1.
Introduction
The GaN HEMTs are anticipated to replace now available GaAs pHEMTs and realize the mainstream application in millimetric waveband due to outstanding performance. Studies of GaN HEMTs have been carried out widely, especially nowadays the reliability research of GaN HEMTs has achieved significant breakthrough[1–3]. GaN HEMTs are currently applied to radar amplifiers, electronic warfare, communication stations and high power RF application fields[4–7].
The self-heating effect is the main factor that limits the power density of GaN HEMTs. When GaN HEMTs devices work at high power, the bias voltages and currents are at high levels, which will produce a considerable quantity of heat. The heat will damage the devices if it cannot be dissipated away immediately[8]. The self-heating effect has seriously limited power density of GaN HEMTs and lowered the device stability[10, 11].
Techniques integrating diamond in close proximity to GaN have been developed to address the thermal limitation and provide a path to higher power GaN devices. The lattice mismatch between GaN and diamond is 11%, so the combination of diamond and GaN is very challenging. Their integration is prone to introducing large defect density and impeding heat dissipation. Therefore, a transition layer is always needed. Since 2010, GaN-on-diamond technology has been included in the DARPA ‘Near Junction Thermal Transport’ project, aiming at minimizing the boundary thermal resistance between GaN and diamond[9]. In 2013, Raytheon and TriQuint have successfully carried out GaN on diamond substrates via Near Junction Thermal Transport (NJTT)[11, 12]. The junction temperature decreased by 40%–45% and radio frequency power density increased three times at the same temperature compared to GaN on SiC. In 2013, GaN on diamond technology has been applied in the defense domain, such as radar and electronic warfare, and the commercial field, such as communication base stations and weather satellites. Meanwhile, for GaN-on-diamond RF power-amplifiers, triple improvement of the surface power density can realize the same RF power on a smaller wafer, which reduces production costs. These fundamental superiorities are anticipated to bring about orders of magnitude with greater reliability and lifespans, smaller size and weight systems due to reduced cooling needs, and significantly cheaper cost of operations due to the system’s dramatically reduced energy consumption[13].
After the fabrication of GaN-on-diamond HEMTs, the channel temperature of GaN HEMTs can be measured by Infrared Microscopy[14]. Stress in GaN integrated with diamond can be conducted by visible and ultraviolet (UV) micro-Raman spectroscopies[15, 16]. Interface thermal resistance in GaN-diamond is an important parameter, which greatly influence the heat dissipation from GaN to diamond, so thermal resistance can be characterized by three-dimensional Raman thermography mapping[17, 18]. All of these parameters have a great influence on the performance of GaN HEMTs.
Several simulations of thermal management in GaN HEMTs on different substrates (SiC, sapphire, diamond) have been studied[19–22]. However, their thermal power is small, and a transition layer between GaN and diamond has not been considered, and only the thermal boundary resistance is simulated in the model. So, the impacts of diamond substrate and transitional layer on the temperature distribution of high power GaN HEMTs are characterized via a theoretical model based on the finite element method (FEM). Also, simulation can predict the temperature distribution of high power GaN HEMTs, and give some suggestions on device fabrication. The structure of the near junction region is taken into account, including the thickness, area and shape of diamond substrate and the thickness and thermal conductivity of the transition layer. The research is carried out through a simulation software COMSOL Multiphysics. The geometry of the multi-fingers model and material properties are presented in Section 2; the numerical results and analyses are shown in Section 3; finally, some conclusions are drawn in Section 4.
2.
Simulation details
In this work, in order to estimate the heat spreading ability induced by diamond substrate, the temperature distribution of GaN-on-diamond HEMTs is simulated by thermal conduction equation[22]:
$$ ho {C_{ m{p}}}frac{{partial T}}{{partial {{t}}}} = nabla cdot kappa nabla T + Q,$$  | (1) |
where
ho $
m{p}}}$
A multi-finger structure model of GaN HEMTs is shown in Fig. 1, which is similar to the simulation model in other studies[19–22]. The model is a multilayer structure. The GaN buffer layer, transition layer and diamond substrate are the main layers. These layers are integrated into a chip and then soldered to a Cu heatsink with a AuSn joint layer. The geometric parameters and physical properties of materials in this model are shown in Tables 1 and 2, respectively.
| Symbol | Definition | Value |
| lCu | Length of Cu | 4 mm |
| wCu | Width of Cu | 4 mm |
| hCu | Thickness of Cu | 2 mm |
| ldiamond | Length of diamond | 2 mm |
| wdiamond | Width of diamond | 1 mm |
| hdiamond | Thickness of diamond | 60–160 μm |
| hAuSn | Thickness of AuSn | 20 μm |
| h1 | Thickness of transition layer | 100–500 nm |
| hGaN | Thickness of GaN layer | 1.2–2.4 μm |
| hg | Thickness of gate | 0.3 μm |
| ld | Gate to gate | 50 μm |
| lg | Length of gate | 0.5 μm |
| hAlGaN | Thickness of AlGaN | 22 nm |
Table1.
