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On the 1f noise in polysilicon emitter bipolar transistors: Coherence between base current noise and emitter series resistance noise
Solid-StateElectronicsVol. 41, No. 3, pp. 441-445. 1997 0 1997 Elsevicr Science Ltd Printed in G&Britain. AU rights reserved 0038-1101/97 $17.00 + 0.00 PII: !soo3&1101(%)00177-3
Pergamon
ON THE l/f NOISE IN POLYSILICON EMITTER BIPOLAR TRANSISTORS: COHERENCE BETWEEN BASE CURRENT NOISE AND EMITTER SERIES RESISTANCE NOISE H. A. W. MARKUS,
Ph. ROCHE
and T. G. M. KLEINPENNING
Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands (Received
10 May 1996; in revised form 18 July 1996)
Abstract-The l/f noise in polysilicon emitter bipolar transistors is investigated. The main l/fnoisc source was found to be located in the oxide layer. This source causes both l/f noise in the base current SI, and l/f noise in the emitter series resistance S,. The l/f noise is ascribed to barrier height fluctuations of the oxide layer resulting in transparency fluctuations for both minority and majority carriers in the emitter, giving rise to Si, and S,,, respectively. This model predicts that Si, and Se are fully correlated. Our experimental results show a correlation factor in the range of 0.30.5. The deviation from full correlation is ascribed to local inhomogeneities in the oxide layer. 0 1997 Elsevier Science Ltd
1. INTRODUCTION
the high current regime was proposed that assumes
Several authors have studied the low-frequency noise in polysilicon emitter BJTs[l-71. The lowfrequency noise always consists of white shot noise and l/f noise. Sometimes burst noise is observed. Kleinpenning[ l] found that the l/f noise was located in the base current S,, and that its spectral density was proportional to the base current ZB. He interpreted the l/f noise in terms of mobility fluctuations. Pong-Fei Lu[2] also found the l/f noise to be located in the base current, but he found 4, _ r;l. Pawlikiewicz et aZ.[3]found S,, - 12,at higher currents and Sr, u Ze at lower currents. SiabiShahrivar et aZ.[4] and Mounib et a[.[51 showed that the l/f noise is strongly related to the surface treatment prior to polysilicon deposition. Wai Shing Lau et a1.[6] found 8, N Z& They suggested that transparency fluctuations of the oxide layer, present at the monosilicon-polysilicon interface, or two-step tunnelling via traps in the oxide is responsible for the observed l/f noise. However, they did not give a detailed quantitative analysis. Recently, a study of the l/f noise in polysilicon emitter bipolar transistors was published in a paper by Markus and Kleinpenning[7]. It was found that the dominant l/f noise generators are the base current 8, and the emitter series resistance noise &. At high currents the l/f noise in the base current was proportional to the base current squared, i.e. Si,ccZ& Only at low currents it was proportional to ZB. The latter was ascribed to mobility fluctuations. A model for
that the fluctuations of the barrier height of the oxide layer, present at the monosilicon-polysilicon interface, lead to fluctuations of the tunneling probability, or transparency, for holes and electrons. The transparency fluctuations give rise to fluctuations in the base current and in the emitter series resistance. The spectral density of the fluctuations has a l/f frequency dependence. Since the bandgap of the oxide layer is constant, we expect that the fluctuations of the transparency for holes and electrons are correlated and thus that the base current noise (at high currents) and the emitter series resistance noise are correlated. The experimental fact that most strongly supports the proposed model, as discussed in Ref. [7], is given in Fig. 1. In this figure the relative l/f noise in the emitter series resistance is plotted vs the relative l/f noise in the base current. Results are presented for transistors having different oxide layer properties. We observe that both l/f noise generators have a similar dependence on the oxide layer properties. However, from Fig. 1 we cannot conclude that both noise generators are correlated. For instance we can have two independent (i.e. uncorrelated) noise sources located in the oxide layer, whose spectral densities have a similar dependence on the oxide properties. The transparency fluctuation model predicts full correlation between both noise generators. Absence of this correlation implies that the results cannot be 441
H. A. W. Markus et al.
I
I
lb
I I
I
I
rh
I I ______
I
__’
-----
Fig. 2. Noise measurement circuit. Internal series resistances are given by the symbol r, and external resistors by R. ‘.._ grown ‘.
