Low-frequency noise in Cr&#8212;SiO<inf>2</inf>&#8212;N-Si tunnel diodes

ACKNOWLEDGMENT surements were made with the mercury thermometer suspended in the center of the reactor with a 10-mil alu- The authorwould like to thankD. S. Enjaian for taking minum wire to thermallyisolate the thermometer from the the experimental measurements and J. M. Welty for a of the thinking. walls. Calculations show that the thermometerwould have major contribution to all aspects REFERENCES read about 20 percent higher were the wire support not [l]S.M. Irving, “A dry photoresist removal method,” in Proceedings of conducting heat from the thermometer. the Kodak Photoresist Seminar, vol. 2,1968, pp. 26-29. At 2.0 torr both the atomicoxygen concentration arid [2] R. L. Bersin, “Automatic plasma machines for stripping photoresist,” Solid S t a t e Technology. 1970, p. 39. the temperature are monotonically increasing functions of the power up to600 W. A t higher pressure the plasma [3] F. K. Kaufman, “Reactionof Oxygen Atoms,” Progress inReaction Kinetics, vol. 1. New York Pergamon Press, 1961, pp. 12-13. requires a higher sustaining voltage for a given power artd [4]A. T. Bell and K. Kwong, “Dissociation of oxygen in radiofrequency electrical discharge,” A.I.Ch.E.J., vol. 18, 1972, p. 990. consequently has alower conductivity and thicker skic.

Abstract-Low-frequency noise of Cr-SiOz-n-Si tunnel dioa es from these states into bound states in theoxide located with about 30-&thick oxides is investigated as function of bias, close to theinterface. The two step modelis employed in frequency, and temperature. Measurements of l/f noise a r e e x of Srrh. this paper to explain l/f noise in Cr-SiOz-n-Si tunnel plained bya theory employing the two step tunneling model measured as Electrons from the Si conduction band are trapped by states at t h e diodes with oxide thickness of about 30 Si-Si02 interface and then tunnel into bound states of the oxide function of bias and temperature. The ac and dc characlocated close to the interface. The oxide states of density Noo c a n teristics of the devices have already been discussed elsebe representedby a frequency dependent parallel admittance ex-where [4].A theory of the low-frequency noise of the MOS hibiting frequency-dependent thermal noise that modulates the d c c u r r e n tI tunneling through the oxide barrier. This generai.estunnel diodes is presented in Section11, sample preparato and in- tion and measuring technique in Section 111, and meaflicker noiseat the device terminals proportional12Noo Section in f and tunnelingarea A . The value surements and their comparison with the theory versely proportional to frequency A = 5 10W3Ao, determined by fitting theoretical and experimen;al IV. a small fractionof the gatearea ‘10, curves atlow frequency, is only since tunneling preferentially occurs through the thinnest pal% 11. THEORY OF LOW-FREQUENCY NOISE of t h e oxide. T h e c u r r e n t I also exhibits full shot noise at high frequency and low current. Qualitative agreement between thcmoA schematic band model of the MOS tunnel diode is 9 decades. Measurements retical and measured noise is found over shown in Fig. l(a). With an appliedforward bias on the at low temperature show additional noise of generation-recombimetal V , = (F, - F,)/q, where F, and F , are the semination centers at larger frequencies and currents.

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I. INTRODUCTION

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U ANDSAH [l] recentlyextendedanearlier proposal of McWhorter [2] to arathersuccessful two-step tunneling modelfor l/f noise in MOS transistors. They assumed as the first step net-recombination of carriers from the semiconductor bands into bound statesa t the Si-Si02 interface bythe Shockley-Read-Hall process [3], and as thesecond step elastic tunneling of the carriers

conductor and metal Fermi levels, respectively, the device current consistsof two components: The first term[ 4 ] ,

is the difference of a forward and a reverse current of electrons tunneling through the oxide between the Si conduction band and the metal. The prefactor Kn A T 2 depends on the tunneling areaA and the temperatureT . The electron tunneling transmissioncoefficient Tn(F,) Manuscript received July 30, 1976; revised September 16,1976. This is bias dependent, and F l ( x ) is a tabulated Fermi-Dirac work was supported by a grant of the NationalScience Foundation. integral function [5].The positions of the silicon and metal The authors are with the Departmentof Electrical Engineering, Lehigh Fermi levels, F, and F , with respect to the energy referUniversity, Bethlehem, PA 18015.

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KUMARANDDAHLKE:NOISE

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ligible since x0 > 1 Y-l I, is adjusted so that the amplifier output voltage increases to N V , in Fig. 2(d). Third, the test device is replaced by its equivalent admittance Y ,which produces only thermal noise a t room temperature, and then the inputnoise is measured again by now adjusting the signal voltage t o Vs,y.The desired equivalent noise current of the testdevice is, G E Re y:

The described techniqueallows us to measure thedevice noise I,, between 5 Hz and 50 kHz with less than 10 percent error.

Iv. RESULTSAND DISCUSSION

The noise pattern of the MOS tunnel diodes was continuously observed on an oscilloscope. Less than 50 percent devices The low-frequency noise of the MOS tunnel diodes has of these devices exhibited clean noise in contrast to exhibiting bursts, i.e., popcorn noise [14], [15], or spikes, been measuredby comparing the device noise with a cali-

B. Noise Measurements

IEEE TRANSACTIONS ONELECTRONDEVICES,

150

FEBRUARY

1977

i.e. microplasma noise [ E ] ; these characteristics were seen in the devices onthe samewafer. Only deviceswith clean noise were used for detailed noise measurements. I

A. Noise Instabilities Our observations of noise instabilities of the tunnel diodes are summarizedas follows: 1) Popcorn noise is already visible at thebeginning o f the test and depends little on the device current. The burst pulse height is of the sameorder of magnitude as the device noise. The pulse width is afew milliseconds. 2) Some devices show no microplasma noise whenbeginning the test at small bias,but exhibit spikes if biased beyond a threshold current,typicdly A. Thischange of the noise pattern is irreversible, althoughdc current and ac admittanceremainunchanged.Thespikeschange magnitude and sign with the device current. Their arnplitude is often morethan ten times larger than thedevice noise, the pulse width is in the order of microseconds. 3) The mechanism of the instabilities is not well understood. It is especially unclear why some devices show both forms of instability, while others do not, although processed in the same manner.

B. Current Dependence of Noise The equivalent noise current I,, of sample 4,type B , measured at room temperature as function of forward and reverse dc currentsI f and Ir with frequency as parameter is presented in Fig. 3(a) and (b). The dashed lines corl*espond to shot and thermal noise calculated from(15)a;ld (16). The measured noise approaches these values a t high frequencies and low currents, where shot noise dominat ?s, as explained in Section 11-B. The measurednoise I,,(It) in Fig. 3(a) can be fairly well represented by a power law I,, IT5, to theleft, and J'eq I!.6,to the rightof the bias marked by an arrow. A t this point the device current switches, as already reported [41, from the recombination controlled component is^ at low bias t o the band-to-band-tunneling component I,, at larger bias, cf. Fig. l(a). In general, I,,(I) can be approximated by the relation

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I0-5

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I,,

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IPl,

p1