- Email: [email protected]
Boron diffusion in polycrystalline silicon layers
sdid-State
Electmnics,
1975. Vol. IS, pp. 529-532.
Perganton Press.
Prinlcd in Great Britain
BORON DIFFUSION IN POLYCRYSTALLINE SILICON LAYERS S. HORIUCHI*and R. BLANCHARD Stanford University, Stanford, California94305,U.S.A. (Received
31 July 1974;in
reoisedfon
5 September
1974)
Abstract-Boron was diffused into the poly Si layers of 5.5 w thickness with boron nitride and diborane as boron sources. The diffusion depth was found to be proportional to the square root of diffusion time. The boron diffusion in the poly Si layers can be expressed in the well known complementary error function. The diffusion coefficient of boron in the poly Si layers is larger when diborane is used than when boron nitride is used as a boron source and is IO-50times larger than that in the single crystal silicon substrates in the experimental range. The diffusion coefficients of boron at 1050°Cin the single crystal silicon substrates with diborane as a boron sourcein the poly Si layers with boron nitride and diborane as boron sources are 8.80 X IO-“, I.17 x IO-‘*and I.95 X IO-‘*cm*/sec, respectively. The activation energies of the diffusion coefficients of boron in the above each case are 3.42, 2.39 and 2.51eV, respectively. NOTATION
impurity concentration at the distance x from the surface at time t surface impurity concentration impurity concentration at xd diffusion coefficient apparent value of D at infinite temperature activation energy function Boltzmann’s constant carrier concentration electron charge absolute temperature time distance from the surface diffusion depth junction depth x, in the single crystal silicon substrates and the diffusion depth x, in the poly Si layers junction depth sheet resistivity of the diffused layers carrier mobility fraction of carrier concentration n = I#IX C variable (= xd/dt)
I.INTRODUCTION
In silicon gate technology [ I], polycrystalline silicon
(poly Si) layers which are used as gate electrodes and interconnections are usually doped by diffusing impurities in the layers after poly Si deposition. Impurities diffuse much faster in poly Si layers than in single crystal silicon substrates because of the grain structure of the poly Si layers[Z, 31. The grain size depends on many factors. Several important factors are the sample preparation before deposition, the deposition temperature and the thickness of the poly Si layers. From the point of view of the practical device fabrication, impurities diffuse from the doped poly Si layers into the gate oxides sometimes resulting in instabilities [4] in silicon gate MOS devices and sometimes even penetrate through the gate oxides down into the single crystal silicon substrates producing the surface conductive layers of the opposite type to the substrates. From the above reason, it is very helpful in the device ‘Present address: Toshiba R & D Center, Kawasaki, Japan.
fabrication to understand the diffusion of impurities in poly Si layers. This paper describes the results of the diffusion of boron in the poly Si layers of the thickness of about 5.5 pm deposited from the thermal decomposition of silane. Diborane and boron nitride were used as boron sources. The work described here is a part of the developmental work on silicon gate technology at the Stanford Integrated Circuits Laboratory.
2. EXPEXIMENTAL METHOD silicon substrates used in these experiments were l-3 fi cm phosphorus doped n-type (100) wafers 2 in. dia. The wafers were oxidized at 1200°C in dry O2 for 13.5 min. The thickness of the oxide was measured to be 820A by an ellipsometer. Following the oxidation, the poly Si layers were deposited on the top of the oxide layers with the flows of 10cm’lmin of silane and 22 I/min of hydrogen at 950°C. The deposition rate was 800 A/min. Since it is difficult to use thin poly Si layers for the diffusion experiments, the poly Si layers of 5.5 pm thickness were deposited. The diffusion was performed in two methods. One was with the flows of 200 cm’lmin of diborane from the tank of 1070ppm of diborane in nitrogen, 5 cm’lmin of oxygen and 16OOcm’lmin of nitrogen. The other was with boron nitride wafers type HBR manufactured by Union Carbide in the flow of 2OOcm’/min of nitrogen. The boron nitride wafers were oxidized at 1050°Cfor 15 min in the flows of 400 cm3/min of nitrogen and 5 cm’/min of oxygen everytime after they were used for more than 4 hr. Before and after the boron nitride wafers were oxidized, boron was diffused in the single crystal silicon test wafers and the sheet resistivity of the diffused layers was checked. No degradation of the boron nitride wafers was found during the experiments. The same quartz tube was used both for boron nitride and diborane. Before the diffusion from boron nitride was carried out after diborane was used, the tube was cleaned by etching it in HF: HZ0 = 1: 1 for 30 min and rinsing it for 30 min with deionized water. The sheet resistivity of the boron diffused layers was measured by using an ordinary four point probe after The
