Investigation on thermo-mechanical responses in high power multi-finger AlGaN/GaN HEMTs R. Zhang a , W.S. Zhao b , W.Y. Yin a,⇑ a Centre for Optical and EM Research, Zhejiang Provincial Key Lab for Sensing Technologies, State Key Lab of MOI, Zhejiang University, Hangzhou 310058, China b Microelectronics CAD Center, Key Lab of RF Circuits and Systems of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China article info Article history: Received 28 July 2013 Received in revised form 13 October 2013 Accepted 15 October 2013 Available online xxxx abstract Both transient temperature and thermal stress responses in high power multi-finger AlGaN/GaN high electron mobility transistors (HEMTs), caused by their self-heating effects, are characterized in the pres- ent study. Instead of using commercial software, self-developed algorithm based on hybrid time-domain finite element method (TD-FEM) is applied for thermo-mechanical co-simulation of such 3-D structure. The temperature-dependent properties of most constitutive parameters of all materials involved, in par- ticular for electrical conductivities, thermal conductivities, thermal expansion coefficients, and Young’s modulus, are described by several sets of nonlinear polynomial expressions. The algorithm accuracy is validated in detail, with good agreement achieved in comparison with the commercial software COMSOL. It is believed that this study will be useful for effectively evaluating the reliability and lifetime of AlGaN/ GaN HEMTs and their monolithic microwave integrated circuits (MMIC) used in high power communica- tion systems and radars. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction High power GaN devices are very important for the develop- ment of various communication and radar systems as they have strong capabilities for operating at high temperature with high output power [1]. On the other hand, their performance degrada- tion and reliability problems caused by self-heating have attracted much attention in the past one decade, and many theoretical and experimental studies have been carried out for characterizing elec- trothermal effects in AlGaN/GaN HEMTs [2–9]. Further, some ad- vanced thermal management methods have been developed to improve their heat dissipation and further suppress their channel temperature rise greatly [10–16]. Physically, it is evident that during the self-heating process taken place inside an AlGaN/GaN HEMT, there are strong multi- physics interactions among electrical, thermal and mechanical fields which do have certain impacts on its performance, reliability and even lifetime [17–19]. Mathematically, as the process of mul- tiphysics interaction occurring in a semiconductor device is time dependent, it is very difficult to develop one hybrid algorithm that can accurately and quickly predict its nonlinear transient thermal stress response in the presence of a periodic power signal. In the study of electrothermal effects in most active devices, it is well known that grid-based methods, such as finite difference method (FDM), finite element method (FEM), and boundary ele- ment method (BEM) have often been adopted for simulation. As the FEM is arithmetically fast and capable of handling irregular structures with high flexibility, it has been recognized as the most popular and efficient computational multiphysics method, as dem- onstrated in our previous studies [20–23]. In this paper, investigation on thermo-mechanical responses of some typical AlGaN/GaN HEMTs in the presence of a periodic sig- nal is performed using our self-developed hybrid TD-FEM algo- rithm. In Section 2, the geometry and layout of an AlGaN/GaN HEMT die is shown, with some analytical expressions for its tem- perature-dependent material parameters given. In Section 3, the hybrid TD-FEM algorithm is outlined and validated. In Section 4, numerical calculations are performed so as to capture both tran- sient temperature and thermal stress responses of the multi-fin- ger AlGaN/GaN HEMT dies. Finally, some conclusions are made in Section 5. 2. Device description 2.1. Device structure Fig. 1(a)–(c) shows the geometry of one AlGaN/GaN HEMT die. In its vertical direction, the substrate is 4H–SiC of 100 lm in thick- ness, while the die attach layer at its bottom is Sn–3.5Ag of 50 lm in thickness. Typically, the thicknesses of GaN, AlGaN, and the met- allization layout (Au) are chosen to be 2, 0.03, and 2 lm, respec- tively. The other parameters of the die are listed in Table 1. 0026-2714/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.microrel.2013.10.017 ⇑ Corresponding author. E-mail address: [email protected](W.Y. Yin). Microelectronics Reliability xxx (2013) xxx–xxx Contents lists available at ScienceDirect Microelectronics Reliability journal homepage: www.elsevier.com/locate/microrel Please cite this article in press as: Zhang R et al. Investigation on thermo-mechanical responses in high power multi-finger AlGaN/GaN HEMTs. Microelec- tron Reliab (2013), http://dx.doi.org/10.1016/j.microrel.2013.10.017
