97.398*, Physical Electronics, Lecture 8. Diode Operation

Transcription

1 97.398*, Physical Electronics, Lecture 8 Diode Oeration

2 Lecture Outline Have looked at basic diode rocessing and structures Goal is now to understand and model the behavior of the device under bias First consider the carrier exchange and interaction between and n materials in equilibrium, and discuss concet of the deletion region Then examine carrier rofiles under forward and reverse bias, and derive a model for the diode current flow in terms of alied otential and hysical arameters Concets of 1D area and doing rofiles from lecture 6 as well as GR and diffusion from lecture 7 are required for current model Page 2

3 Junction Materials Just Before Connection To understand carrier flow in biased diode, first examine behaviour of carriers during establishment of equilibrium between and n materials Start with situation below, where + and n materials are searated, and hence cannot exchange carriers (would be a + imlant diffusion into n substrate structure) Electrons are majority in n-tye (N D ) and minority in -tye (n i2 /N A ), holes are majority in -tye (N A ) and minority in n-tye (n i2 /N D ) Page 3

4 Junction Materials Immediately After Connection After materials are connected, they can exchange carriers Large concentration gradients exist across the metallurgical junction Following slides show enlargement of boxed region Page 4

5 Charge Distributions at t = 0 + Just after connection, the hole and electron distributions are flat in each material (uniform doing) and discontinuous across the metalurgical junction Large concentration gradients exist, so there will be a large comonent of carrier flux due to diffusion, recall Θ= D dc ( x ) dx Page 5

6 Charge Distributions at Later t At some later time, charge redistribution has taken lace Holes move to n-tye, creating +ve charge, electrons move to -tye, creating -ve charge Concentration gradients, and hence diffusion flux, decrease as carriers redistribute Charge redistribution causes electric field which also tends to oose further diffusion of carriers Page 6

7 Charge Distributions for t, Equilibrium After a long time, charge will have redistributed so that the forces due to the concentration gradient and the electric field balance Forces due to diffusion and electric field are still resent, but exactly balance If electrons and holes were not charged, this would not occur (no charge searation, no E) Note that areas away from metallurgical junction are unaffected Page 7

8 Diode Regions Identify two distinct regions in the n-junction structure: The neutral regions are those which are essentially unaffected by the charge redistribution The deletion region is the transition region where charge redistribution has taken lace Page 8

9 Forward Bias Injection Comonents Forward bias raises otential of with resect to n, causes current flow from to n Two current comonents: Injection of holes from to n, in the direction of current Injection of electrons from n to, in the oosite direction to current Note that electrons injected into, holes injected into n, hence the term minority carrier injection for forward bias Page 9

10 Forward Bias Carrier Density Profiles In forward bias, injection of carriers raises the value of the carrier density throughout the device - note linear behavior in thin + region In the neutral regions, the increase is negligible comared to the doing level for moderate bias levels This is therefore a low level injection situation Page 10

11 Current Comonents in Forward Bias Boundary conditions on electron and hole densities are qvd kt n ( x) = n e ( x) = e -del edge o / qvd / kt n n-del edge no Page 11

12 Comonents of Ideal Diode Equation Develo exressions for minority densities, then use diffusion relationshi to derive current comonents due to electron injection J n and hole injection J as J n qdnno qd = = w L qv kt no D/ qvd/ kt ( e 1) J ( e 1) Total current is sum of individual comonents, this is the ideal diode equation (for current density) but illustrating the hysical comonents of the saturation term J D qdnno = + w qd L no qvd / kt ( e 1) Page 12

13 Ideal Diode Equation Total current is sum of individual comonents, this is the ideal diode equation (for current density) but illustrating the hysical comonents of the saturation term J D qdnno = + w qd L no qvd / kt ( e 1) Page 13

14 Saturation Current Density The hysical exression for the saturation current density can be extracted from the revious exression J S n I qd n qd + = = + A w L S + n n o no D This is only valid for a + n junction, since it contains the width of the -tye material, w. For an n + junction with a thin n + -tye region (e.g. an n + imlanted junction) J I qd n qd + = = + A L w S n S + n n o no D n n Page 14

15 Examle 8.1: Saturation Current Density Calculation Find the saturation current density for a + n junction with the 1D doing rofile shown to the right. Assume the minority lifetime is 0.5 µsec, use a uniform doing aroximation and assume the width of the neutral + region is equal to the material width Page 15

16 Examle 8.1: Solution The uniform aroximation to the 1D rofile is shown to the right. Using the uniform aroximation, the doing in the + region is /cm 3, and the doing in the n-tye region is 8x10 15 /cm 3. The width of the + region, from the location of the metallurgical junction on the lot, is 1 µm or 10-4 cm. Page 16

17 Examle 8.1: Solution (con t) Using the values extracted from the uniform doing aroximation 10 ( ) ( ) 2 n o = 10 This gives a saturation current density of (L was calculated last lecture) J 18 2 = / cm = qd n qd + = + w L S n n o = no 11 = A /cm no = / cm 4 Page 17

18 Reverse Bias Injection Comonents Reverse bias raises otential of n with resect to, causes current flow from n to Two current comonents: Injection of holes from n to, in the direction of current Injection of electrons from to n, in the oosite direction to current Note that electrons injected into n, holes injected into, hence the term majority carrier injection for forward bias Page 18

19 Reverse Bias Carrier Density Profiles In reverse bias, injection of majority carriers lowers the value of the minority densities - again note linear behavior in thin + region In the neutral regions, the increase is negligible comared to the doing level for moderate bias levels This is therefore again a low level injection situation + imlant n-tye substrate N A (x) n(x) ND e injection h injection n N i 2 / A n(x) n o no (x) n deletion region carrier densities: equilibrium forward bias n i 2 / N D Page 19

20 Current Comonents in Reverse Bias Because the boundary conditions used in the forward bias case still aly in reverse bias, the revious current exression also still holds J D qdnno = + w qd L no qvd / kt ( e 1) Note that in reverse bias for V D < -3kT/q the exonential term is negligible comared to 1, and J D -J S Page 20

21 Lecture Summary n junction examined in equilibrium, balance between carrier diffusion and oosing electric field Neutral region basically unaffected by carrier exchange, deletion region aroximated as emty of free carriers Injection under bias Minority injection in forward bias Majority injection in reverse bias Saturation current density J S derived as basic structure deendent arameter in ideal diode equation Comutation of J S may require extraction of doing using uniform aroximation Page 21