ISSN 1063-7397, Russian Microelectronics, 2016, Vol. 45, No. 1, pp. 41–53. © Pleiades Publishing, Ltd., 2016.
Original Russian Text © K.S. Grishakov, V.F. Elesin, N.I. Kargin, R.V. Ryzhuk, S.V. Minnebaev, 2016, published in Mikroelektronika, 2016, Vol. 45, No. 1, pp. 44–56.
Effect of a Diamond Heat Spreader on the Characteristics
of Gallium Nitride-Based Transistors
K. S. Grishakov, V. F. Elesin, N. I. Kargin, R. V. Ryzhuk, and S. V. Minnebaev
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Russia
Received April 22, 2015
Abstract⎯A problem, which concerns the effect of the diamond heat-spreading layer on the temperature and
voltage-current characteristics of gallium nitride (GaN) high-electron-mobility transistors (HEMTs) is
solved for the first time in a hydrodynamic model (which includes the continuity equation, Poisson equation,
and equations for electron and lattice temperatures). The mechanism of the occurrence of peak electron and
lattice temperatures (hot spots) is analyzed. It is shown that introducing a heat spreader considerably reduces
the maximum temperature (by 263 K for a sapphire substrate and by 163 K for a silicon carbide substrate) and
improves the voltage-current characteristics. The effectiveness of the heat spreader is evaluated depending on
its thickness, gate size, and substrate material to find the optimum design.
The problem of self-heating in high-electron-
mobility transistors (HEMTs) based on gallium
nitride (GaN) is of great interest: with an increase in
the temperature of such devices, their principal char-
acteristics (such as the drain current, generation rate,
gain, and output power) deteriorate and the transistor
lifetime gets shorter. Therefore, effective methods for
heat removal with the use of substrates, which possess
high thermal conductivity, are of particular interest.
The experimental and theoretical investigations
[1–3] have shown that the power dissipation in GaN
HEMTs results in hot spots, which occur in the neigh-
borhood of the transistor channel and have a size of
about one micrometer; the lattice temperature in these
spots considerably exceeds that in the other areas of
the device. Overheating in the hot spots causes the
degradation of the transistor properties or, sometimes,
irreparable damage of the device.
The use of expensive substrates with high thermal
conductivity allows one to reduce the maximum tem-
perature of the hot spot, but its high spatial inhomoge-
neity remains. This problem can be solved by intro-
ducing the heat spreader  close to the hot spots,
which removes heat directly from them.
In , the effect of the heat spreader has been ana-
lyzed in the heat equation with the hot spots being
simulated by heat sources. In , a thermodynamic
model has been used and it has been shown that a dia-
mond heat spreader considerably reduces the maxi-
mum lattice temperature. However, the mechanism of
the occurrence of hot spots and, therefore, the effect
of the heat spreader still remain underinvestigated.
Such an investigation is difficult to conduct in a ther-
modynamic model, which implies that the electron
temperature is equal to the lattice temperature. The
two, however, can differ considerably (by thousands of
The purpose of this work is to analyze the process
of hot spot occurrence and to investigate the effect of
the heat spreader on this process in a thermodynamic
model, which also allows one to calculate the electron
temperature. It is shown that the electron temperature
rises significantly in a small area, which plays an
important role in the formation of hot spots. This
allows one to optimize the design and parameters of
the heat spreader.
FORMULATION OF THE PROBLEM
AND NUMERICAL TECHNIQUES
In this work, a two-dimensional hydrodynamic
model (HDM) is used. The system of HDM equations
includes the Poisson equation, continuity equation,
and equations for electron and lattice temperatures.
Electron temperature and lattice temperature are
related through a collisional term of the Boltzmann
equation. The solution of the HDM equations allows
one to find the spatial distributions for the tempera-
ture and density of electrons, lattice temperature, elec-
tric fields, and potentials.
Figure 1 shows the two-dimensional geometry of
the GaN HEMT, which is similar to that in . The
semiconductor structure consists of a substrate 5 μm