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Dynamic model of silicon devices with energy-localized trap centers
MicroelecrronicsJOWMI 28 (1997) 93100 Copyright 0 1996 Elsevier Science Limited Printed in Great Britain. All rights reserved 0026-2692/97/$17.00 ELSEVIER
PIkSOO26-2692(96)00064-X
Dynamic mod~el of silicon devices with energy-localized trap centers M. Valdinoci’, and S. Coffa*
L. Colalongo’,
M. Rudan’
‘Diprtimento di Elettronica, Znfoomatiu e Sistemistica, Univetritci di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy. Tel: +39 (51) 644-3016. Fax: f35’ (51) 644-3073. E-mail:[email protected]. it *Co.Ri.M. Me,SGS-Thomson Research Laboratory, Straddle Primosole 50, Z-95121 Catania, Z&y
The effects of deep localized traps on the dynamic behavior of devices is analyzed by adding two more continuity equations to the customary semiconductor-device model. Such equations account for the dynamic variation of the trapped charge. A novel solution method is also proposed, which maintains the same efficiency of the trap-tree case without introducing any approximation in the description of the trap-state dynamics. The model is applied to predict the switching behavior of platinum-doped devices. Copyright 0 1996 Elsevier Science Ltd.
1. Introduction
D
eep impurities like gold or platinum are extensively used in semiconductor technology to improve the switching characteristics of the devices by decreasing the carrier lifetimes. Here a complete motdel is presented, describing the effects of localized traps on the dynamic behavior of devices. Gold or platinum atoms introduce a number of electronic levels localized in the energy gap of silicon. The most irnportant ones are a donor
level in the lower half of the gap and an acceptor level in the upper half [l]. Acting as recombination centers such levels reduce the carrier lifetimes; furthermore, their ionization degrades the concentration of mobile carriers, thus increasing the resistivity of the material. The analysis of this phenomenon in bulk material, along with the comparison with experimental results, has been presented in [2]. While in steady state the deepimpurity effects are accounted for by simply redefining the generation-recombination rate, in transient conditions two more continuity equations are necessary to account for the dynamic variation of the trapped charge. Therefore, from the numerical standpoint the problem is much heavier and calls for an efficient solution scheme. In this paper the derivation of the model is shown and a novel solution method is proposed, which brings the solution of the full system of time-dependent continuity equations to a scheme that maintains the same efficiency as the trap-free case, without introducing any approximation in the description of the trap-state
93
M. Valdinoci
et al/Dynamic
model of silicon devices
dynamics. The model is then applied to predict the switching behavior of platinum-doped devices, along with the degradation in the steadystate output current. Good agreement with experimental results is found. The physical model is derived in Section 2, while the numerical scheme is depicted in Section 3. Finally, in Section 4 the results are shown and the conclusions drawn.
differential in time, but purely algebraic in space; this feature is especially important in view of the numerical solution. The current densities J,, and Jp associated to the band charges are modeled here by the customary drift-diffusion expressions
2. The model
where $(r, t) is the electric potential. The concentration of gap levels considered here is large enough to make the contribution of the trapped charge to the electric potential significant. As a consequence, Poisson’s equation takes the form
When the concentration of trapped charge is significant, and the time-dependent condition is considered, two more continuity equations must be added to the system of the semiconductor equations, yielding
J, = -qp,,ngrad6 + qD, gradn
Jp= -q/y grad+ - @‘, grads
I?\ IJI
-div (E,grad 4) = q(p - n + NIf $-ddivJ,=-U,,
$+idivJP=--Up
(1)
ant=
at
apt - u nt9 at = -up,
(2)
