Analytical solutions for nonlinear transport equations in semiconductors

Journal Article · · Applied Physics Communications; (USA)

OSTI ID:6283723

Abraham-Schauner, B; Bender, C M ^[1]; Zitter, R N ^[2]

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1. Washington Univ., St. Louis, MO (USA)
2. Southern Illinois Univ., Carbondale (USA)

Semiconductor diodes are modeled by nonlinear transport equations for electrons or holes which are the conservation of particle flux, the momentum equation with a constant relaxation time and Gauss's law. The classic cathode boundary conditions, the vanishing of the carrier speed and electric field, are imposed. The transport equations are replaced by a single, second-order, nonlinear ordinary differential equation for the square of the time-independent carrier speed. Approximate solutions of this equation are found in a nonlinear Taylor expansion about extrema of the carrier speed. The Taylor coefficients are calculated exactly in every order for a finite number of terms where the coefficients can be given exactly since a first integral exists for the differential equation. Comparison with the numerical integration of the transport equations is shown. These analytical solutions generalize exact analytical expressions for ballistic transport in semiconductors.

• OSTI ID: 6283723
• Journal Information: Applied Physics Communications; (USA), Journal Name: Applied Physics Communications; (USA) Vol. 10:1-2; ISSN 0277-9374; ISSN APCOD
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
426000* -- Engineering-- Components
Electron Devices & Circuits-- (1990-)
656002 -- Condensed Matter Physics-- General Techniques in Condensed Matter-- (1987-)
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
CALCULATION METHODS
DIFFERENTIAL EQUATIONS
ELECTRICAL PROPERTIES
ELECTRONS
ELEMENTARY PARTICLES
EQUATIONS
FERMIONS
HOLES
LEPTONS
PHYSICAL PROPERTIES
SEMICONDUCTOR DEVICES
SEMICONDUCTOR DIODES