Correlations between 1 /"noise and DC characteristics in bipolar transistors

J. Phys. D: Appl. Phys. 18 (1985) 2269-2275. Printed in Great Britain Correlations between 1 /"noise and DC characteristics in bipolar transistors C T Green and B K Jones Department of Physics. University of Lancaster. Lancaster LA1 4YB, LK Received 7 August 1984, in final form 13 March 1985 Abstract. A statistical analysis is reported of the measured electrical properties of a sample of one type of low-noise npn silicon transistor. The parameters measured were characteristic of the excess noise, the ideal base and transistor action. the non-ideal base and the reverse flow in each junction. Little significant correlation was found between the excess noise parameters and the others. A clear and simple relationship was found between the magnitude and voltage dependence of the non-ideal base. 1. Introduction In an earlier paper (Green and Jones 1985) experiments were reported on the excess noise in npn silicon transistors. The DC characteristics of these devices showed that the base could be represented by the sum of two exponentials IB = -k 1; = Ibo exp(el/,e/mkt) + exp(evbe/kt) (1) where the first term represents the non-ideal base and the second term the ideal base. The ideal base is the component, due to recombination the base region of a proportion of the carriers flowing between the emitter and collector, which contributes to the normal transistor action. The non-ideal component represents the of those carriers which flow between the base and emitter and recombine and degrade the transistor performance. The constant m is found to be independent of VBE and is called the ideality factor. The noise in the devices consisted of the white thermal noise of the device resistances and the white shot noise of the flow through the junctions. Added to these there was excess, l/f, noise with a llf'intensity spectrum. where y -- 1. The results of these experiments showed that the excess noise could be represented by a single generator between the emitter and base junctions with an intensity = KZ;;'Af/fv (2) where Af is the measured bandwidth, K is a constant which is independent of the temperature T, m, Zb/ZB and which gives a measure of the excess noise properties of the transistor. Other evidence was presented to suggest that K = K'/A where K' is another constant and A is the base-emitter contact area. For the devices studied it was found that K' = 60 X cm'. 0022-3727/85/112269 + 07 $02.25 @ 1985 The Institute of Physics 2269

2270 C T Green and B K Jones This result showed an excess noise source with a strong resemblance to other l/f noise sources which are resistance or emission fluctuations with a quadratic dependence on the time-averaged part of the fluctuating variable (here 1;). The results suggest that it is this component which is fluctuating. The present experiment was designed to investigate the relationship between the excess noise and the DC characteristics as they are affected by small variations in the physical properties of the devices, such as doping density and base width, which arise during processing. There were three aims: to indicate which device design parameters and hence processing steps affect the noise and hence could be improved; to determine whether any DC parameter could provide a simpler indicator of excess noise than the slow direct measurement of the noise itself; and finally, to provide more information about the source and mechanism of the llfnoise. The excess noise and the DC characteristics of a sample of 20 specimens were measured. Noise measurements were made on afurther sample of 10. A separate sample of 425 devices was, also used for a limited set of the DC characteristics. For consistency the data are presented for the complete small sample and reference is made to the results on the large sample. The data were analysed by calculating a few key parameters. These were then studied individually to determine the distribution of values and they were then correlated in pairs to determine any relationships. 2. Experimental details The specimens studied were a sample of type BC413P silicon npn transistors made by Ferranti Electronics. These are double-diffused planar devices in a dumb-bell configuration and with a low-concentration phosphorus emitter. They had been selected for a minimum acceptable quality by standard quality control electrical tests and thus did not show a very large range of variability. They were further screened by rejecting any device which showed burst noise above the wide-band white noise when biased at high. This test was done visually using an oscilloscope. The DC measurements were performed on a HP 4140B picoammeter and voltage source which was controlled by an HP85 computer. The data were obtained, stored, processed and reduced by the computer. The noise measurements were performed with the device biased at a collector of 1 pa in the common emitter configuration. After amplification by a low noise preamplifier the noise was measured using an HP 3582A spectrum analyser controlled by an HP85 computer. The average of many repeated spectra was determined by the spectrum analyser. The spectrum was converted into an equivalent noise voltage at the input of the device by dividing by the device gain. To measure this a large noise signal was injected into the device input and the input and output signals were applied to the spectrum analyser which computed the transfer function. To determine the magnitude of the excess noise generator, a large value of source resistance R, was used so that the device noise was converted into an input voltage noise 3 = Rf which dominated all other voltage noise sources at the input. The spectrum was measured between 1 Hz and 25 khz and fitted to the sum of a white noise term and a term varying as l/?. All measurements were made at room temperature. The excess noise parameters used were K and y as defined in equation (2). The value of Zg at the bias point was obtained from the measured DC data.

