5.5 Transient and A-C Conditions5.5.1 Time Variation of Stored Charges5.5.2 Reverse Recovery Transient5.5.3 Switching Diodes5.5.4 Capacitance of p-n Junctions5.5.5 The varactor Diode

5.6 Deviations from the Simple Theory5.6.1 Effect of Contact Potential on Carrier Injection5.6.2 Recombination and Generation in the Transition Region5.6.3 Ohmic Losses5.6.4 Graded Junctions

5.7 Metal-semiconductor Junctions5.7.1 Schottky Barriers5.7.2 Rectifying Contacts5.7.3 Ohmic Contacts5.7.4 Typical Schottky Barriers

5.8 Heterojunctions

)1()1)(( kTqVo

kTqVp

n

nn

p

p eIenL

Dp

L

DqAI //

kTEE

nnvnFep/)(

was neglected at low injection

kTqVi

n

ni

p

pp

n

nn

p

p enL

Dn

L

DqAn

L

qADp

L

qADI 2)( /

• An electron at Er is thermally excited to the conduction band (Gn) and a valance band electron is subsequently excited thermally to the empty state on the recombination level, leaving a hole behind in the valance band (Gp).• Normally, these emission processes are exactly balanced by the corresponding capture processes Rn and Rp. However, in the reverse-bias transition region, generated carriers are swept out before recombination can occur, and net generation results.

• A level near the middle of the band gap is most effective, since for such centers neither Gn nor Gp requires thermal excitation of an electron over more than about half the band gap.• In most materials recombination centers exist near the middle of the gap due to trace impurities or lattice defects. If no recombination level is available, this type of generation is negligible.• Generation from centers within W is most important in materials with large band gaps, for which band-to-band generation in the neutral regions is small.• Generation within W naturally increases linearly with W as reverse bias increases. (The saturation current due to generation in the neutral regions was found to be essentially independent of reverse bias)

• The reduction in junction voltage V lowers the level of injection so that the current increases more slowly with increased bias.• However, the conductivity of each neutral region increases with increasing carrier injection. (conductivity modulation)

GxNN ad

Gxq

NNnpq

dx

dEad

)(

GxNN ad

Gxq

NNnpq

dx

dEad

)(

In a graded junction the usual depletion approximation is often inaccurate.

•If the grade constant G is small, the carrier concentration (p-n) can be important.•The usual assumption of negligible space charge outside the transition region is questionable for small G.

Nevertheless, junction theory is qualitatively applicable to the graded junction, with some alterations in the functional form of the resulting equations.

5.5 Transient and A-C Conditions5.5.1 Time Variation of Stored Charges5.5.2 Reverse Recovery Transient5.5.3 Switching Diodes5.5.4 Capacitance of p-n Junctions5.5.5 The varactor Diode

5.6 Deviations from the Simple Theory5.6.1 Effect of Contact Potential on Carrier Injection5.6.2 Recombination and Generation in the Transition Region5.6.3 Ohmic Losses5.6.4 Graded Junctions

5.7 Metal-semiconductor Junctions5.7.1 Schottky Barriers5.7.2 Rectifying Contacts5.7.3 Ohmic Contacts5.7.4 Typical Schottky Barriers

5.8 Heterojunctions

5.5 Transient and A-C Conditions5.5.1 Time Variation of Stored Charges5.5.2 Reverse Recovery Transient5.5.3 Switching Diodes5.5.4 Capacitance of p-n Junctions5.5.5 The varactor Diode

5.6 Deviations from the Simple Theory5.6.1 Effect of Contact Potential on Carrier Injection5.6.2 Recombination and Generation in the Transition Region5.6.3 Ohmic Losses5.6.4 Graded Junctions

5.7 Metal-semiconductor Junctions5.7.1 Schottky Barriers5.7.2 Rectifying Contacts5.7.3 Ohmic Contacts5.7.4 Typical Schottky Barriers

5.8 Heterojunctions