388 IEEE TRANSACTIONS ON ELECTRON DEVICES, JUNE 1971

concentration, the ni values were not in agreement with those re- ported by Putley and Mitchell [6] . The correction was made by forc- ing the hole-electron mass ratio to be that of McKelvey’s, but adjust- ing the magnitudes until the correct intrinsic concentration was ob- tained.

RAYMOND W A N G JAMES DUNKLEY Motorola Semiconductor Prod. Div, Mesa, Ariz. THOMAS A. DEIL’IASSA LAWRENCE F. JELSMA Arizona State Univ. Tempe, Ariz.

REFERENCES B. E. Deal; E. H. Snow, and C. A. Mead, “Barrier energies in Metal-Sios-Si structures, 1. Phys. Chem. Solids, vol. 27, 1966, pp. 1873-1879. G. G. MacFarlane, T. P. McLean, J. E. Quarrington, and V. Roberts “Fine structure in the absorption-edge spectrum of Si,” Phys. Rev. , vol. 111, Sepi. 1958, pp:, 12: 5- 1 7 L% J . r. LvlcKelvey. Solid .State and Semiconductor Physics, chs. 4 and 9. Kew York: Harper an; Row, 1966. R. Wang, Four terminal MOS device,” Motorola Rep. Aug. 1968. A. S. Grove, B. E. Deal, E. H. Snow, and C. T. Sah. “Investigation of thermally

State Electvon., vol. 8, 1965, pp. 145-163. oxidized Si surface using the metal-oxide-semiconductor structure,” Solid-

E. H. Putley and W. H. Mitchell, “The electrical conductivity and Hall effect of Si,” Puoc. Phys. Soc., vol. 72, 1958, pp. 193-200.

”

Noise Properties of the Dynamic Crossed-Field Photo- multiplier

Abstract-Experimentally measured noise power spectra of the dynamic crossed-field photomultiplier are presented, along with data which describe the sampling characteristics of the device. Sampling is shown to introduce excess noise of the order of 3 dB.

INTRODUCTION The dynamic crossed-field photomultiplier (DCFP) provides cur-

rent amplification by means of secondary emission of electrons, as does a conventional electrostatic photomultiplier. The DCFP uti- lizes a n R F electric field and is a sampling device, sampling the photo- current once each cycle of t he RF electric field. The basic properties of this device have been described elsewhere [1]-[3] and sampling properties have been reported by Leverenz and Gaddy [4]-[6].

The noise properties of the DCFP have not previously been re- ported. In particular, the effect of the sampling property on noise performance has not been investigated. In this correspondence, we present experimentally measured noise properties of the DCFP which show that the noise performance is not significantly different from that of conventional electrostatic photomultipliers. The amplification as a function of frequency may also be inferred from the measured noise power spectra.

The parameters of interest are the dc electric field Eo, the R F elec- tric field E , and the normalized magnetic field parameter r=qB/w where 7 is the electronic charge-to-mass ratio, w is the angular fre- quency of the electric field, and B is the magnitude of the magnetic field. For most values of y , particularly those values which give maxi- mum gain, the sampling properties of the DCFP are nearly indepen- dent of y and depend primarily on the ratio E o / E , while the gain de- pends primarily on the magnitude of E [4]-[6].

The noise in the output of the DCFP is attributable to several sources: amplified shot noise in the photocurrent, secondary emission noise, and the noise introduced by the sampling process. The noise contributed by secondary emission has long been known to be due to the random distribution of the number of secondary electrons emitted per incident electron [7]. The excess noise due to sampling is the result of discard of photocurrent during portions of the sampling cycle. This can also be explained in terms of heterodyning the noise power in the photocurrent in the frequency bands above half the sampling frequency into the baseband output of the device 181.

EXPERIMEKTAL RESULTS One series of experiments was performed with devices designed to

operate with a 200-MHz R F electric field. The electric field in the device was established by an internal shielded-resonator structure of

sponsored by the U. S. Air ForLe unher Grant AF-AFOSR 390-67 and by the Manuscript received August 3 1970, revised January 7 1971. This research was

McDonnell-Douglas Astronautics Company, Eastern Division, St. Louis, Mo.