Please cite this article in press as: Zhang R et al. Investigation on thermo-mechanical responses in high power multi-finger AlGaN/GaN HEMTs. Mictron Reliab (2013), http://dx.doi.org/10.1016/j.microrel.2013.10.017
R. Zhang a, W.S. Zhao b, W.Y. Yin a,⇑a Centre for Optical and EM Research, Zhejiang Provincial Key Lab for Sensing Technologies, State Key Lab of MOI, Zhejiang University, Hangzhou 310058, Chinab Microelectronics CAD Center, Key Lab of RF Circuits and Systems of Ministry of Education, Hangzhou Dianzi University, Hangzhou 310018, China
a r t i c l e i n f o a b s t r a c t
Article history:Received 28 July 2013Received in revised form 13 October 2013Accepted 15 October 2013Available online xxxx
Both transient temperature and thermal stress responses in high power multi-finger AlGaN/GaN highelectron mobility transistors (HEMTs), caused by their self-heating effects, are characterized in the pres-ent study. Instead of using commercial software, self-developed algorithm based on hybrid time-domainfinite element method (TD-FEM) is applied for thermo-mechanical co-simulation of such 3-D structure.The temperature-dependent properties of most constitutive parameters of all materials involved, in par-ticular for electrical conductivities, thermal conductivities, thermal expansion coefficients, and Young’smodulus, are described by several sets of nonlinear polynomial expressions. The algorithm accuracy isvalidated in detail, with good agreement achieved in comparison with the commercial software COMSOL.It is believed that this study will be useful for effectively evaluating the reliability and lifetime of AlGaN/GaN HEMTs and their monolithic microwave integrated circuits (MMIC) used in high power communica-tion systems and radars.
� 2013 Elsevier Ltd. All rights reserved.
1. Introduction
High power GaN devices are very important for the develop-ment of various communication and radar systems as they havestrong capabilities for operating at high temperature with highoutput power [1]. On the other hand, their performance degrada-tion and reliability problems caused by self-heating have attractedmuch attention in the past one decade, and many theoretical andexperimental studies have been carried out for characterizing elec-trothermal effects in AlGaN/GaN HEMTs [2–9]. Further, some ad-vanced thermal management methods have been developed toimprove their heat dissipation and further suppress their channeltemperature rise greatly [10–16].
Physically, it is evident that during the self-heating processtaken place inside an AlGaN/GaN HEMT, there are strong multi-physics interactions among electrical, thermal and mechanicalfields which do have certain impacts on its performance, reliabilityand even lifetime [17–19]. Mathematically, as the process of mul-tiphysics interaction occurring in a semiconductor device is timedependent, it is very difficult to develop one hybrid algorithm thatcan accurately and quickly predict its nonlinear transient thermalstress response in the presence of a periodic power signal.
In the study of electrothermal effects in most active devices, it iswell known that grid-based methods, such as finite difference
method (FDM), finite element method (FEM), and boundary ele-ment method (BEM) have often been adopted for simulation. Asthe FEM is arithmetically fast and capable of handling irregularstructures with high flexibility, it has been recognized as the mostpopular and efficient computational multiphysics method, as dem-onstrated in our previous studies [20–23].
In this paper, investigation on thermo-mechanical responses ofsome typical AlGaN/GaN HEMTs in the presence of a periodic sig-nal is performed using our self-developed hybrid TD-FEM algo-rithm. In Section 2, the geometry and layout of an AlGaN/GaNHEMT die is shown, with some analytical expressions for its tem-perature-dependent material parameters given. In Section 3, thehybrid TD-FEM algorithm is outlined and validated. In Section 4,numerical calculations are performed so as to capture both tran-sient temperature and thermal stress responses of the multi-fin-ger AlGaN/GaN HEMT dies. Finally, some conclusions are madein Section 5.
2. Device description
2.1. Device structure
Fig. 1(a)–(c) shows the geometry of one AlGaN/GaN HEMT die.In its vertical direction, the substrate is 4H–SiC of 100 lm in thick-ness, while the die attach layer at its bottom is Sn–3.5Ag of 50 lmin thickness. Typically, the thicknesses of GaN, AlGaN, and the met-allization layout (Au) are chosen to be 2, 0.03, and 2 lm, respec-tively. The other parameters of the die are listed in Table 1.