In the above equations, n and n, are the concentration of electrons in the conduction band and in the acceptor levels of the gap, respectively, p and pt the concentration of holes in the valence band and in the donor levels of the gap. These quantities are in turn functions of the position and time. At the right hand side, U,, and U,, are the net recombination rates for the conduction band and the acceptor levels, respectively, U, and U,, those for the valence band and the donor levels. Finally, J, and J are the current densities in the conduction an & valence band. The gap levels are spatially localized to such an extent that the probability of hopping transitions is negligible; therefore, they do not contribute to the current transport within the gap. For this reason, the current densities J,, and Jrpt associated with the trapped charges are negligibly small and have not been considered in the continuity equations (2). It is worth observing that in this way the continuity equations for trapped charges are
94
(4)
-K+pt-4
The net recombination rates U, and U, in (1) are easily expressed in terms of the concentrations by generalizing the Shockley-Read-Hall [3] theory to two species of traps, and read &
=
%AbNtA + %D(pt
+
$A(%
-
-
f’w)
-
NtD)
NtA)
%Dnpt
+ -
-
f&Ant
(5)
epDpt
(6)
and Nto are the concentraIn (5) and (6), NtA trap levels, tions of acceptor and donor respectively. In turn, errA, e,A, e,D, e$ are the emission probabilities and are expressed, for the acceptor level, by enA = c~~Au~~N&A epA=apAUthNV(l/XnA)exp eXP(-A&/b&), [(A&A - FEr,)/kBTk]. Here xnA is the entropy factor, whit takes mto account the change m both the vibrational and configurational entropy of the crystal due to the ionization of the level, and AH,, is the corresponding enthalpy change [2]. Similar expressions hold for the donor level. In the above, flnA, 0,~ are the capture crosssections, NC, NV the effective densities of states,
Microelectronics Journal, Vol. 28, No. 7
and
tl,h the
%A
=
UpA,
thermal velocity; finally, it is and similar expressions hold for
bnA%h> %D,
and
a,D.
The system to be solved is made of the five equations (l), (2), (4), where J,, Jr are given by (3). The unknowns of the system are 4, n, p, nt, and pt. The solution of the system is made more straightforward by a few manipulations that are shown in Section 3. Such manipulations lead to a form where nl and pr are expressed, without approximations, as explicit functions of the concentrations M and p of the free-carriers. 3. The solution Combining
sc:heme
Since Nt~ and N,o are independent parameters, (10) leads to the following linear, first-order equations:
(12)
In steady-state conditions the above expressions of n,, pt in terms of n, p become simply algebraic, and the net recombination rates U,,, U, coincide. Equations (12) are more convenient than (2) to express the continuity equations of the trapped charge. They have the form ,+z+gz = Y, whose solution with respect to time is
(1) and (2) and observing that z(t)expG(t)
4~(“+“~-P-P,)=div(J,+J,)
= z(to) +
v(r)expG(r)dr
(7)
(13)
one obtains
Let now PA and F’o be the occupation probabilities of the acceptor and donor trap levels. The concentrations of the trapped carriers in (2) and (4) become nt = N~APA(EA), pr = NtD[l - l+,(E,)], whence
an, dt
N
=
apA fA
dt
Substituting NtA
+
with
dl? --= at
’
-II
D -ND
(9)
g
(5), (6): (9) into (8) yields
(anAn
+
$A>
NtD
(%Dn
-
+
DAPA
el?D)
-
-
apA -
ODpD
at
1 -
When the time discretization is carried out, the time interval At = t - to is taken small enough expansion to allow for the first-order exp G N 1 + G. The integrals are then approximated as
J to
at
r(z)[l + G(r)]dr
Substituting yields
ap~=0
-
(14)
f
1 (10)
N r(t)At[l
+g(t)At]
(14) into (13) and neglecting
(At)*
(15)
i.e. the Backward-Euler scheme. Due to (ll), (12) the coefficients r(t) and g(t) in (15) depend only on the free-carrier concentrations n and p at time t; thanks to this, the right hand side of Poisson’s equation (4) and the net recombination rates U,,, U, (5)) (6) can eventually be
95
M. Valdinoci
et al./Dynamic
model of silicon devices
expressed in terms of YZand p only. This is due to the fact already noted that the continuity equations for yztandp, are not differential in the space coordinates. In this way the solution of the timedependent continuity model can be brought to a scheme that maintains the same efficiency as the trap-free one, without introducing any approximation in the description of the trap-state dynamics. The physical model and the solution scheme have been implemented within the two-dimensional version of the device simulator HFIELDS [4], and the results of some analyses are shown in Section 4.
