IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 39, NO.

12, DECEMBER 1992 2813

On the Reverse Blocking Characteristics of Schottky current of Schottky diodes at large reverse bias is partly due to the
Power Diodes pre-avalanche breakdown impact ionization in the depletion region
of the devices. A new model combining impact ionization with
Shang-hui L. Tu and B. Jayant Baliga thermionic-emission reverse current will be presented to describe
the reverse I-Vcharacteristics of Schottky diodes. The use of power
series approximation for the ionization rates a, and a,, allows an-
Abstract-An analytical model for the reverse blocking characteris-
tics of Schottky power diodes has been obtained by incorporating the alytical calculation of the electron multiplication factor (M,,). This
impact ionization multiplication factor into the thermionic-emission in turns allows the derivation of an analytical expression for the
reverse leakage current with field-dependent Schottky-harrier lower- reverse-leakage current. The reverse I-V curves of Schottky diodes
ing. Excellent agreement has been found between calculated curves and calculated using this new expression are in excellent agreement with
measured data. This model allows for the first time the accurate cal-
measured data even at large reverse-bias values.
culation of the reverse-leakage current of Schottky diodes at high re-
verse voltage.
11. THEORYA N D DISCUSSIONS
I. INTRODUCTION
Schottky power diodes have been used extensively for low-volt-
It is well known that, according to the thermionic-emission the- age power supply applications. The electric field developed in the
ory, the reverse leakage current density of a Schottky diode can be depletion region may be large enough for impact ionization to take
expressed by the following equation: place before avalanche breakdown occurs. T o theoretically dem-
onstrate such an impact ionization effect, two-carrier PISCES sim-
ulations with impact ionization capability [6] were used to simulate
the reverse I-V characteristics of Schottky diodes. The leakage-
where A** is the effective Richardson constant, 4b is the Schottky current density with impact ionization incorporated was found to
barrier height, k is Boltzmann constant, q is the magnitude of elec- be about four times higher than that without impact ionization when
tron charge, and T is absolute temperature. During the reverse the reverse voltage is at 8 0 % of breakdown voltage. The effect of
blocking operation, the reverse current of a Schottky diode in- pre-avalanche impact ionization, as demonstrated by PISCES sim-
creases with increasing reverse bias voltage. This "nonsaturating" ulations, is thus very important in determining the reverse leakage
reverse characteristic of Schottky diodes has been explained pre- current of Schottky diodes at large reverse bias.
viously in term of the lowering of Schottky-bamer height with in- To characterize the effect of impact ionization analytically, con-
creasing electric field at the metal-semiconductor interface [ 11. sider an n-type Schottky power diode under reverse-bias condition.
There are several field-dependent lowering mechanisms [ 11, [2], The dominant source of reverse-leakage current for such a diode
all of which predict that the barrier height decreases with increasing comes from the thermionic emission of electrons over the Schottky
E,,,, the maximum field strength at the barrier. Since E,,,,, in- barrier into the semiconductor [ I ] , [ 5 ] .The current transport inside
creases with reverse voltage VR, it follows that & decreases with a reverse-biased n-type Schottky diode can then be treated as a pure
