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ECSE-6230 Semiconductor Devices and Models I Lecture 10. Prof. Shayla Sawyer Bldg. CII, Rooms 8225 Rensselaer Polytechnic Institute Troy, NY 12180-3590 Tel. (518)276-2164 Fax. (518)276-2990 e-mail: May 24, 2014. . 1.

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ecse 6230 semiconductor devices and models i lecture 10

ECSE-6230Semiconductor Devices and Models ILecture 10

Prof. Shayla Sawyer

Bldg. CII, Rooms 8225

Rensselaer Polytechnic Institute

Troy, NY 12180-3590

Tel. (518)276-2164

Fax. (518)276-2990


May 24, 2014


lecture outline
Lecture Outline

Junction Breakdown

Zener Breakdown

Avalanche Breakdown

PN Junction Switching Characteristics

Charge Control

Constant Current Turn Off

Reverse Bias Turn Off

Midterm notes

junction breakdown
Junction Breakdown

With the increase in reverse voltage across a pn junction, when the voltage reaches the breakdown voltage (BV), a large reverse current starts to flow.

Junction breakdown is due to the high electric field at the junction.

junction breakdown1
Junction Breakdown

Basically, 2 breakdown mechanisms:

If the BV < 4 Eg / q (~ 4V in Si ), carrier tunneling across the junction dominates ( Zener breakdown )

If the BV > 6 Eg / q ( ~ 6V in Si ), carrier multiplication within the depletion region due to impact ionization is the major process ( Avalanche breakdown )

junction breakdown2
Junction Breakdown

Zener breakdown -

Usually occurs in p+/n+ junctions

Electrons tunnel from the valence band through the bandgap to the conduction band

Breaking of the covalent bonds due to high electric field (called field ionization) is the basic mechanism

junction breakdown3
Junction Breakdown

Tunnel barrier is of the triangular shape

Use WKB (Wentzel-Kramers-Brillouin) approximation

Put varying conduction band in terms of electric field

Find tunneling probability

Tunneling current, from either band to empty states in the other

avalanche breakdown
Avalanche Breakdown

Small initiation current leads

to large current due to carrier

multiplication resulting from impact ionization caused by the

high electric field ( > 105 V/cm ) near the metallurgical


avalanche breakdown1
Avalanche Breakdown

Assume Ip0 incident from the left side of the depletion region with width WDm.

With high electric field, e-h pairs are created, Ip will increase with distance and reach MpIpo at x=WDm

  • In will increase from In(WDm)=0 to In(0)=I-Ipo
  • The total current is constant at steady state (I=Ip+In)
  • The incremental hole current is equal to the number of e-h pair generated per second in the distance dx

avalanche breakdown2
Avalanche Breakdown

Boundary condition

When VR  BV, Mp  .

The breakdown condition can be specified as the ionization integral

If the avalanche process is initiated by electrons instead of holes


avalanche breakdown3
Avalanche Breakdown

Since avalanche breakdown does not depend on the carriers or primary current, either ionization integral can be used.

For semiconductors with equal ionization rates ( n = p =  ) such as GaP, the ionization integral reduces

Breakdown voltage for one sided abrupt junctions

Breakdown voltage for linearly graded junctions

avalanche breakdown voltage
Avalanche Breakdown Voltage

With a “universal” expression, accounting for instances where a uniform field over a large distance does not exist, Sze has derived

BV = 60 ( Eg / 1.1 )3/2 ( NB / 1016 )-3/4

for an abrupt junction

 NB-3/4


BV = ( Eg / 1.1 )6/5 ( a/(3 x 1020))-2/5

for a linearly graded junction

However, these expressions are NOT valid for wide bandgap (> 2 eV) semiconductors, such as SiC and GaN. (total voltage must be larger than bandgap)

avalanche breakdown voltage1
Avalanche Breakdown Voltage
  • Calculated breakdown voltage as a function of N for abrupt junctions
  • Dashed line is the upper limit of N for which the avalanche breakdown calculation is valid
  • Based on criterion 6Eg/q; above it tunneling will dominate

avalanche breakdown voltage2
Avalanche Breakdown Voltage
  • For diffused junctions with a linear gradient near the junction and a constant doping on one side the BVlies between two limiting cases
  • For a large a, the BV is given by the abrupt junction results
  • For small a, BV is given by the linearly graded junction and is independent of NB

avalanche breakdown voltage3
Avalanche Breakdown Voltage
  • It is assumed that the semiconductor layer is thick enough to support the maximum depletion-layer width WDm at breakdown
  • If the semiconductor layer W is smaller than WDm the device will be punched through
  • Punchthrough breakdown is earlier

planar junctions
Planar Junctions
  • Actual pn junction have junction curvatures that are cylindrical or spherical, leading to electric field concentrating
  • Breakdown voltages are significantly less than those of the 1-dim, parallel plane junction that we have examined thus far

avalanche breakdown voltage4
Avalanche Breakdown Voltage

With   rj / WDm ,

Cylindrical curvature:

And spherical curvature

As the radius of curvature becomes smaller, so does the breakdown voltage

avalanche breakdown voltage5
Avalanche Breakdown Voltage

transient behavior
Transient behavior

For switching applications the transitions form forward bias to reverse bias and vice versa much be nearly abrupt and the transient time short

The response from forward to reverse is limited by minority carrier charge storage

We investigate the switching of a diode from its forward state to its reverse state

Begin with just from on to off

large signal charge control model
Large-Signal Charge-Control Model

Use the time dependent continuity equation. Obtain each component of the current at position x and time t

Integrate both sides for instantaneous current density

For injection into a long n region from a p+ region, take current xn=0 to be all hole current and Jp at xn=∞ to be zero.

large signal charge control model1
Large-Signal Charge-Control Model

Total injected current including time variations

Hole current injected across the p+ n junction(~ total diode current) is determined by two storage charge effects

(1) usual recombination term, excess carrier distribution is replaced every τp seconds

(2) charge buildup (or depletion term) carriers can be increasing or decreasing in a time dependent problem

charge control equation
Charge Control Equation
  • Solve for stored charge as a function of time for a given current transient
  • Turn off transient, current is suddenly removed at t=0, leaves the diode with stored charge

charge control equation1
Charge Control Equation
  • To solve for v(t) an approximate solution can be obtained by assuming an exponential distribution for δp at every instant during the decay
  • Quasi-steady state approximation neglects distortion due to the slope requirement at xn=0

Non exponential

charge control equation2
Charge Control Equation
  • Not accurate in its details but indicates that the voltage across a pn junction cannot be changed instantaneously
  • Stored charge can present a problem in a diode in switching applications
  • Problems of stored charge can be reduced by
    • Narrow n region (if shorter than hole diffusion length, very little charge is stored
    • Adding recombination centers such as Au to Si

reverse biased turn off of pn junctions
Reverse-Biased Turn-Off of pn Junctions
  • The switch is flipped from VF at t<0 to VR t>0
  • Large reverse current occurs first. Why?

reverse biased turn off
Reverse-Biased Turn-Off
  • Transient time: current drops to 10% of initial reverse current = sum t1 and t2
  • t1 is the constant current phase, t2 is the decay phase
  • During the decay phase, excess charge is being removed primarily by recombination
  • The device approaches steady state dc in the reverse bias condition

large signal charge control model2
Large-Signal Charge-Control Model

Assume p+/n junction with analysis on the n-type side

Continuity equation:

Boundary conditions: initial distribution of holes is a steady state solution to the diffusion equation and under forward bias the voltage across the junction is

reverse biased turn off1
Reverse-Biased Turn-Off

reverse biased turn off2
Reverse-Biased Turn-Off

Reverse-Biased Turn-Off Case

When 0 < t < tS (or t1 ), Cj can be neglected.

Charge control equation

Consider stored charge between 0<t<ts or t1

With the initial conditions i( 0 < t < tS ) = - IR, Qp(0) = IFF

so that

By setting Qstored=0, t1 can be obtained

reverse biased turn off3
Reverse-Biased Turn-Off

Reverse-Biased Turn-Off Case

After t1 , the hole density starts to decrease below its equilibrium value pno. The junction voltage tends to reach –VR and a new boundary condition now holds. This is the decay phase with the initial boundary condition

The solution for t2 is

reverse biased turn off4
Reverse-Biased Turn-Off

Reverse-Biased Turn-Off Case

For a plane junction with the length of the n-type material W much greater than the diffusion length W>>Lp, for a large IR/IF ratio, the transient time can be approximated as

For a a narrow base junction with W<<Lp

midterm short paper
Midterm Short Paper

2-3 pages



Basics of material (if needed)

Basics of operation

How it relates to SDM1

Technical Relevance, Overall Impact, Applications

Future Work

Experimental plan, Milestones

Equipment and/or simulation program

Expected Outcomes (optional)

References (IEEE Style)

midterm short presentation
Midterm Short Presentation

10 minutes total including questions

5-7 slides

All figures must be referenced in the caption if from article or book

Feedback evaluations from Prof. to provide input on speaking and content