4. Results
and conclusions
Numerical simulations have been carried out using HFIELDS on a number of devices, and have been compared with experimental results. The turn off of a p+-n- platinum-doped diode with resistive-inductive load is shown first (Fig. 1). The diode represents the parasitic part of a more complicated structure, which will be described in the second a plication example, and consists of a series of p’-nand n--n+ junctions. The RL load in Fig. 1 represents the measurement setup. The n- concentration is 3 x 10’4cm-3, the device area 10 mm*. The analysis has been repeated at different values of the platinum concentration around the substrate
Fig. 1. Parasitic power diode with resistive-inductive load. The input voltage is brought from 1 to -4” with a 1 ns linear ramp.
96
doping, i.e. Nt = 2 x 1o13, 1o14, and 2 x 1014 cmP3. The diode, initially forward biased at V; = 1 V, is switched off at t = 0.1 ~LS by a 1 ns linear ramp which brings V, to -4V. The bias is then kept at -4V for 1 ps. Figures 2a (experiment) and b (model) show the current flowing through the device. Each figure shows more than one curve corresponding to the different values of the platinum concentration. Figure 2a reproduces the screen of an oscilloscope, and Fig. 2b has been brought to the same scale as Fig. 2a; no parameter fitting has been carried out. One sees that, as the platinum concentration increases, the storage time drops considerably and, at the same time, the forward current is reduced due to the higher substrate resistivity. Figure 3 shows the corresponding anodic voltage Vd. The overshoot with respect to the asymptotic value Vd = -4V is due to the load. The curves also exhibit two changes in the slope during the storage time (this is better visible in the curve at Nt = 0). The phenomenon is due to the successive depleting of the pf-nand n--n+ junctions. To better characterize the degradation in the substrate resistivity-visible, for instance, in Fig. 2-other analyses have been carried out on uniform n-type and p-type silicon samples, in which an increasingly higher concentration of gold or platinum has been added to the starting material. The increase in resistivity becomes relevant when the deep-level concentration is close to, or larger than, that of the shallow levels provided by the dopants [2,6]. The results quantitatively agree with the experiments of [l]. It is found that in n-type samples the effects of platinum and gold are not the same. In fact, the conductivity degradation is mostly due to the capture of conductionband electrons by the acceptor levels. The position of the latter, however, is rather different: while the distance from the edge of the conduction band is 0.23eV for platinum, it is 0.55 eV for gold, namely, the acceptor levels of gold are nearly at the midgap. As a conse-
Microelectronics
Journal,
Vol. 28, No. I
(4
(b)
-6
-a 0
SE-07
1E-06
Time (s) Fig. 2. Parasitic power diode turn-off:
measured (a) and simulated (b) current at different values of platinum
quence, the number of electrons captured by the acceptor levels of gold is much more sensitive to the position of the Fermi level, localized in the upper half of the gap. Instead, for the p-
concentration.
type samples the effect of platinum and gold on conductivity is rather similar; in fact, the position in the gap of the donor levels introduced by these impurities is almost the same.
97
M. Valdinoci
et al./Dynamic
model of silicon devices
I -
N,=O
----
N,=2E+13
.
-
N,=2E+14
.
-4 E 9 -8
-16 0
SE-07 Time (s)
Fig. 3. Parasitic power diode turn-off:
Further analysis has been carried out on the switching behavior of a power MOS; this device consists of multi-MOS cells interconnected in parallel on a single die. The simulated device is the basic cell, and consists of a vertically-diffused silicon-gate structure (VD-MOS) where the current flows vertically from the drain to the source [5]. The cross-section is shown in Fig. 4. The VD-MOS contains the parasitic diode described in the first example. In some applications, such as motor-speed control, the internal diode is used as a free-wheeling device. However, its slow recovery results in a significant increase in the switching power losses of the VD-MOS, thus limiting the performance of the latter [5]. Therefore, in many applications, the parasitic diode should be characterized by low values of the reverse recovery time (turn-off time during which minority carriers leave the nregion). The storage time depends mainly on the minority carrier lifetimes, hence can substantially be reduced by introducing deep levels in the silicon bandgap. To investigate the effect of platinum doping the VD-MOS turn-off has
98
1E-06
simulated anodic voltage.
