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Fig. 2.5 shows the typical structure for a p-i-n diode. A lightly doped N- layer is grown on the top of a heavily doped N+ substrate. The typical doping concentration for each layer is shown on the figure. In high power applications, the requirement for reverse blocking voltage is normally very high. To avoid the avalanche break down, the electric field in the depletion layer needs to be kept belowE_{BD. According to Eqns. 2.40and2.42, the maximum}

electric field will decrease if the doping concentration decreases. Therefore, the lightly doped drift region is designed to absorb the depletion layer of the reverse biased P+_N− _junction.

Considering that the breakdown voltage VBD is much higher than contact potential ψc, it

can be estimated from Eqns. 2.39 and 2.42, as shown in 2.54.

VBD ≈ εE2

BD

2qNd

(2.54) The depletion layer width is also highly dependent on the doping concentration according to Eqn. 2.39. Therefore, the most of the depletion layer contains in the lightly doped drift region. This parameter is very important for the design of non-punch-through (NPT) devices, since the width of drift region must be longer. The reverse blocking voltage is considered as the dark area shown in Fig. 2.6. Therefore, the minimum drift region width Wd required

P+ N- Drift region N+ Substrate Depletion layer Anode Cathode Wd

Typical doping level: P+: Na=1019cm-3

N-: N_d=1014_cm-3

N+: Nd=1019cm-3

Figure 2.5: Cross section view of a typical p-i-n diode. Wd indicates the drift region width.

Wd≥W(VBD) =

2VBD

E_BD (2.55)

For power diode used in high voltage applications, the drift region width for NPT devices needs to be relatively long in order to accommodate the depletion layer, hence more Si is needed for the production of such device. Punch-through (PT) devices are designed to overcome this problem. Fig. 2.6 shows the distribution of depletion layer in NPT and PT devices. The same blocking voltage capability can be obtained with shorter drift region. In the case of PT devices, the increase of reverse voltage can not extend beyond the N- region thickness (Wd). The electric field at the edge of N-N+ junction starts to rise. When the

doping concentration of the N- drift region is very low, the shape of the electric field is flatten out and becomes more rectangular, as shown in Fig. 2.6b. It is clear that the required drift region width for the PT devices are approximately one-half of that required for the NPT devices.

According to Eqn. 2.41, the depletion layer width of the drift region will be quite large because of the low doping level. This would appear to lead to high on-state resistance hence

E EBD Wd x VBD P+ N- N+ E Wd x V_BD P+ N- N+

(a) NPT p-i-n diode (b) PT p-i-n diode EBD

Figure 2.6: The distribution of depletion layer in (a) NPT and (b) PT p-i-n diode. limit the forward conduction capability of power diode. However as a bipolar device, a large amount of excess holes are injected into the drift region from the forward biased PN junction during on-state. When the injected hole density (∆p) is greater than the thermal equilibrium electrons of the drift regionnn0, it cannot be neutralised by the electrons of the drift region.

The positive space charge attracts the electrons to be inject into the drift region from the N+ region. When ∆p _≫ nn0, the excess hole and electron densities are approximately

equal. This double injection process is termed conductivity modulation. Such a mechanism reduces the on-state resistance of the drift region hence ensures the design of N- drift region practically valuable.

Fig. 2.7 shows the spatial distribution of the excess carrier caused by conductivity mod- ulation. In the drift region, it is flattened if the diffusion length L is greater than the Wd.

The current in the drift region can be written approximately as Eqn. 2.56 by assuming the electric field distribution in the drift region is uniform and the voltage across it is not high enough to cause carrier velocity to saturate. Here, Vd is the voltage over the drift region, A is the cross section area of the drift region, n is the excess carrier density defined in the

p(x)=n(x)=n

n

p

_p

n

n

(x)

p

(x)

N-

P+

N+

hole injection

electron injection

x

Figure 2.7: Conductivity modulation.

figure, and Qd is the stored charge in the drift region. Therefore, Vd can be derived and is

shown, Eqn. 2.57. The on-state voltage drop VF across the diode is the sum of the voltage

drop over PN junction Vj and Vd. Vj can be estimated according to Eqn. 2.50, hence VF

can be summarized as Eqn. 2.58. Js, τ and µ are highly temperature dependent values as

discussed before, henceVF varies with temperature. IF ≈qµnaAEd= qµnaAVd Wd ≈ Qd τ ≈ qnaAWd τ (2.56) Vd≈ W2 d µτ (2.57) VF =Vj+Vd≈ kT q ln( JF Js ) + W 2 d µτ (2.58)

limited by Wd and the current density. Therefore, the larger reverse blocking capability, the

greater on-state power loss. In the case of high-level injection, the excess carrier density gets larger than the doping density, the band-to-band recombination in the drift region increase significantly and become dominant instead of the trap recombination. Therefore, the carrier lifetime decreases and lead to the increase of Vd. Furthermore, carrier mobilities decreases

with the increasing excess carrier density. In the case of high-level injection when excess carrier densities reach a certain level, the Coulomb scattering between free carriers increases significantly hence limits the mobility.