529
S. HORIIJCHI and R.
530
dipping the samples in an oxide etchant. The diffusion layers were stained by two staining etchants following beveling. One is an ordinary staining etchant which contains a few drops of HNOs in 100cm’ of HF: HZ0 = 1: 1. The other etchant consists of 500mg of H2PtC16in 100cm’ of HF:H*O = 1: 1[2]. The diffusion depth was measured by a fringing microscope and both the staining etchants always gave the same results.
BLANCHARD
POLY BN
5-
DIFFUSION TEMF! PC) 0-o 1050 x-x 1000
3. EXPERIMENTAL RESULTS
In Fig. 1, the diffusion depth in the poly Si and single crystal silicon samples which were put side by side on the quartz boat during the diffusion with diborane as a boron source is plotted against the square root of diffusion time. Figure 2 shows the relationship between the square root of diffusion time and the diffusion depth in the poly Si layers with boron nitride as a boron source. A larger amount of scattering in the data of the diffusion depth is seen in the poly Si layers than in the single crystal silicon samples and when diborane is used than when boron nitride is used as a boron source in the poly Si layers. However, the general tendency can be found. The diffusion proceeds faster in the poly Si layers than in the single crystal silicon layers and when diborane is used than when boron nitride is used as a boron source in the poly Si layers. In Fig. 3, the sheet resistivity of the diffused layers in the poly Si layers and single crystal silicon substrates with diborane as a boron source is plotted against diffusion time. In Fig. 3 is also shown the relationship between the diffusion time and the sheet resistivity of the poly Si layers with boron nitride as a boron source. No significant difference between with diborane and boron nitride as boron sources can be seen in the sheet resistivity. The sheet resistivity of the diffused layers in the single crystal silicon samples is higher than that in the ---
x--x 1000 o--o 1050
ii 1%
/
0/
f
/ !I P 0
I
x
/-’ ,,,...
0
/x--
.’
_a--
__--__-n---->===___
0
TIME+
(HOUR+)
Fig. 2. Square root of diffusion time vs diffusion depth in the poly Si layers with diffusion temperature as a parameter. BN was used as a boron source.
poly Si layers except when the diffusion temperature is low or the diffusion time is short. 4. ANALYSIS OF THE EXPERIMENTAL RESULTS
By assuming that the surface concentration C,, is invariable with diffusion time and the diffusion coefficient D, is independent of the impurity concentration as supported by Figs. 1 and 2, the impurity concentration C(x, t), at the distance x from the surface at time t, can be expressed in the form of the well known complementary error function, (1)
This means that though the grain size and preferred orientation of the poly Si layers vary with the thickness of the layers[2], they have little effects on the diffusion coefficients in the experimental range. First of all, the impurity concentration Cs at the diffusion depth xd, was examined by the same method as is described in ref. [2]. The epitaxial layers and the poly Si layers were grown on the single crystal silicon substrates and the oxide layers thermally grown on the single crystal silicon wafers respectively in the epitaxial reactor at 9SO”Csimultaneously. The growth time was IOmin and for the first 5 min, these layers were grown without doping and during the last 5 min, they were doped with diborane. The doping level was varied from run to run in the range of 10’6-10’9/cm3in the epitaxial layers. There was no difference in the growth rate between the epitaxial layers and the poly Si layers. The growth rates of the doped and the undoped layers both are the same in the epitaxial layers and the poly Si layers in the range of the doping
‘,’ ___o______o___----oc
_A
0
c’
Ic
IO
C(x.t)=C.xF(~~=C,erfc(~).
900 950 0 / 0
Cl
05 (DIFFUSION
POLY BzHs SINGLE E2Hs
DIFFUSION TEMP PC1
A-A 0-n
0
x’--
&+__---
P-
A__--
I
0.5 (DIFFUSION
x-
_/-
__--
1.0 TIME+
1.5
(HOUR+)
Fig. 1. Square root of diffusion time vs diffusion depth in the poly Si layers and single crystal silicon substrates with diffusion temperature as a parameter. B&Lwas used as a boron source.
level examined.
