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Moustakas and M. State Comm. As, D. Schikora, A. Greiner, M. Lubbers, J. Mimkes, and K. B, 54 RR Barin, O. Knacke, and O. Bermudez, C. Wu, A. Bermudez, T. Jung, K. Doverspike, and A. Bernardini, V. Bhapkar and M. Bloom, G. Harbeke, E. Meier, I. Solidi, 66, Boguslawski, E. Briggs, and J. Brandt, J. Mullhauser, B. Yang, H. Yang, and K. Bu, D. Ciplys, M. Shur, L. Schowalter, S. Schujman, and R. Gaska, "Surface acoustic waves in single crystal bulk aluminum nitride" Appl.
Bykhovski, B. Gelmont, and M. Chernyak, A. Osinsky, A. Chin, T. Tansley, and T. Chu, D. Ing, and A. State Electron. Davis, A. Roskowski; E. Preble, J. Speck, B. Heying, J. Freitas, Jr. Glaser, ; and W. Davydov, A. Klochikhin, R. Seisyan, V. Emtsev, S. Ivanov, F. Bechstedt, J. Furthmuller, H. Harima, A. Mudryi, J. Aderhold, O.
Semchinova, and J. Evidence of Narrow fundamental band gap" Phys. Klochikhin, V. Emtsev, D. Kurdyukov, S. Ivanov, V. Vekshin, F. Furthmuller, J. Aderhold, J. Graul, A. Mufrui, H. Hashimoto, A. Yamomoto, and E. Davydov, Yu. E Kitaev, I. Goncharuk, A. Smirnov, J. Graul, O. Semchinova, D. Uffmann, M. Smirnov, A. Mirgorodsky, and R. B, 58 Davydov, V.
N Goncharuk, A. Petrikov, V. Mamutin, V. Vekshin, S. Ivanov, M. Smirnov, and T. Klochkin, V. Mudryi, A. Yamamoto, J. Graul, and E. Deger, E. Born, H. Angerer, O. Ambacher, M. Stutzmann, J. Hormsteiner, E. Riha, and G. Demiryont, L. Thompson, and G. Optics, 25, — Dingle, D.
Sell, S. Stokowski, P. Dean and B. B, 3 Dmitriev and A. Brandt, and R. Symposium Proc. Edwards, K. Kawabe, G. Stevens, and R. Fan, M. Li, and T. Fanciulli, T. Lei, and T. B, 48 Fernandez, V.
Chitta, E. Abramof, A. Ferreira da Silva, J. Leite, A. Tabata, D. As, T. Frey, D. Schikora, and L. Soc, Florescu, V. Asnin, F. Pollak, R. Molnar, and C. Francis and W. Gaskill, L. Rowland, K. Geidur and A. Goldhan, S. Manasreh, H. Gorczyca, A. Svane, and N. Research 2 Article 18 Gotz, N. Moustakas, editors, , Academic Press, p Guo, M. Nishio, H. Ogawa, and A. B, 55, RR Guo and A. Guy, S. Muensit, and E. Matter 14 RR, Heying, I. Smorchkova, C. Poblenz, C. Elsass, B. Fini, S. DenBaars, U. Mishra, and J. Speck, "Optimization of the surface morphologies and electron mobilities in GaN grown by plasma-assisted molecular beam epitaxy", Appl.
Holst, L. Eckey, A. Hoffmann, I. Broser, B. Schottker, D. Schikora and K. Inushima, V. Ivanov, T. Sakon, M. Motokowa, and S. Ohoya, Physical properties of InN with the band gap energy of 1. Growth, Jenkins and J. Jiang, J. Lin, and W. Jones, R. French, H. Mullejans, A. Dorneich, S. Loughin, and P. Joo, H. Kim, S. Kim, and S. Kampfe, B. Eigenmann, O. Vohringer, and D. Lohe, High temperature material processes, 2, Kasic, M.
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Gierlotka, S. Stelmach, B. Palosz, S. Porowski, and P. Solids, 59 Lambrecht and B. B, 47 Lan, X. Chen, Y. Cao, Y. Xu, L. Xun, T. Xu, and J. Growth, , Leszczynski, H. Teisseyre, T. Suski, I. Grzegory, M. Bockowski, J. Jun, S. Porowski, K. Baranowski, C. Foxon, and T. Liufu, and K. A, 16 Look, C. Stutz, R. Molnar, K. Saarinen and Z. Lu, W. Schaff, J. Jasinski, and Z. Loughin S. Matsuoka, H.
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Harima, and E. McNeil, M. Grimsditch, and R. Mohammad, A. Salvador, and H. Monemar, J. Bergman, H. Amano, I. Akasaki, T. Detchprohm, K. Hiramatsu and N. Material Sci. Moore, J. B, 56 Lee, S. Park, and J. Muth, J. Brown, M. With input from Robin J. Jones of Silvaco. International the mesh points were redu ced and the spacing increased. Reducing nodes. The first attempt at running the new. The x. The z-axis spacing was doubled and that produced , nodes which. This still resulted in run time errors when running the file.
