Lecture4 - 11/9/2010 11/9/2010 2 PreparationforDevices...

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11/9/2010 1 LECTURE 4: PN JUNTION DIODES EECS 170A 11/9/2010 1 Preparation for Devices After understanding the quasi Fermi levels and non equilibrium condition we may proceed to simple semiconductor devices. Before we move on let’s remember the basic postulates of thermal equilibrium There are two types of charged carriers in a semiconductor, electrons and holes, and current is generated ONLY by diffusion or drift of these carriers 11/9/2010 2 JJ J qD n q E n  Semiconductor reaches equilibrium when diffusion, drift, generation and recombination balances each other and hence the probability of finding electron at a given energy level is always constant at any point along the crystal. Hence 0 FFF dE dE dE dx dy dz  || nn d i f fn d r i pp d i f fp d r i f t p tn n p f J JJ q D pq p E     Preparation for Devices (2) Semiconductor is under non equilibrium condition if there is an external perturbation in the form of generation, diffusion, drift and recombination. These perturbations add excess carriers that varies in space and in time as defined by continuity equations. 11/9/2010 3 Diffusion by carrier gradient Drift due to external field Recombination Carrier generation 2 2 P p L dp d D dx d x p G dt p      Drift due to external field Diffusion 2 2 p n N dn D dx dx dt   Carrier generation by carrier gradien Recombination n L t G n  P N Junctions: Basic postulates So far we were dealing with bulk semiconductors with fixed type (p type or n type) Now we would like to understand what will happen if we have two different semiconductors are brought together 11/9/2010 4 P TYPE N TYPE X E C E V E i E F E C E V E i E F
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11/9/2010 2 P N Junctions: Basic postulates (2) To simplify the process let’s make some assumptions Both the P type and N Type are uniformly doped semiconductors Both have the same bandgap energy Both semiconductors are under equilibrium and charge neutrality holds before the junction is formed as: 11/9/2010 5 Charge Density = ( ) 0 DA qp N n N   0 0 Also Gauss Law holds 0 Where, is the permitivity of free space and is the dielectric constant S S K K  P N Junctions: Basic postulates (2) Simplifying assumptions (Cont) The contact point (metallurgical junction) is perfectly smooth and sharp and we have a step junction in which semiconductor type switches from p type to n type abruptly at x=0 Length of semiconductors are much larger than diffusion length of carriers Excess carriers do not change the equilibrium condition points too far from the junction Assume that the junction is created at t=0 by bringing two semiconductors together 11/9/2010 6 P TYPE N TYPE X E C E V E i E F E C E i E F Junction and band diagram at t=0 P N Junctions: Equilibrium
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Lecture4 - 11/9/2010 11/9/2010 2 PreparationforDevices...

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