Mapping nonlinearities over the active regions of semiconductor devices

PROCEEDINGS LETTERS 1635

Fig. 1. A photomicrograph of the silicon interdigitated UHF transistor used for thermal mapping showing the surface topology.

Fig . 2. A photograph of the display screen $10 the enhanced 1.15- fim hotoresponse due to hot-spot operation-e hot-spot region is the {right region, approximately in the center.

technique which should be mentioned. Analysis [6] shows that the There are several features of the electronic temperature mapping

resolution is equal to the laser spot diameter. The 3- resolution demonstrated is several times better than that obtained from most, if not all, of the commercial infrared radiometers used for noncontacting measurements of device temperatures. These radiometers determine temperatures by integrating the IR radiated in a wavelength interval from the specimen. This interval extends from about 1.8 pm to about 5.6 fim for the usual case in which the radiometer employs an InSb detector. Because the scanner uses a monochromatic source at a wavelength shorter than 1.8 l m , its diffraction-limited resolution is better than that achievable by the radiometer. Another feature is that very little specimen preparation is required. The operating mechanism is the change in photoexcitation with temperature, and the fraction of the incident 1.15- radiation which reaches any portion of the structure is quite immaterial. Of course, the initial, eg., room temperature, signal from the portion of the structure to be measured must be large enough to use. Furthermore, the emissivity of the various portions of the transistor surface do not have to be taken into account, and special coatings to control emissivity need not be used when measuring temperatures. Finally, the utility of the technique d e s m i is not re- stricted to high-frequency devices, since the trend in modem device

design seems to be toward interdigitation, which allows access by infrared radiation to active regions of the device, even for a power supply transistor.

It is possiile to assign temperature values to 1.15- photoresponse enhancement such as shown in Fig. 2. A description of this work is being prepared for publication [ 6 ) .

ACMOWLEDOMENT The authors are pleased to acknowledge helpful discussions with

D. L. Blackburn, W. M. Bullis, and F. F. Oettinger of the National Bureau of Standards’ Electronic Technology Division; 0. pitzalis and R. Gilson of the US. A m y Electronics Technology aud Devices Labora- tory, Fort Monmouth, NJ; and Prof. H. P. D. Lanyon of the Electrical Engineering Department of the Worcester Polytechnic Institute, Wor- cester, MA.

REFERENCES [ 11 D. E. Sawyer and D. W. Berning, “Semiconductor measurement

technology: A laser scanner for semiconductor devices,’’ NBS S cial Publication p g 400-424, in preparation.

[Z] C“N. Potter and 0. . Sawyer, “A flylagspot scanner,”Rev. Sd. IMncm. , vol. 39, pp. 180-183,1968.

[ 31 W. C. Dash and R. Newman, “Intrinsic o tical absor tion in singlecrystal germanium and silicon at 77 an%300 K,” P&s. Rev., vol.

[4] W. Bf udau and A. Onton, “Temperature dependence of the band

[ 5 ] H. P. D. Lanyon, Electrical Engineenng Department, Worcester gap of silicon,” J. Appl. Phys., vol. 45, ep. 1846-1848.1974.

Polytechnic Institute, Worcester, MA, private communication. [ a ] D. E. Sawyer and H. P. D. Lanyon, ‘‘Lam scanning for tem-

perature measurements of active semiconductor devices,’’ in preparation.

99,p . 1151-1155,1955.