Fig. 1. Data for the 200-MHz DCFP with dc gain of 105. (a) and (d) are noise

frequency) and the vertical scale representing relative noise power at 10 dB/div. power spectra with horizontal frequency scale of 10 MHz/div (50-MHz center

horizontal scale of 1 ns/div and a vertical scale of 2 mV/div. (c) and (f) are (b) and (e) are sampling oscilloscope traces of collector current pulses with a

oscilloscope traces of the convolution of the sampling function of the mode-locked laser pulses with horizontal scale 1 psldiv. Operating conditions are for (a), (b), and (c). Eo/E = 1 . 5 and y =0.872; for (dl. (e), and (f). Eo/E = 2 and y =0.925.

different design from the structures used by Leverenz and Gaddy [SI, [6]. The length of the dynode was 35 cm and the separation of the electrodes was 1.4 cm. The collector was of coaxial geometry with response flat to several GHz.

I n the measurement of the noise performance of the experimental devices, the S-4 photocathode was illuminated with light from an incandescent bulb and the photocurrent was adjusted to some con- venient value. The operating parameters of the device were then ad- justed to give the desired value of amplification and sampling charac- teristics. The noise power spectra were recorded with a Hewlett- Packard Model 8551 spectrum analyzer and the output current pulses were observed with a Tektronix Model 545 oscilloscope with 1S1 sampling plug-in unit. With the same operating conditions, the dura- tion of the sampling function was determined using the technique of Leverenz and Gaddy [5], [6], in which a mode-locked helium-neon laser was used as the light source. The output of the DCFP, after passing through a low-pass filter, then gives the convolution of the laser light pulses and the sampling function of the DCFP. The dura- tion of the sampling function may be inferred from this experiment.

Fig. 1 presents a typical set of data from these experiments. Parts (a) and (d) of this figure show noise power spectra. The baselines in the spectra show the sensitivity limit of the spectrum analyzer. The two center pictures [ (b) and (e)] show sampling oscilloscope traces of the output current pulses due to the phase focusing property of the device, and the two lower pictures [(c)] and (f)] show the convolution of the sampling function and the laser light pulses. Zero output cur- rent corresponds to the top graticule line for the output current pulse photographs and the bottom line for the convolution photographs. In each case the dc output current was 100 @A. The convolution data show that the sampling function duration decreases E o / E is increased. The noise spectra became considerably flatter with increasing Eo/E.

with changes in Eo/E. The shape of the output current pulses was essentially unchanged

These measurements were repeated with another 200-MHz DCFP which was similar to the device described above, with the exception that the dynode was divided into two sections to allow independent adjustment of the values of dc electric field at the photocathode and

CORRESPONDENCE 389

( c ) (e)

Fie. 2. Data for the solit dvnode ZOO-MHz DCFP with Eo,/E =1 and Y =0.91. ~I

(a). (b). and (c) are convolution function photographs. yd) and (e) are noise power spectra. For (a), Eos/E =2.75; for (b) and (d), &,/E =2.42; for (c) and (e), Eo,IE =2.25. Horizontal and vertlcal scales are the same as the corresponding

. -

data presented in Fig. 1.

along the remainder of the dynode, as in the devices described by Leverenz and Gaddy [6]. The section of the dynode containing the photocathode was 20 percent of the total dynode length. The elec- tric field at the photocathode Eo. could then be adjusted to give the desired sampling properties, while the electric field along the remain- der of the dynode Eou could be adjusted to maximize the gain. Typical results of noise power spectrum and convolution measurements on this device, presented in Fig. 2, show the result of variation of EO, with all other parameters held constant. The noise spectrum for each set of operating parameters is shown adjacent to the convolution of the laser light pulse and sampling function obtained for that set of parameters. The gain of the DCFP under the conditions that pro- duced the extremely narrow sampling function of Fig. 2(a) was in- sufficient to produce a noise spectrum measurable with the equipment at hand.

Two devices mere also constructed to measure the noise behavior of the DCFP a t microwave frequencies; one operated with an RF drive frequency of 2.25 GHz and the other at a drive frequency of 4.05 GHz. The distance from photocathode to collector for the 2.52-GHz drive device was 20 mm, and the distance between electrodes was 0.76 mm. Both microwave devices used dynodes of Be0 and S-4 photocathodes. The same design wide-band coaxial collector was also used. These devices were employed in experiments to determine the frequency response in the microwave region and also to measure the noise behavior of the DCFP a t frequencies low compared to the drive frequency. Noise power spectra for both devices for several values of Eo/E are shown in Fig. 3. I n all cases current amplification was lo5.

