6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 11-1 Lecture 1 2 - Carrier Flow (cont.) March 2, 2007 Cont ents: 1. Transport in space-charge and high-resistivity regions 2. Carrier multiplicati on and avalanche breakdown Reading assignment : del Alamo, Ch. 5, §5.7 Seminar: Matthias Passlack (Freescale Semiconductor) High Mo-bili ty III-V MOSFET Technology.March6, 2007, 4-5 PM (reception at 3:30 PM). Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 11-2 Key questions • What ch a racterizes space-charge-region-type situations? • How does impact ionization a ffect space-charge-region type sit-uations? Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 11-3 1. Transport in space-charge and high-resistivity regions In regions with very low carrier concentrations: • dielectric relaxation time long → majority carriers take a long time to screen out charge perturbations i.e.: for 1012 cm−3 Si (ρ � 104 Ω · cm), τd � 10 ns • Debye length long → net charge can exist over substantial spa-tial extent i.e.: for 1012 cm−3 Si, LD � 4 µm Transport physics quite different from QN regions. Key approximation: E independent of n, p: • E imposed f rom outside (i .e. high resistivity region under bias), or • E set by spatial distribution of dopants (depletion region) Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 11-4 Overview of simplified carrier flow formulations General drift-diffusion� situation� (Shockley's equations) 1D approx. Quasi-neutral� situation� (negligible volume� charge) Majority-carrier � type situation� (V=0, n'=p'=0) Space-charge� situation� (field independent� of n, p) Minority-carrier � type situation� (V=0, n'=p'=0, LLI) Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 11-5 Example: Drift in a high-resistivity r egion under external electric field +V + + --gl + -ε 0 Lx J qgl 0 Jt Je Jh 0 xo Lx n',p' 0 x0 L n' p' xo Electric field sepa rates photogenerated carriers: Je = qgl for x < xo Jh = qgl for x > xo Jt = qgl everywhere Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 11-6 3. Carrier mu ltiplication and avalanche breakdown If E high, impact ionization may take place → carrier multiplication ε + -Ec Ev If E high enough, carrier avalanche possible → avalanch e break-down • Dominant breakdown mechanis m in semiconductor devices → imposes limit to maximum voltage • Noisy Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.7205/3.435 - Integrated Microelectronic Devices - Spring 2007 Impact ionization + new generation mechanism: a, - - electron impact ionization rate (emp1) ah -- hole impact ionization rate (emp1) a - average number of ionizations per unit length per carrier l/a mean distance between I1 events per flowing carrier a is strongly dependent on I: Cite as: leslis del Alamo, course materials for 6.7201 Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month W]6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 11-8 Example: carrier multiplication in a high-resistivity region with uniform e lectric field High-resistivity uniformly-doped sample under E: +V --gl + -ε J Jt=qgl 0 qgl Je=qgl Jh=00 xL no impact ionization J impact ionization with αe>αh Jt 0 qgl Je Jh 0 L x Jt = qglM ≥ qgl M ≡ Mu l tiplication coefficient [n.u . ] Two limits to M: • if E small, M → 1 • for hig h enough E, M diverges: avalanch e breakdown Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 11-9 Calculation for 1 µm long Si sampl e: 0 5 10 15 20 Multiplication factor, M (cm-1 ) 1E-09 1E-08 1E-07 1E-06 1E-05 1E-04 1E-03 1E-02 1E-01 1E+00 1E+01 1E+02 M-1 (cm-1 ) M-1 M 0E+00 1E+05 2E+05 3E+05 4E+05 5E+05 Electric Field (V/cm) For example above: • critical breakdown field: Eb = 4. 9 × 105 V/cm • Breakdown voltage: BV = 49 V Cite as: Jesús del Alamo, course materials for 6.720J Integrated Microelectronic Devices, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].6.720J/3.43J - Integrated Microelectro nic Devices - Spring 2007 Lecture 11-10 Key c onclusions • In a quasi-neutral, ch a rge redistribution takes place in scale of dielectric relaxation time. • Majority -carrier type situations can be consi dered quasi-static. • Minority-carrier type situations show subs tantial memory. • Time constants in minority-carrier type situations: – carrier lifetime – transit time ∝ L2/D – which ever one is smallest dominates • SCR/high-resistivity