transistors bipolar in l/f noise 2271 Noise measurements were also used to determine the value of the device geometric base resistance rhb. The device was biased at an optimum with a source resistance of 1 R. - The white noise is then determined by the thermal noise of rbb and the shot noise of re, U, = 4kT(Yhh + re/2)af. Since the emitter junction slope resistance re = kt/ele can be calculated the value of Ybb can be found (see Green and Jones (1985) and Unwin and Knott (1980)). The lc - V, curve was used to determine Zco using the equation: zc = I C0 exp(ev,,/kt). (3) The ZB - V, curve enabled Zbo, Zbo and m to be determined using equation (1). The data were fitted over the of range about 0.15 V to 0.65 V by an iterative least-squares analysis assuming that the ideal component had the same voltage variation I,. as The ideal gain HFE Ico/Zbo = Zc/Zb was used as a parameter. The measured gain is Zc/ZB which decreases at low s from the maximum, ideal value because ZB is larger because of the added contribution of the non-ideal and at high s because of high injection and collector series resistance effects. The reverse I-Vcharacteristics were measured for each junction separately with the third terminal open-circuit. A power law I = Vawas found at lowvoltages. The exponent LY = d(lg Z)/d(lg V) was evaluated for each junction and called EB slope and CB slope. As a measure of the magnitude of the reverse leakage the values at 1 V were determined, lg I,,,( 1 V) and lg ZCBO( V). 3. Results The parameters chosen to describe the properties of the devices are shown in table 1 with their measured mean and standard deviation. They have been divided into four groups to describe the excess noise parameters and the junction forward and reverse parameters. These data were produced on a sample of 20 specimens. Similar results for some of the parameters were found on a separate larger sample of 425 specimens. A typical distribution for the parameter rbb is shown in figure 1. For this Table 1. The mean and standard deviations of the parameters of the 20 devices. deviation Excess noise Ig K K Y Non-ideal m Ig Go Ideal Ig IC, k 4 0 HFE E IC0 /rio rbdq 1 Reverse Ig I,,, (1V) Ig IC,, (1V) EB slope CB slope Mean -8.67 4.28 x 1.18 1.32-14.4-13.9-16.4 263 76-12.1-11.6 0.24 0.39 Standard 0.95 14.5 x lo-* 0.175 0.093 (bimodal) 0.62 (bimodal) 0.12 0.056 57 40 0.40 0.30 0.40 0.34

2272 C T Green and B K Jones 50 75 100 125 150 175 rdb IQ1 Figure 1. The histogram of the frequency distribution of the measured base resistance the large sample of 425 devices. rbb for parameter the mean of the smaller distribution lies only just within the larger distribution but we have no reason to believe that the former specimens are typical. not The standard deviation of K is large and the histogram of the data for the larger sample shows that the distribution is not normal. A normal distribution was found for lg K so this parameter was also included and should probably be preferred. The distributions for both non-ideal parameters (rho and m) were found to 180 (a I 60 40 20 A 1.01.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 U C m 3 U E LL Figure 2. The histogram of the frequency distribution of the two non-ideal base parameters, (a) ideality factor m, and (6) lgibo the non-ideal base amplitude. A bimodal distribution is shown in both cases.

Zlf noise transistors in bipolar 2273 be not normal. The histograms of the data taken on the larger sample showed a bimodal distribution and are shown in figure 2. The values of y and m are typical of those reported in the literature. It should be noted that the distributions are not perfectly 'natural' since some selection has been undertaken in the initial quality control screening. In the next stage of the analysis, correlation coefficients were calculated between each Fir ofparameters. These are shown as percentages in table 2. The coefficient used was ( XY)~/X* 7. Table 2. The percentage correlation between the parameters numbers refer to the extended sample of 30 devices. of the 20 devices. Starred Excess noise Non-ideal Ideal Reverse i"" m i Ig ICB0(lv) EB slope CB slope 50 25 25 0 9 * 2 0 0 9 19 6 X X 35 12 18 0 6 * 1 1 0 0 8 3 0 10 7 0 5 40 13 0 13 9 020 58 0 11 2 15 11 2 53 24 16 0 25 26 0 78 43 X 9 6 13 36 13 1 18 9 20 17 7 0 2 2 2 5 X 4. Discussion We will consider initially the correlations within each group of parameters. Within the excess noise parameters there is very little correlation. This suggests that the use of equation (2) is suitable and that the data fitting procedure is appropriate. The non-ideal parameters show an exceptionally high correlation of 87%. This was confirmed on the larger sample and the correlation plot is shown in figure 3. This result is significant and will be discussed later. The ideal parameters show little correlation except lg I,, and lg Zbo and lg l,, and H, which is to be expected from the definitions. The reverse parametershow a large correlation only between lg lcbo(lv) and CB slope which shows probably that these have not been chosen fully independent as parameters. This high correlation was not repeated in the larger sample. The significant correlations between the parameters of the DC characteristic groups are between lg Ibo and m, lg Zbo. This possibly reflects the difficulty of fitting the base perfectly to these three parameters. may It however, indicate a common source for the recombination processes in Z;3 and 1;. The 40% correlation between m and CB slope was not sustained in the larger sample.