(c)Fig. 1. (a) Schematic diagram of a AlGaN/GaN MMIC die, (b) multi-gate HEMT structure showing source (S), gate (G), and drain (D) fingers, and (c) cross-sectional view of theAlGaN/GaN HEMT die [13].
Table 1Geometrical parameters of the AlGaN/GaN HEMT MMIC die.
Parameters Definitions Value (lm)
Ldie Length of MMIC die 2000wdie Width of MMIC die 700LA Length of HEMT array 1100w Width of HEMT array 150Lp Gate-to-gate pitch spacing 50Lg Gate length 0.5tAu Thickness of metallization layer 2hAlG Thickness of AlGaN layer 0.03hGaN Thickness of GaN layer 2hSiC Thickness of SiC layer 100hDA Thickness of die attach Sn–3.5Ag 50
2 R. Zhang et al. / Microelectronics Reliability xxx (2013) xxx–xxx
2.2. Material parameters
In the AlGaN/GaN HEMT, most material parameters involvedare temperature-dependent, in particular for electrical conductiv-ity r (S/m), thermal conductivity j (W/m K), thermal expansioncoefficient a (ppm/K), and Young’s modulus E (GPa). However,the material density q (kg/m3), specific heat c (J/kg K), and Pois-son’s ratio t are not sensitive to temperature variation, and theycan be treated as temperature-independent. The related materialproperties at room temperature are listed in Table 2.
Using the technique of curve fitting, their temperature-depen-dent properties, denoted by x(T), can be expressed by
xðTÞ ¼X4
n¼0
cnTn; TL 6 T 6 TH ð1Þ
where cn (n = 0, 1, 2, 3 and 4) are the fitting coefficients of thepolynomial coefficients, T is temperature (K), and [TL, TH] is the
Table 2Material parameters in the AlGaN/GaN HEMT at room temperature (T = 300 K).
Please cite this article in press as: Zhang R et al. Investigation on thermo-mechatron Reliab (2013), http://dx.doi.org/10.1016/j.microrel.2013.10.017
applicable temperature range [21]. Table 3 summarizes all valuesof cn of the most materials involved [20–27], with their applicabletemperature ranges shown [21].
3. Outline of numerical method and validation
3.1. Hybrid TD-FEM algorithm
Although the simulation process of a realistic AlGaN/GaN HEMTusing some commercial software are very time consuming, mostresearchers still would like to use them for its 3-D electrothermalcharacterization. While for its transient thermo-mechanical simu-lation, even with the help of ANSYS or COMSOL software, very fewstudies have been reported till now. Here, the self-developed hy-brid TD-FEM algorithm is adopted to investigate the transientself-heating effects in the AlGaN/GaN HEMT die, which has beenimplemented successfully in the study of 3-D high density inter-connects, LDMOSFET, and through-silicon vias in the authors’ pre-vious studies [20–23].
With one time-dependent signal applied, the time-dependenttemperature distribution over the AlGaN/GaN HEMT die, contrib-uted by its self-heating effects, can be described by a 3-D differen-tial equation, i.e.
qc @Tð~r;tÞ@t þr½�jðTÞrTð~r; tÞ� ¼ f1ð~r; T; tÞ
TjCa¼ Ta
@T@n
��Cq¼ �hðT � TaÞjCq
8>><>>: ð2Þ
where Tð~r; tÞ is the 3-D temperature distribution, f1ð~r; T; tÞ is thetransient heat generation rate of the heat source, h is the convectioncoefficient (in W/m2 K), Ta is the ambient temperature, Ca and Cq
are the Dirichlet and Neumann boundaries, respectively, and o/@nis the normal derivative operator along the outward direction of Cq.
To solve (2), we need to transform it into the matrix form, i.e.