The sheet resistivity
of the epitaxial
531
Boron diffusion in silicon layers TEMPERATURE o-0 n-0
IIf”
IO DIFFUSION
I
111’
TIME
POW POLY
100
SN a*y
1050
I
1000
(“c)
950
I
I
900
I
a
fmin)
Fig. 3. Diffusion time vs sheet resistivity. BN poly, B,Hs poly and B&single.
5t 7.5
layers was measured with a four point probe but the sheet resistivity of the poly Si layers grown at the same time was typically too high to measure with a four point probe. The thickness of the doped epitaxial layers and the doped poly Si layers was measured using a fringing microscope after beveling and staining. From the measurements of the sheet resistivity and thickness of the doped epitaxial layers, the impurity concentration of boron in the doped poly Si layers was estimated. The poly Si layer of the lowest doping level that corresponds to 101%m3 in the epitaxial layer grown at the same time was able to be stained with the etchants. It can be concluded from the results that the impurity concentration of boron at the edge of the stained poly Si layers is less than 10’6/cm’. Next, the diffusion coefficients of boron in the poly Si layers were calculated by using equation (1) and the results in Figs. 1 and 2. C, in the poly Si layers was taken to be the same as that in the single crystal silicon substrates diffused at the same time and Ca to be 10’6/cm3. This does not introduce any serious error in the calculation considering that Ca is less than 10’6/cm3and C, might be larger in the poly Si layers than in the single crystal silicon substrates and argerfc C&/C, is a very slow decreasing function with Ce/Cs in this range. The decrease of two orders of magnitude in G/C, gives less than 20 per cent increase in argerfc G/C,. C, in the single crystal silicon substrates was calculated using the measured xd and p5 and Irvin’s[S] curves. The obtained C, is a little bit larger than the published data[6] of the solid solubility limit of boron in single crystal silicon substrates. In Table 1, the values of the slope xd/.\lt in Figs. 1 and 2, C,, G/C,, argerfc Cs/C,, VD, D are summarized. In Fig. 4, the square roots of the diffusion coefficients of boron in the poly Si layers and single crystal silicon
substrates are plotted against diffusion temperature. The published data[7] of the diffusion coefficient of boron in the single crystal silicon substrates is also presented in Fig. 4 for reference. D varies exponentially with reciprocal absolute temperature l/T in each case as
TEMPERATURE
,
I
8.0
8.5 1 I/T?K))
I x10-4
Fig. 4. Diffusion temperature vs square root of diffusion coefficient.
shown in Fig. 4 and is expressed in the form,
(2) where k is the Boltzmann’s constant, E. is an activation energy and Do is an apparent value of D at infinite temperature. The activation energies and apparent values of D at infinite temperature were calculated using equation (2) and Fig. 4 are shown in Table 2. The activation energy in the single crystal silicon substrates agrees very well with that of the published data[7]. The activation energy in the poly Si layers does not depend on the kinds of boron sources and takes almost the same value in both cases of boron nitride and diborane and is about 1.4 times smaller than that in the single crystal silicon layers. The sheet resistivity, p,, of the diffused layers is related to the carrier concentration n, by X’ -1 = Ps wn dx (3) I0 where q is the electron charge and p is the carrier mobility which is a function of only the carrier concentration in the single crystal silicon substrates and is a function of the carrier concentration and distance in the poly Si layers due to the grain structure. x’ is the junction depth in the single crystal silicon substrates and is the diffusion depth in the poly Si layers. The carrier concentration n is a fraction 4 of the impurity concentration and is written, n = $Jx C(x, t).
(4)
Using equations (l), (3) and (4) and introducing a new
S.
