for example) should be indicated.
5- Explain the purpose of the 700 KeV implant of Al. Is it for lattice damage?
6- For the RIE, how do you protect the 2DEG, does the AlN act as an etching stopper? Lack of clarity confuses the readers.
7- In line 157, the authors mentioned 3 heterostructure samples, with and without AlN barrier layer. Where is the cartoon showing these structures? A cartoon showing the 3 structures should be provided, even if they have been shown in another reference. Without these structures, it is hard to understand the paper with certainty.
8- Fig 2 caption fails to link curves to their own samples, since the structures of the samples are not shown. Please draw the structure of every sample used in this study.
9- Line 155, is confusing? Please clarify!
10- The authors indicate that ΔRc is proportional to I5 but linearly proportional to power Pc. Is this assumption based on analytical analysis, or it is just experimental observation? Can this be explained? Explain this behavior based on the law of physics.
11- The paper states that the contact temperature reaches 700 K or 400 C. Was there any metal migration in the semiconductor, degradation of the 2DEG layer, or change in the metal morphology?
12- Fig 9 is not clear. The figure contains plots for 3 samples. One is AlGaN/GaN (squares), and the other two are AlGaN/AlN/GaN. How can we have one structure for two samples? Show a drawing for all structures.
13- There are some minor English mistakes. Examples: (A) line 323 where the word “it” is missing. (B) Line 361: rewrite “the shorter the pulse the weaker…” There are more typos in the paper.
Author Response
The following points need to be addressed.
Question 1: The authors describe the material structure of the DUT in the 1st paragraph of section 2, lines 86 to 96. In the text, there are layers that are not shown in the figure. For example, there is a mention of high resistivity GaN and UID GaN, in the text. But only one GaN layer is shown in the figure. Is this GaN layer the high resistivity layer, UID layer, or a doped layer? It is not clear.
Answer 1: We thank Reviewer for this question from content of which we assume that Reviewer talks about Figure 1 b. In this figure the intersection of the AlGaN/GaN with 2DEG channel is illustrated, showing the active part of the epitaxial structure with two electrodes only. Most top part of unintentionally doped (UID) GaN layer and AlGaN barrier is illustrated in Fig. 1 b. This is explained now in the revised manuscript (inserted at line 96):
"Figure 1 (b) illustrates top part of the unintentionally doped (UID) GaN layer and AlGaN barrier required for 2DEG formation. "
In addition, caption of Fig. 1 b is also modified:
"intersection illustration of the typical AlGaN/GaN herostructure with the 2DEG channel, showing the active part of the epitaxial heterostructure, and involving only two electrodes (b)."
Question 2: Also, there is a mention of a GaN cap, but it is not shown in the figure. Is this GaN cap grown on top of the GaAlN to form a good ohmic contact?
Answer 2: Not exactly, caps of GaN and SiNx are used to finish the AlGaN/GaN heterostructure layers in order to provide stability of 2DEG layer in respect to environmental change, for example humidity. Cap layers has no impact on the results of this work therefore they are not shown in illustration of the active part of the heterostructure.
Question 3: What is the doping of the UID GaN? Would it affect the channel resistance?
Answer 3: UID GaN layer is undoped. Residual doping of this layer is usually in the range of 1015 cm-3 depending on the MOCVD method used for comercial groth of AlGaN/GaN heterostructures. This layer has insignificant influence on the channel resistance.
Question 4: The device structure explained in the text should be illustrated in the graph and their physical parameters (doping for example) should be indicated.
Answer 4: We believe that most important layers are illustrated in Fig. 1 b (see also our comments answering to the Question 1). Physical parameters used to characterize AlGaN/GaN HEMT structures are density and mobility of 2DEG. We add sentence in the revised manuscript discussing values of the physical parameters (inserted at line 104):
"The Hall effect experiments in Van der Paw geometry at temperature of 300 K revealed the density n_2DEG and mobility μ_2DEG values of 2DEG in used samples to be of 8.3×1012 cm−2 and 9.3×1012 cm−2 and of 1.9×103 cm2/Vs and 1.9×103 cm2/Vs, respectively. "
Question 5: Explain the purpose of the 700 KeV implant of Al. Is it for lattice damage?