Mapping Nonlinearities Over the Active Regions of Semiconductor Devices

D. E. SAWYER AND D. W. BERNING

ALmmct-A Leper scanner e m p l a y i a modulated lowpower 0.633- mHe-Nelrserhrsbeenusedinawndrmrgiagmrnnertoloute portions of a silicon bipolar UHF tmaistor which electriany behave m a nonlina manner at a s@d frequency of 470 MHz. In effect, the method UMS the device sunned as a frequency convert= to produce au IF output for a displry scffen whenever the laser spot is i n d e n t on nonliaerr@m

A technique has been developed to reveal the portions of semiconductor devices which operate nonlinearly at UHF. Signals at two frequencies are applied to the device, and s u m and difference frequencies produced by square-law nonlinearities appear at the output. One of the signals is applied electrically at the usual input port. The other is applied as modulation of a scanning light spot focussed on the exposed device surface. The light spot creates hole-electron pain nondestruc- tively within the device. W~th an IF amplifier connected to the device output port and tuned to the difference frequency between the two signals, an IF output is detected only when the light spot is incident on a region of nonlinearity; The device, in effect, serves as its own mixer. With the light spot deflected in synchronism with the trace on a cathode- ray display screen and with the IF amplifier connected to suitably modulate the screen, a map of the nonlinearities is presented.

The scanning system, which is described in detail elsewhere [ l ] , is quite simple in concept. Briefly, the beam from a low-power 0.633- pm CW He-Ne laser is sequentially deflected from two scanning mirrors to generate a scanning raster, and this is focussed on the specimen under investigation. A scanning system of this type has been descnid previ- ously [2]. For the observations which will be described it was not necessary to modulate the laser with a signal source, but simply to utilize the laser modulation already present. During normal operation, the laser produces optical radiation not at just one discrete wavelength, but at a series of discrete wavelengths determined by the allowed axial modes and centered about the nominal wavelength. Mixing of these modes modulates the laser radiation in multiples of a fundamental modulating frequency. For the 0.633-pm laser used, the fundamental

Manuscript received October 30, 1975; revised June 21, 1976. This work was conducted as part of the National Bureau of Standards pro- gram on Semiconductor Measurement Technology, with principal fund- ing from the Defense Advanced Research Projects Agency through ARPA Order 2397.

Bureau of Standards, Washington, DC 20234. The authors are with the Institute for Applied Technology, National

1636 PROCEEDINGS OF THE IEEE, NOVEMBER 1976

frequency is approximately 500 MHz, and this SOO-MHz modulation was used for the detection of nonlinearities.

Production of the IF component can be understood on a c h a r p control basis. The relationship between minority carrier density in ex- cess of equilibrium within the base and the internal base current quite geqeraUy can be represented by a power series. For devices, or device portions, which are operating linearly, the power series (exclusive of a possible constant) is a single term linear in the current and the characteristics are described by a straight line. For this case, there is no variation in the minority carrier distribution within the device at frequencies other than the two input ones, and so only these two frequencies will a m in the electrical output. However, if the charae teristics are not linear, frequency mixiug may be detected at the output. Specificdly, if the square term is present, and this is the next term in the power series after the linear one, frequencies which are the sum and the difference of the two inputs will be produced. The two inputs, of course, are the electrically applied signal, and the signal due to carrien photogenerated within the device to a depth of a few mi- crometers (for silicon) by the 0.633um laser [3].

The nonlinearities in several silicon bipolar transistors designed to furnish 5 W at frequencies up to 1000 MHz were investigated. These transistors are comprised of four in-line cells electrically connected in parallel with a total active area 1200 pm X 150 pm, and the surface topology is shown in Fig. l(a) as revealed by a reflected-t detector circuit which is incorporated in the laser samer. The emitter and base fingers are interdigitated with the emitter fingers coming in from the left in this photograph, and the base fingers in from the right. The fin- ger metallization stripes am 2 pm wide and are separated by 8 pm. This separation allows access of the laser light to the device inner regions. To map the nonlinearities, the transistor was operated in a simple

common emitter circuit fed with a supply voltage of 30 V. The dc base drive was adjusted to allow the transistor to be biased anywhere between cutoff and a saturation current of 475 mA.

