6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-1 Contents: Lecture 13 - Carrier Flow (cont.), Metal-Semiconductor Junction October 2, 22 1. Transport in space-charge and high-resistivity regions 2. Carrier multiplication and avalanche breakdown 3. Ideal metal-semiconductor junction in TE Reading assignment: del lamo, Ch. 5, 5.8-5.1; Ch. 6, 6.1 nnouncements: Quiz 1: October 1, Rm. 5-34 (Walker), 7:3-9:3 PM; lectures #1-13 (up to metal-semiconductor junction). Open book. Calculator required.
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-2 Key questions What characterizes space-charge-region-type situations? How does impact ionization affect space-charge-region type situations? What happens when you bring together a metal and a semiconductor in intimate contact?
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-3 1. Transport in space-charge and high-resistivity regions In regions with very low carrier concentrations: dielectric relaation time long majority carriers take a long time to screen out charge perturbations i.e.: for 1 12 cm 3 Si (ρ 1 4 Ω cm), τ d 1 ns Debye length long net charge can eist over substantial spatial etent i.e.: for 1 12 cm 3 Si, L D 4 µm Transport physics quite different from QN regions. Key approimation: E independent of n, p: Eimposed from outside (i.e. high resistivity region under bias), or Eset by spatial distribution of dopants (depletion region)
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-4 Overview of simplified carrier flow formulations General drift-diffusion situation (Shockley's equations) 1D appro. Quasi-neutral situation (negligible volume charge) Space-charge situation (field independent of n, p) Majority-carrier type situation (V=, n'=p'=) Minority-carrier type situation (V=, n'=p'=, LLI)
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-5 Eample: Drift in a high-resistivity region under eternal electric field g l +V - + - + + ε - L J qg l Je Jt Jh o L n',p' p' n' o L Electric field separates photogenerated carriers: J e = qg l for < o J h = qg l for > o J t = qg l everywhere
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-6 2. Carrier multiplication and avalanche breakdown If E high, impact ionization may take place carrier multiplication ε + - E c E v If E high enough, carrier avalanche possible avalanche breakdown Dominant breakdown mechanism in semiconductor devices imposes limit to maimum voltage Noisy
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-7 Impact ionization new generation mechanism: G ii = α e F e (drift) + α h F h (drift) α e electron impact ionization rate (cm 1 ) α h hole impact ionization rate (cm 1 ) α average number of ionizations per unit length per carrier 1/α mean distance between II events per flowing carrier α is strongly dependent on E: 1E-6 1E-5 1E-4 1E-3 1E-2 1E-1 1E+ 1E+1 1E+2 1E+3 E+ 1E-5 2E-5 3E-5 1/electric field (cm/v) Impact ionization coefficient (cm -1 ) α e T=3 K α h Gas Si
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-8 Eample: carrier multiplication in a high-resistivity region with uniform electric field High-resistivity uniformly-doped sample under E: g l +V + ε - - - J no impact ionization J t =qg l J e =qg l J h = L qg l J impact ionization with αe>αh J t Je J h qg l L J t = qg l M qg l M Multiplication coefficient [n.u.] Two limits to M: if E small, M 1 for high enough E, M diverges: avalanche breakdown
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-9 Calculation for 1 µm long Si sample: 2 1E+2 1E+1 1E+ Multiplication factor, M (cm -1 ) 15 1 5 M-1 M 1E-1 1E-2 1E-3 1E-4 1E-5 1E-6 1E-7 M-1 (cm -1 ) 1E-8 1E-9 E+ 1E+5 2E+5 3E+5 4E+5 5E+5 Electric Field (V/cm) For eample above: critical breakdown field: E b =4.9 1 5 V/cm Breakdown voltage: BV =49V
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-1 3. Ideal metal-semiconductor junction in TE First, ideal metal-metal junction in TE: Eo Eo WM1 WM2 EF2 EF1 a) two metals far apart Eo EF1 WM1 WM2 Eo EF2 b) two metals just before contact Eo q bi WM1 WM2 EF c) two metals in intimate contact dipole charge at interface built-in potential
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-11 r o e o f o f bi E p qf bi Spatial etent of SCR in MM junction: a few nm
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-12 Can define local work function Think of photoelectric eperiment vs. position: - hυ hυth metal 1 metal 2 W M1 W M2 hυth metal 1 metal 2 WM1 WM2 Can define local vacuum energy E o Shape of E o identical to potential energy φ bi = 1 q (W M1 W M2 )
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-13 Key conclusions SCR/high-resistivity regions: electric field independent of carrier concentrations behavior of electrons and holes independent of each other and of the background carrier concentrations Carrier multiplication can lead to avalanche breakdown at high fields limit to maimum voltage: breakdown voltage. Junction of dissimilar materials dipole charge at interface built-in potential.
6.72J/3.43J - Integrated Microelectronic Devices - Fall 22 Lecture 13-14 Self study Simplification of Shockley s equations for space-charge and highresistivity regions Comparison between SCR and QNR transport.