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An analytical model of the breakdown voltage and minimum epi layer length for RESURF pn diodes
Solid-State Electronics Vol. 39, No. 8, pp. 1247-1248, 1996 Copyright 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 003%1101(95)004254 0038-I 101/96 $15.00 + 0.00
Pergamon
NOTE AN ANALYTICAL MODEL OF THE BREAKDOWN VOLTAGE AND MINIMUM EPI LAYER LENGTH FOR RESURF pn DIODES (Received 20 October
1995; in revised form I December
I. INTRODUCTION
The RESURF (reduced surface field) technique[l] has been very useful for realizing high breakdown voltage in power integrated circuit devices. This method utilizes the thin expitaxial layer which gives a reduced lateral electric field if the proper concentration and thickness of the epi layer are used. Since the on resistance and area efficiency of the device are determined by its epi layer length, a minimum length of the epi layer is desirable for a given breakdown voltage. A relationship between breakdown voltage and epi layer length has been reported in two-dimensional simulation[2] as well as in an experimental investigation[2,3]. In this note, an analytical model for calculating the minimum epi layer length of RESURF pn diodes is presented by employing the breakdown voltage derived as a function of the device parameters. Experimental results as well as numerical simulations reported for the RESURF devices[2,3] are shown to support the present model. 2. ANALYTICAL
where a = 1.8 x 10-‘5. In the case of yd,/y,> 0.2 which is reasonable in practice, second term in the bracket, (1 - yd,/y,)*/(l + y) may be neglected. Thus, depletion width at breakdown is given by yBPf(!$J1
!%(&_y), ~cV,+vrX I
(4)
(1 - yd, ly,,Y 1+y I’
VB”
(5)
where N,, = N,,,l(I + l/y).
The lateral electric field distribution of the RESURF pn diode based on PISCES IIB simulation is shown as the solid
MODEL
E(Y) t
forOGy
for-d,
sy
CO
and the applied voltage, V, is
va=; +61
(_$+2y,d,-yd;),
[
(‘)
tb)
(2)
+p[l_(1 -;?fQ8]=1,
jWY
E(x) t Approx. Electric
where q is the electronic charge, t, is the permittivity of silicon, NW,and Nsvbare concentration of the epi layer and the substrate, respectively, y is the ratio of Ncp,to NIYband yp represents the depletion width in the p- substrate. The avalanche breakdown voltage can be derived using Fulop’s ionization coefficient for silicon[4] which is given by a,, = 1.8 x IO-“[El’. Substituting eqn (1) into breakdown condition, pd, u0dy = 1, we have
tz~y(I
+;)I-““.
From eqns (2) and (4), the breakdown voltage due to the vertical electric field is found to be
A schematic cross-section of the RESURF pn diode is illustrated in Fig. l(a). In the present study, the epi layer length is defined as the n _ type region length, Leplbetween the n + cathode and p+ anode. dePiis the thickness of the epi layer with uniform doping concentration, Ncpiwhile _x,is the junction depth of the anode and cathode. Assuming that the epi layer is completely depleted to satisfy the RESURF condition[l], the breakdown takes place along the vertical path of the one-dimensional n +n -p - junction. From the Poisson’s equation, the electric field distribution at breakdown can be expressed by
NY)= *fis”b
1995)
(3)
Field
(c)
Fig. 1. RESURF pn diode. (a) Cross-section. (b) Electric field distribution of the vertical n+n-p- junction. (c) Bow tie approximation for the lateral electric field.
1247
1248
Note 800
3. DISCUSSION
The breakdown voltage is plotted in Fig. 2 as a function of epi layer length, Lepi, varied from 20 pm to 90pm. For a given set of parameters, increasing the epi layer length increases the breakdown voltage which is expected in eqn (8) up to a constant value determined by the vertical n +n-pjunction breakdown. The analytical results obtained from eqns (5), (7) and (8) are compared with the simulation and the experimental ones reported by Colak[Z] and Wildi ef al. [3] for the breakdown voltage and minimum epi layer length. For the parameters of Nep, = 1 x lO”cm-‘, N_s = 1.5 x lOI cm-‘, d, = 13 pm, the analytical results of breakdown voltage and minimum epi layer length are 414 V and 29 pm, respectively, while the simulation ones are 415 V and 30 pm, respectively. Also, the experimental value of the breakdown voltage is 427 V in this case. Excellent agreement is shown. For the case of Nepl = 1.5 x lOI crnm3, Ns.,, = 4 x 10’4cm-3. d, = 7.2 pm, the analytical results are in good agreement with the experimental ones. A slight discrepancy between the analytical and experimental values may be contributed to the first-order approximation of the lateral electric field.