532
HORIUCHI and R. BLANCHARD
Table 1. Diffusion coefficient of boron in the poly crystalline and single crystal silicon layers Diffusion x,/v/t pm/hr”’ arg erfc C,/C, CrllC, temp. C, Poly Poly Poly Poly Poly Poly Poly (“C) (cmm3)B,Hs BN Single B&L, BN Single B2H6 BN Single B,H, 900 950 1000 1050
x 1020 4.5 5.0 5.5 6.0
1.31 2.34 3.45 5.67
1.16 1.91 2.94 4.40
0.182 0.405 0.692 1.26
xlo-J xlo-5 xlo-6 2.22 2.22 6.67 3.34 3.34 2.00 280 6.00 3.36 3.36 1.82 1.82 5.45 3.375 3.375 1.67 1.67 5.00 3.39 3.39
3.51 3.53 3.54 3.55
0.1% 0.346 0.511 0.837
D
BN
Single
Poly B,H,
cm*/sec Poly BN Single
x lo-” x 10-l” 0.173 0.0259 0.963 0.834 0.283 0.0574 3.33 2.22 0.435 0.0971 7.25 5.26 0648 0.178 19.5 11.7
x lo-‘” 0.186 0.915 2.62 8.80
C, in the poly crystalline silicon layers and in the single crystal silicon samples is taken to be lOI cm-’ and 3 x 10” cm?, respectively. C, in the poly crystalline silicon layers is assumed to be the same as that in the single crystal silicon samples. Table 2. Activation energy and apparent diffusion coefficient at infinite temperature E. teV)
DO
(cm’ set-‘)
fi,,
(pm x hr-I’*)
Poly BIH6 Poly BN
2.51 2.39
6.01 x lo-’ 1.51x lo-’
4.65 x 10’ 2.33 x 10’
Single Single[l4]
3.42 3.42
9.10x lo-’ 6.38x IO-’
5.72x 10’ 4.79x IO5
variable n =x/g diffused layers,
yield the sheet resistivity in the
As shown in Fig. 3, ps-’ is proportional to fi
resulting in that p is a slightly dependent function on x even in the poly Si layers except for low diffusion temperature and short diffusion time. As described betore, ps in the poly Si layers is higher than that in the single crystal silicon substrates when the diffusion temperature is low or the diffusion time is short even though the diffusion depth is deeper in the poly Si layers than in the single crystal silicon layers. These facts show that diffusion proceeds along the grain boundaries in poly Si layers and after they are filled with impurities and the barrier height is lowered[8], some parts of the impurities start to contribute to conduction. 5. SUMMARY gives a good understanding in device fabrication to know the diffusion mechanism of boron in poly Si layers since poly Si layers are usually doped by diffusion of boron in p-channel Si gate MOS devices. Boron was diffused with diborane and boron nitride as boron sources into the poly Si layers of 5.5 pm thickness which were deposited at 950°C from the thermal decomposition of It
silane in hydrogen ambient. The diffusion depth was found to be proportional to the square root of time in the single crystal silicon substrates and in the poly Si layers with boron nitride and diborane as boron sources. The boron diffusion in the poly Si layers can be expressed in the well known complementary error function. The diffusion coefficient of boron in the poly Si layers is larger when diborane is used than when boron nitride is used as a boron source and is also 10-50 times larger than that in the single crystal silicon substrates in the experimental range. The activation energies in the single crystal silicon substrates and in the poly Si layers when boron nitride is used and when diborane is used as a boron source are 3.42,2-39 and 2.51 eV, respectively. The sheet conductivity of the diffused poly Si layers is proportional to the square root of diffusion time and is lower than that of the diffused layers in the single crystal silicon substrates except when the diffusion temperature is low and/or the diffusion time is short. Acknowledgements-The authors wish to thank all the colleagues in the Stanford Integrated Circuits Laboratory for their assistance.
REFERENCES 1. L. L. Vadasz, A. S. Grove, T. A. Rowe and G. E. Moore, IEEE Specr. 6, 28 (1969). 2. T. I. Kamins, J. Manoliu and R. N. Tucker, J. appl. Phys. 43.83 (1972). 3. C. C. Mai, T. S. Whitehouse, R. C. Thomas and D. R. Goldstein, J. Electrochem. Sot. 118, 331 (1971). 4. F. Faggin, D. D. Forsythe and T. Klein, Proc. Eighteenth Ann. Reliability Physics Conf. p. 35 (1970). 5. J. C. Irvin, Be/f Sysr. Tech. J. 41, 387 (1962). 6. H. F. Wolf, Silicon Semiconductor Data, p. 155, Pergamon Press, Oxford (1969). 7. H. F. Wolf, Silicon Semiconductor Data, p. 141, Pergamon Press, Oxford (1%9). 8. T. I. Kamins, J. appl. Phys. 42, 4357 (1971).