A good measure of the noise performance of the DCFP is the ratio of the noise power density at low frequencies to the power density expected if the shot noise on the input current were amplified by a noiseless amplifier. The power ratio, expressed in dB, is called the noise figure. For the DCFP with 2.52-GHz drive frequency, data were taken at an output frequency of 30 MHz. Noise figure as a func- tion of E o / E with gain constant of lo5 is presented in Fig. 4 (curve A ) . The noise figure contribution due to the secondary emission noise was calculated and subtracted from the total. The remainder, also shown in Fig. 4 (curve B ) is the noise figure contribution due to sampling. In

Fig. 3. Noise power spectra for the microwave DCFP. Frequency scale: 200 MHz/div (1.0 GFIz center frequency). Vertical scale: 10 dB/div. (a), (b). and (c) were obtained with the 4.05-GHz device and (dl. (e). and (f) with the 2.25- GHz device. ODeratinn conditions are for (a) and (d), Ea/E =0.5; for (b) and (e), Eo/E =l.O;^and fo; (c) and (f), Ea/E =1.5.

" 0 0.5 1.0 1.5 2.0 E,/ E

Fig. 4. Measured noise figure a t 30 M€1z versus Eo/E for the 2.52-GHz DCFP with dc gain of 106. Curve A is total noise figure and curve B is noise figure due to sampling.

all of these experiments the value of the magnetic field was main- tained at the value that provided maximum gain. The same experi- ments performed on the DCFP with 4.55-GHz drive frequency yielded similar results.

DISCUSSION OF RESULTS The measured noise performance of the DCFP described above

has yielded results that are in close agreement with expected results. An analysis of the noise performance of this device has been carried out by Schaeffer [lo]. The excess noise due to sampling is found to be consistent with the sampling characteristics, increasing with de- creasing sampling function duration. The noise power spectra of the microwave devices are consistent with the results obtained with the 200-MHz devices, indicating that scaling to higher frequencies should cause no unexpected noise or frequency response problems.

390 IEEE TRANSACTIONS ON ELECTRON DEVICES. JUNE 1971

For a given photomultiplier, noise figure decreases with increasing gain due to decreasing secondary emission noise. The total noise figure decreases with increasing Eo/E, as shown in Fig. 4. The high- frequency response of the DCFP also improves under this condition, as shown in Figs. 1 and 3. The results of the experiments with the split-dynode DCFP show that flat high-frequency response depends on maintaining a high value of Eae/E. The value of Eo./E may then be varied over a wide range, allowing a variety of sampling functions from very wide to very narrow.

Schaeffer has shown [ 101 that the primary cause of the degradation of the high-frequency response of the DCFP is collection of portions of more than one group of electrons at the output because of small step size. a4nalysis of the electron dynamics of the DCFP shows that the size of the displacement of electrons along the dynode increases with increasing Eo/E, as does the electron arrival energy. Thus operation a t high values of Eo/E provides good separation between steps and high values of secondary emission yield. The high value of secondary emission yield is desirable to hold secondary emission noise to a minimum. In practice the noise figure is minimized by operating the DCFP with as large a value of Eo/E as possible while maintaining the desired value of gain.

ACKNOWLEDGUEXT The authors thank A . B. \T'ilson, K. Kuehl, E. Boose, B. Williams,

11. Swanson, and B. Neumann for technical assistance. Helpful dis- cussions with D. F. Holshouser and D. J . Leverenz are also gratefully acknowledged. Part of the equipment used in this research was pro- vided by the Industrial Affiliates Program in Physical Electronics at the University of Illinois, Urbana.

E . M. SCHAEFFER~ 0. L. GADDY Dep. Elec. Eng. Univ. Illinois Urbana, Ill. 61801

REFEREWES [I] 0. L;, Gaddy, "Microwave crossed-field secondary emission photomultiplica-

tion, Ph.D. dissertation. University of Illinois, Urbana-Champaign, June

121 0. L. Gaddy and D. F; Hohhouser, "A microwave irequency dynamic crossed- 1962.

131 ---, "Some aspects of electron motion in biased DCFEM operation,'' field photomultiplier, P r o c . I E E E , vol. 51. Jan. 1963, pp. 153-162.

[4] D. J. Leverenz, .4 study of the sampling process in DC biased dynamic Proc. I E E E (Corysp . ) , vol. 52, Apr. 1964, pp. 413-414.

crossed-field electron multiplier." Ph.D. dissertation, University of Illinois, Urbana-Champaign, 1969.

1.51 D. J. Leverenz and 0. L. Gaddy, '"Measurement of the duration oi the samp!ing function in the dynamic crossed-field photomultiplier." P r o c . I E E E (Lett.), vol. 57, Dec. 1969. pp. 2153-2154.

161 --, "Subnanosecond gating properties of the dynamic crowfield photo- multiplier." Pmc. I E E E , vol. 58: Oct. 1 9 i 0 , pp. 1487-1490.