2274 C T Green and B K Jones Ideality factor m Figure 3. The correlation between lg (Ibo), the non-ideal amplitude. and the ideality factor m. The regression line is shown with 98% coefficient. The data are for the histograms shown in figure 2. The correlation between the excess noise parameters and the DC parameters show that y has a uniformly low correlation. There is not a large correlation between K or lg K and the non-ideal parameters which suggests that the method of analysis given by equation (2) is appropriate. The moderate correlations are not larger than might one expect from the curve fitting procedure. There is also not a large correlation between K or lg K and the reverse emitter-base junction parameters. Many models ascribe both the reverse bias leakage, forward recombination and excess noise to impurity centres in the junction so that the lack of correlations shown here is not expected but is consistent. The fairly high correlation between K and lg K with CB slope is surprising and is not reflected in the magnitude of the leakage, lg ZcBO(lV). We assume that it is therefore not significant since it is difficult to produce logical a model of the noise to include these two parameters. 5. Conclusions No significant correlation was found between the excess noise of a set of bipolar transistors and the DC parameters. The lack of correlation is significant. Excess noise generally found to be dependent on the quality of the device and varies between devices, processes etc. Previous work has suggested that it is a fluctuation of the non-ideal recombination. These observations suggest that there should be a correlation with the impurity or defect concentration in the device. The reverse leakage and non-ideal forward properties of the diodes are also usually assumed to depend on these properties. To account for the lack of correlation it may be that the parameter used for excess the noise, K, has already removed any explicit dependence of the non-ideal and the other DC parameters are not affected by the particular defect property which controls K and Zbo. The significant positive result of this correlation experiment is the very high correlation found between the non-ideal parameters m and lg Zbo. On the larger sample the distributions of both parameters are clearly bimodal. The correlation is shown in

Ilf noise in bipolar transistors 2275 figure 3. The data fall on the line lg Zg, = 5.46m - 21.3. (3) The reason for the double peaked distribution not known and no other parameter was found to have such a distribution. This result is significant because present theories of the non-ideal are based on recombination centres in the base-emitter spacecharge region. In all theories the magnitude of I;io is due to the number (quantity) of the centres and m is due to their distribution in energy or space (quality) (e.g. Lefferts 1981, Sah er a1 1957, Sah 1962, Dhariwal and Srivastava 1977, Nussbaum 1973). This high correlation does not support this simple distinction. There are other problems with the simple recombination centre modelsince they do not predict a constant value of m over a wide range of V,, as observed and no mechanism has been proposed to produce a low-frequency fluctuation of the recombination rate, which is necessary if this is the source of the llfnoise. Simulations have been made using the basic recombination model but in which a distribution of traps, in space and energy, has been added. These produce values of m between 1 and 2 which are constant over a range of VBE (Lefferts 1981, Buckingham and Faulkner 1969, Ashburn et a1 1975). Such a distribution of energies or time constants is also typical of one class of llfnoise theory. The simple correlation result found suggests that the parameters of the Z;io-m relationship may give a simple measure of the distribution of such traps. Acknowledgments This work was supported in part by Ferranti Semiconductors and SERC. We are grateful for the help given by Dr M J Turner and 0 A Jiagbogu. References Ashburn P, Morgan D V and Howes M J 1975 Solid State Electron. 18 569-77 Buckingham M J and Faulkner E A 1969 Radio Electron. Eng. 38 33-9 Dhariwal S R and Srivastava G P 1977 Solid State Elecrron. 20 476-7 Green C T and Jones B K 1985 J. Phys. D: Appl. Phys. l8 77-91 Lefferts R B 1981 PhD rhesis Stanford University Nussbaum A 1973 Phys. Stat. Solidi a19 441-50 Sah C T 1962 IRE Trans. Electron Deu. ED-9 94-108 Sah C T, Noyce R N and Shockley W 1957 Proc. IRE 45 1228-43 Unwin R T and Knott K F 1980 IEE Proc. 127 53-61