For the results shown, a 470-MHz signal generator was coupled to the base lead, and a 30-MHz IF amplifier and detector modulating the display screen was connected across the cdector load resistor having a nominal value of 60 S2. If squareqaw nonlinearities are present within the transistor, frequency mixing of the 470-MHz signal and the 500- MHz laser modulation occurs and a 3 0 - m ~ difference frequency output is produced. It might be anticipated that mixing would occur with the transistor biased near saturation, near cutoff (the characteristics near cutoff resemble those of a mixer diode), and to a lesser extent in regions inbetween.

Fig. 2 shows the IC versus IB characteristic for the transistor when operated between cutoff and saturation. The photographs in Fig. 1 are keyed to Fig. 2 and show the display at the operating points indicated by the arrows. For the results given in the photographs in Fig. 1, the electrical response of the transistor has been overlayed on a reflected- light image of the device being scanned. Since both a reflectedqight image and a photoresponse image of the device can be obtained at the same time, these are superimposed dectronically so that it is possible to locate the exact point of origin of the photoresponse signals.

In Fig. l(a), the transistor is completely turned off and no photoresponse signal due to mixing is possible. In Fig. 1@), the transistor is in partial cutoff and a strong IF output is obtained uniformly. Accord- ing to the graph in Fig. 2, the base-cokctor current characteristics are quite linear at the point where Fig. l(c) was obtained, but some localized points of strong nonlinearity are revealed nevertheless. In Fig. l(d), the third cell down on the transistor is more nonlinear than the others, and some of the strong localized nonlinearities that were present in Fig. l(c) are still there. In Fig. l(e), the transistor is nearing the saturation region and the overall nonlinearity increases. Fig. l(f) was taken with the transistor driven further into saturation. It is interesting to note that the strong nonlinearity present at the top and bottom edges of the active area, as revealed by the photos in Fig. l(b)-l(e), seems to have been reduced. Perhaps this is so because the gain of the transistor is very low here, and it may be that the overall nonlinearity is really much stronger than that indicated in Fig. l(f).

Fig. 3 shows the display when the cdlector supply voltage was raised to 40 V so as to cause the transistor to form a hot spot [4] . The operating point was between C and D in Fig. 2 before the collector voltage was raised. The hot spot is the dark area on the left-hand emitter side. It is interesting to see that operation in the hot-spot regime can influ- ence linearity in cells other than just the one or ones with a hot spot. The gain settings for the equipment used to measure the nonlinearities was kept constant for all of the results given in Figs. 1 and 3.

In summary, a technique has been developed which utilizes the mix-

Fig. 1. Photographs of the scanner display screen showing nonlinearities in a UHF transistor while it is operating at the bias points indicated by arrows in Fig. 2. The nonlinearities are overlaid on a reflected li t ima e of the device surface obtained at the same time. (a) Hard region. o g (b) #ear cutoff. (c) and (d) Linear region. (e) and ( f ) Saturation

ing property inherent in nonlinear operation to map these nonlinearities over the active regions of semiconductor devices. This is accomplished in a nondestructive manner by scanning the device with modulated light while the device is functioning within its normal frequency range. It was found that localized regions of strong nonlinearity and broad regions of lesser amounts of nonlinearity could be detected even though there was little indication of this behavior in a base currentcollector current graph. Devices showed nonlinear regions which varied in degree and location from device to device, but the presence of these nonlinearities could not, in general, be ascertained through the use of the usual sorts of external electrical measurements designed to assess device quality.

One application of the technique described might be for design and selection of devices for systems in which a large number of devices are cascaded throughout a communications link, or for systems in which several channels of widely differing signal strangths are used simulta-

PROCEEDINGS LETTERS 1637

USE CURWIT [=A]

Fig. 2. Collector-base characteristics for the UHF transistor of Fig. 1 connected in the common emitter circuit used for that figure.

Fig. 3. Photograph of the display screen for transistor operation in the hot-clpot regime.

neously, such as CATV. Even the smallest amount of nonlinearity is to be avoided, since it will produce crosstalk. Another application might be for predicting certain types of device failure modes, as nonlinearities often indicate stfess points in any s t r u c t u r e .