Answer 5: The purpose of the 700 KeV implant of Al is mesa formation. This is explained in manuscript text (see from line 98 till 101).
Question 6: For the RIE, how do you protect the 2DEG, does the AlN act as an etching stopper? Lack of clarity confuses the readers.
Answer 6: Hard mask of photo-resist was used to protective all AlGaN/GaN heterostructure layers during RIE. The RIE process was done using well calibrated procedure on template samples.
Question 7: In line 157, the authors mentioned 3 heterostructure samples, with and without AlN barrier layer. Where is the cartoon showing these structures? A cartoon showing the 3 structures should be provided, even if they have been shown in another reference. Without these structures, it is hard to understand the paper with certainty.
Answer 7: Two cartoons one for each group of TLM samples are presented as insets of Fig.2 and discussed in text (see also our answer to Question 7) in the revised manuscript.
Question 8: Fig 2 caption fails to link curves to their own samples, since the structures of the samples are not shown. Please draw the structure of every sample used in this study.
Answer 8: We modified Fig. 2 caption in the revised manuscript.
Figure 2. The dependence of the low-field total resistance R on the channel length L. Data for group of TLM samples 1, fabricated of AlGaN/GaN (bottom inset), are shown by rectangles, meanwhile, triangles as well as circles demonstrate results of different two groups of TLM samples 2, made of AlGaN/AlN/GaN (top inset).
Question 9: Line 155, is confusing? Please clarify!
Answer 9: We revised text in the manuscript in order to avoid confusion (please see from line 155):
"The parasitic capacitance (parallel to the channel) for the shortest channel was found to be less than ~ 50 fF. Meanwhile, measurements of S11 spectra of normal TLM structures with 2DEG layer (i.e. channel not etched) revealed the serial inductance value to be of ~ 30 pH.‘"
Question 10: The authors indicate that ΔRc is proportional to I5 but linearly proportional to power Pc. Is this assumption based on analytical analysis, or it is just experimental observation? Can this be explained? Explain this behavior based on the law of physics.
Answer 10: Indeed, the ΔRc is proportional to Pc, at least in the range from 1 to 10 W/mm, however, ΔRc is not proportional to current density but follows I5 law in the range of high current densities. This was mentioned in the manuscript (line 219): "The Rc(I) dependence is nonlinear and develops a steep increase, which approaches and exceeds ΔRc(I) ~ I5 (see lines in Fig. 4(a)) at highest currents".
Both dependencies are related to the self-heating effects, as discussed in the manuscript. In theory and experiment, fast increase of Rc(I) and ΔRc(I) could be obtained even without pronounced self-heating as in the case of bulk (and weakly doped) GaN, where well known current (and electron drift velocity) saturation-like dependence develops at high electric field E. Weak dependence of I on E (or voltage U) means high R, and in representation of dependence on I, it shows fast increase. This is even more pronounced in GaN-based 2DEG channels due to known hot-LO-phonon effect (i.e. LO-phonon self-heating). Crystal temperature increase due to dissipated electrical power, i.e. Joule heat, also increases the resistance (i.e. acoustic phonon self-heating).
The proportionality to Pc could be explained in such a way, that the excess temperature ΔT of Rc is proportional to Pc, if heat capacitance CV is nearly constant (see also discussion from line 383). Apart of proportionality of ΔT ~ Pe, we then also need ΔRc ~ ΔT (or Rc ~ T) proportionality to be correct as well. The latter is not obvious for Authors from the point of theory. In Ref. [28] given Rc~T0.8 experimental dependence would almost suite our requirement (0.8-1), however, in the same reference, for other sample, T1.8 dependence is obtained. In Ref.[60] almost linear Rc~T dependence is found up to 250 C.
Question 11: The paper states that the contact temperature reaches 700 K or 400 C. Was there any metal migration in the semiconductor, degradation of the 2DEG layer, or change in the metal morphology?
