Peak Electric Field Junction breakdown occurs when the peak electric field in the P junction reaches a critical value. For the + P junction, qa E ( x) ( xp x), s W dep 2 s ( bi Vr ) 2 s potential barrier x q q ( is the lighter doping density in a one-sided junction) qa qa 2 s( bi Vr ) 2q Ep E (0) xp ( bi Vr ) s s q s 1/ 2 p 2q E crit ( bi V B ) s 1/ 2 6 E crit : 10 / V cm for Si 2q 2 Es crit V B bi The field distribution in a one-side P junction. (a) + P junction with x 0 and (b) electric field profile.
Tunneling Breakdown (Zener Process, Field Ionization) Tunneling: purely quantum mechanical nature (no classical analogy) Two major requirements for tunneling to occur There must be filled states on one side of the barrier and empty states on the other side of the barrier at the same energy. The width of the potential energy barrier, d, must be very thin, (d < 100Å ), and the height, h, must be low for higher of probability of tunneling.
Tunneling Breakdown (Zener Process, Field Ionization) Dominant breakdown mechanism when is very high and V B is quite low. Heavily doped junction at zero bias E Fp h E g e - bi Vr Available empty states for tunneling E Fn reverse bias with electron tunneling from valence band to conduction band Available filled states for tunneling d W V : slow increase with V (< 100Å ) ( E E )/ kt ( qv )/ kt dep bi r r # of available electrons for tunneling in valence band n e e Fn Fp r : fast increase with V r H / E 1/ E p Tunneling current, J Ge e where H E m 3/ 2 1/ 2 E p g n, p (G and H are constant for a given semiconductor) p More tunneling current can flow as increasing reverse bias. The breakdown voltage decreases as the temperature goes up, because the tunneling probability increases.
Avalanche Breakdown (Impact Ionization) When the peak electric field, E p, reaches a critical field, E crit, carrier multiplication rate due to impact ionization and the reverse current rise abruptly. This is called avalanche breakdown. Carriers are not much accelerated during mean free path between collision. E E E g E E g E multiplication factor, 1 M 1 V / V Carrier multiplication due to impact ionization B n, n3 ~ 6 at small reverse bias at large reverse bias mean free path (~10-6 cm) W dep W dep The energy transferred per collision becomes sufficient to ionize a semiconductor atom, called impact ionization Electron jumps from valence band to conduction band, creating electron-hole pair.
E E 2q 2q 2 2 s crit s crit V B bi 0.6 17 10 VB ( V ) 15 1/ In general, it is necessary and effective to reduce the junction doping concentration(s) if a larger breakdown voltage is desired. V ( GaAs) V ( Si) V ( Ge) B B B The energy required to initiate the impact ionization increases (and therefore, E crit, also increases) with increasing band gap energy, E g. E crit 510 V / cm at 10 cm and ~ 0.6 5 17 3 0.2 V V at cm B 17 3 15 10. VB, ast The lattice scattering increases as the temperature increases. Increasing lattice scattering means a smaller mean free path (not much time to get sufficient energy from the field), a larger critical electric field for avalanching, and hence a higher breakdown voltage.
Qualitative Description of Ideal Diode Equation At equilibrium (V = 0) electron diffusion E E electron drift D C (E)f(E) q bi - E C E F q bi E V hole drift hole diffusion p-to-n-side drift electron current precisely balances the n-to-p side diffusion electron current under equilibrium, vice versa for hole. (J n = 0, J p = 0 J = 0)
At forward bias ( V > 0) Large electron diffusion (due to exponentially increased electron concentration) q V bi electron drift unchanged E C E Fn E Fp q V bi E V hole drift unchanged Large hole diffusion (due to exponentially increased hole concentration) # of carriers that have sufficient energy to surmount the potential barrier goes up exponentially with V (because barrier height decreases linearly with V). net electron flow net hole flow Large and exponentially increasing current flow J = J n,diffusion + J p,diffusion
At reverse bias ( V < 0) q V bi electron drift unchanged negligible hole and electron diffusion J n,diffusion + J p,diffusion 0 q V bi hole drift unchanged net electron flow net hole flow current flow J = J n,drift + J p,drift : small and constant current flow at all biases
The supply of minority carriers on each side of the junction required to participate in the drift component of current is generated by thermal excitation of electron-hole pair, called the generation current. I rectifier I I diffusion V exp( ) V ref V V=0, at equilibrium I gen I drift constant, called reverse saturation current ote that the minority carrier drift currents are not affected by the height of the potential hill (constant current regardless of applied reverse bias) Water fall anology kt if Vref : thermal voltage q I I e : Ideal Diode Equation ( qv / kt 1) 0 Same amount of water flows regardless of the height of the water fall
Carrier Injection under Forward Bias: Quasi-Equilibrium Boundary Condition Assumptions: 1) Steady state 2) ondegenerately uniformly doped 1-D step junction 3) Low level injection in the quasi-neutral region (minority carrier concentration << majority carrier concentration) 4) o other processes other than drift, diffusion, and thermal recombinationgeneration ( E )/ ( EFp EV )/ kt C EFn kt nce, p Ve ( E )/ ( EFp EV )/ kt C EFn kt np Ce Ve e C ne V 2 qv / kt i ( E E )/ kt C V e ( E E )/ kt Fn Fp : Law of the junction x A forward bias reduces the junction barrier to ϕ bi V and allows electrons and holes to be injected over the reduced barrier. xp
Quasi-Equilibrium Boundary Conditions n( x ) p( x ) n e 2 qv / kt P P i n n p n n( xp) e e n e e p( x ) p( x ) where p( x ) p Similarly, P 2 2 i qv / kt P0 P0 qv / kt qv / kt i qv / kt P0 P P a P0 This is because majority carrier concentration at depletion edge remains almost unchanged from its equilibrium value under low level injection. n n p n p( x) e e p e e n( x ) n( x ) 2 2 i qv / kt P0 P0 qv / kt qv / kt i qv / kt 0 d n n( xp) np0e e 2 qv / kt i qv / kt a qv / kt 2 ni qv / kt p( x) p0e e or d n at x p (electron density at the edge of the neutral P region) is determined by E c E fn. Similarly, p at -x is determined by E v E Fp. Quasi-equilibrium boundary condition (or Shockley boundary condition) for minority carrier at depletion edge - / qv kt n( x ) n x n n ( e 1) P P P0 P0 p x p x p p e qv / kt ( ) ( ) 0 0( 1) Quasi-equilibrium boundary condition for excess minority carrier at depletion edge