Asymptotic analysis of the Gunn effect with realistic boundary conditions

Abstract

A general asymptotic analysis of the Gunn effect in n-type GaAs under general boundary conditions for metal-semiconductor contacts is presented. Depending on the parameter values in the boundary condition of the injecting contact, different types of waves mediate the Gunn effect. The periodic current oscillation typical of the Gunn effect may be caused by moving charge-monopole accumulation or depletion layers, or by low-or high-field charge-dipole solitary waves. A new instability caused by multiple shedding of ͑low-field͒ dipole waves is found. In all cases the shape of the current oscillation is described in detail: we show the direct relationship between its major features ͑maxima, minima, plateaus, etc.͒ and several critical currents ͑which depend on the values of the contact parameters͒. Our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation. ͓S1063-651X͑97͒04708-9͔ PACS number͑s͒: 05.45.ϩb, 72.20.Ht, 85.30.Fg

Semiconductor superlattices: a model system for nonlinear transport

“…The shape of the current-field relation is thus typically of N-type and domain formation effects are likely to occur (see [45] for a general overview). The prototype of an extended device with N-shaped current-field relation is the Gunn diode which exhibits selfsustained current oscillation due to traveling field domains [160][161][162][163][164][165][166]. A similar behavior has been suggested for semiconductor superlattices [18,167], and oscillatory behavior has indeed been found experimentally in the last years [19,168] with frequencies over 100 GHz [20,169].…”

“…In contrast c dep (I) is positive for all currents for the sample parameters used. These functions c acc (I), c dep (I) have been shown to be very helpful to understand and analyze Gunn oscillations [166,189]. Here they are applied in the context of semiconductor superlattices where some peculiarities can be found.…”

Photorefractive Gunn effect

“…It is due to periodic shedding and motion of charge dipole waves (high field domains) at a boundary or a nucleation site. It is intrinsically nonlinear [3][4][5][6][7][8] so that the relevance of linear approximations such as those used in [1] is questionable. We think that Kroemer's NL criterion implies that for a given model (equations, bias, boundary and initial conditions) it can be proved that no oscillatory instability is possible unless the NL product (where L is semiconductor length and N is doping density) is above a certain number.…”

“…During the formation of a new wave at the injecting boundary the displacement current plays a crucial role and can not be neglected. Thus, we use an ohmic condition at the injecting contact, E = ρ J total [5][6][7][8], and ∂E/∂z = 0 at the receiving contact (which is thus passive and integration time is saved). When ρ is such that E/(ρqN A ) intersects v(E) on its decreasing branch, the Gunn effect is found for m = 0 and appropriate values of the bias V [4,5].…”

Multiple steady state current–voltage characteristics in drift–diffusion modelisation of N type and semi-insulating GaAs Gunn structures

“…Analytical expression for the steady state ambipolar transport, including generation/recombination, diffusion current and field dependent mobilities, is elusive but for very specific physical cases. Experimental [6-9,17,21,24-26], analytical [24,[26][27][28][29][30] and numerical results [6][7][8][9][31][32][33] have been obtained either in the steady state or for time dependent transport under dc voltage bias or constant current bias. These results deal mainly with unipolar transport in N type SC.…”