Answer 11: As it is discussed in the paragraph starting at line 354, interpretation depends on whether hot-electron effect is pronounced (Te_TLO>>TL, applicable for Rc2D), or not pronounced (Te_TL, applicable for the metallike conductor). For the first case, the contact noise temperature is a measure of hot-electron temperature only, and in the latter case, it is a measure also of lattice temperature. So, for metal migration / degradation, probably only the second case could be important. In reality, the situation probably is somewhere in between because the noise temperature of Rc depends on noise temperature of Rc2D and of ρc. We have not done any research on metal migration. Degradation experiment, in terms of pulsed measurements, when duty cycle is so low (10-5), is problematic. Degradation depends on stress duration, which is short when low duty cycle is used. In this work, we needed to do measurements on different length channels from the same TLM. On the one hand, we were trying to reach higher voltages, on the other hand, we were trying to avoid any burn-out of the channel/electrode. If we will degrade/burn-out, then the total resistance of the next length channel (which shares the same electrode) also could be perturbed.
Two sections in the revised manuscript text from (starting from line 255):
"Self-heating of the contact resistance also follows from the noise experiment (see Fig. 6) under the assumption that noise temperature Tnc is a measure of the contact resistance temperature Tc, i.e. Tnc » Tc. The excess noise temperature of contact resistance (squares) approaches ~ 700 K.
The assumption Tnc » Tc is realistic because it is based on the experiments with the GaN-based 2DEG channels, where the microwave noise temperature of hot electrons Tn is approximately equal to hot-electron temperature Tn»Te [52]."
were modified to:
"Self-heating of the contact resistance is also seen from the noise experiment (see Fig. 6) under the assumption that noise temperature Tnc is a measure of electron gas temperature Tec in the contact resistance, i.e. Tnc » Tec. The excess noise temperature of contact resistance (squares) approaches ~ 700 K.
The assumption Tnc » Tec is realistic because it is based on the experiments with the GaN-based 2DEG channels, where the microwave noise temperature of hot electrons Tn is approximately equal to hot-electron temperature Tn » Te [52]. "
Question 12: Fig 9 is not clear. The figure contains plots for 3 samples. One is AlGaN/GaN (squares), and the other two are AlGaN/AlN/GaN. How can we have one structure for two samples? Show a drawing for all structures.
Answer 12: Two groups of TLM samples (labeled as TLM samples 2) were fabricated of AlGaN/AlN/GaN heterostructure, while third group of TLM samples (labeled as TLM samples 1) were made of AlGaN/GaN material. Two cartoons one for each group of TL:M samples are presented in insets of Fig.2 and discussed properly in the revised manuscript.
Question 13: There are some minor English mistakes. Examples: (A) line 323 where the word “it” is missing. (B) Line 361: rewrite “the shorter the pulse the weaker…” There are more typos in the paper.
Answer 13: We thank Reviewer for spotting typos. We corrected the sentence (lines 323, 361) and revised all the manuscript properly.
line 323:"Indeed, from Fig. 9 can be concluded that, above threshold, the increase of Rc is faster than that of R2D."
line 361: "..decrease [38]; thermal quenching is weaker when shorter pulse is used."
Reviewer 3 Report
This paper investigated the contact resistance of Ti/Al/Ni/Au ohmic metal stacks for GaN-based HEMTs under pulsed voltage bias. The results of I-V measurements based on the transmission line structure and the noise temperature measurements indicated that the increase of contact resistance due to self-heating is significant. In my opinion, this article is suitable to be published in the Applied Sciences after a minor revision.
1. The abbreviation “TLM” was defined twice in the main text, one for the “transfer-length-model” and another one for the “Transmission line method”.
2. The “Pc” in the x-axis label in fig. 7 should be “Pc”
3. The linearity in fig. 4, fig. 6, fig. 7, and fig. 8 are presented in log-log plots. But in the main text, the authors described the linearity without mentioning the log-log plot. This may cause confusion. For example, the statement in the conclusion part “It was found that the change of Rc from its low-field value is proportional to the electric power dissipated in the contacts.”