been simulated including the load (Fig. 5). The source is grounded, V0 is set to 10 V and, at t = 0.1 p, the gate voltage Vi is brought from 10 to OV in 1 ns and then kept constant. In Fig. 6 the drain current of the undoped device and that
n+
+
b
D
Fig. 4. Cross-section
of the simulated VD-MOS.
Microelectronics
Fig. 5. VD-MOS
switching:
bias circuit.
Journal,
Vol. 28, No. 7
time along with a reduction in the on-current due to the increase in the substrate resistance. In Fig. 7 the corresponding drain voltage is shown. From this figure the reduction in the parasiticdiode storage time is evident. From t = 0 to 0.1 ,us the VD-MOS is on and the parasitic diode is off. As soon as Vi reaches OV, a voltage oscillation occurs, due to the external RCL load (the first peak reaches about 800V and is only partially shown in Fig. 7). Then the negative peak in the drain voltage is cut off by the parasitic diode, which at negative drain voltages is forward biased. The drain voltage remains negative until all minority carriers leave the p+-njunction; this happens at about 0.3 and 0.5 ,us for the platinum-doped and the undoped device, respectively. In other terms, in the case of the platinum-doped device the switching delay is about halved. In conclusion, the analysis of the dynamic behavior of devices doped with deep impurities two has been carried ou; by implementing more continuity equations accounting for the
of the platinum-doped one are compared. The platinum concentration is NI = 1015 cmP3. One can see the reduction in the VD-MOS switching 0.04
I
-
----
0.02
3 9-F
0
-0.02
------
-0.04 fi 0
N,=lE+15
5E-07
lE-06
Time (s) Fig. 6. VD-MOS
switching:
drain current.
M. Valdinoci
et al./Dynamic
model of silicon devices
OE+OO
5E-07
Time (s) Fig. 7. VD-MOS
dynamic variation of the trapped charge. The solution has been carried out by devising a method which exploits the form of the continuity equations of the traps. In this way, the implementation in an existing device-analysis code has become easier, and the numerical efficiency of the trap-free case kept. The applications shown here consisted in the prediction of the switching behavior of platinum-doped devices.
switching:
[2]
[3] [4]
[5]
Acknowledgements M. Valdinoci and L. Colalongo fellowships provided by Co.Ri.M.Me Thomson, respectively.
profit by and SGS[6]
References [I]
100
M.F. Catania, L. Calcagno, S. Coffa, S.U. Campisano, M. Raspagliesi and G. Ferla, Compensating effects of
drain voltage.
platinum in n- and p-type silicon, Applied Physics A, 52 (1991) 119-122. M. Valdinoci, L. Colalongo, A. Pellegrini and M. Rudan, Analysis of conductivity degradation in gold/ platinum-doped silicon, IEEE Trans. Electron Devices (to appear). S.M. Sze, Physics ofSemiconductor Devices, 2nd edn, John Wiley & Sons, New York, 1981. G. Baccarani, R. Guerrieri, P. Ciampolini and M. Rudan, HFIELDS: a highly flexible 2-D semiconductor-device analysis program, in J.J.H. Miller (ed.), Proc. of the NASECODE IV Conference, Boole Press, Dublin, 1985, pp. 3-12. M.F. Catania, F. Frisina, N. Tavolo, G. Ferla, S. Coffa and S.U. Campisano, Optimization of the tradeoff between switching speed of the internal diode and on-resistance in gold- and platinumimplanted power metal-oxide-semiconductor devices, IEEE Trans. Electron Devices, 39( 12) (1992) 2745-2749. M. Valdinoci, L. Colalongo, S. Coffa and M. Rudan, A dynamic model of gold/platinum-doped devices, in H.C. de Graaffand H. van Kranenburg (eds), Pm. of the 1995 ESSDERC Conference, Edition Frontiers, Paris, 1995, pp. 71-74.
