Chapter 6 P-N DODES Junctions between n-and p-type semiconductors are extremely important foravariety of devices. Diodes based on p-n junctions produce nonlinear current voltage characteristics which can be exploited for numerous applications.
P-N DODE: NONLNEAR CURRENT-VOLTAGE An ideal diode is conducting in one direction of bias and non-conducting in the reverse bias case. V C, the cut-in voltage in forward bias should approach zero. o, the reverse bias current, should be zero. V Conducting in forward bias mode p n o V C V Non-conducting in reverse bias mode Diode symbol
NON-DEAL EFFECTS N A P-N DODE A built-in voltage arises when a p-n junction is formed. n V bi = n p p k B T ln n2 i E vac E vac eχ eχ eφ sn eφ sp E c E c E Fn E Fp E v a) E v Hole density, p p Electron density, n p Electron density, n n Hole density, p n E vac Junction formation E c Drift Depletion of mobile charge Diffusion of electrons E vac E v Holes Diffusion Electrons E c Fermi level is flat p-type W p W n Drift n-type b) E v Mobile carriers electrons on n-side, diodes on p-side) are swept away from the depletion region.
DEPLETON REGON AND CURRENT FLOW A p-n diode has a depletion region on the n-side and on the p-side. W p V) = 2ε V bi V) e N d N a N a N d ) 1/2 Neutral p-region Neutral n-region W n V) = WV) = 2ε V bi V) e 2ε V bi V) e N a N d N d N a ) N a N d N a N d 1/2 1/2 W p 0 W n a) negatively charged region positively charged region F Electric field direction Holes { Diffusion particle flow Drift particle flow Diffusion current flow Drift current flow Electrons { Diffusion particle flow Drift particle flow b) Diffusion current flow Drift current flow There are four terms in the current flow, as shown. At zero bias the total current is zero. At forward bias the minority current injected over the junction increases exponentially. At reverse bias the current saturates.
BAND PROFLE N A P-N DODE EQULBRUM FORWARD BAS REVERSE BAS V f V r p n p n p } Depletion region a) n V bi V n V bi V f V bi V r V p b) E Fn E Fp E E Fn ev Fn E f Fp E Fp EFp E Fp ev r E Fn E Fn c) FORWARD BAS: Depletion region decreases. Minority carriers injected electrons injected from the n-side into the p-region holes injected from the p-side into the n-region) control the current. REVERSE BAS: Depletion region width increases. Saturation current is made up of holes diffusing into the p-side from the n-side) and electrons diffusing into the n-side from the p-side.
CURRENT FLOW N A P-N DODE UNBASED DEVCE Electron density in the p-side depletion edge E Fp Fraction of electrons able to be injected into the n-side } Fraction of holes able to be injected into the n-side } Electron density versus energy on the n-side depletion edge E Fn Zero bias: Diffusion current = drift current FORWARD BAS Current increases exponentially with applied bias E Fp Fraction of electrons able to be injected into the n-side V Fraction of holes able to be injected into the n-side E Fn Zero bias: Diffusion current >> drift current Current saturates REVERSE BAS E Fp Negligible density of holes able to cross the barrier V Negligible density of electrons able to cross the barrier E Fn Reverse bias: Diffusion current ~ 0
MNORTY CHARGE DSTRBUTON AND CURRENT N A FORWARD BAS DODE a) p Depletion region W p 0 W n n Excess holes are injected into the n-side. Excess electrons are injected into the p-side. nx) n p n p px) δnx) = nx) n p p n p n δpx) = px) p n b) Minority current holes in n- side, electrons in p-side) decreases exponentailly in a long diode and linerly in a narrow diode. n p p n Equilibrium minority x charge Hole current Total current Electron current c) Electron current minority) Position Hole current minority) x
CURRENT VOLTAGE N A P-N DODE Reverse bias voltage across the diode is limited to V Z due to breakdown effects Forward current V o R L V z V p n Reverse saturation current V out = V z Reverse current = V o V z )/R L a) Zener diode) Forward bias: = S exp ev 1 nk B T n: non-ideality factor n = 1 in ideal diode Vertical: Horizontal: 5 ma/div 5 V/div b)
NON-DEAL EFFECTS N A P-N DODE Recombination-generation effects in the depletion region allow current flow which has a behavior ev GR = GR exp 1 2k B T The total current voltage relation has the form shown below 10 3 10 6 Region 1 Dominated by generationrecombination Region 2 Region 3 = HGH NJECTON REGON Diode behaves like an ohmic resistor V D r S CURRENT A) 10 9 ev exp 1 k B T 10 12 ev exp 1 2kB T 10 15 0.2 0.4 0.6 0.8 FORWARD BAS, V volt) Diode current: = S ev exp 1 nk B T n poor quality diodes n ~ 2 n high quality diodes n ~ 1
MPORTANT SSUES CONTROLLNG SWTCHNG SPEEDS N P-N DODES T = 0 Excess minority charge is injected in a forward bias diode. This charge has to be removed to reverse-bias the diode. δ p x) ncreasing time x Device response in minority carrier devices How fast can minority charge be altered? Recombination with majority carriers. τ ~ 10 6 sec for indirect gap materials τ ~10 9 sec for direct gap materials Recombination via impurities or defects. τ can approach a few picoseconds Narrow width devices to extract charge through contacts. τ dominated by transit time effects
Excess minority charge TURN-ON OF A P-N DODE it) V F R vt) 0 V R a) t 1 Time F ~V F R Current in the diode reaches F it) b) t 1 Time t p n ncreasing time Minority carrier density builds up on the n-side as the diode is forward biased t< t 1 c) 0 n-side axis x vt) V 1 ~k B T n F o ) Voltage across the diode builds up to its final value d) t 1 Time t
Excess minority charge TURN-OFF OF A P-N DODE MPORTANT TME CONSTANTS: Minority carrier lifetime long diode) or minority carrier transit time to the contacts narrow diode) RC time constants for the reverse biased diode. it) R vt) V F 0 t 2 V R Time t a) Diode current in time Diode current path F Static current it) 0 t 2 t 3 t T/2 i F Switching current V a τ sd τ t 0 0 R b) R p n t< t 2 Excess minority charge is removed in a time τ sd p no t = ncreasing time c) 0 n-region x Diode voltage vt) V 0 t 2 τ sd τ t t Voltage across the diode remains positive until all of the excess minority charge is extracted. τ sd is the storage delay time and τ t is the RC time constant V R d) Time
A MODEL FOR A P-N DODE USED N SPCE = R S v D C D i D = S exp ) ev D nk B T 1 C D = eτ T k B T ev S exp D nk B T 1 v D m C j0 /1 V0 ) ) ) ) a) Top contact p n epitaxy p n epitaxy p n n p n body n buried layer p substrate b) Back contact c) DODE CAPACTANCE: Diffusion capacitance important in forward bias) junction capacitance C diff = C j = Aε W e k B T = τ; τ = minority carrier lifetime long diode) τ = transit time to contact narrow diode) C jo 1 V V bi ) m m = 1/2 for abrupt doped diode = 1/3 for linearly graded junctions
A MODEL FOR A P-N DODE USED N SPCE APPLCATONS OF DODES ELECTRONCS OPTOELECTRONCS Logic Circuits Diode Transistor Logic DTL) Voltage clamps to avoid swings in voltage Detectors Avalanche photodetectors Rectifiers for wave shaping Modulators Varactor diodes for tuning circuits, mixers Light emitting diodes Tunnel diodes Microwave diodes Semiconductor lasers