Geometric parameters of GaN MMIC.
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| Symbol | Definition | Value |
| lCu | Length of Cu | 4 mm |
| wCu | Width of Cu | 4 mm |
| hCu | Thickness of Cu | 2 mm |
| ldiamond | Length of diamond | 2 mm |
| wdiamond | Width of diamond | 1 mm |
| hdiamond | Thickness of diamond | 60–160 μm |
| hAuSn | Thickness of AuSn | 20 μm |
| h1 | Thickness of transition layer | 100–500 nm |
| hGaN | Thickness of GaN layer | 1.2–2.4 μm |
| hg | Thickness of gate | 0.3 μm |
| ld | Gate to gate | 50 μm |
| lg | Length of gate | 0.5 μm |
| hAlGaN | Thickness of AlGaN | 22 nm |
| Material | k(W/(m·K)) | ρ (kg/m3) | Cp (J/(kg·K)) | |
| GaN | 130 | 6070 | 490 | |
| Cu | 401 | 8960 | 384 | |
| Diamond | 1800 | 3515 | 516 | |
| AuSn | 57 | 14700 | 128 | |
| AlGaN | 25 | 6070 | 490 |
Table2.
Material properties used in simulation.
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| Material | k(W/(m·K)) | ρ (kg/m3) | Cp (J/(kg·K)) | |
| GaN | 130 | 6070 | 490 | |
| Cu | 401 | 8960 | 384 | |
| Diamond | 1800 | 3515 | 516 | |
| AuSn | 57 | 14700 | 128 | |
| AlGaN | 25 | 6070 | 490 |
The calculations are implemented by three dimensional finite element analysis with COMSOL Multiphysics. The GaN devices can provide RF output power on the order of 10–12 W/mm[7], so the thermal power density and thermal power are set to 10 W/mm and 40 W, respectively. The environment and initial temperature are set to 293.15 K, and the rest of the surfaces are set to natural air convection of h = 20 W/m2K (natural air convection is about 5–25 W/m2K, so 20 W/m2K is chosen)[23]. Thermal boundary resistance (TBR) of GaN-on-diamond is set to 12 m2K/GW[18]. Only a quarter of the model shown in Fig. 1 is simulated on account of its structural symmetry.
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Figure1.
(Color?online)?Schematic diagram of GaN HEMTs. (a) Cross section of GaN HEMTs. (b) Top view of GaN HEMTs. (c) Partial enlarged drawing of GaN HEMTs.
3.
Numerical result and discussion
The effects of transition layer and diamond substrate have on the thermal performance of GaN HEMTs are examined in detail in this section. Meanwhile, some results are obtained and discussed to illustrate the transition layer’s applicability for thermal management.
3.1
Temperature distribution
The thermal power is 40 W, and the thickness of GaN buffer layer, transition layer and diamond substrate are 2, 0.1 and 100 μm, respectively. Thermal conductivity of the transition layer is 60 W/mK. Under these conditions, the maximum temperature is 444 K, as is shown in Fig. 2(a), and heat is not uniformly distributed and concentrates in the multi-finger area (active region), which serves as the heat source. Fig. 2(b) is an enlarged view of the heat source, including diamond substrate, transition layer, GaN buffer layer and multi-finger area. The bottom temperature of diamond substrate is 320 K, temperature drops from 444 to 320 K along the vertical direction, indicating that diamond substrate has a good heat transfer capability. Fig. 2(c) is an isothermal diagram of the GaN surface, which is active-region-centric and propagates as an ellipse. The isothermal becomes sparse when it comes to the edge, indicating the drop of temperature slows down near the edge. Fig. 2(d) is a temperature profile of a lateral finger. The maximum temperature of the lateral finger is 432 K, which is lower than that in the middle, because the heat in the middle gate is hard to spread, while the heat on the edge of the gate is easy to spread. The temperature of the multi-fingers decreases from the middle to the edge.
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Figure2.
(Color?online)?Temperature distribution of (a) the overall module, (b) diamond and GaN, (c) GaN surface, and (d) a specific finger.
Fig. 3 is the cross section of the temperature distribution. The structure consists of GaN, transition layer and diamond substrate, omitting AuSn and Cu heatsink. Fig. 3(a) shows the temperature is dropping in the vertical direction. By comparing Figs. 3(b) and 3(c), channel temperature in the middle is higher than that of the edge, and the shape of heat propagation is also different, because the channel in the middle is greatly affected by the adjacent channel, while the channel near the edge is little affected by the adjacent channel.