oxide 7 5 1 A,: = 3 8x3 pm’
10-9t 1O“O
9
S,!Z,’(Hz~‘) at I Hz
current and in the emitter series resistance., are given by Ref. [l]: AVe = AZsRB= Re ]r. + B(r. + Z$llAZk - ZEArc
Fig. 1. Relative l/f noise in the emitter series resistance vs the relative lynoise in the base current. AE is the emitter area. Details on the devices are given in Section 2.
A VE = AIERE =
interpreted in terms of the transparency fluctuation model. The purpose of the work presented in this paper is to obtain experimental evidence for the correlation between l/f noise in the base current and l/f noise in the emitter series resistance. 2. DEVICES
The transistors are made by Philips Electronics. The oxide layer at the polysilicon-monosilicon interface was removed using an HF/H20 vapour etch in a cluster tool. A new layer was grown thermally. According to the manufacturer the average thickness of this layer is 7.5 A and 8 A. We studied two devices with an emitter area of 0.3 x 48 pm2 and two with an emitter area of 1.3 x 48 pm’. With the help of the Gummel plots and the white noise measurements, we determined the values of the base series resistance, the emitter series resistance and the current gain. The results are presented in Table 1. More details can be found in Ref. [7].
RE
kc- fib
-I- RdlAL Z
Z = r, + RB + rb + t/3 + ~)(RE + rJ.
AV BN -R
BAZbe-eAr BRE
=
A VEx [” - kb •t Ra)l AI, _ ZEA,.e. B The cross product can be approximated (AV,
AVE) x RF,
Tl T2 T3 T3
(0.3 (0.3 (1.3 (1.3
x x x x
48 48 48 48
Oxide thickness pm>) pm’) pmz) pmz)
7.5 8 8 7.5
(A)
by:
1
(Arf) - Z&AL Are> . (3)
The values of (Af,) and (Arc’) were measured as described in Ref. [7j. Assuming a correlation factor r between AZ, and Ar,, i.e. (AZ, Ar,) = we can calculate the three contriZ-J?z5G& butions of (Al’,), (Ari), and (AZ, Ar.) in eqn (3). In Fig. 3 the absolute value of the sum of the contributions owing to (Aebb) and (AT:), and the absolute value of the contribution owing to
Table 1. Transistor parameters and correlation factor Transistor
(2)
r. - P(; + Rd (A&)
MEASUREMENTS
The correlation spectra were measured by putting the transistor in the circuit given in Fig. 2. The correlation spectra1 density was measured between the voltage fluctuations at the base contact and at the emitter contact. The formulae for the voltage fluctuations at the base and emitter contacts, taking only the l/f fluctuations into account in the base
(1)
Here r. = dV&/d& is the dynamic input resistance, fi is the dynamic current gain, AZ, and Ar, are the spontaneous l/f fluctuations in the base current and in the emitter series resistance, respectively. b-r our experiments we took RE>>rer rb, RB, r. so that 2 z (/? + ~)RE. For eqn (1) we then obtain with /I>>l:
+ & 3. CORRELATION
- (fl+ l)ZEAr,
B
ra (Q
r. (Q)
r
315 530 650 330
494 410 430 433
9 11 7 3
0.4 0.3 0.5 0.4
On the I/fnoise in polysilicon emitter bipolar transistors
443
resistance. From the experimental results in Fig. 1 it is found that y a 0.3. The sign in eqn (5) is positive because an increase in the barrier height for electrons is coupled to a decrease in the barrier height for holes. So, an increase in the emitter resistance is accompanied by an increase of the base current. Substitution of eqn (5) in eqn (4) yields:
These conditions have to be satisfied to obtain:
emitter current (A) Fig. 3. Absolute value of the sum of the contributions owing to (A&) and (Ar:) in eqn (3) (solid line), and absolute value of the contribution owing to (AL Ar,) taking r = 1 in eqn (3) (dotted line), both divided by e.
