4.3. CURRENT FLOW: P-N DIODE UNDER BIAS 157
4.3.1 DriftandDiffusionCurrentsintheBiasedDiode .............
Thep-ndiode characteristics are dominated by minority carrier flow i.e. electrons entering
thep-side and holes entering from thep-side. When the diode is forward biased the barrier that
electrons (holes) need to overcome to enter thep-side (n-side) from then-side (p-side) decreases.
This allows a higher minority charge injection. In reverse bias, the minority carrier injection is
suppressed. This is shown schematically in figure 4.6. The presence of the bias increases or
decreases the electric field in the depletion region. However, under moderate external bias, the
electricfieldinthedepletionregionisalwayshigherthanthefieldforcarriervelocitysaturation
(E>∼10kV cm−^1 )for most semiconductors.Thusthechangeinelectricfielddoesnotalterthe
driftpartoftheelectronorholecurrentinthedepletionregionandthemagnitudeisdetermined
bytherateofsupplyofminoritycarriersbydiffusionfromthebulktothedepletionregionas
willbedescribedinsection4.5. When no bias is applied we have
pp 0
pn 0= exp (eVbi/kBT) (4.3.3)In the presence of the applied bias, under the assumptions of quasi-equilibrium, we get
p(−Wp)
p(Wn)= exp (e(Vbi−V)/kBT)∼=pp 0
p(Wn)(4.3.4)
We have assumed that the injection of mobile carriers is small (low-level injection) so that the
majority carrier densities are essentially unchanged because of injection, i.e.,p(−Wp)=pp 0.
Taking the ratio of the two equations
pn(Wn)
pn 0= exp (eV /kBT) (4.3.5)This equation suggests that the hole minority carrier density at the edge of then-side depletion
region can be increased or decreased dramatically by applying a bias.
A similar consideration gives, for the electrons injected as a function of applied bias,
np(−Wp)
np 0
= exp (eV /kBT) (4.3.6)From these equation we can see that theexcesscarrierscreatedduetoinjection across the deple-
tion regions are
Δpn=p(Wn)−pn=pn 0 ( exp (eV /kBT)−1) (4.3.7)
Δnp=np(−Wp)−npo=npo( exp (eV /kBT)−1) (4.3.8)
The excess minority carriers that are introduced will decay into the majority region due to
recombination with the majority carriers. For long diodes, the decay is simply given by the ap-
propriate diffusion lengths (Lpfor holes,Lnfor electrons). Using results derived in section 3.9,
δp(x)=Δpnexp ((−(x−Wn)/Lp))
= pn 0 [ exp (eV /kBT)−1]·exp [−(x−Wn)/Lp] (4.3.9)