increasing VR. The most common form of field-dependent barrier electron-initiated injection process. In this process, a certain amount
lowering is that due to image force [ l ] . The amount of barrier height of electrons, as determined by thermionic emission theory, are in-
lowering A 4 b in this lowering mechanism has been shown to be jected across the metal-semiconductor interface into the semicon-
proportional to Eke and, in tum, to I/;/'. In addition to image- ductor depletion region. If the electric field in the depletion region
force lowering, another lowering mechanism has also been pro- is high enough for impact ionization to occur, the amount of elec-
posed for silicon-silicide Schottky diode [2]. In this mechanism, trons will increase with distance through the depletion region. The
the barrier height lowering is expressed in an empirical form 46, total electrons that reach the edge of depletion region will be larger
= CUE,,, with proportionality constant a in the range of 15-35 A . than those injected into the region by a factor of M,, the electron
Using the aforementioned field-dependent lowering models, an multiplication factor [ 11. Consequently, if the reverse-current den-
increase in the reverse-leakage current of Schottky diodes with in- sity corresponding to the electron emission at the Schottky inter-
creasing reverse-bias voltage has been calculated in most cases at face is denoted as .ITF, this initial electron current will be multiplied
low reverse voltage [ 11-[4]. At large reverse-bias values, however, by the factor M , after impact ionization where
it has been noticed that the actual reverse-leakage current of
Schottky diodes is much larger than that predicted by the field-
dependent lowering mechanisms [5]. Such discrepancy is most no-
ticeable in Schottky power diodes. As an example, for a Schottky with &O the barrier height at zero voltage and A4,(VR) the barrier
diodes with 50-V blocking capability, the measured reverse-leak- height lowering a s a function of reverse voltage V,. At large re-
age current can be 3 to 4 times higher than that predicted by image- verse bias, the factor M,, will be greater than one. This in turn
force-induced lowering when the device is operated at a reverse results in larger total reverse current density JL as compared to that
voltage of 40 V [5]. Since, in most power systems, the Schottky predicted by thermionic emission ( J T E ) .
power diodes are required to operate at large reverse bias during The reverse-current density J,- can be obtained only if M,, can be
reverse blocking mode, the field-dependent lowering models are calculated as a function of reverse-bias voltage. The ionization rates
not sufficient for predicting their reverse I-V characteristics. have been shown [ 7 ] , [8] to have the exponential form a(,,,,) =
In this brief, it will be shown that the increase in reverse-leakage A(,,,,, exp ( - B , n , , , ) / E ) , where A and B are constants and E the
electric field. If such an exponential form is used, the factor M,,
Manuscript received December 27, 1991; revised June 19, 1992. The can only be solved by numerical techniques. In order to calculate
review of this brief was arranged by Associate Editor T.P. Chow.
The authors are with the Power Semiconductor Research Center, North the reverse-current density J I analytically without resorting to a
Carolina State University, Raleigh, NC 27695-7924. time-consuming numerical process, the following approximation to
IEEE Log Number 9203857. ionization rates a,t and aDis proposed: 1) they can be expressed in

