# Three Dimensional Electro-Thermodynamic

Analysis for GaN Light Emitting Diodes

**Abstract**

Improvement in temperature characteristics of GaN LEDs is important for realizing
reliable devices operating at high temperatures. In this article, the thermal
characteristics of GaN LEDs have been analyzed by using the ** ATLAS**
three dimensional thermal conduction model and thermal heat model. Maximum operation
temperature has also been calculated. It was shown that the distribution of
lattice temperature using the conventional structure.

**Introduction**

Nitride-based compound wide bandgap semiconductor materials such as GaN, InGaN and AlGaN or AlInGaN have been attract the greatest interest as materials for high performance light emitting devices in the blue to ultraviolet wavelength region light emitting diodes(LEDs), and laser diodes. These LEDs are used extensively as back lighting in liquid-crystal displays, traffic light lamps, and indoor or outdoor displays.

Analysis of thermal characteristics for GaN LEDs have been carried out by using the three-dimensional thermal conduction model. In this article, three-dimensional analysis introduced the thermal conduction model and the self-heating effect as well.

**Simulation Model**

The polarization of the wurtzite materials with built-in electrical fields in semiconductors is characterized with two components, spontaneous polarization, Psp, and piezoelectric polarization, Ppi.

**Polarization in Wurtzite Materials**

eq. 1 eq. 2

where E31 and E33 are piezoelectric constants, and the a0 parameter is the lattice constant of the material layer in question (as is the substrate value).

**Self Heating Effect**

The heat flow equation added to the primary equation such as poisson and carrier continuous equation for the device characteristics.

eq. 3 eq. 4

where C is the heat capacitance per unit volume, and k is the thermal conductivity,
and H is the heat generation, Tl is the local lattice temperature and Cp is
the specific heat and is the density
of the material.

**Heat Generation**

When carrier transport is handled in the drift-diffusion the heat generation term, H, used in equation 3 has

eq. 5 is the Joule heating term

is the Recombination and Generation Heating and Cooling term

accounts for the Peltier and Thomson Effects.

**Simulation Results for Thermal Resistance**

A schematic three dimensional structure shows in Figure 2. This structure is the conventional LED structure GaN-sapphire. The structure combinated with GaN/AlGaN/InGaN/GaN on sapphire.

Figure 1. Thermal conductivity and specific heat for
metal and semiconductor materials |

Figure 2. Simulated GaN LED structure. |

Based on the calculation results, the thermal resistance Rth of the device was derived using the following equation,

eq. 6 eq. 7

where the Tact is temperature rise
in the active layer and Qtotal is the total heat generation. The definition
is practical because the entire input power is included in Qtotal. However,
it should be noted that the thermal resistance calculated by Eq.6 is a lumped
value and differ depending on the spacial distribution of the heat source.

In Figure 3, the maximum temperature 419 K distributed around the active layer and the edge of the mesa. On two dimensionally, the lattice temperature shows along the active layer vertically.

Figure 3. Lattice Temperature Distribution on the
LED at Anode Current 600mA. |

Figure 4. Lattice Temperature on the center of the
InGaN active layer on 2 dimension at Anode Current is 600mA. |

In Figure 5, the junction heating effect on LEDs can be further interpreted using the variation injection currents. When the driving current increased from 0.2 to 0.6A, the peak wavelength of LEDs showed a drastic red shift from 565nm to 576nm.

Figure 5. Peak Wavelength as a function of injection
current. |

**Conclusions**

Thermal characteristics of GaN LEDs have been analyzed by using the ** ATLAS**,
three-dimensional thermal heat flow and heating model. The dependence of the
thermal resistance and the current flow effect is more effective the maximum
operation temperature Tmax. This depend on the conductivity of material and
device structure. This operation temperature depend on the injection current
makes the peak wavelength red shift.