I(AVBAVE)I ~~
x
RezE(Ab ,/WAIZ,))G
Are)
(AL Are>
=Jw=r.
(7)
4. EXPERIMENTAL RESULTS AND DISCUSSION
Ar,) with r = 1 are plotted versus ZE for a 1.38 x 48 pm2 transistor. For the sake of readability of Fig. 3 the power spectral densities are divided by G. From this plot we can determine the emitter current range where the contribution owing to (AI& Arc) can be dominant in eqn (3), in this current range we have to perform the correlation measurement. From Fig. 3 we also have an impression of the detection limit of the correlation factor r. In the case of the transistor presented in Fig. 3, correlation factors of 0.1 and higher can be accurately detected in the emitter current range of 1O-s-1O-’ A. With the help of Fig. 3 the emitter current range where the contribution owing to (AL Ar,) is dominant can be determined graphically. For this emitter current range we want to have analytical expressions for the conditions to impose on the emitter current and on the values of the external resistances. If r = 1 the cross product term in eqn (3) is dominant if we choose eqn (2): (AL
If these conditions are satisfied eqns (2) and (3) reduce to AVs x RB AI,, AVE z -ZE Ar,, and (AVBAVE) = -R&(AkArc), SO that (A&), (Arz), (AZkAre), and thus r, can be obtained directly from the measurement of (Av’,), (AI?), and (AVB AVE). When Ar, and AI, are fully correlated we have: AI, -= Is
Ar, YI,.
Here, y is a factor that can be determined from the ratio between the relative noise in the base current and the relative noise in the emitter series
With the transistor parameters given in Table 1 it is possible to satisfy the conditions of eqn (6). We measured the correlation factor r of all transistors at different biasing conditions. The correlation factor proved to be independent of the current, within the studied current range. The value of r is given in Table 1. The transparency fluctuation model predicts the value of r to be one. If in addition to the transparency fluctuations there are contributions of other noise generators that do not lead to a correlated contribution to Si, and SE, we get a lower overall correlation factor. However, we found no experimental evidence for the presence of such an extra noise source, whose influence is large enough to account for the low correlation factor. At low currents we found a second l/f noise source for Si, that we ascribed to mobility fluctuations, but its contribution is negligible in the current range where we performed the correlation measurements. If transparency fluctuations are the only noise source for both Si, and S, we can explain the deviation from r = 1 by supposing the presence of local inhomogeneities in the oxide layer. In Ref. [7] it was concluded that the l/f noise sources were homogeneously distributed across the emitter area. This conclusion was based on the emitter area dependence of the l/f noise in both base current and emitter series resistance. However this method cannot show (local) inhomogeneities that could be present on a smaller scale than the smallest emitter area studied in Ref. [7], which is 1 pm’. In case of local inhomogeneities, parts of the emitter area contributing most to the measured base current l/fnoise do not necessarily coincide with the areas that contribute most to the emitter series resistance l/‘noise. As a result, even if there is full correlation between the local l/fnoise sources of the base current and emitter series resistance, one can get
H. A. W. Markus et al.
444
an overall correlation factor that is lower than one. In other words if the ratio between the relative noise in the base current and the relative noise in the emitter series resistance is position dependent, an overall correlation factor lower than one will be found. Below we shall present arguments for local inhomogeneities and derive an expression for f. In order to find a physical explanation or origin for the local inhomogeneities we have to consider the expression for Sr, and S, that were derived in Ref. [7]:
Fig. 4. Correlation factor F as a function of (x. y).
