Page 174 - Semiconductor For Micro- and Nanotechnology An Introduction For Engineers

Systems and Ensembles
systems as they are found in microsystem devices: photons, electrons and
holes, quasiparticles. We end the chapter with applications of the statisti-
cal results, and show how they characterize the particles and quasiparti-
cles that we encounter in describing the behavior of semiconductor-based
devices.

5.1.1 Microcanonical Ensemble
An isolated system (see Figure 5.1a) in equilibrium, with a fixed num-
A

a)
System Environment Microcanonical

S E S E

Exchange

b) c)
Canonical Grand canonical

S E S E

Heat Heat, particles (mass), …
Figure 5.1. Characterization of systems according to the way they interact with the envi-
ronment.

ber N of components, which resides in a fixed volume , assumes dif-
V
ferent microscopic implementations in the small energy interval
E < E < E + δE . The index counts the different implementations. A
i
i
large number of identical such systems A is called a microcanonical
ensemble. An implementation is characterized by its energy E and a
i
i
detailed description of the state of each of the N subsystems. We can
think of the components as particles. Each particle then has a given
j
N
vector momentum p and vector position q ; each vector in turn has
j j
Semiconductors for Micro and Nanosystem Technology 171