Although the results presented here are qualitative, it should be possible to quantify the degree of nonlinearity for any device portion by separately measuring the amplitudes of the two exciting frequencies and the difference frequency, and from these one can determine the square-law coefficient

ACKNOWL~DOMENT The authors wish to thank R. A. Gilson and 0. Pitzalis, Jr., of the U.S.

Army Electronics Technology and Devices Laboratory, Ft. Monmouth, NJ, for providing the transistors used.

REFERENCES

D. E. Sawyer, and D. W. Berning, “A laser scanner for semiconductor devices,” Semiconductor Measurement Technology, NBS Special Publication 400-24 (in preparation). C. N. Potter, and D. E. Sawyer, “A flying-spot scanner,”Rev. Sci. In&um.,vol. 39, p. 180-183, 1968. W. C. Dash, an8R Newman, “Intrinsic optical absorption in singlecrystal germanium and silicon at 77 and 300 K,”Phys. Rev.,

D. E. Sawyer, and D. W. Berning, “Thermal mapping of transistors with a laser scanner,’’ thia h u e , pp. 1634-1635.

V O L 99, pp. 1151-1155, 1955.

I-Y chanrcteristics of a Thin-Fitm Transistor with Graded channel Thidcness

TUNG H. WENG

A-t-The expredon for mam-duin . . Of 8 lhip

Btmlr&mktawithliQ€mdygradsdchmneleiFhranirpredentsdba#l aPadepletiObtypeopantiasmradmcementmoda Thesltp1.tion

Manuscript received December 3,1975;revised March 22.1976. The author is with the School of Engineering, Oaklaud University,

Rochester. MI 48063.

v=o x - 0 v=vo

V‘Vd

Fig. 1. Phyaical model of a graded-channel thin-film transistor.

vdm dexived trOm &el-Y expmdon was found to deueaae signia a n ~ , a s c o m p o r e d t o d ~ c h m n e l ~ c o m p ~ ~ du~fihthicLrnegasthesomcedoffhegndedcbmna.

Studies [l] of the saturation voltage of a thin-W transistor with uniform channel thickness mhte that, for a given semiconductor doping level, l5e saturation voltage increases parabolidy with in- creasing film thickness. This is to be expected since the saturation occufs when the channel near the drain electrode is completely de- pleted. In order to obtain a low saturation voltage or pentode-like characterigtics for the transistor, it is necessary to reduce the channel thickness. This may result m reducing the carrier mobility due to scattering m a thinner W which, m turn, can reduce the transconduc- tame of the transistor. To minimize this contlicting effect, it is mg- gested that the channel thickness be varied m such a way that the semiconductor film near the drain is thinner than that near the source. A simple physicat configuration to achieve this objective is that of a linearly graded channel as shown m Fig. 1. This configuration would retain high carrier mobility and at the same time result in low saturation voltage.

To obtain an expression for the source-drain characteristics, we based on the physical model, also shown m Fig. 1, of a depletion-type operating in an enhancement mode. In this model, the channel cau be represented by two distiact regions, namely, the enhancement region and the depletion region. If an n-type channel is assumed, then the enhancement region is characterized by Vg > V and the depletion region by Vg < V. Accordingly, the conductance changes m these two regions as a result of the applied gate voltage should be considered separately. Using Weimer’s result [ 21 , the conductance function m the enhancement region can be expressed as

The conductance function m the depletion region is given [3] by

where N is the initial carrier concentration, p is the carrier mobility, w is the chaunel width, q is the electron charge, d is the thickness of the depletion layer, and E i is the permittivity of insulator. The d e pletion layer thickness d was found [4] to be related to the following expression:

Nqd2 Nqdt Y-V,=-+- - 2€$ El

where e$ is the permittivity of semiconductor; h(x) can be expressed as

h(x)=a+-x. b - a

L (4)

Solving d from (3) and substituting it along with h(x) into (2), we have

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Mapping nonlinearities over the active regions of semiconductor devices