In this paper we study a driftdiffusion semiconductor model with variable electron mobility. General driftdiffusion theory of the current density in. Jp drift q p vd and jn drift q n vd area a hole drift current density electron drift current density. Introduction of bipolar junction transistor, terminal characteristics, forward active bias, current gain.
Now an electric field is created within in the depletion region. Analysis and design of such semiconductor devices as bipolar and fieldeffect transistors now relies, in part, on the assumption that current flows by drift and diffusion. They can be easily deduced from maxwells equations 8. Im trying to simulate basic semiconductor models for pedagogical purposesstarting from the drift diffusion model. To facilitate this analysis, we present here a simplified driftdiffusion model, which. Jul 30, 2016 descritxt the concepts of drift current and diffusion current in a semiconductor material. These equations are also called the basic semiconductor equations. What is difference between drift current and diffusion. What is the difference between drift and diffusion. Considering electrons as carriers but the same can be said for holes, the current density in a semiconductor can be expressed by the drift diffusion transport equation. Apr 29, 2016 in this note, we study a fractional poissonnernstplanck equation modeling a semiconductor device. A semiconductor is not diffusion or driftbased, those are two phenomena always taking place in the same semiconductor. The direction of diffusion current is same or opposite to that of the drift current.
Diffusion current occurs without an external voltage or electric field applied. The drift velocity, and resulting current, is characterized by the mobility. Quantumcorrected driftdiffusion models for transport in. What links here related changes upload file special pages permanent link page.
What is difference between drift current and diffusion current. When the diode is reverse biased diffusion is negligible, but drift remains constant. The flow of charge carriers, which is due to the applied voltage or electric field is called drift current. Combined electromagnetic and drift diffusion models for microwave semiconductor device. The minute size of existing devices raises questions about the appropriateness of this assumption, however, because an internal region critical to device performance may. Consider a piece of nonuniformly doped semiconductor at equilibrium no external elect. Lecture 3 electron and hole transport in semiconductors.
A semiconductor is not diffusion or drift based, those are two phenomena always taking place in the same semiconductor. Evx ecx ef ntype semiconductor decreasing donor concentration ntype semiconductor qe kt n e internal electric field due to nonuniform doping that opposes the diffusion making net current zero is there an assumption that we. An augmented driftdiffusion model in a semiconductor device. The drift diffusion model of a semiconductor is frequently used to describe semiconductor devices. When the diode is forward biased drift current is present, but because diffusion current grows exponentially, it dominates. Unlike drift, diffusion has nothing to do with the charge of the.
With graded semiconductors one needs to include a quasidrift term that takes into. The diffusion process leaves a depletion region near the such that as the charges build up, a net positive charge and net negative charge are created at the p and the nside respectively. This kind of current is different from drift currentwe call this current diffusion current. There can still be current flow in a silicon lattice, even if there is no electric field applied to it. In this note, we study a fractional poissonnernstplanck equation modeling a semiconductor device. Electrons and holes in semiconductors are mobile and charged.
Pdf driftdiffusion current in organic diodes researchgate. Digital logic concepts, inverter characteristics, logic levels and noise margins, transient. Unlike drift, diffusion has nothing to do with the charge of the carrier and arises whenever there is a nonuniform concentration, or concentration gradient, of charges in a medium. The method is based on the use of a mixed finite element method for the approximation of the electric field and a discontinuous upwinding finite element method for the approximation of the electron and hole concentrations. The term is most commonly used in the context of electrons and holes in semiconductors, although the same concept also applies to metals, electrolytes, and so on drift current is caused by the electric force. Posted 2 years ago in an ntype semiconductor bar, there is an increase in electron concentration from left to right and an electric field pointing to the left. They may not be occurring at the same time, but the equation is still valid. Lecture notes microelectronic devices and circuits. Pdf because the conductivity of organic semiconductors is very low, a useful model for the organic diode consists of treating the organic layer.
Diffusion current for electrons and holes duration. For the decoupled solution of the two models, we introduce a functional iteration technique that extends the classical gummel algorithm widely used in the iterative solution of the dd system. Fermidirac distribution x density of states carrier concentration probability of. In this paper we study a drift diffusion semiconductor model with variable electron mobility. Drift and diffusion current in semiconductors ee311. Instances when driftdiffusion equation can represent the trend or predict the mean behavior of the transport properties feature length of the semiconductors smaller than the mean free path of the carriers instances when drift diffusion equations are accurate quasisteady state assumption holds no transient effects. Since biasing and hence electric field only generates majority carriers, not the minority, thats why drift currnet is independent of biasing.
Find materials for this course in the pages linked along the left. The corresponding biases of these junctions are vjs and vjd, respectively. Does diffusion current in semiconductor always exist. Drift and diffusion currents electric current diffusion scribd. Under equilibrium conditions, the current density should be zero because there shouldnt be any drastic changes occurring, like applying an electric field or changing the carrier. Drift is the motion of charge carriers caused by an electric field. The driftdiffusion model of a semiconductor is frequently used to describe semiconductor devices. The flow of charge ie current through a semiconductor. Starting with chapter 3, we will apply the drift diffusion model to a variety of different devices.