Electmnics,
1975. Vol. IS, pp. 529-532.
Perganton Press.
Prinlcd in Great Britain
BORON DIFFUSION IN POLYCRYSTALLINE SILICON LAYERS S. HORIUCHI*and R. BLANCHARD Stanford University, Stanford, California94305,U.S.A. (Received
31 July 1974;in
reoisedfon
5 September
1974)
Abstract-Boron was diffused into the poly Si layers of 5.5 w thickness with boron nitride and diborane as boron sources. The diffusion depth was found to be proportional to the square root of diffusion time. The boron diffusion in the poly Si layers can be expressed in the well known complementary error function. The diffusion coefficient of boron in the poly Si layers is larger when diborane is used than when boron nitride is used as a boron source and is IO-50times larger than that in the single crystal silicon substrates in the experimental range. The diffusion coefficients of boron at 1050°Cin the single crystal silicon substrates with diborane as a boron sourcein the poly Si layers with boron nitride and diborane as boron sources are 8.80 X IO-“, I.17 x IO-‘*and I.95 X IO-‘*cm*/sec, respectively. The activation energies of the diffusion coefficients of boron in the above each case are 3.42, 2.39 and 2.51eV, respectively. NOTATION
impurity concentration at the distance x from the surface at time t surface impurity concentration impurity concentration at xd diffusion coefficient apparent value of D at infinite temperature activation energy function Boltzmann’s constant carrier concentration electron charge absolute temperature time distance from the surface diffusion depth junction depth x, in the single crystal silicon substrates and the diffusion depth x, in the poly Si layers junction depth sheet resistivity of the diffused layers carrier mobility fraction of carrier concentration n = I#IX C variable (= xd/dt)
I.INTRODUCTION
In silicon gate technology [ I], polycrystalline silicon
(poly Si) layers which are used as gate electrodes and interconnections are usually doped by diffusing impurities in the layers after poly Si deposition. Impurities diffuse much faster in poly Si layers than in single crystal silicon substrates because of the grain structure of the poly Si layers[Z, 31. The grain size depends on many factors. Several important factors are the sample preparation before deposition, the deposition temperature and the thickness of the poly Si layers. From the point of view of the practical device fabrication, impurities diffuse from the doped poly Si layers into the gate oxides sometimes resulting in instabilities [4] in silicon gate MOS devices and sometimes even penetrate through the gate oxides down into the single crystal silicon substrates producing the surface conductive layers of the opposite type to the substrates. From the above reason, it is very helpful in the device ‘Present address: Toshiba R & D Center, Kawasaki, Japan.
fabrication to understand the diffusion of impurities in poly Si layers. This paper describes the results of the diffusion of boron in the poly Si layers of the thickness of about 5.5 pm deposited from the thermal decomposition of silane. Diborane and boron nitride were used as boron sources. The work described here is a part of the developmental work on silicon gate technology at the Stanford Integrated Circuits Laboratory.
2. EXPEXIMENTAL METHOD silicon substrates used in these experiments were l-3 fi cm phosphorus doped n-type (100) wafers 2 in. dia. The wafers were oxidized at 1200°C in dry O2 for 13.5 min. The thickness of the oxide was measured to be 820A by an ellipsometer. Following the oxidation, the poly Si layers were deposited on the top of the oxide layers with the flows of 10cm’lmin of silane and 22 I/min of hydrogen at 950°C. The deposition rate was 800 A/min. Since it is difficult to use thin poly Si layers for the diffusion experiments, the poly Si layers of 5.5 pm thickness were deposited. The diffusion was performed in two methods. One was with the flows of 200 cm’lmin of diborane from the tank of 1070ppm of diborane in nitrogen, 5 cm’lmin of oxygen and 16OOcm’lmin of nitrogen. The other was with boron nitride wafers type HBR manufactured by Union Carbide in the flow of 2OOcm’/min of nitrogen. The boron nitride wafers were oxidized at 1050°Cfor 15 min in the flows of 400 cm3/min of nitrogen and 5 cm’/min of oxygen everytime after they were used for more than 4 hr. Before and after the boron nitride wafers were oxidized, boron was diffused in the single crystal silicon test wafers and the sheet resistivity of the diffused layers was checked. No degradation of the boron nitride wafers was found during the experiments. The same quartz tube was used both for boron nitride and diborane. Before the diffusion from boron nitride was carried out after diborane was used, the tube was cleaned by etching it in HF: HZ0 = 1: 1 for 30 min and rinsing it for 30 min with deionized water. The sheet resistivity of the boron diffused layers was measured by using an ordinary four point probe after The