HeT@TeðtÞ@t
þ KeTðTÞT
eðtÞ ¼ Q eTðT; tÞ ð3Þ
where HeT , Ke
T , and Q eT are the heat capacity, thermal conductivity,
and thermal load vector matrices, respectively, and they are furthercalculated by
HeT ¼
ZvðeÞ
qcNT Ndv ð4aÞ
nical responses in high power multi-finger AlGaN/GaN HEMTs. Microelec-
R. Zhang et al. / Microelectronics Reliability xxx (2013) xxx–xxx 3
KeTðTÞ ¼
ZvðeÞ
jðTÞr � NTr � Ndv þZ
CðeÞq
NT NhdS ð4bÞ
Q eTðtÞ ¼
ZvðeÞ
flðT; tÞNdv þZ
CðeÞq
hTambientNdS ð4cÞ
where v(e) and Ceq denote the volume and convective boundary of
each element, and N represents the selected shape function.The thermal stress over the die can be described by the differ-
ential equation as follows:
q @2ui@t2 þ l @ui
@t ¼ fi þ@rij
@xj
eij ¼ eEij þ eTh
ij
eEij ¼ ð@ui=@xj þ @uj=@xiÞ=2
eThij ¼ aðTÞDTdij
rij ¼ DijkleEkl ði; j; k; l ¼ 1;2;3Þ
uijCu¼ ui
rijnjjCr¼ ki
8>>>>>>>>>>>>><>>>>>>>>>>>>>:
ð5Þ
where q is the material density, l is the thermal stress dampingcoefficient, ui is the thermal displacement component, rij is thethermal stress tensor, eij is the strain tensor, DT is the change intemperature vector, fi is the applied stress, and the forth-order ten-sor Dijkl is the elastic constant [21]. Here, the plastic expansion inthe die is excluded in our simulation.
In (5), the fourth-order tensor Dijkl is the elastic constant calcu-lated by
Dijkl ¼EðTÞ1þ t
dikdjl þEðTÞt
ð1þ tÞð1� 2tÞ dijdkl ð6Þ
where dij is the Kronecker Delta function, and
rij ¼1; i ¼ j
0; i–j
�ð7Þ
To solve (5), it should also be transformed into the matrix form,i.e.
MeF@2ae
@t2 þHeF@ae
@tþ Ke
F ae ¼ PeF ð8Þ
where MeF , Ke
F , HeF , and Pe
F are the mass, stiffness, damping, and heatload matrices, respectively. They are further expressed by
MeF ¼ q
ZvðeÞ
NT Ndv ð9aÞ
Please cite this article in press as: Zhang R et al. Investigation on thermo-mechatron Reliab (2013), http://dx.doi.org/10.1016/j.microrel.2013.10.017
HeF ¼ l
ZvðeÞ
NT Ndv ð9bÞ
KeF ¼
ZvðeÞ
BT DðTÞBdv ð9cÞ
PeF ¼
ZvðeÞðBT DðTÞeTh þ NT�f ðT; tÞÞdv þ
ZCðeÞr
NT�kdC ð9dÞ
where B and D are the strain and elasticity matrices, respectively.The transient thermal stress is finally calculated by
rij ¼12
Dijklðlk;l þ ll;kÞaðTÞDTDijkldkl ð10Þ
In summary, according to (2), (3), (4a)–(4c), (5)–(8), (9a)–(9d),(10), and applying the boundary conditions, both linear systemequations derived from the heat conduction and the thermal stressfield functions can be expressed as
Ax ¼ b ð11Þ
where the matrix A is symmetric and positive-definite.Further, such two sets of coupled linear matrix equations can be
co-solved using a preconditioned conjugated gradient technique(PCG) with an element by element approximate factorizationadopted [20,21]. In the solution of them, direct and indirect meth-ods can be applied, respectively. In the direct method, two sets ofequations should be assembled into a large one, and it takes a lotof computer memory. While in the indirect method, two sets ofequations are solved sequentially, where the result of the formerserves as the condition of the latter one. This iterative process isnot terminated until the solution meets the convergence criterions,and it is unconditionally stable. Therefore, both static and transienttemperature and thermal stress distributions over the above struc-ture can be captured numerically.
3.2. Algorithm validation
At first, we validate our hybrid TD-FEM algorithm by calculatingthe static temperature distribution on the surface of a six-finger Al-GaN/GaN HEMT, as plotted in Fig. 2. In our simulation, the dissi-pated power at each source-drain channel is chosen to be 3 W/mm, and the thermal conductivity of air in the upper space is equalto 0.02624 W/m K [28]. The thicknesses of AlGaN, GaN, SiC, and Cuare 20 nm, 1.5 lm, 400 lm, and 1 cm, respectively. The size of heatsource shown in one rectangular geometry is 4 lm wide and 10 nm
nical responses in high power multi-finger AlGaN/GaN HEMTs. Microelec-
Fig. 2. Simulated surface temperature distribution of an AlGaN/GaN HEMT with sixgate fingers. Red line: our FEM result, and empty square dot: Fig. 5 of referencepaper [28]. (For interpretation of the references to colour in this figure legend, thereader is referred to the web version of this article.)