The z-axis. This mesh was. The next part of the research was to determine the mobility equations to use. Albrecht had used a Monte Carlo. T is the temprature in Kelvin. I is the ionized donor concentration cm - 3. Albrecht had found that this was a viable equation to use from a range of to. This thesis implement. Albrecht had assigned constants to the. Newham  had altered the values of the.
The work for the 2D model encompasses. The constant values are listed,. This code was written to l ook at the effects of changes in temperature on. Figure 11 shows the effects of mobility versus temperature for the sum of. Figure 12 shows part A of the equation, ionized impurity scattering,. Part A of the equation is not only. For this test of. Figure 13 shows part B of the e quation, acoustic phonon limited mobility,. Figure 14 shows part C of the equation,. For this model ionized donor concentration will not be used because.
The vertical axis for the plots in Figure s is defined as mobility in units of. The results of this show that part A had the most effect on mobility, but parts. B and C together are more effected by change s in temperature. The overall combination. This is. The self-. Berkeley Device. The top curve on Figure 9 has a negative slope for current which. There were no temperature readings. The self-heating effects. The two dimensional. This was attempted to be incorporated in this thesis model for.
The result of attempting this method of simulation of the self-heating effects was. The doping levels at that concentration pr oved to create a short. Attempts to lower the. A doping level of. Many manipulations of the Schott ky work function were. This method for incorporating the self-heating effect s was not successful. The use of the new. These attempts were unsuccessful, which may be due to. Therefore a sheet charge was. The sheet charge for this model will.
The value of. This value is also concurrent with those found in the. For thermal conductivity and he at capacity for th e material, it was determined that. Newham had used the standard model. This was. Shown in Table 5 ar e the default parameters for GaN . The thermal properties also have an effect on the heating of the device.
The self. Kelvin for a similar power device for 20 volts applied. The only way found to. This was done by changing the TC. A parameter in the material. This resulted in a matching th e temperature effect as seen by Freeman. This was done. MAX designation from the GaN region statement. This allows for the simulation of. This concluded the changes th at were implemented by Silvaco for GaN. This resulted in a current of approximately four.
The value chosen. The results of adding this contact resistance brought the current to a level that. The bandgap curves matched the theoretical expectations fo r a GaN device and the result. The mode ling results will be discussed fu rther in the next section. The model was initially run in two dimensi ons with an auto mesh width set at one.
Running the model in two dimens ions first allowed it to run quicker in. The initial runs did not incorp orate the self heating affects. The peak temperature in the channel was only. The results. The plot was. In order to do the overlay the actual measured. The Green line is the. The Red line is the device measurements. Kelvin for this data run. The rest of the simulation runs incorporated changing the.
I A -V curves comparing act ual vs. The simulation of the self heating effects is compared to the actual device at room. Figure 18 shows the results for a gate voltage of -1 at the top and stepped. The red lines are the device measurements at the same. The picture shows the peak temp at the drain side of the gate which agrees with. Peak temperature. The simulated device for the room temperature curve did correlate to. Figur e 20 shows the resulting simulated I-V for.
Several more runs were conducted and matche d to various gate bias and temperature. The dark blue line is the simulate d device being compared to the red line of. The light blue line is the simulated device being. The results match to less than a.
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The simulated results correlate well with the UC Berkeley device measurements. Kelvin above room temperature. This could be attributed to the possibility of not.
This also could be due to. With the model set in two dimensions th e simulation was then converted to three. The model was changed to include the z- axis component to make a one hundred. The 3D model run could not find. The LOG file. The contact. The model was run with the implemented change to the. The 2D modeling system resulted in. The resi stance was then changed to a lump input. The inability to get a convergence was due to a high temperature variations from. This result led to the need to reduce the channel current. The mobility was lowered by one third by multiplying each.
The thermal c onductivity for the GaN laye rs was returned to. The 3D. This was then compar ed to the 2D results at the -1 volt gate. Figure 21 shows the comparison of the I-V curves for the. The first thing examined was the difference in the numerical solver used between.
The 2D model was then. The result was an instability in the Newton solver. Figure 22 shows the I-V curves for the 2D model using Block red. Figure 23 shows the global device temperature differences. These results show a divergence between the. Comparison of global device temperature K for Block and Newton solvers. This was now looked at as in issue that may affect the 3D modeling, since the. This led to consulting with Robin. Jones at Silvaco International, to be able to determine the differences.
The problem that. It is recommended to. The recommended solver for the. The effect of running non-isothermal models wa s done in order to verify the same results. The 2D and 3D models were converted to isothermal models by removing the. TEMP from the model statement.
The Models used the same values for the. This same. Figure 24 shows the. This result shows that the solvers are. Comparison of isothermal models for 2D and 3D. The previous results of the 3D model with the heating effects compared to the 2D. Th e results of the 3D model for the heating.
