Joseph A. Elias, PhD 1

Class 04: Device Physics I

Topics:1. Introduction2. NFET Model and Cross Section with Parasitics3. Band Diagrams4. Depletion region, Voltage, Field5. Deriving Vbi6. Vbi as a function of doping7. Depletion region8. Forward, Reverse Biasing Band Diagrams9. Thermal Equilibrium10. Forward Bias11. Reverse Bias12. Junction Capacitance13. Diode Equation

Joseph A. Elias, PhD 2

Class 04: Device Physics I

•Goal is to understand the parasitic regions and terms shown in the model and cross section•Question - where are the pn junctions?

NMOS Model and Cross Section with Parasitics (Martin p.101)

Joseph A. Elias, PhD 3

Class 04: Device Physics IPN Junctions - Band Diagrams (Yang p.73)

•When two dissimilar materials are joined, there is an offset in the energy levels•The Fermi levels must align, and the band diagrams show how this is done via band bending•The x-axis is linear dimension, and the y-axis is energy

Before contact

Fermi Level alignment

Space-Charge distribution

Joseph A. Elias, PhD 4

Class 04: Device Physics IPN Junctions - Depletion, Voltage, Field (Yang p.72, Neudeck p.22,24, Mason)

•When p-type and n-type materials are joined, diffusion occurs. Excess holes in p-typeregion diffuse to n-type, and excess electrons inn-type diffuse to p-type region

•This diffusion is opposed by the resulting electric field ofthe uncovered ionic charges. The positive ion coresin the n-type region oppose the diffusion of the p-typecarriers from the p-type region, and vice-versa.

•The exposed ionic cores in the p-type region (negative, Na)must be matched by the exposed ionic cores in the n-type region(positive, Nd), leaving a net charge-neutral device:

q A xp NA = q A xn ND

•If A is the same on both sides, then

xpNA = xnNDmeaning the depletion depth is greater for a more lightly doped region

•The ionic charge results in an E-field, which causes abuilt-in potential to form. This Vbi will oppose thediffusion and it will match the -qVbi in the band diagrams.

Joseph A. Elias, PhD 5

Class 04: Device Physics IPN Junctions - Deriving Vbi (Neudeck p.26,27)

•Electron current density is a combinationof drift and diffusion currents, which mustbe zero to maintain charge neutrality

•Solving for the E-Field, and using the Einsteinrelationship between diffusion and mobility, givesthe E-field as a function of temperature

•Integrating from one bulk region to the other

•Vbi as a function of the electron carrierconcentration in the n- and p-type material

•By using the approximations:

•Built-in Potential across an abrupt pn junction

Joseph A. Elias, PhD 6

Class 04: Device Physics IPN Junctions - Vbi as a function of doping (Sze p.88)

Joseph A. Elias, PhD 7

Class 04: Device Physics IPN Junctions - Depletion Region (Neudeck p.36,40)

From course notes, and various textbooks,one can derive the depletion width.(Where Vbi is the built-in potential,Ks is the relative permittivity, ε is thepermittivity of free space, Na is theacceptor concentration, and Nd is thedonor concentration)

As the applied bias (Va) becomes morepositive with respect to the n-type region,the Vbi barrier is overcome, and thedepletion width becomes narrower.Conversely, as Va becomes more negativewith respect to the n-type region, thedepletion width will increase.

One can also see, as the doping of oneside is much greater than the other, thedepletion width depends on the lightlydoped region.

Joseph A. Elias, PhD 8

Class 04: Device Physics IPN Junctions - Forward, Reverse Biasing (Neudeck p.38,39)

Forward bias Reverse bias

Depletion widthnarrows

Total chargedecreases

E-fielddecreases

Potentialdecreasesby amount

of bias

Depletion widthwidens

Total chargeincreases

E-fieldincreases

Potentialincreases

by amountof bias

Joseph A. Elias, PhD 9

Class 04: Device Physics IPN Junctions - Thermal Equilibrium (Neudeck p.46)

•Jdrift - Jdiff = 0

•Density of states gives the number of free carriers available in theconduction band that are above qVbi energy

Joseph A. Elias, PhD 10

Class 04: Device Physics IPN Junctions - Forward Bias (Neudeck p.50)

•Va is negative with respect to the p-type (or positive wrt the n-type region)

•The energy bands bend so that the qVaenergy increases the amount of diffusioncarriers available in the density of states.

The drift current remains constant, as theavailable carriers have not changed(electrons in the p-type region, holes in the n-type region)

Forward bias current is therefor dependenton the number of majority carriers available in the conduction band, whichis an exponential relationship. This is morethan the thermal equilibrium condition.

Jdiff > Jdrift, so large positive current

Joseph A. Elias, PhD 11

Class 04: Device Physics IPN Junctions - Reverse Bias (Neudeck p.51)

•Va is positive with respect to the p-type (or negative wrt the n-type region)

•The energy bands bend so that the qVaenergy decreases the amount of diffusioncarriers available in the density of states.

•The drift current remains constant, as theavailable carriers have not changed(electrons in the p-type region, holes in the n-type region)

•Reverse bias current is therefor dependenton the number of majority carriers available in the conduction band, whichis an exponential relationship. This is lessthan the thermal equilibrium condition.

Jdrift > Jdiff, so small negative currentlimited by minority carrier supply

Joseph A. Elias, PhD 12

Class 04: Device Physics IPN Junctions - Junction Capacitance (Martin p.75-77)

To find the junction capacitance, start with the depletion width for an abrupt junction:

The charge in the depletion region (per cross sectional area) is the depletion widthtimes the concentration of ionic charge (qN). For the p-type region, and assuming that Na >> Nd:

The junction capacitance can be derived by differentiating Q wrt Vr:

For a one-sided diode (Na>>Nd):

Joseph A. Elias, PhD 13

Class 04: Device Physics IPN Junctions - Diode Equation (Neudeck p.63-65)

Ideal or Shokley Diode Equation

Who cares?Reverse diode leakage is relatedto off-state leakage of an IC

•Current proportional to the diode junction areaand inversely proportional to doping(why you want lightly doped substrates)

•Reverse current dependent on theminority carrier diffusion coefficient (Dn,p),minority carrier diffusion length (Ln,p),and minority carrier concentration (np, pn)