4 R. Zhang et al. / Microelectronics Reliability xxx (2013) xxx–xxx
thick, and it is separated by 100 lm from its neighbor one. Becauseof its symmetry, only half of the structure is simulated here. It isevident that the predicted temperature distribution obtained usingour simplified TD-FEM algorithm agrees well with that shown inFig. 5 in the reference paper [28].
Secondly, our algorithm is validated by simulating the transienttemperature response of a single-finger AlGaN/GaN HEMT asshown in Fig. 3(a) [29]. The dissipation power in its channel isknown with its duty cycle and frequency set to be 50% and50 kHz, respectively. The thicknesses of GaN, AlGaN, and SiC sub-strate are 2, 0.025, and 100 lm, respectively, where the tempera-ture of substrate bottom is kept to be 300 K and the othersurfaces are set to be thermal insulation. It is observed that thecaptured transient maximum channel temperature using our TD-FEM algorithm agrees well with that of commercial software, andthe maximum relative error is about 3.1% [29].
Finally, we validate our hybrid TD-FEM algorithm by simulatingthe transient maximum temperature and thermal stress responseof a copper interconnect as shown in Fig. 4(a). A double exponen-tial EMP is injected into such an interconnect, and it is given by
EðtÞ ¼ E0kðe�at � e�btÞ ð12Þ
where the pulse amplitude E0 = 10 kV/m, k = 1 is the correction fac-tor, a = 7 � 10�6/s, and b = 2 � 10�9/s.
-
Pow
er
Density
(W/u
m)
(a)Fig. 3. (a) Cross-sectional view of a single-finger AlGaN/GaN HEMT, and (b) its maximumperiodic pulse of duty cycle 50% and frequency 50 kHz [29].
Please cite this article in press as: Zhang R et al. Investigation on thermo-mechatron Reliab (2013), http://dx.doi.org/10.1016/j.microrel.2013.10.017
For comparison, both maximum temperature and thermalstress of the interconnect are plotted in Fig. 4(b), which aresimulated using our algorithm and the commercial software COM-SOL, respectively, with good agreement also obtained betweenthem. In our simulation, the bottom surface of silicon substrate iskept to be 300 K, while the other surfaces are set to be thermalinsulation, respectively.
4. Numerical results and discussion
In this section, thermo-mechanical co-simulations are per-formed using our developed hybrid TD-FEM algorithm to predictself-heating effects in the multi-finger AlGaN/GaN HEMT dies withhigh power handling capability.
4.1. Thermo-mechanical responses
We at first carry out static thermo-mechanical studies on the 4-,12-, 22-, and 24-finger AlGaN/GaN HEMTs with a uniform gatepitch spacing of 50 lm and 5 W/mm heat dissipation along theirgates assumed. By taking the structure symmetry into account,only a quarter of each geometry is plotted in Fig. 5(a) and (b),respectively.
During our thermo-mechanical co-simulation, as shown inFig. 5(a), the thermal conductivities, thermal expansion coeffi-cients, and Young’s modulus of the materials involved are treatedto be temperature-dependent (see Table 3) and independent(T = 300 K), respectively. The heat convection coefficient at thedie bottom of micro-channel wall is set to be 5 W/cm2 K [13],and the other boundaries are assumed to be thermal insulation,respectively. It is observed that the temperature-dependent prop-erties of the materials must be taken into account in the co-simu-lation, and otherwise, the maximum temperature of the AlGaN/GaN HEMT is under estimated seriously.
Fig. 5(b) shows the temperature distributions on the top of 4-,12-, and 24-finger AlGaN/GaN HEMTs, respectively. It is obviousthat the larger finger number of the transistor, the higher the max-imum temperature will be, while the heat is mainly produced inthe gate close to the drain contact where most of the potential dropoccurs in these transistors. The non-uniform temperature distribu-tion on the top of AlGaN/GaN HEMT, in particular for larger fingernumber, does degrade its electrical performance or reliability. Un-der such circumstances, we should optimize its layout by employ-ing a non-uniform gate pitch design [13].
Fig. 6(a) and (b) shows the 3-D temperature and thermal stressdistributions of the 22-finger AlGaN/GaN HEMT, respectively,
450 460 470 480 490 500 5100.001
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
Maxim
um
Tem
pera
ture
(K)
Power Density
Time (µs)
340
360
380
400
420
440
460
480
500
520
540
Reference ResultTD-FEM
(b)temperature response with its dissipation power density known and described by a
nical responses in high power multi-finger AlGaN/GaN HEMTs. Microelec-
(b)(a)Fig. 4. (a) Geometry of an interconnect with an EMP applied, and (b) its maximum temperature and thermal stress responses.
