ECSE-6230 Semiconductor Devices and Models I Lecture 10

1. 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 e-mail: sawyes@rpi.edu May 24, 2014 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html 1

2. Lecture Outline Junction Breakdown Zener Breakdown Avalanche Breakdown PN Junction Switching Characteristics Charge Control Constant Current Turn Off Reverse Bias Turn Off Midterm notes

3. 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. sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

4. 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 ) sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

5. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

6. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

7. 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 junction. sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

8. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

9. 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 is sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

10. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

11. 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 and 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) sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

12. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

13. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

14. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

15. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

16. Avalanche Breakdown Voltage With   rj / WDm , Cylindrical curvature: And spherical curvature As the radius of curvature becomes smaller, so does the breakdown voltage sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

17. Avalanche Breakdown Voltage sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

18. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

19. 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. sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

20. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

21. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

22. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

23. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

24. 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? sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

25. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

26. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

27. Reverse-Biased Turn-Off sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

28. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

29. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

30. 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 sawyes@rpi.edu www.rpi.edu/~sawyes/courses.html

31. Midterm Short Paper 2-3 pages Introduction Background 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)

32. 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