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# Nonlinear carrier transport in semiconductors

DOI link for Nonlinear carrier transport in semiconductors

Nonlinear carrier transport in semiconductors book

# Nonlinear carrier transport in semiconductors

DOI link for Nonlinear carrier transport in semiconductors

Nonlinear carrier transport in semiconductors book

## 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 @[email protected] < 0 ð@[email protected] < 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 @[email protected] and/or @[email protected] < 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.