Fig. 6. (a) 3-D temperature and (b) 3-D thermal stress distributions of the 22-fingerAlGaN/GaN HEMT with 5 W/mm heat dissipation along its gates.
20
40
60
80
100
120
140
160
180
Tem
pera
ture
(o C)
Tem
pera
ture
(o C)
Position (µm) Position (µm)
T-dep. para T-indep. para
22 23 24 25 26 27 28100
120
140
160
180
0 200 400 600 800 1000 0 200 400 600 800 100020
40
60
80
100
120
140
160
180
22 23 24 25 26 27 28306090120150180
24 HEMTs12 HEMTs
4 HEMTs
(a) (b)Fig. 5. Temperature distributions on the top of (a) 22-, and (b) 4-, 12-, and 24-finger AlGaN/GaN HEMTs, respectively.
R. Zhang et al. / Microelectronics Reliability xxx (2013) xxx–xxx 5
where the maximum temperature and the maximum thermalstress are captured and given by 435 K and 455 MPa, respectively.
Please cite this article in press as: Zhang R et al. Investigation on thermo-mechatron Reliab (2013), http://dx.doi.org/10.1016/j.microrel.2013.10.017
Further, the impacts of finger number and dissipated power onthe maximum temperature and thermal stress are examined andplotted, as shown in Fig. 7(a) and (b), respectively. It is evident thatthe larger the finger number of the AlGaN/GaN HEMT, the higher ofits maximum temperature as well as its maximum thermal stresswill be reached. In particular, for the 22-finger case, its non-uni-form thermal stress distribution does degrade its electrical perfor-mance and reliability. Under such circumstances, we need tooptimize its layout by employing a non-uniform gate pitch design[13].
4.2. Response to periodic power pulse
The time-dependent maximum temperature and thermal stressof the AlGaN/GaN HEMT die in the presence of a periodic pulsepower signal are further simulated here, and its duty cycle and per-iod are set to be 50% and 20 ls, respectively [29]. Mathematically,it is described by
PðtÞ ¼ c þ ae�bt ; nT 6 t 6 ð0:5þ nÞT0; ð0:5þ nÞT < t 6 ðnþ 1ÞT
(ð13Þ
where a = 0.7172 � 10�3, b = 0.3121 � 106, c = 0.56 � 10�2, and Trepresents its period (n = 0, 1, 2, . . .). We also choose the AlGaN/GaN HEMT with 22 fingers as an example, where most materialparameters are treated to be temperature-dependent in our simula-tion. The heat convection coefficient at the die bottom of micro-channel wall is set to be 5 W/cm2 K [13], and the other boundariesare also assumed to be thermal insulation, respectively. On theother hand, the innermost and bottom surfaces of the micro-chan-
nical responses in high power multi-finger AlGaN/GaN HEMTs. Microelec-
(a) (b)Fig. 7. Maximum temperature and maximum thermal stress of the AlGaN/GaN HEMT as functions of its (a) finger number and (b) dissipated power density, respectively.
0 10 20 30 400
1
2
3
4
5
6
Time (µs) Time (µs)
Pow
er
Density
(W/m
m)
300
320
340
360
380
Maxim
um
Tem
pera
ture
(K)
10 20 300 400
1
2
3
4
5
6
Pow
er
Density
(W/m
m)
0
100
200
300
400
Maxim
um
Therm
alS
tress
(MP
a)
A
B
A
B
(a) (b)Fig. 8. (a) Maximum temperature and (b) maximum thermal stress responses of the 22-finger AlGaN/GaN HEMT die under the impact of a periodic pulse power signal.
Fig. 9. (a) 3-D temperature and (b) 3-D thermal stress distributions at t = 15 ls ofthe 22-finger AlGaN/GaN HEMT die under the impact of a periodic pulse powersignal.