529
S. HORIIJCHI and R.
530
dipping the samples in an oxide etchant. The diffusion layers were stained by two staining etchants following beveling. One is an ordinary staining etchant which contains a few drops of HNOs in 100cm’ of HF: HZ0 = 1: 1. The other etchant consists of 500mg of H2PtC16in 100cm’ of HF:H*O = 1: 1[2]. The diffusion depth was measured by a fringing microscope and both the staining etchants always gave the same results.
BLANCHARD
POLY BN
5-
DIFFUSION TEMF! PC) 0-o 1050 x-x 1000
3. EXPERIMENTAL RESULTS
In Fig. 1, the diffusion depth in the poly Si and single crystal silicon samples which were put side by side on the quartz boat during the diffusion with diborane as a boron source is plotted against the square root of diffusion time. Figure 2 shows the relationship between the square root of diffusion time and the diffusion depth in the poly Si layers with boron nitride as a boron source. A larger amount of scattering in the data of the diffusion depth is seen in the poly Si layers than in the single crystal silicon samples and when diborane is used than when boron nitride is used as a boron source in the poly Si layers. However, the general tendency can be found. The diffusion proceeds faster in the poly Si layers than in the single crystal silicon layers and when diborane is used than when boron nitride is used as a boron source in the poly Si layers. In Fig. 3, the sheet resistivity of the diffused layers in the poly Si layers and single crystal silicon substrates with diborane as a boron source is plotted against diffusion time. In Fig. 3 is also shown the relationship between the diffusion time and the sheet resistivity of the poly Si layers with boron nitride as a boron source. No significant difference between with diborane and boron nitride as boron sources can be seen in the sheet resistivity. The sheet resistivity of the diffused layers in the single crystal silicon samples is higher than that in the ---
x--x 1000 o--o 1050
ii 1%
/
0/
f
/ !I P 0
I
x
/-’ ,,,...
0
/x--
.’
_a--
__--__-n---->===___
0
TIME+
(HOUR+)
Fig. 2. Square root of diffusion time vs diffusion depth in the poly Si layers with diffusion temperature as a parameter. BN was used as a boron source.
poly Si layers except when the diffusion temperature is low or the diffusion time is short. 4. ANALYSIS OF THE EXPERIMENTAL RESULTS
By assuming that the surface concentration C,, is invariable with diffusion time and the diffusion coefficient D, is independent of the impurity concentration as supported by Figs. 1 and 2, the impurity concentration C(x, t), at the distance x from the surface at time t, can be expressed in the form of the well known complementary error function, (1)
This means that though the grain size and preferred orientation of the poly Si layers vary with the thickness of the layers[2], they have little effects on the diffusion coefficients in the experimental range. First of all, the impurity concentration Cs at the diffusion depth xd, was examined by the same method as is described in ref. [2]. The epitaxial layers and the poly Si layers were grown on the single crystal silicon substrates and the oxide layers thermally grown on the single crystal silicon wafers respectively in the epitaxial reactor at 9SO”Csimultaneously. The growth time was IOmin and for the first 5 min, these layers were grown without doping and during the last 5 min, they were doped with diborane. The doping level was varied from run to run in the range of 10’6-10’9/cm3in the epitaxial layers. There was no difference in the growth rate between the epitaxial layers and the poly Si layers. The growth rates of the doped and the undoped layers both are the same in the epitaxial layers and the poly Si layers in the range of the doping
‘,’ ___o______o___----oc
_A
0
c’
Ic
IO
C(x.t)=C.xF(~~=C,erfc(~).
900 950 0 / 0
Cl
05 (DIFFUSION
POLY BzHs SINGLE E2Hs
DIFFUSION TEMP PC1
A-A 0-n
0
x’--
&+__---
P-
A__--
I
0.5 (DIFFUSION
x-
_/-
__--
1.0 TIME+
1.5
(HOUR+)
Fig. 1. Square root of diffusion time vs diffusion depth in the poly Si layers and single crystal silicon substrates with diffusion temperature as a parameter. B&Lwas used as a boron source.
level examined.