(9) Here, fh is the tunneling probability for holes, s,,, is the metal contact recombination velocity, W,,,,p and L& are the width and the diffusivity of holes in the monosilicon and polysilicon emitter region, &h is the effective mass of electrons and holes in the oxide, Fti,h is the barrier height of the oxide for electrons and holes, L is the thickness of the oxide layer, AE is the emitter area, and tan(b) is the loss tangent of the oxide. Possible inhomogeneities resulting in a position dependent relative l/‘noise in the base current and emitter series resistance are a position dependent band line-up between oxide and silicon, a position dependent barrier height (both through VOe.h and fh), and a position dependent oxide layer thickness (through t,,). A calculation of the correlation factor of an inhomogeneous oxide layer is made in the Appendix. In this calculation we consider an inhomogeneous oxide layer that is modelled with two homogeneous parts with different properties. The resulting expression for r is:
y = g#.
(10)
Here, the indices 1 and 2 refer to the two different parts of the oxide area. A plot of F versus the parameters x and y is presented in Fig. 4. We observe that F-values in the range of 0.3-0.5 can only be obtained for limited areas in the x, y plane. It should be noted that eqn (10) applies for the most elementary case of inhomogeneity. Stronger inhomogeneity leads to lower values of r.
5. CONCLUSIONS
The l/f noise of polysilicon emitter bipolar transistors with a continuous oxide layer can be explained in terms of transparency fluctuations of the oxide layer. These transparency fluctuations lead to base current fluctuations and emitter series resistance fluctuations. This model predicts that the fluctuations in the base current and the emitter series resistance are fully correlated. The correlation factor between the l/J noise in the base current and the l/f noise in the emitter series resistance was measured. Experimentally the correlation factor was found to be in the range of 0.3-0.5. The fact that the correlation factor is smaller than one can be ascribed to local inhomogeneities in the oxide layer. REFERENCES 1. T. G. M. Kleinpenning, Location of low-frequency noise sources in submicrometer bipolar transistors, IEEE Trans. Electron Dwices 39, 1501-1506 (1992). 2. Pong-Fei Lu, Low-frequency noise in self-aligned bipolar transistors, J. App. Phys. 62, 1335-1339 (1987). 3. A. H. Pawlikiewicz, A. van der Ziel, G. S. Kousik, and C. M. van Vliet, Fundamental l/f noise in silicon bipolar transistors, Solid-State Elecfron. 31, 831-834 (1988). 4. N. Siabi-Shahrivar, H. A. Kemhadjian, W. RedmanWhite, P. Ashbum, and J. D. Williams, The effects of scaling and rapid thermal annealing on the l/f noise of polysilicon emitter bipolar transistors, Microelectronic Engineering 15, 533-536 (1991). 5. A. Mounib, F. Balestra, N. Mathieu, J. Brim, G. Ghibaudo, and A. Chovet, Low-frequency noise sources in polysilicon emitter bipolar transistors: influence of hot-electron-induced degradation, in Noise in Physical Systems and l/f Fluctuations, ed. P. H. Handel and A. L. Chung, AIP Conference Proceedings 285, New York, USA, American Institute of Physics, 1993, pp. 288-291. 6. W. S. Lau, E. F. Chor, C. S. Foo, and W. C. Khoong, Strong low-frequency noise in polysilicon bipolar transistors with interfacial oxide due to fluctuations in tunneling probabilities, Jpn. J. Appl. Phys. 31, LlO21-L1023
(1992).
On the I/fnoise in polysilicon emitter bipolar transistors 7. H. A. W. Markus
and T. G. M. Kleinpenning, Low-Frequency Noise in Polysilicon Emitter Bipolar Transistors, IEEE Trans. Electron Devices 42(4),
445
With full correlation in each part we obtain:
720-727 (1995). (A4) APPENDIX: COHERENCE IN AN INHOMOGENEOUS OXIDE LAYER
Let us suppose that we can model the local inhomogeneities by dividing the oxide into two parts. Each part is homogeneous and has full correlation between AIk and Ar,. The quantities in each part are referred to with an index 1 and 2. We have: Ah = A&I + A&.
After some manipulation we find:
p =
KX+K-IV+2 KX
+
K-IV
XV +
and
K-‘-XV
+
r=$$.
K
,
(45)
(Al)
Since I/r, = l/r,) + l/rrl we obtain:
According to the definition in eqn (7) the correlation factor F becomes:
From eqn (AS) we can obtain the following expression for r:
‘=J*.
