ABSTRACT
In physics, various types of nonequilibrium phase transitions are encountered, which can be classified as either first order or second order [1]. In a first-order phase transition, the physical variable (state variable) shows a discontinuous transition when the control parameter is varied continuously, while for a second-order phase transition the state variable is continuous but its derivative shows discontinuity at the transition point. This chapter is concerned with the nonequilibrium phase transition of first order, which can be seen in the semiconductor carrier transport [2]. The steady-state solution of the current density J at an electric field E is given by a well-known formula:
J ¼ E: ð2:1Þ
Here, electrical conductivity is given by
¼ ene for n-type semiconductors; ð2:2Þ eph for p-type semiconductors; ð2:3Þ
where nðpÞ is free electron (free hole) density, eðhÞ is the electron (hole) mobility, and e is the magnitude of elementary charge. For the double injection diode [3], ¼ eðne þ phÞ. There are typically two types of J-E characteristics (Fig. 2.1). As is apparent from Fig. 2.1, there is an unstable region @J=@E < 0 ð@=@E < 0Þ, followed by S-shaped negative differential conductivity (SNDC) in Fig. 2.1a, and N-shaped negative differential
conductivity (NNDC) in Fig. 2.1b. For n-type semiconductors,
@
@E ¼ e e @n
@E þ n @e
@E
< 0: ð2:4Þ
The NDC means @n=@E and/or @e=@E < 0. The SNDC is typical in the impact ionization avalanche of neutral impurities, leading to spatial formation of a current filament. The NNDC is seen in the Gunn diode, leading to the formation of a high-field domain, where intervalley scattering of free electrons as well as polar optical phonon scattering and acoustic phonon scattering play an important role [4, 5]. Both NDCs exhibit oscillatory instability. In order to understand the
nonequilibrium phase transition and the dynamical behaviors, it is necessary to know the fundamental properties of the carrier transport theory [6, 7]. This chapter will cover the important parts of the theory that may be helpful for the present interests. Readers who are familiar with the carrier transport theory may skip the first section of this chapter. In sections 2.2 and 2.3, the experimental and theoretical studies of NNDC and the SNDC will be introduced.