Starting with chapter 3, we will apply the driftdiffusion model to a variety of different devices. Short base approximation, steady state diffusion equation with currents in pn junction. Double sided diffusion and drift of lithium ions on large. Questionability of driftdiffusion transport in the. The drift velocity of the carriers in the medium is a direct function of the electric. We obtain conditions under which the electron density is bounded above and bounded away from 0 below. Considering electrons as carriers but the same can be said for holes, the current density in a semiconductor can be expressed by the driftdiffusion transport equation. Combined electromagnetic and drift diffusion models for. Semiconductors are made up of two types of material i. See driftdiffusion equation for the way that the drift current, diffusion current, and carrier generation and recombination are combined into a single equation. Drift current depends on temperature also current passing through a square centimeter area perpendicular to the direction of flow. The total current flowing through the depletion region under forward biasing is made up of mostly majority carrier diffusion.
Why do minority carriers form a diffusion current not a drift current after they cross the potential barrier. Total current p n n n drift n diffusion n n p p drift p diffusion p p. On a driftdiffusion system for semiconductor devices. The injected currents of each junction are isd from the ds junction and ids from the dd junction. Assume that,in an ntype semiconductor att 300k,the electron concentration varies linerly from1. This is the current which is due to the transport of charges occurring because of nonuniform concentration of charged particles in a semiconductor. Sometimes, this drift diffusion term is gathered into. Although i dont want to use an offtheshelf semiconductor simulatorill be learning other common, recent or obscure models, i do want to use an offtheshelf pde solver. It contains all the features described in this chapter.
Driftdiffusion and hydrodynamic modeling of current. Given current density j ij x area flowing in a semiconductor block with. Drift and diffusion currents free download as word doc. In a semiconductor, there are two types of charge carriers, they are electrons and holes. Drift current is generated by minority carriers in pn junction, and this is equal to diffusion current but flows in opposite direction in equlibrium. The current density distribution is obtained from the solution of the drift diffusion model 11,12. Writing a book on semiconductor device physics and design is never complete and probably never completely satisfying. Descritxt the concepts of drift current and diffusion current in a semiconductor material. Both drift current and diffusion current make up the total current in a semiconductor. Diffusion current is a current in a semiconductor caused by the diffusion of charge carriers holes and or electrons.
Inside the depletion region, both diffusion current and drift current are present. To learn two current conduction mechanisms of drift current and diffusion current, and einstein relation the relationship between diffusion constant and mobility in thermal equilibrium. Driftdiffusion currents of holes in semiconductors are usually written as. Given current density j ij x area flowing in a semiconductor block with face area a under the influence of electric field e, the component of j due to drift of carriers is. The driftdiffusion equations are derived introducing the mobility e m. The diffusion coefficient d is also introduced, and the resulting driftdiffusion current expressions for electrons and holes. Diffusion current is a current in a semiconductor caused by the diffusion of charge carriers. An explicit finite element method for numerically solving the driftdiffusion semiconductor device equations in two space dimensions is analyzed. A driftdiffusion model for semiconductors with temperature. This is according to all the microelectronics book im currently reading.
It is counterintuitive that the main current is diffusion when there is an applied electric field. Diffusion current is a current in a semiconductor caused by the diffusion of charge carriers holes andor electrons. In this case, the mobilities to describe drift currents and diffusion coefficients to describe diffusion currents are not independent to each other. This point of view gives us a model of particle behavior at atomistic level. Drift current and diffusion currents in semiconductors. Drift diffusion currents of holes in semiconductors are usually written as. We prove several decay estimates for the lebesgue and sobolev norms in one, two and three dimensions. Dn xx g for the electron concentration n, where g is a function not only of n x. Current flow in semiconductors university of north. Pdf on a driftdiffusion system for semiconductor devices. Drift current occurs with the application of an electric field to the medium. Concept of drift current and diffusion current comes in the semiconductor material. Diffusion and drift of charge carriers the next step in understanding the operation of semiconductors is the concept of diffusion and drift of the charge carriers.
The electric field causes a net, or directed, movement of carriers in the medium. An augmented driftdiffusion model in a semiconductor. The second contribution to current is known as diffusion. Im trying to simulate basic semiconductor models for pedagogical purposesstarting from the driftdiffusion model.
Carrier transport, drift velocity, drift current density, diffusion current density. When an electric field is applied across a semiconductor, the carriers start moving, producing a current. Drift current in a biased pn junction is independent of biasing,in unbiased pn junction minority carriers can cross the barrier and it produces drift current and is balanced by equal diffusion current. The drift and diffusion processes actually displace charge carriers in space, and thus are responsible for the current. An augmented version of the driftdiffusion model in an nsemiconductor device is considered. Driftdiffusion and hydrodynamic modeling of current collapse.
Drift current is the electric current caused by particles getting pulled by an electric field. To facilitate this analysis, we present here a simplified drift diffusion model, which. Drift current drift is, by definition, charged particle motion in response to an applied electric field. The drift completion moment is fixed by sharp increase of inversed current. The driftdiffusion ratio of the mos transistor drain current 81 the equivalent circuit is based on the charge sheet model 4. Note that the nature, amount and regional location of these charge carriers can be be manipulated according to the intentions of the chip designers.
1310 267 986 458 1525 821 785 943 1159 1337 1150 644 768 1172 663 466 1183 1080 1363 1434 21 28 454 165 280 897 45 1455 1133 667 74 121 683 1152 36 105 55 242 1271 761 65 872