6 R. Zhang et al. / Microelectronics Reliability xxx (2013) xxx–xxx
Please cite this article in press as: Zhang R et al. Investigation on thermo-mechatron Reliab (2013), http://dx.doi.org/10.1016/j.microrel.2013.10.017
nel wall are set to be moved freely, while the other boundaries arefixed with no displacement. The captured time-dependent maxi-mum temperature and thermal stress are plotted in Fig. 8(a) and(b), respectively. It is observed that the temperature and thermalstress responses follow the similar periodic variation trends withchanging the dissipated power. At t = 15 ls (Point A), the 3-D tem-perature and thermal stress distributions of such 22-finger AlGaN/GaN HEMT die are plotted in Fig. 9(a) and (b), respectively, wherethe net temperature rise with the first pulse injected is only aboutDTmax|t=15 ls � (306–300) K = 6 K, and the corresponding maximumthermal stress Fmax|t=15 ls � 32 MPa. While at t = 30 ls (Point B), thenet maximum temperature rise is as high as DTmax|t=30 ls � (370–300) K = 70 K. In comparison with Point A, the residual thermalstress DFmax = Fmax (t = 30 ls) � Fmax(t = 15 ls) � (328–32)MPa = 296 MPa, and its concentration region is mainly in the chan-nel of multi-finger AlGaN/GaN HEMT.
5. Conclusion
In this paper, using our developed hybrid TD-FEM algorithm in-stead of the commercial software, both temperature and thermalstress responses of the multi-finger AlGaN/GaN HEMT die, in par-ticular for the applied periodic pulse power signal, have beeninvestigated numerically in this paper. In our simulations, the tem-perature-dependent properties of most constitutive parameters,such as electrical conductivities, thermal conductivities, thermalexpansion coefficients, and Young’s modulus of all materials in-volved, have been taken into account appropriately. With its fur-ther implementation, we can accurately predict the effects of the
nical responses in high power multi-finger AlGaN/GaN HEMTs. Microelec-
R. Zhang et al. / Microelectronics Reliability xxx (2013) xxx–xxx 7
applied pulse period, width, repetition frequency and its magni-tude on the maximum temperature, maximum thermal stress aswell as their accumulation regions in the multi-finger AlGaN/GaNHEMT die. All these information will be useful and furtherexploited for its effective thermal management and physicalprotection.
Acknowledgments
This work was supported in part by the National NSFC underGrant 61171037, the Specialized Research Fund for the DoctoralProgram of Higher Education (SRFDP) under Grant20100101110065, and the State Key Lab of MOI, Zhejiang Univer-sity, China.
References
[1] Mishra UK, Parikh P, Wu YF. AlGaN/GaN HEMTs – an overview of deviceoperation and applications. Proc IEEE 2002;90(12):1022–31.
[2] Ardaravicius L, Liberis J, Matulionis A, Eastman LF, Shealy JR, Vertiatchikh A.Self-heating and microwave noise in AlGaN/GaN. Phys Status Solidi A2004;201(2):203–6.
[3] Turin VO, Balandin AA. Electrothermal simulation of the self-heating effects inGaN-based field-effect transistors. J Appl Phys 2006;100(5). 054501-054501-8.
[4] Hu WD, Chen XS, Quan ZJ, Xia CS, Lu W, Ye PD. Self-heating simulation of GaNbased metal-oxide-semiconductor high-electron-mobility transistorsincluding hot electron and quantum effects. J Appl Phys 2006;100(7).074501-074501-9.
[5] Kuball M, Riedel GJ. Time resolved temperature measurement of AlGaN/GaNelectronic devices using micro-Raman spectroscopy. IEEE Electron Dev Lett2007;28(2):86–9.
[6] Heller ER, Crespo A. Electro-thermal modeling of multifinger AlGaN/GaNHEMT device operation including thermal substrate effects. MicroelectronReliab 2008;48(1):45–50.
[7] Vitusevich SA, Kurakin AM, Klein N, Petrychuk MV, Naumov AV, Belyaev AE.AlGaN/GaN high electron mobility transistor structures: self-heating effect andperformance degradation. IEEE Trans Dev Mater Reliab 2008;8(3):543–8.
[8] Wang XD, Hu WD, Chen XS, Lu W. The study of self-heating and hot-electroneffects for AlGaN/GaN double-channel HEMTs. IEEE Trans Electron Devices2012;59(5):1393–401.
[9] Heller E, Choi S, Dorsey D, Vetury R, Graham S. Electrical and structuraldependence of operating temperature of AlGaN/GaN HEMTs. MicroelectronReliab June 2013;53(6):872–7.
[10] Binari SC, Ikossi K, Roussos JA, Kruppa W, Doewon P, Dietrich HB, et al.Trapping effects and microwave power performance in AlGaN/GaN HEMTs.IEEE Trans Electron Dev Mar 2001;48(3):465–71.
