6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-1 Contents: Lecture 5 - Carrier generation and recombination (cont.) September 12, 2001 1. G&R rates outside thermal equilibrium 2. Surface generation and recombination Reading assignment: del Alamo, Ch. 3, 3.4, 3.6
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-2 Key questions What happens to the balance between generation and generation when carrier concentrations are perturbed from thermal equilibrium values? How is this balance upset for each G&R mechanism? What are the key dependencies of this imbalance in G&R rates? How can surface G&R be characterized?
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-3 1. G&R rates outside equilibrium In thermal equilibrium: n = n o p = p o G oi G o = R oi = R o Outside thermal equilibrium (with carrier concentrations disturbed from thermal equilibrium values): n n o G i p p o R i G R n o n=no G o = R o G = R E v E v p o p=p o thermal equilibrium outside thermal equilibrium
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-4 If G R, carrier concentrations change in time. Useful to define net recombination rate, U: U = R G Reflects imbalance between internal G&R mechanisms: if R>G U>0, net recombination prevails if R<G U<0, net generation prevails If there are several mechanisms acting simultaneously, define: U i = R i G i and U =ΣU i What happens to the G&R rates of the various mechanisms outside thermal equilibrium?
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-5 a) Band-to-band optical G&R n o n>no G o,rad = R o,rad p o E v E v G rad = G o,rad R rad > R o,rad p>p o thermal equilibrium with excess carriers optical generation rate unchanged since number of available bonds unchanged: G rad = g rad = r rad n o p o optical recombination rate affected if electron and hole concentrations have changed: define net recombination rate: R rad = r rad np U rad = R rad G rad = r rad (np n o p o ) if np > n o p o, U rad > 0, net recombination prevails if np < n o p o, U rad < 0, net generation prevails note: wehaveassumedthatg rad and r rad are unchanged from equilibrium
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-6 b) Auger G&R Involving hot electrons: n o n>no G o,eeh = R o,eeh p o E v E v G eeh > G o,eeh R eeh > R o,eeh p>p o thermal equilibrium with excess carrier G eeh = g eeh n R eeh = r eeh n 2 p If relationship between g eeh and r eeh unchanged from TE: U eeh = R eeh G eeh = r eeh n(np n o p o ) Involving hot holes, similarly: Total Auger: U ehh = r ehh p(np n o p o ) U Auger =(r eeh n + r ehh p)(np n o p o )
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-7 c) Trap-assisted thermal G&R n o n>n o E t E v r o,ec =r o,ee r o,ec >r o,ee r o,hc =r o,he E t E v r o,hc >r o,he p o p>p o thermal equilibrium with excess carriers Out of equilibrium, if rate constants are not affected: r ec = c e n(n t n t ) r ee = e e n t = c e n i n t r hc = c h pn t r he = e h (N t n t )=c h n i (N t n t ) Recombination: capture of one electron + one hole net recombination rate = net electron capture rate = net hole capture rate U tr = r ec r ee = r hc r he From this, derive n t, and finally get U tr : U tr = np n o p o τ ho (n + n i )+τ eo (p + n i )
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-8 d) All processes combined U = U rad + U Auger + U tr
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-9 Special case: Low-level Injection Define excess carrier concentrations: n = n o + n p = p o + p LLI: Equilibrium minority carrier concentration overwhelmed but majority carrier concentration negligibly disturbed thermal equilibrium low-level injection high-level injection po ni n o log n' p' -forn-type: p o n p n o -forp-type: n o n p p o
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-10 In LLI: np n o p o = n o p o + n o p + p o n + n p n o p o (n o + p o )n All expressions of U follow the form: U i n τ i τ i is carrier lifetime of process i, a constant characteristic of each G&R process: τ rad = 1 r rad (n o + p o ) τ Auger 1 (r eeh n o + r ehh p o )(n o + p o ) τ tr τ hon o + τ eo p o n o + p o Under LLI, net recombination rate depends linearly on excess carrier concentration through a constant that is characteristic of material and temperature.
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-11 If all G&R processes are independent, combined process: with U n τ 1 τ =Σ1 τ i The G&R process with the smallest lifetime dominates. Physical meaning of carrier lifetime: U is rate of net recombination rate in unit volume in response to excess carrier concentration n (linear in n ) 1 U is mean time between recombination events in unit volume τ = n U is mean time between recombination event per excess carrier, or average time excess carrier will survive before recombining constant characteristic of material
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-12 For n-type material, n o p o : τ rad = 1 r rad n o τ Auger = 1 r eeh n 2 o τ tr = τ ho 1 N t log τ τ Auger τ rad τ tr n ō 2 n ō 1 log n o
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-13 Trap recombination (n-type material): Lifetime does not depend on n o [trap occupation probability rather insensitive to n o ] E t E F E v rhc is bottleneck Lifetime depends on trap concentration as τ N 1 t
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-14 Measurements of carrier lifetime in Si at 300 K 1E-1 1E-1 1E-2 1E-2 1E-3 1E-4 n-si T=300 K 1E-3 1E-4 p-si T=300 K carrier lifetime (s) 1E-5 1E-6 carrier lifetime (s) 1E-5 1E-6 1E-7 1E-7 1E-8 1/τ=7.8x10-13 N D +1.8x10-31 N D 2 1E-8 1/τ=3.5x10-13 N A +9.5x10-32 N A 2 1E-9 1E-9 1E-10 1E+13 1E+14 1E+15 1E+16 1E+17 1E+18 1E+19 1E+20 1E+21 donor concentration (cm-3) 1E-10 1E+13 1E+14 1E+15 1E+16 1E+17 1E+18 1E+19 1E+20 1E+21 acceptor concentration (cm-3) For low doping levels, N A,D < 10 17 cm 3, τ tr dominates: τ depends on material quality and process wide data scatter N t correlated with N A,D τ N 1 A,D For high doping levels, N A,D > 10 18 cm 3, τ Auger dominates: intrinsic recombination: tight data distribution τ N 2 A,D
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-15 2. Surface generation and recombination Surface: severe disruption of periodic crystal lots of traps (G&R centers) lots of traps semiconductor bulk Under LLI: U s Sn (s) S surface recombination velocity (cm/s) note units: U s (cm 2 s 1 )=S(cm s 1 ) n (cm 3 ) S is perpendicular component of velocity with which excess carriers dive into the surface to recombine.
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-16 Key conclusions Excess np product is driving force for net generation/recombination. Under low-level injection: with τ carrier lifetime. U n τ Carrier lifetime: mean time that an average excess carrier survives before recombining. In Si around 300K, τ N 1 for low N (trap-assisted recombination), τ N 2 for high N (Auger recombination). Order of magnitude of key parameters for Si at 300K: τ 1 ns 1 ms, depending on doping
6.720J/3.43J - Integrated Microelectronic Devices - Fall 2001 Lecture 5-17 Self study Carrier extraction, generation lifetime