McAlister . The manipulation of changing the thermal constants that was done for 2D. This work uses the results from the 2D best match for the UC. Berkeley device to develope a best fit 3D model. The I-V characteristic curves were used to make the comparison between 2D and. This was done by using the same multiplication factor for each of the.
The best fit 2D model was run with the thermal properties removed. Several co mparisons were done with the. The best fit matched. I-V curves between 2D and 3D is shown in Figure This set of constants will be used. The results of the thermal 3D modeling. The heating effects of the device can be seen in the I-V characteristic curves.
This is similar to the he ating effects seen in the actual device I-V. This shows that as the average channel temperature increases the. This is the same result that was. The isothermal model curve is shown in. Comparison of the thermal model a nd isothermal model I A -V curves. The thermal picture for the 3D is show n in Figure This shows the thermal. The he at production on the drain side of the gate is shown in. The passivation oxide layer was hidden to be able to view this better. The device modeling can allow for other device characteristics to be looked at in. Figure 29 shows the electron concen tration in 3D the red plane is the 2DEG.
Figure 30 show s the thermal heating in the middle of the. Figure 31 shows the temperature profile of the device through the channel. Temperature K profile of th e device across the channel. The investigation to use the 3D system to model a diamond substrate was done by. The actual substrate was not manufactured and will be left to model as. The sapphire in the material statement was changed to diamond and this. This was so the elec trical properties of th e diamond would not be.
This was in serted into the model by changing TC. The final 3D model is shown in Appendix C. The results show the effect of heat removal from the channel of the device and the. Figure 32 shows the I-V curve comparison between the. The global device. This is the. The global device temperature comp arison is shown in Figure 33 showing. Comparison diamond and sapphire substrate I A -V curves. Comparison of global device Temperature K. The source of the heating wa s still at the drain side of the gate. Figure 34 shows. Figure 35 show the temperature profile. The channel temperature is lower resulting in a higher.
The electri c field peak occurs at the. The electric field pr ofile is shown in Figur e The peak self-. Thermal image of diamond substrate HEMT. Diamond substrate model channel temperature profile. The 2D modeling showed a better predictive ability. The 3D modeling better showed the actual ther mal effects that are.
Though the actu al device temperatures were not measured,. Through the comparison of several model runs and the testing of. The issues in this thesis were mainly seen when switching from a 2D model to a. The matching of th e 2D model was easily done based on the data of the actual. The 3D model was harder to match due to the time it took to run a simulation. There was an increase of about six to ten tim es longer than the 2D counterpart. The lack. ATLAS program resulted in process slowdow n.
The other issue that could not be. The effects of self-heating and thermal dissipation were key focuses for this. The operation of the device is clearly effected by the average channel. The temperature in the device with a diamond substr ate was modeled with. The results of the modeling show that improved. The improvement in temperature can be related to improved reliability. Arrhenius equation correlates th e failure rate to temperatur e in electronic components. Equation 5 is the Arrhenius equation used to solve for failure rate. The activation. Th e value of 1. Singhal et al. The value of 1.
The equation was solved using the final simulated. The result of the. Where; R is the failure rate, A is the empirical rate constant, E a is the activation energy. This thesis was successful in showi ng the modeling of the operation of GaN. The comparison of the two different modeling techniques. The 3D modeling is more accurate when.
This also shows that w ith improved thermal. The modeling that was done for this thesis incorporated a direct switch from a. Th is is not what is actually being produced for. GaN substrates. This substrat e is created on a silicon. The GaN will then be grown. The future modeling needs to incorporate this. If possible, thermal information should be obt ained as another mean s of verification of. Future modeling should be do ne in 3D due to bett er incorporation of.
The resu lts should also be compared to those of. Felbinger  who also tested GaN on Diam ond substrate. The bonding process used for. The effect of the. The different numerical solvers should be looked at more closely to ensure the. Also the different parts of the thermal equation should be. Future modeling should use the functions.
The data for the UC Berkeley. This will. July Management Conference , Houston, Kimerley, H. Wallace, and M. Sugimoto, H. Ueda, T. Uesugi, and T. Conference, April Postgraduate School, Monterey, California, Vargaftman, J. Meyer, L. Semiconductors and Semimetals , Volume 57, pp , Kisielowski, J. Kruger, M. Leung, R. Klockenbrink, H. Fujii, T. Maeda, T. Nishida, N. Kobayashi and M. Applied Physics Letters , Volume 73, Number 13, pp. Mastro, J. LaRoche, N. Bassim, C. Eddy Jr. Microelectronics Journal 36 , pp. Ambacher et al. Bernardini and V.
B Vol. October Albrecht, P. Ruden, S. Binari, and M. Electron Devices , vol. Singhal, T. Li, A. Hanson, R. Therri en, J. Johnson, W. Nagy, J. Marquart, P. Rajagopal, J. Roberts, E. Piner, I. Kizily alli, and K. Feldbinger, M. Chandra, Y. Sun, and L. Electron Device Letters , D x plane meshing x. Region Definitions. Defense Technical Information Center Ft. Belvoir, Virginia. Professor Todd R.
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