(A6)
Note that for the homogeneous case, i.e. J = v = K = I, we obtainF=l.Forxv#lwehaver
Pergamon
ON THE l/f NOISE IN POLYSILICON EMITTER BIPOLAR TRANSISTORS: COHERENCE BETWEEN BASE CURRENT NOISE AND EMITTER SERIES RESISTANCE NOISE H. A. W. MARKUS,
Ph. ROCHE
and T. G. M. KLEINPENNING
Department of Electrical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands (Received
10 May 1996; in revised form 18 July 1996)
Abstract-The l/f noise in polysilicon emitter bipolar transistors is investigated. The main l/fnoisc source was found to be located in the oxide layer. This source causes both l/f noise in the base current SI, and l/f noise in the emitter series resistance S,. The l/f noise is ascribed to barrier height fluctuations of the oxide layer resulting in transparency fluctuations for both minority and majority carriers in the emitter, giving rise to Si, and S,,, respectively. This model predicts that Si, and Se are fully correlated. Our experimental results show a correlation factor in the range of 0.30.5. The deviation from full correlation is ascribed to local inhomogeneities in the oxide layer. 0 1997 Elsevier Science Ltd
1. INTRODUCTION
the high current regime was proposed that assumes
Several authors have studied the low-frequency noise in polysilicon emitter BJTs[l-71. The lowfrequency noise always consists of white shot noise and l/f noise. Sometimes burst noise is observed. Kleinpenning[ l] found that the l/f noise was located in the base current S,, and that its spectral density was proportional to the base current ZB. He interpreted the l/f noise in terms of mobility fluctuations. Pong-Fei Lu[2] also found the l/f noise to be located in the base current, but he found 4, _ r;l. Pawlikiewicz et aZ.[3]found S,, - 12,at higher currents and Sr, u Ze at lower currents. SiabiShahrivar et aZ.[4] and Mounib et a[.[51 showed that the l/f noise is strongly related to the surface treatment prior to polysilicon deposition. Wai Shing Lau et a1.[6] found 8, N Z& They suggested that transparency fluctuations of the oxide layer, present at the monosilicon-polysilicon interface, or two-step tunnelling via traps in the oxide is responsible for the observed l/f noise. However, they did not give a detailed quantitative analysis. Recently, a study of the l/f noise in polysilicon emitter bipolar transistors was published in a paper by Markus and Kleinpenning[7]. It was found that the dominant l/f noise generators are the base current 8, and the emitter series resistance noise &. At high currents the l/f noise in the base current was proportional to the base current squared, i.e. Si,ccZ& Only at low currents it was proportional to ZB. The latter was ascribed to mobility fluctuations. A model for
that the fluctuations of the barrier height of the oxide layer, present at the monosilicon-polysilicon interface, lead to fluctuations of the tunneling probability, or transparency, for holes and electrons. The transparency fluctuations give rise to fluctuations in the base current and in the emitter series resistance. The spectral density of the fluctuations has a l/f frequency dependence. Since the bandgap of the oxide layer is constant, we expect that the fluctuations of the transparency for holes and electrons are correlated and thus that the base current noise (at high currents) and the emitter series resistance noise are correlated. The experimental fact that most strongly supports the proposed model, as discussed in Ref. [7], is given in Fig. 1. In this figure the relative l/f noise in the emitter series resistance is plotted vs the relative l/f noise in the base current. Results are presented for transistors having different oxide layer properties. We observe that both l/f noise generators have a similar dependence on the oxide layer properties. However, from Fig. 1 we cannot conclude that both noise generators are correlated. For instance we can have two independent (i.e. uncorrelated) noise sources located in the oxide layer, whose spectral densities have a similar dependence on the oxide properties. The transparency fluctuation model predicts full correlation between both noise generators. Absence of this correlation implies that the results cannot be 441
H. A. W. Markus et al.
I
I
lb
I I
I
I
rh
I I ______
I
__’
-----
Fig. 2. Noise measurement circuit. Internal series resistances are given by the symbol r, and external resistors by R. ‘.._ grown ‘.
oxide 7 5 1 A,: = 3 8x3 pm’
10-9t 1O“O
9
S,!Z,’(Hz~‘) at I Hz
current and in the emitter series resistance., are given by Ref. [l]: AVe = AZsRB= Re ]r. + B(r. + Z$llAZk - ZEArc
Fig. 1. Relative l/f noise in the emitter series resistance vs the relative lynoise in the base current. AE is the emitter area. Details on the devices are given in Section 2.
