E E 339 - CN11-pn jucntion-equilibrium

E E 339 - CN11-pn jucntion-equilibrium - 1 P-N Junction:...

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Unformatted text preview: 1 P-N Junction: Equilibrium Conditions P N Junction: Equilibrium Conditions 1 roles of p-n junctions; a reminder Abrupt junction approximation Contact potential and equilibrium band bending Outline Contact potential and equilibrium band-bending Depletion approximation, and total and partial depletion region widths One-sided junctions Summary 2 2 p-n junctions, just the connection between n-type and p-type regions, are used individually in devices such as, for example, voltage rectifiers, and Definition and uses of p-n junctions voltage-variable capacitors as to be considered here. Modified p-n junctions are also be used as photocells (including solar cells), light emitting diodes and lasers and two or more p-n junctions are used in devices such as bipolar junction transistors, field-effect transistors of various types Although in these latter cases the qualitative behavior can vary quite a bit from that of the simple p-n junction to be considered here. 3 The important universal qualitative behaviors of p-n junction can be demonstrated by considering simple abrupt junctions formed by bringing together uniformly p-doped (N a ) and n- doped (N d ) pieces of the same semiconductor material Abrupt isolated homogeneous p-n junction (a starting point) doped (N d ) pieces of the same semiconductor material Such a simple junction can be formed epitaxially or, in many more E F E c E v E v E c E F E x cases, effectively by diffusion or ion implantation of one-sided junctions, TBD. Quantitative differences for graded junctions will be considered later. 4 3 E F E c E v E v E c E F E x In Equilibrium, E F / x 0 such that Contact Potential V o and equilibrium band bending E F E c,p,o E v,p,o voltage drop E x V band bending that by some means TBD must occur to satisfy E F / x 0 E c ( x ) E v ( x ) E v,n,o E c,n,o o o n i o p i qV E E , , , , E i E i E i ( x ) V o V electrostatic x x tic electrosta dx x x V ' ) ' ( ) ( where E i,p,o E i,n,o = E c,p,o E c,n,o etc. is the band bending and V o is the contact potential = equilibrium electrostatic potential drop from the n to the p-side (positive by definition). 5 Away form the junction, in the essentially charge neutral regions after the electric field has been (somehow, TBD) screened out, on the p-side T k E E o p B F o p i e n p ) ( , , (1a) Value of contact potential (electrostatic potential in units of Volts) or And, similarly, on the n-side i o p , (1b) (2) i o p B F o p i n p T k E E , , , ln i o n B o n i F n n T k E E , , , ln Therefore, adding (1b) and (2), the total band bending E i,p,o E i,n,o is (3) 2 , , , , , , , , ln ln ln i o n o p B i o n B i o p B o n i o p i n n p T k n n T k n p T k E E 6 4 The contact potential is defined as (see preceding diagram)...
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E E 339 - CN11-pn jucntion-equilibrium - 1 P-N Junction:...

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