Eel732 Hw Vii

Home Assignment - VII (EEL732)Adersh Miglani

Adersh.Miglani@gmail.com13-Sep-2013

Assignment: Submit a report on how Lateral Merged Dou-ble Schottky (LMDS [1]) rectifier work and solve leakagecurrent and forward voltage drop problems. Also explain howLMDS rectifier lowers image force barrier lowering (IFBL)effect.

Solution: In case of conventional Schottky barrier rectifier,the common non-ideal effect is IFBL also called Schottkyeffect. The other two desirable outcome from a rectifier arelow leakage current and low forward voltage drop. First, theseeffects are explained and, later, we discuss how these effectsare reduced in case of LMDS over conventional Schottkybarrier, lateral low barrier Schottky (LLBS) and lateral highbarrier Schottky (LHBS) rectifiers.

1) Image Force Barrier Lowering: In an ideal case forSchottky barrier rectifier, the potential barrier to the elec-tron flowing from metal to semiconductor is unchanged.But, the barrier height, φB0 = (φm − χs) where φmis metal work function and χs is electron affinity forsemiconductor, also depends on the applied voltage.Within the semiconductor an electron at a distance +xinduces a positive charge on the metal surface as if animage charge +e is located at the same distance −xfrom the metal surface. The force of attraction betweenthese two charges is called image force and is

F =(−e)(+e)4πεs(2x)2

=−e2

16πεsx2

The potential energy of an electron at a distance +x is

E(x) =

∫ x

∞F dx =

e2

16πεsx

The potential at point +x is

−φ(x) = E(x)

−e=

−e16πεsx

With an applied electric field E the net potential is

−φ(x) = −e16πεsx

− E x

Thus, peak potential barrier is lowered. This effect iscalled image force barrier lowering (IFBL) or Shottkybarrier lowering as shown in Fig. 1. This effect dom-inates when Schottky barrier rectifier is under reversebias. The lowering effect4φ and its position from metalsurface xm can be computed by the following condition[3].

d(e φ(x))

dx= 0

Fig. 1. Energy band diagram of a metal-semiconductor junction. φm is metalwork function. The effective barrier φB is lowered by 4φ when an electricfield E is applied. (From [2])

e

16πεsx2m− E = 0⇒ xm =

√e

16πεsE

Use xm in equation for φx, we get

−4φ =−e

16πεs√

e16πεsE

− E√

e

16πεsE

−4φ = 2

√eE

16πεs=

√eE

4πεs

2) Reverse Leakage Current and Forward VoltageDrop: If Schottky barrier height is reasonably smallerthan the band gap, the reverse current (JR) wouldincrease gradually with increase in reverse bias voltage.The dependence of JR on reverse bias voltage before thebreakdown voltage is not a desired behavior. The reverseleakage current should be as minimum as possible. Also,in conventional Schottky barrier rectifier, the reversebreakdown is relatively slow because the peak electricfield is large at the metal-semiconductor contact. Theforward voltage drop (VF ) of Schottky barrier rectifieris a function of barrier height. Though VF is less thanthe conventional PN junction diode, it can be furtherreduced if barrier lowering effect is reduced. Thus,barrier lowering effect is undesired behavior.

LMDS Rectifier: In schottky barrier rectifier, the differencein the work function of metal and electron affinity of semi-conductor plays the key role in achieving desired forward andreverse bias characteristics. The LMDS provides reduction inreverse leakage current by about three orders of magnitude

between 100 to 1000 V reverse bias with low forward voltagedrop. The reverse breakdown voltage is also increased withsharp reverse bias characteristics. While reviewing LMDS, wewould refer the forward and reverse bias characteristics oflateral low barrier Schottky (LLBS) and lateral high barrierSchottky (LHBS) rectifiers. The reason is that LLBS provideslow forward voltage drop and LHBD provides good reversecharacteristics.

1) If a metal is chosen such that the barrier height is low-ered, the forward voltage drop, VF , would be loweredbut the reverse leaking current JR would be higher.Conversely, if barrier height is more, reverse leakagecurrent JR is reduced but forward voltage drop, VF ,would become higher. So, there is a trade off betweenthe VF and JR. To summarize, the forward voltagedrop should be lower and reverse breakdown should besharp with low reverse leakage current because Schottkyrectifiers are generally used in power integrated circuits.

2) In LMDS, anode consists of Titanium (Ti), a metalwith lower Schottky barrier height (= 0.85 V ) inbetween two trenches of Nickel (Ni), a metal with highSchottky barrier height (= 1.5 V ). The cathode contactis contacted with N+ region on both the sides of thedevice.

3) Barrier Height Lowering: The LMDS has a simplemodel for barrier height lowering as given by

4φB = a [Eavg]12 + b (1)

where Eavg is the average electric field at the Schottkycontact and a and b are constants. These constants aresimulated such that desired reverse bias behavior can beachieved. Therefore, modeling of LMDS is importantin determining a and b. These constants should becomputed for Ni and Li metals separately.

Fig. 2. Forward bias characteristics for LMDS, LLBS and LHBS. (From[1])

4) Forward Characteristics: The forward voltage drop forLMDS rectifier is very close to LLBS rectifier as shownin Fig. 2. In forward bias, the effect of low barrierSchottky height (Ti) dominate over high barrier Schottkyheight (Ni) in case of LMDS. Thus, under forward bias,LMDS behaves as a LLBS.

Fig. 3. Reverse bias characteristics for LMDS, LLBS and LHBS. (From [1])

5) Reverse Characteristics: The Fig. 3 shows that reversebias characteristics strongly depends on the Schottkybarrier height. The reverse leakage current increasesvery rapidly in case of LLBS and LHBS rectifiers. But,in case of LMDS rectifier, the reverse leakage currentincreases merely in an order or 2 to 3 as reverse bias isincreased from 100 to 1000 V. Also, LLBS and LHBShas slow reverse breakdown but LMDS shows sharpreverse break down which is the desired behavior.

6) Effect of Barrier Height Lowering: As reverse voltageincreases, the barrier lowering increases faster for LLBSrectifier. This results in large leakage current. But, the% lowering for LHBS rectifier is lesser as compared toLLBS rectifier. This causes low reverse leakage currentfor LHBS rectifier. In case of LMDS rectifier, the regionbetween two HBS trenches experiences pinch-off underreverse bias and this results in a very small change inbarrier lowering with increase in reverse bias voltage.Thus, the reverse leakage current increases by a factorof 2 to 3 only between 100 to 1000 V.

The Schottky barrier diode is a majority carrier device. Itmeans that there is no diffusion capacitance [3]. While switch-ing from forward to reverse bias, there are no minority carriersstored and minority carrier storage time is zero. This makesSchottky barrier rectifiers as fast switching applications. Alongwith various advantages in Schottky barrier rectifiers over PNjunction, LMDS provides additional better forward and reversebias characteristics which makes it suitable for low-loss, high-voltage and high-speed power IC applications.

REFERENCES

[1] Y. Singh, “A new 4h-sic lateral merged double schottky (lmds) rectifierwith excellent forward and reverse characteristics,” IEEE TRANSAC-TIONS ON ELECTRON DEVICES, vol. 48, 2001.

[2][3] D. A. Neamen and D. Biswas, Semiconductor Physics and devices, 4th ed.

Tata McGraw Hill, ISBN(13): 978-07-107010-2, 2012.