PIkSOO26-2692(96)00064-X
Dynamic mod~el of silicon devices with energy-localized trap centers M. Valdinoci’, and S. Coffa*
L. Colalongo’,
M. Rudan’
‘Diprtimento di Elettronica, Znfoomatiu e Sistemistica, Univetritci di Bologna, Viale Risorgimento 2, I-40136 Bologna, Italy. Tel: +39 (51) 644-3016. Fax: f35’ (51) 644-3073. E-mail:[email protected]. it *Co.Ri.M. Me,SGS-Thomson Research Laboratory, Straddle Primosole 50, Z-95121 Catania, Z&y
The effects of deep localized traps on the dynamic behavior of devices is analyzed by adding two more continuity equations to the customary semiconductor-device model. Such equations account for the dynamic variation of the trapped charge. A novel solution method is also proposed, which maintains the same efficiency of the trap-tree case without introducing any approximation in the description of the trap-state dynamics. The model is applied to predict the switching behavior of platinum-doped devices. Copyright 0 1996 Elsevier Science Ltd.
1. Introduction
D
eep impurities like gold or platinum are extensively used in semiconductor technology to improve the switching characteristics of the devices by decreasing the carrier lifetimes. Here a complete motdel is presented, describing the effects of localized traps on the dynamic behavior of devices. Gold or platinum atoms introduce a number of electronic levels localized in the energy gap of silicon. The most irnportant ones are a donor
level in the lower half of the gap and an acceptor level in the upper half [l]. Acting as recombination centers such levels reduce the carrier lifetimes; furthermore, their ionization degrades the concentration of mobile carriers, thus increasing the resistivity of the material. The analysis of this phenomenon in bulk material, along with the comparison with experimental results, has been presented in [2]. While in steady state the deepimpurity effects are accounted for by simply redefining the generation-recombination rate, in transient conditions two more continuity equations are necessary to account for the dynamic variation of the trapped charge. Therefore, from the numerical standpoint the problem is much heavier and calls for an efficient solution scheme. In this paper the derivation of the model is shown and a novel solution method is proposed, which brings the solution of the full system of time-dependent continuity equations to a scheme that maintains the same efficiency as the trap-free case, without introducing any approximation in the description of the trap-state
93
M. Valdinoci
et al/Dynamic
model of silicon devices
dynamics. The model is then applied to predict the switching behavior of platinum-doped devices, along with the degradation in the steadystate output current. Good agreement with experimental results is found. The physical model is derived in Section 2, while the numerical scheme is depicted in Section 3. Finally, in Section 4 the results are shown and the conclusions drawn.
differential in time, but purely algebraic in space; this feature is especially important in view of the numerical solution. The current densities J,, and Jp associated to the band charges are modeled here by the customary drift-diffusion expressions
2. The model
where $(r, t) is the electric potential. The concentration of gap levels considered here is large enough to make the contribution of the trapped charge to the electric potential significant. As a consequence, Poisson’s equation takes the form
When the concentration of trapped charge is significant, and the time-dependent condition is considered, two more continuity equations must be added to the system of the semiconductor equations, yielding
J, = -qp,,ngrad6 + qD, gradn
Jp= -q/y grad+ - @‘, grads
I?\ IJI
-div (E,grad 4) = q(p - n + NIf $-ddivJ,=-U,,
$+idivJP=--Up
(1)
ant=
at
apt - u nt9 at = -up,
(2)