The sheet resistivity
of the epitaxial
531
Boron diffusion in silicon layers TEMPERATURE o-0 n-0
IIf”
IO DIFFUSION
I
111’
TIME
POW POLY
100
SN a*y
1050
I
1000
(“c)
950
I
I
900
I
a
fmin)
Fig. 3. Diffusion time vs sheet resistivity. BN poly, B,Hs poly and B&single.
5t 7.5
layers was measured with a four point probe but the sheet resistivity of the poly Si layers grown at the same time was typically too high to measure with a four point probe. The thickness of the doped epitaxial layers and the doped poly Si layers was measured using a fringing microscope after beveling and staining. From the measurements of the sheet resistivity and thickness of the doped epitaxial layers, the impurity concentration of boron in the doped poly Si layers was estimated. The poly Si layer of the lowest doping level that corresponds to 101%m3 in the epitaxial layer grown at the same time was able to be stained with the etchants. It can be concluded from the results that the impurity concentration of boron at the edge of the stained poly Si layers is less than 10’6/cm’. Next, the diffusion coefficients of boron in the poly Si layers were calculated by using equation (1) and the results in Figs. 1 and 2. C, in the poly Si layers was taken to be the same as that in the single crystal silicon substrates diffused at the same time and Ca to be 10’6/cm3. This does not introduce any serious error in the calculation considering that Ca is less than 10’6/cm3and C, might be larger in the poly Si layers than in the single crystal silicon substrates and argerfc C&/C, is a very slow decreasing function with Ce/Cs in this range. The decrease of two orders of magnitude in G/C, gives less than 20 per cent increase in argerfc G/C,. C, in the single crystal silicon substrates was calculated using the measured xd and p5 and Irvin’s[S] curves. The obtained C, is a little bit larger than the published data[6] of the solid solubility limit of boron in single crystal silicon substrates. In Table 1, the values of the slope xd/.\lt in Figs. 1 and 2, C,, G/C,, argerfc Cs/C,, VD, D are summarized. In Fig. 4, the square roots of the diffusion coefficients of boron in the poly Si layers and single crystal silicon
substrates are plotted against diffusion temperature. The published data[7] of the diffusion coefficient of boron in the single crystal silicon substrates is also presented in Fig. 4 for reference. D varies exponentially with reciprocal absolute temperature l/T in each case as
TEMPERATURE
,
I
8.0
8.5 1 I/T?K))
I x10-4
Fig. 4. Diffusion temperature vs square root of diffusion coefficient.
shown in Fig. 4 and is expressed in the form,
(2) where k is the Boltzmann’s constant, E. is an activation energy and Do is an apparent value of D at infinite temperature. The activation energies and apparent values of D at infinite temperature were calculated using equation (2) and Fig. 4 are shown in Table 2. The activation energy in the single crystal silicon substrates agrees very well with that of the published data[7]. The activation energy in the poly Si layers does not depend on the kinds of boron sources and takes almost the same value in both cases of boron nitride and diborane and is about 1.4 times smaller than that in the single crystal silicon layers. The sheet resistivity, p,, of the diffused layers is related to the carrier concentration n, by X’ -1 = Ps wn dx (3) I0 where q is the electron charge and p is the carrier mobility which is a function of only the carrier concentration in the single crystal silicon substrates and is a function of the carrier concentration and distance in the poly Si layers due to the grain structure. x’ is the junction depth in the single crystal silicon substrates and is the diffusion depth in the poly Si layers. The carrier concentration n is a fraction 4 of the impurity concentration and is written, n = $Jx C(x, t).
(4)
Using equations (l), (3) and (4) and introducing a new
S.
