CurrentEquations

CurrentEquations - EE471 Course Notes: Week 2 Tewksbury 2....

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EE471 Course Notes: Week 2 Tewksbury 2. Transport in Semiconductors Chapter 3 of the textbook covers carrier transport (current) in semiconductors. Two equations were developed - the current equation and the current continuity equation . These two equations capture the relationships between currents and carrier densities for all semiconductors and all electrical devices made using semiconductors. 2.1 Current Equation The current is the rate of flow of charge across the device area. In particular, I = q ! R Q = Q t where Q is the total charge passing through the area in time t . The electrons and holes contribute separate currents I n and I p , respectively and the total current is the sum of these two currents, I = I n + I p . As the cross sectional area A increases, more charge flows across the larger area, with the current being proportional to the cross sectional area. To obtain general equations independent of this area, the current density (represented by J ) is used. The current (amps) and current density ( amps/cm 2 ) are related by J = I / A . The current due to a given carrier type (electron or hole) has two contributions - one due to electric fields (and called the drift current ) and the other due to a gradient in the carrier density (which causes diffusion of carriers into lower density region) and called the diffusion current . 2.1A Drift Current To obtain the drift current, it was necessary to obtain the velocity of carriers due to an electric field E . We discussed the "cloud" of carriers (moving at high velocities in random directions and scattering from scattering points caused by deviations of the silicon crystal from a perfect crystal). When an electric field is applied, this "cloud" of carriers moves (drifts), with the cloud of holes drifting in the direction of the electric field and the "cloud" of electrons drifting in the direction opposite to the electric field direction. From this, we established that carriers have a "drift velocity" proportional to the electric field, with the mobility of the carriers being the proportionality constant. In particular (using vector notation to capture the drift direction), the electron and hole drift velocities, respectively, are r v n = ! μ n r E and r v p = + p r E . Here, the electron and hole mobilities are, for silicon at 300K n = 1450 cm 2 /volt - sec and p = 505 cm 2 /volt - sec . The electron, hole and total drift current densities (J) and the corresponding currents (I) are J n = q n nE J p = q p pE J = J n + J p I n = J n ! A = q n ( ) A I p = J p ! A = q p ( ) A I = I n + I p . (3A) Here, we have left off the sign and eliminated the vector notation (the two currents simply add and, when considering currents in electrical circuits, we represent electrons flowing in one
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direction as current flowing in the opposite direction). Don't worry about these details - just use the equations above.
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This note was uploaded on 10/27/2009 for the course ECE 5 taught by Professor Chavez during the Spring '09 term at Stevens.

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CurrentEquations - EE471 Course Notes: Week 2 Tewksbury 2....

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