A VE = AIERE =
interpreted in terms of the transparency fluctuation model. The purpose of the work presented in this paper is to obtain experimental evidence for the correlation between l/f noise in the base current and l/f noise in the emitter series resistance. 2. DEVICES
The transistors are made by Philips Electronics. The oxide layer at the polysilicon-monosilicon interface was removed using an HF/H20 vapour etch in a cluster tool. A new layer was grown thermally. According to the manufacturer the average thickness of this layer is 7.5 A and 8 A. We studied two devices with an emitter area of 0.3 x 48 pm2 and two with an emitter area of 1.3 x 48 pm’. With the help of the Gummel plots and the white noise measurements, we determined the values of the base series resistance, the emitter series resistance and the current gain. The results are presented in Table 1. More details can be found in Ref. [7].
RE
kc- fib
-I- RdlAL Z
Z = r, + RB + rb + t/3 + ~)(RE + rJ.
AV BN -R
BAZbe-eAr BRE
=
A VEx [” - kb •t Ra)l AI, _ ZEA,.e. B The cross product can be approximated (AV,
AVE) x RF,
Tl T2 T3 T3
(0.3 (0.3 (1.3 (1.3
x x x x
48 48 48 48
Oxide thickness pm>) pm’) pmz) pmz)
7.5 8 8 7.5
(A)
by:
1
(Arf) - Z&AL Are> . (3)
The values of (Af,) and (Arc’) were measured as described in Ref. [7j. Assuming a correlation factor r between AZ, and Ar,, i.e. (AZ, Ar,) = we can calculate the three contriZ-J?z5G& butions of (Al’,), (Ari), and (AZ, Ar.) in eqn (3). In Fig. 3 the absolute value of the sum of the contributions owing to (Aebb) and (AT:), and the absolute value of the contribution owing to
Table 1. Transistor parameters and correlation factor Transistor
(2)
r. - P(; + Rd (A&)
MEASUREMENTS
The correlation spectra were measured by putting the transistor in the circuit given in Fig. 2. The correlation spectra1 density was measured between the voltage fluctuations at the base contact and at the emitter contact. The formulae for the voltage fluctuations at the base and emitter contacts, taking only the l/f fluctuations into account in the base
(1)
Here r. = dV&/d& is the dynamic input resistance, fi is the dynamic current gain, AZ, and Ar, are the spontaneous l/f fluctuations in the base current and in the emitter series resistance, respectively. b-r our experiments we took RE>>rer rb, RB, r. so that 2 z (/? + ~)RE. For eqn (1) we then obtain with /I>>l:
+ & 3. CORRELATION
- (fl+ l)ZEAr,
B
ra (Q
r. (Q)
r
315 530 650 330
494 410 430 433
9 11 7 3
0.4 0.3 0.5 0.4
On the I/fnoise in polysilicon emitter bipolar transistors
443
resistance. From the experimental results in Fig. 1 it is found that y a 0.3. The sign in eqn (5) is positive because an increase in the barrier height for electrons is coupled to a decrease in the barrier height for holes. So, an increase in the emitter resistance is accompanied by an increase of the base current. Substitution of eqn (5) in eqn (4) yields:
These conditions have to be satisfied to obtain:
emitter current (A) Fig. 3. Absolute value of the sum of the contributions owing to (A&) and (Ar:) in eqn (3) (solid line), and absolute value of the contribution owing to (AL Ar,) taking r = 1 in eqn (3) (dotted line), both divided by e.