:-‘?gig
600
15
3
14
3
. /
dx /
d,
= 13 urn
A
_
Analytical
. Simulation
- -
30
40
50 Lepi
Fig. 2. The analytical and the experimental
[2]
A
Experimental
[2]
n
Experimental
[3]
60
70
80
4. CONCLUSION
90
[uml
(solid line), the simulated (dotted line) breakdown voltage, as a function of epi layer length.
line in Fig. l(c). A first-order approximation for the lateral field illustrated as dotted lines in Fig. l(c) is expressed by
(6)
Substituting
eqn (6) in the breakdown
condition
gives (7)
For the RESURF pn diode, the minimum length, L,, of the epitaxial layer may be determined when P’s, approaches V sv, allowing L In,”= 2 .57 x 10+2;.
(8)
Analytical expressions for the breakdown voltage and minimum epi layer length of RESURFpn diodes are derived as a function of the doping concentration and thickness of the epitaxial layer and substrate concentration. It is concluded that the analytic formulas presented in this note will provide a good tool for designing the RESURF devices such as LDMOS and LIGBT. Acknowledgements-This research was carried out at the Electrical Engineering and Science Research Center and suuoorted bv the Korea Electric Power Co. under grant no. 941062. Department of Electronics Engineering, Ajou University, &won -City, 442- 749. Korea
Seung-Youp
Han
Jong-Min
Na
Yearn-Ik
Choi
Jin-Cheol
Shin
Sang-Koo
Chung
REFERENCES
1. J. A. Appels, M. G. Collet, P. A. H. Hart, H. M. J. Vaes and J. F. C. M. Verhoeven, Philips J. Res. 35, 1 (1980). 2. S. Colak, IEEE Trans. Electron Devices ED-28 1455 (1981). 3. E. J. Wildi, P. Gray, T. P. Chow and H. R. Chang, Proc. IEDM, pp. 268 (1982). 4. W. Fulop, Solid-St. Electron. 10,39 (1967).
Pergamon
NOTE AN ANALYTICAL MODEL OF THE BREAKDOWN VOLTAGE AND MINIMUM EPI LAYER LENGTH FOR RESURF pn DIODES (Received 20 October
1995; in revised form I December
I. INTRODUCTION
The RESURF (reduced surface field) technique[l] has been very useful for realizing high breakdown voltage in power integrated circuit devices. This method utilizes the thin expitaxial layer which gives a reduced lateral electric field if the proper concentration and thickness of the epi layer are used. Since the on resistance and area efficiency of the device are determined by its epi layer length, a minimum length of the epi layer is desirable for a given breakdown voltage. A relationship between breakdown voltage and epi layer length has been reported in two-dimensional simulation[2] as well as in an experimental investigation[2,3]. In this note, an analytical model for calculating the minimum epi layer length of RESURF pn diodes is presented by employing the breakdown voltage derived as a function of the device parameters. Experimental results as well as numerical simulations reported for the RESURF devices[2,3] are shown to support the present model. 2. ANALYTICAL
where a = 1.8 x 10-‘5. In the case of yd,/y,> 0.2 which is reasonable in practice, second term in the bracket, (1 - yd,/y,)*/(l + y) may be neglected. Thus, depletion width at breakdown is given by yBPf(!$J1
!%(&_y), ~cV,+vrX I
(4)
(1 - yd, ly,,Y 1+y I’
VB”
(5)
where N,, = N,,,l(I + l/y).
The lateral electric field distribution of the RESURF pn diode based on PISCES IIB simulation is shown as the solid
MODEL
E(Y) t
forOGy
for-d,
sy
CO
and the applied voltage, V, is
va=; +61
(_$+2y,d,-yd;),
[
(‘)
tb)
(2)
+p[l_(1 -;?fQ8]=1,
jWY
E(x) t Approx. Electric
where q is the electronic charge, t, is the permittivity of silicon, NW,and Nsvbare concentration of the epi layer and the substrate, respectively, y is the ratio of Ncp,to NIYband yp represents the depletion width in the p- substrate. The avalanche breakdown voltage can be derived using Fulop’s ionization coefficient for silicon[4] which is given by a,, = 1.8 x IO-“[El’. Substituting eqn (1) into breakdown condition, pd, u0dy = 1, we have
tz~y(I
+;)I-““.