0018-9383/92$03.00 0 1992 IEEE

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2814 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 39, NO. 12. DECEMBER 1992

10
I alytical expression given in ( 3 ) and numerical values obtained from
PISCES simulations.
Drift regionthickness: 3.0pm After solving the factor M, analytically, the reverse leakage JL
Breakdown voltage: 55 V
Temperature:3 d K
can be calculated as a function of reverse-bias voltage. In Fig. 2,
the reverse I-V curve calculated from these equations is compared
PISCES simulation
___.- with measured data taken on 50-V Schottky-barrier diodes. The
~ Eq (3) image-force-induced bamer lowering was used for A&( VR)as given
in ( 2 ) for calculating the I-V curve in Fig. 2 . It can be seen in Fig.
2 that excellent agreement is obtained between the analytically cal-
culated results and the measured data.

111. CONCLUSIONS
The impact ionization effect has been shown to contribute to an
o 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.8 1 increase in the reverse-leakage current of Schottky power diodes
REVERSE VOLTAGVBREAKWWN VOLTAGE
with increasing reverse-bias voltage. The combining effect of
Fig. I . Comparison of the values of electron multiplication factor (M,r) thermionic emission leakage current, field-dependent barrier low-
calculated using (3) with those obtained from PISCES simulation. Grant’s ering, and multiplication factor due to impact ionization allows the
empirical model was used in PISCES simulation. reverse blocking characteristics of Schottky power diodes to be
completely described. The use of power-series approximation for
electron and hole ionization rates allows the reverse current density
Drift region doping: 1xl0”cmJ to be calculated analytically. Excellent agreement between theo-
Drift regionthickness: 2.5 pm retically calculated values and experimental data has been found.
0.4 - Device active area: 0.042 U?
This new analytical model for predicting the reverse blocking char-
I--
acteristics of Schottky power diodes will be useful for analyzing
H4 0.3 - - Calculated CUNB the performance and thermal stability of these diodes.
0 0 Measured data
% REFERENCES
9
9 0.2 - [I] S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York:
W Wiley, 1981, pp. 281-288.
U [2] J. M. Andrews and M. P. Lepselter, “Reverse current-voltage char-
g 0.1 - acteristics of metal-silicide Schottky diodes,” Solid-State Electron.,
vol. 13, pp. 101 1-1023, 1970.
131 T. Arizumi and M. Hirose, “Transport properties of metal-silicon
01 I
Schottky barriers,” Japan. J . Appl. Phys., vol. 8, no. 6, pp. 749-
10 20 30 40 50 60 754, 1969.
REVERSE BIAS VOLTAGE, (V) (41 M. Missous, E. H. Rhoederick, and K . E. Singer, “The effect of
Fig. 2. Comparison of analytically calculated room-temperature reverse I- vacuum conditions on epitaxial AI/GaAs contacts formed by molec-
V curve with measured data taken on 50-V Schottky-barrier diodes. ular-beam epitaxy,” J. Appl. Phys., vol. 60, pp. 2439-2444, 1986.
[5] B. J. Baliga, Modern Power Devices. New York: Wiley, 1987, pp.
427-429.
power-series form with a, = CE“ and a,, = yCE“, where C and n [ 6 ] M. E. Pinto, C. S. Rafferty, and R. W. Dutton, “PISCES 11: Poisson
are constants; 2) the ratio y = aP/a,,is constant and independent and continuity equation solver,” Stanford Univ., Stanford, CA, Tech.
Rep., Sept. 1984.
of E. One existing set of data on ionization rates pertaining to such [7] G . A . Baraff, “Distribution junctions and ionization rates for hot
approximation is given in [9]. Fitting the values of apand a, given electrons in semiconductors,” Phys. Rev., vol. 128, p. 2507, 1962.
in [9] with a power-series expansion in the electric field range re- 181 R. Van Overstraeten and H . De Man, “Measurement of the ionization
quired for the analysis of Schottky power diodes, the following rates in diffused silicon p-n junctions.” Solid-State Electron., vol.
empirical equations were obtained: 13, pp. 583-608, 1970.
[9] S. K. Ghandhi, Semiconductor Power Devices. New York: Wiley,
C,, = 6.6 X n = 4.93 r = 0.344 1977, pp. 39-40.
1101 W. Fulop, “Calculation of avalanche breakdown of silicon p-n junc-
at 2 x lo5 V / c m < E < 5 x IO5 V/cm. It is worth pointing out tion,” Solid-State Electron., vol. 10. pp. 39-43, 1967.
that the approximation aeff= a, = a,,= CE” [ 101 is not used here
for the multiplication factor calculation. Such assumption on ion-
ization rates may be used for breakdown voltage calculations but Entirely Gate-Surrounded MOS Capacitor to Study
not for the calculation of the multiplication factor, since, in the the Intrinsic Oxide Quality
latter case, the ratio y plays an important role [SI.
Using these functions, an analytical expression for electron mul- Martin Kerber
tiplication factor can be obtained
Abstract-In this study the intrinsic dielectric strength of gate oxides
is investigated by MOS capacitors which are designed so that the gate
poly does not cross the field oxide edge. Using the charge to breakdown

The value of M, calculated using the above equation as a function Manuscript received January 25, 1992; revised June 20, 1992. The re-
view of this brief was arranged by Associate Editor K . Shenai.
of reverse-bias voltage is shown in Fig. 1, along with numerical
The author is with Siemens AG, Corporate Research and Development,
results deducted from PISCES simulation for comparison. As can 8000 Munich 83, Germany.
be seen from this figure, good agreement is found between the an- IEEE Log Number 9203856.

0018-9383/92$03.00 O 1992 IEEE

Authorized licensed use limited to: NXP Semiconductors. Downloaded on December 20,2020 at 04:45:06 UTC from IEEE Xplore. Restrictions apply.