4. There should be a term of 1 missing in the equation in line 186.
5. What might be the physical implication of the linear dependences of on and in fig. 4(a) and fig. 4(b)?
6. In fig. 7, the curves of the relative contact resistance vs. dissipated power for different samples nearly overlap with each other. This is somewhat striking considering the absolute values in fig. 4(b) are very different. What might be the explanation?
7. The statement in 266, “This suggests that the self-heating of Rc and Rch have much in common”, is kind of hand-waving. I think this is better to be removed unless further explanation can be provided.
8. The discussion in the paragraph of line 335-353 is problematic. In my opinion, it is better to be removed.
a. The statement, “The stronger self-heating of Rc2D compared to R2D and on the same time on average smaller current density in Rc2D compared to R2D, might seem surprising.”, is hard to understand. Maybe some grammar problem here?
b. The statement “The properties of the 2DEG channel of Rc2D and R2D are expected to be similar with the only difference that the processing of ohmic contacts can increase Rc2D due to the decrease of electron mobility without modification of the 2DEG density. Indeed, the 2DEG density mostly depends on material properties, like the difference in polarization between AlGaN and GaN layers”. In my opinion, this statement is not right. The 2DEG density depends on many things. For example, fluoride treatment on the surface can change the surface fermi level and completely deplete the 2D channel. The deposition and annealing of the Ohmic metal can surely change the surface chemistry and cause diffusion of metal atoms. These factors can all potentially change the density of the 2D channel.
Comments for author File: 
Comments.pdf
Author Response
This paper investigated the contact resistance of Ti/Al/Ni/Au ohmic metal stacks for GaN-based HEMTs under pulsed voltage bias. The results of I-V measurements based on the transmission line structure and the noise temperature measurements indicated that the increase of contact resistance due to self-heating is significant. In my opinion, this article is suitable to be published in the Applied Sciences after a minor revision.
Question 1. The abbreviation “TLM” was defined twice in the main text, one for the “transfer-length-model” and another one for the “Transmission line method”.
Answer 1: We thank Reviewer for spotting this confusion. We described abbreviation “TLM” once and properly in the revised manuscript (at line 32).
"The contact resistance Rc usually is estimated from the transmission line model (TLM) measurements [21,22]."
Question 2. The “Pc” in the x-axis label in fig. 7 should be “Pc”
Answer 2: We thank Reviewer for spotting this typo, which was corrected in the revised manuscript.
Question 3. The linearity in fig. 4, fig. 6, fig. 7, and fig. 8 are presented in log-log plots. But in the main text, the authors described the linearity without mentioning the log-log plot. This may cause confusion. For example, the statement in the conclusion part “It was found that the change of Rc from its low-field value is proportional to the electric power dissipated in the contacts.”
Answer 3: For ΔRc(I) ~ I5 line in Fig. 4(a), please see the answer to Reviewer 2 comment 10, where in response we modified also the sentence at line 219. Lines in Fig.6(a) is just to guide the eyes as it is noted in the caption of the figure. Please note, that linear dependences in Figures 4(b), 7 and 8 would be linear in log-log representation and in linear-linear representation (it would not for ~ I5).
Question 4. There should be a term of 1 missing in the equation in line 186.
Answer 4: We thank Reviewer for this important comment, the equation is correct now.
Question 5. What might be the physical implication of the linear dependences of on and in fig. 4(a) and fig. 4(b)?
Answer 5: The ΔRc is proportional to Pc, at least in the range from 1 to 10 W/mm, however, ΔRc is not proportional to current density but follows I5 law in the range of high current densities. This was mentioned in the manuscript (line 219): "The Rc(I) dependence is nonlinear and develops a steep increase, which approaches and exceeds ΔRc(I) ~ I5 (see lines in Fig. 4(a)) at highest currents".
Both dependencies are related to the self-heating effects, as discussed in the manuscript. In theory and experiment, fast increase of Rc(I) and ΔRc(I) could be obtained even without pronounced self-heating as in the case of bulk (and weakly doped) GaN, where well known current (and electron drift velocity) saturation-like dependence develops at high electric field E. Weak dependence of I on E (or voltage U) means high R, and in representation of dependence on I, it shows fast increase. This is even more pronounced in GaN-based 2DEG channels due to known hot-LO-phonon effect (i.e. LO-phonon self-heating). Crystal temperature increase due to dissipated electrical power, i.e. Joule heat, also increases the resistance (i.e. acoustic phonon self-heating).