In the above equations, n and n, are the concentration of electrons in the conduction band and in the acceptor levels of the gap, respectively, p and pt the concentration of holes in the valence band and in the donor levels of the gap. These quantities are in turn functions of the position and time. At the right hand side, U,, and U,, are the net recombination rates for the conduction band and the acceptor levels, respectively, U, and U,, those for the valence band and the donor levels. Finally, J, and J are the current densities in the conduction an & valence band. The gap levels are spatially localized to such an extent that the probability of hopping transitions is negligible; therefore, they do not contribute to the current transport within the gap. For this reason, the current densities J,, and Jrpt associated with the trapped charges are negligibly small and have not been considered in the continuity equations (2). It is worth observing that in this way the continuity equations for trapped charges are
94
(4)
-K+pt-4
The net recombination rates U, and U, in (1) are easily expressed in terms of the concentrations by generalizing the Shockley-Read-Hall [3] theory to two species of traps, and read &
=
%AbNtA + %D(pt
+
$A(%
-
-
f’w)
-
NtD)
NtA)
%Dnpt
+ -
-
f&Ant
(5)
epDpt
(6)
and Nto are the concentraIn (5) and (6), NtA trap levels, tions of acceptor and donor respectively. In turn, errA, e,A, e,D, e$ are the emission probabilities and are expressed, for the acceptor level, by enA = c~~Au~~N&A epA=apAUthNV(l/XnA)exp eXP(-A&/b&), [(A&A - FEr,)/kBTk]. Here xnA is the entropy factor, whit takes mto account the change m both the vibrational and configurational entropy of the crystal due to the ionization of the level, and AH,, is the corresponding enthalpy change [2]. Similar expressions hold for the donor level. In the above, flnA, 0,~ are the capture crosssections, NC, NV the effective densities of states,
Microelectronics Journal, Vol. 28, No. 7
and
tl,h the
%A
=
UpA,
thermal velocity; finally, it is and similar expressions hold for
bnA%h> %D,
and
a,D.
The system to be solved is made of the five equations (l), (2), (4), where J,, Jr are given by (3). The unknowns of the system are 4, n, p, nt, and pt. The solution of the system is made more straightforward by a few manipulations that are shown in Section 3. Such manipulations lead to a form where nl and pr are expressed, without approximations, as explicit functions of the concentrations M and p of the free-carriers. 3. The solution Combining
sc:heme
Since Nt~ and N,o are independent parameters, (10) leads to the following linear, first-order equations:
(12)
In steady-state conditions the above expressions of n,, pt in terms of n, p become simply algebraic, and the net recombination rates U,,, U, coincide. Equations (12) are more convenient than (2) to express the continuity equations of the trapped charge. They have the form ,+z+gz = Y, whose solution with respect to time is
(1) and (2) and observing that z(t)expG(t)
4~(“+“~-P-P,)=div(J,+J,)
= z(to) +
v(r)expG(r)dr
(7)
(13)
one obtains
Let now PA and F’o be the occupation probabilities of the acceptor and donor trap levels. The concentrations of the trapped carriers in (2) and (4) become nt = N~APA(EA), pr = NtD[l - l+,(E,)], whence
an, dt
N
=
apA fA
dt
Substituting NtA
+
with
dl? --= at
’
-II
D -ND
(9)
g
(5), (6): (9) into (8) yields
(anAn
+
$A>
NtD
(%Dn
-
+
DAPA
el?D)
-
-
apA -
ODpD
at
1 -
When the time discretization is carried out, the time interval At = t - to is taken small enough expansion to allow for the first-order exp G N 1 + G. The integrals are then approximated as
J to
at
r(z)[l + G(r)]dr
Substituting yields
ap~=0
-
(14)
f
1 (10)
N r(t)At[l
+g(t)At]
(14) into (13) and neglecting
(At)*
(15)
i.e. the Backward-Euler scheme. Due to (ll), (12) the coefficients r(t) and g(t) in (15) depend only on the free-carrier concentrations n and p at time t; thanks to this, the right hand side of Poisson’s equation (4) and the net recombination rates U,,, U, (5)) (6) can eventually be
95
M. Valdinoci
et al./Dynamic
model of silicon devices
expressed in terms of YZand p only. This is due to the fact already noted that the continuity equations for yztandp, are not differential in the space coordinates. In this way the solution of the timedependent continuity model can be brought to a scheme that maintains the same efficiency as the trap-free one, without introducing any approximation in the description of the trap-state dynamics. The physical model and the solution scheme have been implemented within the two-dimensional version of the device simulator HFIELDS [4], and the results of some analyses are shown in Section 4.