I(AVBAVE)I ~~
x
RezE(Ab ,/WAIZ,))G
Are)
(AL Are>
=Jw=r.
(7)
4. EXPERIMENTAL RESULTS AND DISCUSSION
Ar,) with r = 1 are plotted versus ZE for a 1.38 x 48 pm2 transistor. For the sake of readability of Fig. 3 the power spectral densities are divided by G. From this plot we can determine the emitter current range where the contribution owing to (AI& Arc) can be dominant in eqn (3), in this current range we have to perform the correlation measurement. From Fig. 3 we also have an impression of the detection limit of the correlation factor r. In the case of the transistor presented in Fig. 3, correlation factors of 0.1 and higher can be accurately detected in the emitter current range of 1O-s-1O-’ A. With the help of Fig. 3 the emitter current range where the contribution owing to (AL Ar,) is dominant can be determined graphically. For this emitter current range we want to have analytical expressions for the conditions to impose on the emitter current and on the values of the external resistances. If r = 1 the cross product term in eqn (3) is dominant if we choose eqn (2): (AL
If these conditions are satisfied eqns (2) and (3) reduce to AVs x RB AI,, AVE z -ZE Ar,, and (AVBAVE) = -R&(AkArc), SO that (A&), (Arz), (AZkAre), and thus r, can be obtained directly from the measurement of (Av’,), (AI?), and (AVB AVE). When Ar, and AI, are fully correlated we have: AI, -= Is
Ar, YI,.
Here, y is a factor that can be determined from the ratio between the relative noise in the base current and the relative noise in the emitter series
With the transistor parameters given in Table 1 it is possible to satisfy the conditions of eqn (6). We measured the correlation factor r of all transistors at different biasing conditions. The correlation factor proved to be independent of the current, within the studied current range. The value of r is given in Table 1. The transparency fluctuation model predicts the value of r to be one. If in addition to the transparency fluctuations there are contributions of other noise generators that do not lead to a correlated contribution to Si, and SE, we get a lower overall correlation factor. However, we found no experimental evidence for the presence of such an extra noise source, whose influence is large enough to account for the low correlation factor. At low currents we found a second l/f noise source for Si, that we ascribed to mobility fluctuations, but its contribution is negligible in the current range where we performed the correlation measurements. If transparency fluctuations are the only noise source for both Si, and S, we can explain the deviation from r = 1 by supposing the presence of local inhomogeneities in the oxide layer. In Ref. [7] it was concluded that the l/f noise sources were homogeneously distributed across the emitter area. This conclusion was based on the emitter area dependence of the l/f noise in both base current and emitter series resistance. However this method cannot show (local) inhomogeneities that could be present on a smaller scale than the smallest emitter area studied in Ref. [7], which is 1 pm’. In case of local inhomogeneities, parts of the emitter area contributing most to the measured base current l/fnoise do not necessarily coincide with the areas that contribute most to the emitter series resistance l/‘noise. As a result, even if there is full correlation between the local l/fnoise sources of the base current and emitter series resistance, one can get
H. A. W. Markus et al.
444
an overall correlation factor that is lower than one. In other words if the ratio between the relative noise in the base current and the relative noise in the emitter series resistance is position dependent, an overall correlation factor lower than one will be found. Below we shall present arguments for local inhomogeneities and derive an expression for f. In order to find a physical explanation or origin for the local inhomogeneities we have to consider the expression for Sr, and S, that were derived in Ref. [7]:
Fig. 4. Correlation factor F as a function of (x. y).
(9) Here, fh is the tunneling probability for holes, s,,, is the metal contact recombination velocity, W,,,,p and L& are the width and the diffusivity of holes in the monosilicon and polysilicon emitter region, &h is the effective mass of electrons and holes in the oxide, Fti,h is the barrier height of the oxide for electrons and holes, L is the thickness of the oxide layer, AE is the emitter area, and tan(b) is the loss tangent of the oxide. Possible inhomogeneities resulting in a position dependent relative l/‘noise in the base current and emitter series resistance are a position dependent band line-up between oxide and silicon, a position dependent barrier height (both through VOe.h and fh), and a position dependent oxide layer thickness (through t,,). A calculation of the correlation factor of an inhomogeneous oxide layer is made in the Appendix. In this calculation we consider an inhomogeneous oxide layer that is modelled with two homogeneous parts with different properties. The resulting expression for r is:
y = g#.