[ 7 ] W. Shockley and J . R. Pierce, A theory of noise for electron multipliers," P?m. I R E , vol. ;46, Mar. 1938, pp. 321-332.

[ 8 ] W. R. Bennett, Methods of solving noise problems," P ~ o c . I R E , vol. 44, Ma>- 1956, pp. 609-638.

[Y] R. W. Iverson and 0. L. Gaddy, "A simple method of preparing magnesium oxide secondary emission surfaces," Rev. Sci. Iwstr.. vol. 39, Dec. 1968, pp. 1950-1951.

(101 E,, M . Schaeffer, "Xoise processes in the dynamic crossed-field photomulti- pller," Pl1.D. dissertation. University of Illinois, Urbana-Champaign, June 1970.

I r\'ow mill1 Bell Telephone Laboratories. Indian Hill, I11

Static Negative Resistance in Gunn Effect Materials with Field-Dependent Carrier Diffusion

Abstract-A numerical study of the equations governing the elec- tric field in Gunn effect materials under constant bias shows that static negative resistance (SNR) can occur a s a bulk effect when cer- tain conditions regarding carrier diffusion are satisfied. This result places an important limitation on Shockley's positive conductance theorem in that a completely general extension of the theorem to cases where diffusion is field dependent cannot exist.

product, devices in resistive bias circuits have a saturated, static I-V characteristic, or oscillate in a traveling domain mode. Shockley [ 1 ] has shown also that negative differential mobility by itself always leads to a positive differential conductance. This result has recently been generalized to arbitrary geometries and impurity distributions by Kroemer [ Z ] .

Qualitatively different behavior may occur, however, when carrier diffusion plays a more dominant role, and is field dependent. In heavily doped materials, for example, field-dependent diffusion can substantially affect the velocity of high-field domains. I n extreme cases where the diffusion coefficient D ( E ) increases with field well above threshold, mathematical analysis predicts the possibility of backward-traveling domains [ 3 ] - [ j ] and depletion layers [6].

A special class of behavior occurs when the field derivative D'(E) of the diffusion coefficient, evaluated in a region of field above thresh- old, lies close to the critical value wo/pno, where zto= J/qno is the average carrier velocity in regions of uniform field, e is the material permittivity, and p is the carrier charge. In this case, the material exhibits a static I-Vcharacteristic, regardless of the noL value. hlore-

both d ( E ) <O and D'(E) >0, the I-I/ characteristic has negative over, for bias voltages corresponding to average electric fields where

slope. This correspondence presents calculated static I- V characteristics

showing this negative resistance (SNR) behavior. The results were obtained from numerical solutions of the current equation and Poisson's equation in one dimension and time, where v(E) was chosen for convenience to approximate that of n-GaAs, and D ( E ) was freely specified.

NUMERICAL ASALYSIS

The following equations were solved numerically by a method de- scribed elsewhere [7] :

J ( t ) = qn(x, t ) F ( E ) + €Et(%, t ) - q [ D ( E ) n ( x , t ) I z (1)

The boundary conditions imposed were

where 1 1 6 is the bias voltage and no(x) is the doping profile, specified with a small notch, and a tenfold increase at the ends to simulate contacts. The subscripts x and t denote partial derivatives. The u(E) and D ( E ) characteristics used are shown in Fig. 1. The field values El and En in Fig. l (b ) could be varied, as well as the slope D' in that interval. Static I-Vcharacteristics were calculated in cases where the electric field distribution was stationary, by evaluating (1) to obtain J for specified values of the parameter Vb.

RESULTS TKO sets oi calculations are described. The first demonstrates that

solutions of (1)-(5) exist which exhibit SNR as a bulk effect. D ( E ) was specified so that El=&, and E%>E,, where E, was the peak field in the sample, typically 4-10 times threshold. The slope D' in this interval \vas made equal to Ez'o/yno for a bias Vb about 30 percent above threshold, and then held constant. The calculated internal field under this condition was found to be stable regardless of the noL value. The value of D' could be specified about 10 percent higher or lower with essentially the same result. The current density J found from (1) was thus time independent, and static current-voltage curves were obtained as shown in Fig. 2. These curves correspond to noL values ranging from 5x10'0 to 2x10'2 cm-2. A doping level of 10l4 cmW3 was used for the curves in Fig. 2 , but similar results were obtained a t l O I 5 and 1016 cm-3. One notes that each curve shows a region of negative slope, occurring, except for the shortest sample, for bias voltages corresponding to average fields where u'(E) (0.

I t is evident both from measurements [SI and calculations usinrc