``Alles Vergängliche ist nur ein Gleichnis.''
Johann Wolfgang von Goethe2.1
MANY challenges faced in modern semiconductor devices are related to heating phenomena. Since shrinking the device feature size causes higher power loss densities and therefore higher and faster temperature evolution inside the device structure, many additional problems occur due to material-related constraints because the produced heat cannot be transported to the heat sink fast enough. Hence the surrounding device structure heats up and the global microelectronic chip heats up globally.
Since the absolute temperature is not zero, matter is in steady
motion at least in terms of BROWN's2.2 molecular movements.
Therefore, the most probable consequence is that the number of possible states
of a closed system, e.g the quantum states, is increasing until a temporary
state of thermal equilibrium has been reached. Hence, also the entropy which
represents the information about the reachable states in a system is
not decreasing spontaneously.
This fundamental theorem of thermodynamics and its derivations challenge today's
electronic devices including the decrease of the device feature size on the
wafer while the ITRS request that the operational current density remains the
same. Correspondingly, the power loss density increases quadratically with the
reduction of the feature size.
Two possible alternatives to overcome these problems are to reduce the supply
voltage or the use of alternative materials which produce and inherit less
To describe the general behavior of the electro-magnetic system, fundamental
electro-magnetic field equations are given by
MAXWELL2.3 [58,59,60] as
The heat conduction equation (2.9) has some critical quantities: the heat generation term, the thermal conductivity , and the specific heat capacitance . The heat generation term is mostly represented by JOULE's2.5 power loss (cf. Section 2.2.3). For the thermal conductivity and the specific heat capacitance several tables of material parameters exist, which have also different ranges of validity (cf. Section 2.2.1).
In order to describe the behavior of semiconductor devices more specifically, the necessary equations can be derived from MAXWELL's equations . Equation (2.3) and (2.2) are used to derive the continuity equation between the charge carrier current for space charge
By introducing an electrical potential as
More problem-specific models have to be introduced instead of the generally used ones to described the discrepancies between reality and the observed model behavior. For instance, if the transient behavior of a clock frequency shift of an oscillator has to be considered during different operation conditions, many additional thermal and transient phenomena occur and influence the device behavior significantly . Therefore, the applied simulation models have to be adapted for each particular case appropriately to achieve an accurate problem description.
The following part of this chapter gives an overview of the most important parts of the thermodynamics in semiconductor devices with respect of their application to industrial-relevant examples [65,66,62,67,68,69].