532
HORIUCHI and R. BLANCHARD
Table 1. Diffusion coefficient of boron in the poly crystalline and single crystal silicon layers Diffusion x,/v/t pm/hr”’ arg erfc C,/C, CrllC, temp. C, Poly Poly Poly Poly Poly Poly Poly (“C) (cmm3)B,Hs BN Single B&L, BN Single B2H6 BN Single B,H, 900 950 1000 1050
x 1020 4.5 5.0 5.5 6.0
1.31 2.34 3.45 5.67
1.16 1.91 2.94 4.40
0.182 0.405 0.692 1.26
xlo-J xlo-5 xlo-6 2.22 2.22 6.67 3.34 3.34 2.00 280 6.00 3.36 3.36 1.82 1.82 5.45 3.375 3.375 1.67 1.67 5.00 3.39 3.39
3.51 3.53 3.54 3.55
0.1% 0.346 0.511 0.837
D
BN
Single
Poly B,H,
cm*/sec Poly BN Single
x lo-” x 10-l” 0.173 0.0259 0.963 0.834 0.283 0.0574 3.33 2.22 0.435 0.0971 7.25 5.26 0648 0.178 19.5 11.7
x lo-‘” 0.186 0.915 2.62 8.80
C, in the poly crystalline silicon layers and in the single crystal silicon samples is taken to be lOI cm-’ and 3 x 10” cm?, respectively. C, in the poly crystalline silicon layers is assumed to be the same as that in the single crystal silicon samples. Table 2. Activation energy and apparent diffusion coefficient at infinite temperature E. teV)
DO
(cm’ set-‘)
fi,,
(pm x hr-I’*)
Poly BIH6 Poly BN
2.51 2.39
6.01 x lo-’ 1.51x lo-’
4.65 x 10’ 2.33 x 10’
Single Single[l4]
3.42 3.42
9.10x lo-’ 6.38x IO-’
5.72x 10’ 4.79x IO5
variable n =x/g diffused layers,
yield the sheet resistivity in the
As shown in Fig. 3, ps-’ is proportional to fi
resulting in that p is a slightly dependent function on x even in the poly Si layers except for low diffusion temperature and short diffusion time. As described betore, ps in the poly Si layers is higher than that in the single crystal silicon substrates when the diffusion temperature is low or the diffusion time is short even though the diffusion depth is deeper in the poly Si layers than in the single crystal silicon layers. These facts show that diffusion proceeds along the grain boundaries in poly Si layers and after they are filled with impurities and the barrier height is lowered[8], some parts of the impurities start to contribute to conduction. 5. SUMMARY gives a good understanding in device fabrication to know the diffusion mechanism of boron in poly Si layers since poly Si layers are usually doped by diffusion of boron in p-channel Si gate MOS devices. Boron was diffused with diborane and boron nitride as boron sources into the poly Si layers of 5.5 pm thickness which were deposited at 950°C from the thermal decomposition of It
silane in hydrogen ambient. The diffusion depth was found to be proportional to the square root of time in the single crystal silicon substrates and in the poly Si layers with boron nitride and diborane as boron sources. The boron diffusion in the poly Si layers can be expressed in the well known complementary error function. The diffusion coefficient of boron in the poly Si layers is larger when diborane is used than when boron nitride is used as a boron source and is also 10-50 times larger than that in the single crystal silicon substrates in the experimental range. The activation energies in the single crystal silicon substrates and in the poly Si layers when boron nitride is used and when diborane is used as a boron source are 3.42,2-39 and 2.51 eV, respectively. The sheet conductivity of the diffused poly Si layers is proportional to the square root of diffusion time and is lower than that of the diffused layers in the single crystal silicon substrates except when the diffusion temperature is low and/or the diffusion time is short. Acknowledgements-The authors wish to thank all the colleagues in the Stanford Integrated Circuits Laboratory for their assistance.
REFERENCES 1. L. L. Vadasz, A. S. Grove, T. A. Rowe and G. E. Moore, IEEE Specr. 6, 28 (1969). 2. T. I. Kamins, J. Manoliu and R. N. Tucker, J. appl. Phys. 43.83 (1972). 3. C. C. Mai, T. S. Whitehouse, R. C. Thomas and D. R. Goldstein, J. Electrochem. Sot. 118, 331 (1971). 4. F. Faggin, D. D. Forsythe and T. Klein, Proc. Eighteenth Ann. Reliability Physics Conf. p. 35 (1970). 5. J. C. Irvin, Be/f Sysr. Tech. J. 41, 387 (1962). 6. H. F. Wolf, Silicon Semiconductor Data, p. 155, Pergamon Press, Oxford (1969). 7. H. F. Wolf, Silicon Semiconductor Data, p. 141, Pergamon Press, Oxford (1%9). 8. T. I. Kamins, J. appl. Phys. 42, 4357 (1971).