Please cite this article in press as: Zhang R et al. Investigation on thermo-mechatron Reliab (2013), http://dx.doi.org/10.1016/j.microrel.2013.10.017
[11] Braga N, Mickevicius R, Gaska R, Hu X, Shur MS, Khan MA, et al. Simulation ofhot electron and quantum effects in AlGaN/GaN heterostructure field effecttransistors. J Appl Phys 2004;95(11):6409–13.
[12] Calame JP, Myers RE, Wood FN, Binari SC. Simulations of direct die attachedmicrochannel coolers for the thermal management of GaN-on-SiC microwaveamplifiers,. IEEE Trans Compon Pack Technol 2005;28(4):797–809.
[13] Garven M, Calame JP. Simulations and optimization of gate temperatures inGaN-on-SiC monolithic microwave integrated circuits. IEEE Trans ComponPackag Technol 2009;32:63–72.
[14] Hu WD, Chen XS, Yin F, Zhang JB, Lu W. Two-dimensional transientsimulations of drain lag and current collapse in GaN-based high-electronmobility transistors. J Appl Phys 2009;105(8). 084502-084502-7.
[15] Lin CH, Merz TA, Doutt DR, Hetzer MJ. Nanoscale mapping of temperature anddefect evolution inside operating AlGaN/GaN high electron mobilitytransistors. Appl Phys Lett 2009;95(3). 033510-033510-3.
[16] King JB, Brazil JT. Nonlinear electrothermal GaN HEMT model applied to high-efficiency power amplifier design. IEEE Trans Microw Theory Technol Jan.2013;61(1):444–54.
[17] Bykhovski A, Gelmont B, Shur M. The influence of the strain-induced electricfield on the charge distribution in GaN–AlN–GaN structure. J Appl Phys1993;74(11):6734–9.
[18] Rivera C, Muñoz E. The role of electric field-induced strain in the degradationmechanism of AlGaN/GaN high-electron-mobility transistors. Appl Phys Lett2009;94(5). 053501-053501-3.
[19] Ancona MG, Binari SC, Meyer DJ. Fully coupled thermoelectromechanicalanalysis of GaN high electron mobility transistor degradation. J Appl Phys2012;111(7). 074504-074504-16.
[20] Ren Z, Yin WY, Shi YB, Liu QH. Thermal accumulation effects on the transienttemperature responses in LDMOSFETs under the impact of a periodicelectromagnetic pulse. IEEE Trans Electron Dev 2010;57(1):345–52.
[21] Wang XP, Yin WY, He S. Multiphysics characterization of transientelectrothermomechanical responses of through-silicon vias applied with aperiodic voltage pulse. IEEE Trans Electron Dev 2010;57(6):1382–9.
[22] Yi M, Yin WY. Electrothermomechanical analysis of partially insulated field-effect transistors using hybrid nonlinear finite element method. MicroelectronReliab 2011;51(5):895–903.
[23] Zhao WS, Wang XP, Yin WY. Electrothermal effects in high density through-silicon via (TSV) arrays. Prog Electromagn Res 2011;115:223–42.
[24] Burgemeister EA, Muench VW, Pettenpaul E. Thermal conductivity andelectrical properties of 6H silicon carbide. J Appl Phys 1979;50(9):5790–4.
[25] Reeber RR, Wang K. Lattice parameters and thermal expansion of GaN. J MaterRes 2000;15(1):40–4.
[26] Reeber RR, Wang K. High temperature elastic constant prediction of somegroup III-nitrides. MRS Internet J Nitride Semiconduct Res 2001;6(3):1–5.
[27] Zou J, Kotchetkov D, Balandin AA, Florescu DI, Pollak FH. Thermal conductivityof GaN films: effects of impurities and dislocations. J Appl Phys2002;92(5):2534–9.
[28] Ko G, Kim J. Thermal modeling of graphene layer on the peak channeltemperature of AlGaN/GaN high electron mobility transistors. ElectrochemSolid-State Lett 2009;12(2):H29–31.
[29] Zhang YM, Feng SW, Zhu H, Zhang JW, Deng B. Two-dimensional transientsimulations of the self-heating effects in GaN-based HEMTs. MicroelectronReliab 2013;53(5):694–700.
nical responses in high power multi-finger AlGaN/GaN HEMTs. Microelec-