4. Results
and conclusions
Numerical simulations have been carried out using HFIELDS on a number of devices, and have been compared with experimental results. The turn off of a p+-n- platinum-doped diode with resistive-inductive load is shown first (Fig. 1). The diode represents the parasitic part of a more complicated structure, which will be described in the second a plication example, and consists of a series of p’-nand n--n+ junctions. The RL load in Fig. 1 represents the measurement setup. The n- concentration is 3 x 10’4cm-3, the device area 10 mm*. The analysis has been repeated at different values of the platinum concentration around the substrate
Fig. 1. Parasitic power diode with resistive-inductive load. The input voltage is brought from 1 to -4” with a 1 ns linear ramp.
96
doping, i.e. Nt = 2 x 1o13, 1o14, and 2 x 1014 cmP3. The diode, initially forward biased at V; = 1 V, is switched off at t = 0.1 ~LS by a 1 ns linear ramp which brings V, to -4V. The bias is then kept at -4V for 1 ps. Figures 2a (experiment) and b (model) show the current flowing through the device. Each figure shows more than one curve corresponding to the different values of the platinum concentration. Figure 2a reproduces the screen of an oscilloscope, and Fig. 2b has been brought to the same scale as Fig. 2a; no parameter fitting has been carried out. One sees that, as the platinum concentration increases, the storage time drops considerably and, at the same time, the forward current is reduced due to the higher substrate resistivity. Figure 3 shows the corresponding anodic voltage Vd. The overshoot with respect to the asymptotic value Vd = -4V is due to the load. The curves also exhibit two changes in the slope during the storage time (this is better visible in the curve at Nt = 0). The phenomenon is due to the successive depleting of the pf-nand n--n+ junctions. To better characterize the degradation in the substrate resistivity-visible, for instance, in Fig. 2-other analyses have been carried out on uniform n-type and p-type silicon samples, in which an increasingly higher concentration of gold or platinum has been added to the starting material. The increase in resistivity becomes relevant when the deep-level concentration is close to, or larger than, that of the shallow levels provided by the dopants [2,6]. The results quantitatively agree with the experiments of [l]. It is found that in n-type samples the effects of platinum and gold are not the same. In fact, the conductivity degradation is mostly due to the capture of conductionband electrons by the acceptor levels. The position of the latter, however, is rather different: while the distance from the edge of the conduction band is 0.23eV for platinum, it is 0.55 eV for gold, namely, the acceptor levels of gold are nearly at the midgap. As a conse-
Microelectronics
Journal,
Vol. 28, No. I
(4
(b)
-6
-a 0
SE-07
1E-06
Time (s) Fig. 2. Parasitic power diode turn-off:
measured (a) and simulated (b) current at different values of platinum
quence, the number of electrons captured by the acceptor levels of gold is much more sensitive to the position of the Fermi level, localized in the upper half of the gap. Instead, for the p-
concentration.
type samples the effect of platinum and gold on conductivity is rather similar; in fact, the position in the gap of the donor levels introduced by these impurities is almost the same.
97
M. Valdinoci
et al./Dynamic
model of silicon devices
I -
N,=O
----
N,=2E+13
.
-
N,=2E+14
.
-4 E 9 -8
-16 0
SE-07 Time (s)
Fig. 3. Parasitic power diode turn-off:
Further analysis has been carried out on the switching behavior of a power MOS; this device consists of multi-MOS cells interconnected in parallel on a single die. The simulated device is the basic cell, and consists of a vertically-diffused silicon-gate structure (VD-MOS) where the current flows vertically from the drain to the source [5]. The cross-section is shown in Fig. 4. The VD-MOS contains the parasitic diode described in the first example. In some applications, such as motor-speed control, the internal diode is used as a free-wheeling device. However, its slow recovery results in a significant increase in the switching power losses of the VD-MOS, thus limiting the performance of the latter [5]. Therefore, in many applications, the parasitic diode should be characterized by low values of the reverse recovery time (turn-off time during which minority carriers leave the nregion). The storage time depends mainly on the minority carrier lifetimes, hence can substantially be reduced by introducing deep levels in the silicon bandgap. To investigate the effect of platinum doping the VD-MOS turn-off has
98
1E-06
simulated anodic voltage.
been simulated including the load (Fig. 5). The source is grounded, V0 is set to 10 V and, at t = 0.1 p, the gate voltage Vi is brought from 10 to OV in 1 ns and then kept constant. In Fig. 6 the drain current of the undoped device and that
n+
+
b
D
Fig. 4. Cross-section
of the simulated VD-MOS.