The proportionality to Pc could be explained in such a way, that the excess temperature ΔT of Rc is proportional to Pc, if heat capacitance CV is nearly constant (see also discussion from line 383). Apart of proportionality of ΔT ~ Pe, we then also need ΔRc ~ ΔT (or Rc ~ T) proportionality to be correct as well. The latter is not obvious for Authors from the point of theory. In Ref. [28] given Rc~T0.8 experimental dependence would almost suite our requirement (0.8-1), however, in the same reference, for other sample, T1.8 dependence is obtained. In Ref.[60] almost linear Rc~T dependence is found up to 250 C.
Question 6. In fig. 7, the curves of the relative contact resistance vs. dissipated power for different samples nearly overlap with each other. This is somewhat striking considering the absolute values in fig. 4(b) are very different. What might be the explanation?
Answer 6: Yes, this result is striking (and important) and we mention at line 252, that „Actually, dissipated power in contacts controls the change of Rc what is evident from Fig. 7, where relative contact resistance change is plotted; the dependencies of different samples almost coincide when are plotted versus Pc.“
If we want to find some quantity, which controls the change of the Rc, then first, we need to isolate this change, therefore we take Rc-Rc0. On the other hand, if we use dissipated power Pc as a control parameter, we need consider that it is additive; lets say we have two resistances Rc0/2 + Rc0/2, therefore we will need 2 x more Pc to achieve the same affect compared to just Rc0/2 resistance. Therefore, we arrive at the point, that if we want to compare different Rc, we can try relative change, ΔRc/Rc0. It is strong argument, that Pc (and associated self-heating) controls experimentally observed phenomena.
Question 7. The statement in 266, “This suggests that the self-heating of Rc and Rch have much in common”, is kind of hand-waving. I think this is better to be removed unless further explanation can be provided.
Answer 7: We thank Reviewer for this important comment, this statement and a following sentence were removed:
This suggests that the self-heating of Rc and Rch have much in common. For example, the 2DEG channel contributes to both resistances.
Question 8. The discussion in the paragraph of line 335-353 is problematic. In my opinion, it is better to be removed.
Question 8a. The statement, “The stronger self-heating of Rc2D compared to R2D and on the same time on average smaller current density in Rc2D compared to R2D, might seem surprising.”, is hard to understand. Maybe some grammar problem here?
Question 8b. The statement “The properties of the 2DEG channel of Rc2D and R2D are expected to be similar with the only difference that the processing of ohmic contacts can increase Rc2D due to the decrease of electron mobility without modification of the 2DEG density. Indeed, the 2DEG density mostly depends on material properties, like the difference in polarization between AlGaN and GaN layers”. In my opinion, this statement is not right. The 2DEG density depends on many things. For example, fluoride treatment on the surface can change the surface fermi level and completely deplete the 2D channel. The deposition and annealing of the Ohmic metal can surely change the surface chemistry and cause diffusion of metal atoms. These factors can all potentially change the density of the 2D channel.
Answer 8a+b: We modified this section in the revised manuscript (text from line 335):
"Let’s first discuss the option that the self-heating of Rc is caused by the self-heating of Rc2D (see Eq. 7), while ρc self-heating is negligible. The current density in Rc2D is smaller than in R2D, therefore, the stronger self-heating of Rc2D compared to R2D, might seem surprising. The current profile is illustrated in Fig. 1 (b), where the horizontal current vector magnitude gradually decreases as the current branches toward the electrodes. A detailed description of the current dependence on the distance can be found elsewhere [22]. We could suppose, that Rc2D > R2D due to lower electron mobility or lower sheet electron density under the electrodes. In this case dissipated power per unit area P2D at given current density j will be higher because P2D ~ Rc2D j2. Higher dissipated power in the contact resistance result in higher self-heating of Rc2D. The next option is the self-heating of rc… "
Please also see the attachment.
Round 2
Reviewer 2 Report
Revisions are acceptable.