From eqns (2) and (4), the breakdown voltage due to the vertical electric field is found to be
A schematic cross-section of the RESURF pn diode is illustrated in Fig. l(a). In the present study, the epi layer length is defined as the n _ type region length, Leplbetween the n + cathode and p+ anode. dePiis the thickness of the epi layer with uniform doping concentration, Ncpiwhile _x,is the junction depth of the anode and cathode. Assuming that the epi layer is completely depleted to satisfy the RESURF condition[l], the breakdown takes place along the vertical path of the one-dimensional n +n -p - junction. From the Poisson’s equation, the electric field distribution at breakdown can be expressed by
NY)= *fis”b
1995)
(3)
Field
(c)
Fig. 1. RESURF pn diode. (a) Cross-section. (b) Electric field distribution of the vertical n+n-p- junction. (c) Bow tie approximation for the lateral electric field.
1247
1248
Note 800
3. DISCUSSION
The breakdown voltage is plotted in Fig. 2 as a function of epi layer length, Lepi, varied from 20 pm to 90pm. For a given set of parameters, increasing the epi layer length increases the breakdown voltage which is expected in eqn (8) up to a constant value determined by the vertical n +n-pjunction breakdown. The analytical results obtained from eqns (5), (7) and (8) are compared with the simulation and the experimental ones reported by Colak[Z] and Wildi ef al. [3] for the breakdown voltage and minimum epi layer length. For the parameters of Nep, = 1 x lO”cm-‘, N_s = 1.5 x lOI cm-‘, d, = 13 pm, the analytical results of breakdown voltage and minimum epi layer length are 414 V and 29 pm, respectively, while the simulation ones are 415 V and 30 pm, respectively. Also, the experimental value of the breakdown voltage is 427 V in this case. Excellent agreement is shown. For the case of Nepl = 1.5 x lOI crnm3, Ns.,, = 4 x 10’4cm-3. d, = 7.2 pm, the analytical results are in good agreement with the experimental ones. A slight discrepancy between the analytical and experimental values may be contributed to the first-order approximation of the lateral electric field.
:-‘?gig
600
15
3
14
3
. /
dx /
d,
= 13 urn
A
_
Analytical
. Simulation
- -
30
40
50 Lepi
Fig. 2. The analytical and the experimental
[2]
A
Experimental
[2]
n
Experimental
[3]
60
70
80
4. CONCLUSION
90
[uml
(solid line), the simulated (dotted line) breakdown voltage, as a function of epi layer length.
line in Fig. l(c). A first-order approximation for the lateral field illustrated as dotted lines in Fig. l(c) is expressed by
(6)
Substituting
eqn (6) in the breakdown
condition
gives (7)
For the RESURF pn diode, the minimum length, L,, of the epitaxial layer may be determined when P’s, approaches V sv, allowing L In,”= 2 .57 x 10+2;.
(8)
Analytical expressions for the breakdown voltage and minimum epi layer length of RESURFpn diodes are derived as a function of the doping concentration and thickness of the epitaxial layer and substrate concentration. It is concluded that the analytic formulas presented in this note will provide a good tool for designing the RESURF devices such as LDMOS and LIGBT. Acknowledgements-This research was carried out at the Electrical Engineering and Science Research Center and suuoorted bv the Korea Electric Power Co. under grant no. 941062. Department of Electronics Engineering, Ajou University, &won -City, 442- 749. Korea
Seung-Youp
Han
Jong-Min
Na
Yearn-Ik
Choi
Jin-Cheol
Shin
Sang-Koo
Chung
REFERENCES
1. J. A. Appels, M. G. Collet, P. A. H. Hart, H. M. J. Vaes and J. F. C. M. Verhoeven, Philips J. Res. 35, 1 (1980). 2. S. Colak, IEEE Trans. Electron Devices ED-28 1455 (1981). 3. E. J. Wildi, P. Gray, T. P. Chow and H. R. Chang, Proc. IEDM, pp. 268 (1982). 4. W. Fulop, Solid-St. Electron. 10,39 (1967).