Microelectronics
Fig. 5. VD-MOS
switching:
bias circuit.
Journal,
Vol. 28, No. 7
time along with a reduction in the on-current due to the increase in the substrate resistance. In Fig. 7 the corresponding drain voltage is shown. From this figure the reduction in the parasiticdiode storage time is evident. From t = 0 to 0.1 ,us the VD-MOS is on and the parasitic diode is off. As soon as Vi reaches OV, a voltage oscillation occurs, due to the external RCL load (the first peak reaches about 800V and is only partially shown in Fig. 7). Then the negative peak in the drain voltage is cut off by the parasitic diode, which at negative drain voltages is forward biased. The drain voltage remains negative until all minority carriers leave the p+-njunction; this happens at about 0.3 and 0.5 ,us for the platinum-doped and the undoped device, respectively. In other terms, in the case of the platinum-doped device the switching delay is about halved. In conclusion, the analysis of the dynamic behavior of devices doped with deep impurities two has been carried ou; by implementing more continuity equations accounting for the
of the platinum-doped one are compared. The platinum concentration is NI = 1015 cmP3. One can see the reduction in the VD-MOS switching 0.04
I
-
----
0.02
3 9-F
0
-0.02
------
-0.04 fi 0
N,=lE+15
5E-07
lE-06
Time (s) Fig. 6. VD-MOS
switching:
drain current.
M. Valdinoci
et al./Dynamic
model of silicon devices
OE+OO
5E-07
Time (s) Fig. 7. VD-MOS
dynamic variation of the trapped charge. The solution has been carried out by devising a method which exploits the form of the continuity equations of the traps. In this way, the implementation in an existing device-analysis code has become easier, and the numerical efficiency of the trap-free case kept. The applications shown here consisted in the prediction of the switching behavior of platinum-doped devices.
switching:
[2]
[3] [4]
[5]
Acknowledgements M. Valdinoci and L. Colalongo fellowships provided by Co.Ri.M.Me Thomson, respectively.
profit by and SGS[6]
References [I]
100
M.F. Catania, L. Calcagno, S. Coffa, S.U. Campisano, M. Raspagliesi and G. Ferla, Compensating effects of
drain voltage.
platinum in n- and p-type silicon, Applied Physics A, 52 (1991) 119-122. M. Valdinoci, L. Colalongo, A. Pellegrini and M. Rudan, Analysis of conductivity degradation in gold/ platinum-doped silicon, IEEE Trans. Electron Devices (to appear). S.M. Sze, Physics ofSemiconductor Devices, 2nd edn, John Wiley & Sons, New York, 1981. G. Baccarani, R. Guerrieri, P. Ciampolini and M. Rudan, HFIELDS: a highly flexible 2-D semiconductor-device analysis program, in J.J.H. Miller (ed.), Proc. of the NASECODE IV Conference, Boole Press, Dublin, 1985, pp. 3-12. M.F. Catania, F. Frisina, N. Tavolo, G. Ferla, S. Coffa and S.U. Campisano, Optimization of the tradeoff between switching speed of the internal diode and on-resistance in gold- and platinumimplanted power metal-oxide-semiconductor devices, IEEE Trans. Electron Devices, 39( 12) (1992) 2745-2749. M. Valdinoci, L. Colalongo, S. Coffa and M. Rudan, A dynamic model of gold/platinum-doped devices, in H.C. de Graaffand H. van Kranenburg (eds), Pm. of the 1995 ESSDERC Conference, Edition Frontiers, Paris, 1995, pp. 71-74.