(10)
Here, the indices 1 and 2 refer to the two different parts of the oxide area. A plot of F versus the parameters x and y is presented in Fig. 4. We observe that F-values in the range of 0.3-0.5 can only be obtained for limited areas in the x, y plane. It should be noted that eqn (10) applies for the most elementary case of inhomogeneity. Stronger inhomogeneity leads to lower values of r.
5. CONCLUSIONS
The l/f noise of polysilicon emitter bipolar transistors with a continuous oxide layer can be explained in terms of transparency fluctuations of the oxide layer. These transparency fluctuations lead to base current fluctuations and emitter series resistance fluctuations. This model predicts that the fluctuations in the base current and the emitter series resistance are fully correlated. The correlation factor between the l/J noise in the base current and the l/f noise in the emitter series resistance was measured. Experimentally the correlation factor was found to be in the range of 0.3-0.5. The fact that the correlation factor is smaller than one can be ascribed to local inhomogeneities in the oxide layer. REFERENCES 1. T. G. M. Kleinpenning, Location of low-frequency noise sources in submicrometer bipolar transistors, IEEE Trans. Electron Dwices 39, 1501-1506 (1992). 2. Pong-Fei Lu, Low-frequency noise in self-aligned bipolar transistors, J. App. Phys. 62, 1335-1339 (1987). 3. A. H. Pawlikiewicz, A. van der Ziel, G. S. Kousik, and C. M. van Vliet, Fundamental l/f noise in silicon bipolar transistors, Solid-State Elecfron. 31, 831-834 (1988). 4. N. Siabi-Shahrivar, H. A. Kemhadjian, W. RedmanWhite, P. Ashbum, and J. D. Williams, The effects of scaling and rapid thermal annealing on the l/f noise of polysilicon emitter bipolar transistors, Microelectronic Engineering 15, 533-536 (1991). 5. A. Mounib, F. Balestra, N. Mathieu, J. Brim, G. Ghibaudo, and A. Chovet, Low-frequency noise sources in polysilicon emitter bipolar transistors: influence of hot-electron-induced degradation, in Noise in Physical Systems and l/f Fluctuations, ed. P. H. Handel and A. L. Chung, AIP Conference Proceedings 285, New York, USA, American Institute of Physics, 1993, pp. 288-291. 6. W. S. Lau, E. F. Chor, C. S. Foo, and W. C. Khoong, Strong low-frequency noise in polysilicon bipolar transistors with interfacial oxide due to fluctuations in tunneling probabilities, Jpn. J. Appl. Phys. 31, LlO21-L1023
(1992).
On the I/fnoise in polysilicon emitter bipolar transistors 7. H. A. W. Markus
and T. G. M. Kleinpenning, Low-Frequency Noise in Polysilicon Emitter Bipolar Transistors, IEEE Trans. Electron Devices 42(4),
445
With full correlation in each part we obtain:
720-727 (1995). (A4) APPENDIX: COHERENCE IN AN INHOMOGENEOUS OXIDE LAYER
Let us suppose that we can model the local inhomogeneities by dividing the oxide into two parts. Each part is homogeneous and has full correlation between AIk and Ar,. The quantities in each part are referred to with an index 1 and 2. We have: Ah = A&I + A&.
After some manipulation we find:
p =
KX+K-IV+2 KX
+
K-IV
XV +
and
K-‘-XV
+
r=$$.
K
,
(45)
(Al)
Since I/r, = l/r,) + l/rrl we obtain:
According to the definition in eqn (7) the correlation factor F becomes:
From eqn (AS) we can obtain the following expression for r:
‘=J*.
(A6)
Note that for the homogeneous case, i.e. J = v = K = I, we obtainF=l.Forxv#lwehaver