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Figure3.
(Color?online)?Cross section of temperature distribution. (a) The overall module. (b) The channel in the middle. (c) The channel near the edge.
The maximum temperature in the simulation model is 444 K (~151 °C), which is consistent with the temperature distribution in the experiment made by Liu et al.[24]under the similar conditions. They fabricated the 3-inch GaN-on-diamond HEMTs with device-first transfer technology, and the thermal power density was 10 W/mm. So, it indicates that the simulation model is accurate and credible.
3.2
Diamond substrate thickness
The temperature distribution on diamond substrate is simulated by varying diamond thickness from 60 to 160 μm at the thermal power of 40 W. Transition layer thickness, GaN buffer layer thickness and thermal conductivity of transition layer are 100 nm, 2 μm and 60 W/mK, respectively. As shown in Fig. 4, temperature mainly focuses on the region directly under heat sources. The peak temperatures exist exactly in finger regions and vary from different positions. The temperature difference between the inner and outer peak is 15 K, which indicates a considerable variation in temperature between the fingers. Meanwhile, the results show that temperature decreases with the rise of diamond substrate thickness but with a decreasing trend. Fig. 4(b) is a partially enlarged drawing of Fig. 4(a). The region represents the area underneath two fingers and clearly shows the temperature varies with the thickness of the diamond. Along the direction of the dotted line shown in Fig. 4(a), the temperature reduces rapidly from 364 to 359 K with diamond thickness increasing from 60 to 80 μm and comparatively slowly from 352 to 351 K with diamond thickness from 140 to 160 μm. This is because the temperature gradient along the vertical direction of the diamond decreases with the increase of diamond thickness, as Fig. 5 shows, which leads to the slower heat dissipation rate.
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Figure4.
(Color?online)?Temperature distribution along the horizontal position of the diamond substrate for variable diamond thickness.
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Figure5.
(Color?online)?Temperature distribution along the vertical position of the diamond for different diamond thickness.
3.3
Diamond substrate area
Two common methods of increasing diamond substrate size are introduced in order to study the effects of diamond area on GaN HEMTs temperature. Method 1 increases the diamond area disproportionately (as Table 3 shows), while Method 2 increases the diamond area with an equal proportion of active region. The thermal power is 40 W and the thermal conductivity of the transition layer is 60 W/mK. The thicknesses of GaN buffer layer, transition layer and diamond substrate are 2, 0.1 and 100 μm, respectively. The results are shown in Fig. 6. The maximum temperature of GaN HEMTs reduces with the rise of diamond substrate size. Maximum temperature drops about 85 K using Method 2 and 95 K using Method 1 when the diamond substrate is three times the size of the active region. The increase of diamond area enables heat to diffuse not only in the vertical direction, but also in the horizontal direction, thus the device temperature drops rapidly. The downtrend of the maximum temperature becomes smaller when there is a further increase diamond area. When the diamond area reaches a certain extent, the generated heat dissipates in the planar direction without being limited by the edge, but diamond thickness gradually becomes the main factor that limits the thermal diffusion in the vertical direction. Different methods of increasing diamond substrate area cause the different maximum temperature of the GaN HEMT device, so the shape of diamond substrate affects device temperature. The reason is set out in Section 3.4.
| Diamond area (μm2) | Area ratio | Maximum temperature (K) | Diamond area (μm2) | Area ratio | Maximum temperature (K) |
| 1000 × 200 | 1 | 565 | 2000 × 600 | 6 | 456 |
| 1000 × 400 | 2 | 492 | 2000 × 700 | 7 | 451 |
| 1000 × 600 | 3 | 470 | 2000 × 800 | 8 | 449 |
| 1000 × 800 | 4 | 461 | 2000 × 900 | 9 | 445 |
| 1000 × 1000 | 5 | 457 | 2000 × 1000 | 10 | 444 |
Table3.
Increase the area of diamond with Method 1.
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| Diamond area (μm2) | Area ratio | Maximum temperature (K) | Diamond area (μm2) | Area ratio | Maximum temperature (K) |
| 1000 × 200 | 1 | 565 | 2000 × 600 | 6 | 456 |
| 1000 × 400 | 2 | 492 | 2000 × 700 | 7 | 451 |
| 1000 × 600 | 3 | 470 | 2000 × 800 | 8 | 449 |
| 1000 × 800 | 4 | 461 | 2000 × 900 | 9 | 445 |
| 1000 × 1000 | 5 | 457 | 2000 × 1000 | 10 | 444 |
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Figure6.
(Color?online)?Dependence of maximum temperature on the area ratio of diamond and GaN.
3.4
Diamond substrate shape
Thermal investigation on diamond shape is carried out to identify the effects on device temperature and the results are shown in Fig. 7. The area ratio of diamond and GaN is settled as 5, the temperature distribution and isotherm are simulated. Fig. 7 shows diamond shape has a certain impact on the temperature distribution. When the diamond substrate size is 1000 × 1000 μm2, the maximum temperature is 431 K. The isotherm spreads from the active region and distributes approximately parallel in the y axis direction and becomes sparser when getting away from the active region. When diamond substrate size is 2000 × 500 μm2, the maximum temperature is 437 K, which is higher than the former. The isotherm propagates as an ellipse in the active region and distributes approximately parallel in the x axis direction and becomes sparser when getting away from the active region. So, the heat dissipating performance of the former shape diamond is better.
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Figure7.
(Color?online)?Isothermal planforms based on two different diamond shapes. (a) 1000 × 1000 μm2. (b) 2000 × 500 μm2.
Fig. 8 is the temperature distribution of GaN surface along the horizontal position of GaN. The figure shows when diamond substrate size is 1000 × 1000 μm2, temperature is uniformly distributed, and the temperature distribution on the edge is nearly the same as that in the middle. For this diamond shape, there is abundant heat dissipation space in the y axis direction, so the overall temperature will be lower. Nevertheless, when diamond substrate size is 2000 × 500 μm2, the temperature on the edge is obviously smaller than that in the middle, which indicates that the heat on the edge can be quickly spread out, meanwhile, the heat cannot be diffused timely and the heat accumulation is caused due to the size limitation of the middle section in the y axis direction.
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Figure8.
(Color?online)?Temperature distribution along the horizontal position of GaN for different diamond shapes.
As a result, the temperature distribution of GaN HEMTs relates to the area and shape of diamond substrate. To achieve a favorable heat dissipation effect with settled diamond substrate area, the shape of diamond should contain as many isothermal curves as possible when the isothermal gradient is constant, just as shown in Fig. 9. In the figure, heat generated by the active region is transmitted to the edge of the substrate evenly, so heat gathering will not happen and the overall temperature of the device will be lower.
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Figure9.
(Color?online)?An ideal temperature distribution diagram.
3.5
Transitional layer thickness and thermal conductivity
As Fig. 10 shows, when thermal power is 40 W, the maximum temperature of GaN HEMTs is simulated as a function of thermal conductivity of the transition layer. The maximum temperature is reduced by increasing the thermal conductivity of the transition layer and drops quickly when thermal conductivity ranges from 1 to 10 W/mK. When the thickness of the transition layer is 500 nm, temperature drops 150 K with the thermal conductivity changing from 1 to 10 W/mK. When the thickness is only 100 nm, the corresponding temperature drop is 50 K. This indicates that thickness becomes the main factor that influences the maximum temperature of the device when the thermal conductivity of the transition layer is low. The maximum temperature drop becomes much slower when the thermal conductivity exceeds 10 W/mK. Under the same thermal conductivity, a thicker transition layer can further hinder thermal diffusion and result in a higher temperature of the device, which is especially pronounced when the thermal conductivity of the transition layer is small. When the thermal conductivity of the transition layer is over 40 W/mK, the maximum temperature of the device hardly decreases anymore. This is because the thermal boundary resistance is the main factor that prevents the thermal diffusion. Study on the effects that thermal conductivity and thickness of transition layer have on device temperature contributes to the choice of transition layer as the bonding layer of GaN on diamond.
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Figure10.
(Color?online)?Dependence of maximum temperature on thermal conductivity and thickness of transition layer.
4.
Conclusion
A theoretical thermal model based on the finite element method is presented for the heat spreading capability of GaN-on-diamond HEMTs. Also, we predict the temperature distribution of high power GaN-on-diamond substrate for HEMT applications. The results indicate that the diamond substrate and transition layer have certain influences on the temperature distribution and heat spreading capability. The existence of the transition layer will result in an increase in temperature, simply because the interface acts as a thermal resistance due to its low thermal conductivity. The results also show that the maximum temperature reduces with increasing diamond substrate thickness but with a decreasing trend, which shows a saturation behavior for a thicker diamond layer. The shape of diamond substrate also affects temperature performance. To achieve a favorable heat dissipation with settled diamond area, the shape of diamond substrate should contain as many isothermal curves as possible with a settled isothermal gradient.
From the simulation results, in order to weigh the cost and heat dissipation, the thickness of diamond and transition layer should be 100 μm and 100 nm, the area ratio of diamond and GaN should be 5, and the thermal conductivity of the transition layer should be higher than 40 W/mK. Under these conditions, the cost of diamond and the performance of the device are acceptable and balanced.
