The noise characteristics of Baritt diodes with trapsV.M. Harutunian and V.V. Buniatian

Indexing terms: Baritt diodes, Electron device noise

Abstract: The noise characteristics of a semiconductor punchthrough structure are examined for operationunder low-field conditions, i.e. constant mobility, and for trap levels in the bandgap of the semiconductor.It is shown that the noise measure is decreased under the influence of trapping of injected carriers, for thesmall-signal injection approximation. With the increase of the concentration of traps, the noise measuredecreases, but the frequency band, where it takes place, narrows and is displaced to a lower frequency.

1 Introduction

In recent years great attention has been paid to the theo-retical basis and the practical developments of a new typeof punchthrough transit-time diode, termed Baritt.1"9 TheBaritts are distinguished from the Impatt diode by themechanism of carrier-current injection into the drift space.The lower noise level than for Impatt diodes permits theuse of injection-transit-time diodes as low-noise high-frequency generators, heterodynes for c.w.-frequencymodulation and in automatic frequency-tuning devices.

Theoretical and experimental investigations of the noisecharacteristics of such devices have been discussed in severalpaper.8~17> 19 The object of this paper is the investigationof the influence of the injected carriers in the dirft space ofthe traps, which are inevitably present in real materials,on the noise characteristics of Baritt diodes.

2 Theoretical considerations

When studying the noise characteristics of p-n-p structures,as described below, the p-layers are looked upon as heavilydoped and, in the uniformly doped n-type central region,it is assumed that the existence of impurities creates traplevels for holes. A concentration of traps Nt in the lowerhalf of the forbidden gap near the top of the valence bandis assumed. In such a semiconductor structure some of theinjected carriers are captured by the traps, creating amotionless space charge which can essentially change theform of the current/voltage characteristics and the im-pedance of the injection-transit-time diode.18 In the presenttreatment it is assumed that the voltage applied to thestructure is greater than the voltage which is necessary torealise the punchthrough condition and also that theelectric-field intensity is not high enough for the field toempty the traps. With such low fields the relation betweenfree and captured carriers changes because of the injectionof free carriers.

We shall confine ourselves to the cases of the small-signal injection approximation, when P<Pt where P isthe concentration of holes, Pt is the Shockley-Read statefactor (the concentration of holes in the valence bandwhen the imref coincides with the trap level), and thehigh-signal injection (when P>Pt) approximation.18

One can assume that the most probable sources of noisein Baritts are shot (fluctuation) and diffusion (thermal)noise. The technique of calculation of the noise measure8

is described below and for the impedance the results ofReference 18 were used.

Paper T3S8 S, received 18th December 1978Prof. Harutunian and Dr. Buniatian are with the Institute of Radio-physics and Electronics, Academy of Sciences of the Armenian WSSR, Ashtarak, K. Marx Politechnical Institute, Yerevan, USSR

SOLID-STATE AND ELECTRON DEVICES, SEPTEMBER 1979, Vol. 3, No. 5

If we express the alternating component of voltageUu in terms of the total current density Iu and of theconvection current density Ipi in the injection source planewe can obtain18

-Uu = IuKi(u) + IPM<>>) 0 )

The case with / = 1 corresponds to small-signal injectionand with / = 2 to high-signal injection.

e oof/0

eco,/0

0, - /

A =

eco2/0

/00,

D +X2(02 - /<

Bo =

Co =

202(202 - 0 , +/0f32)

700 , (1+0 , - /0 j32) [ 70(0, - 0 , ) e x p 0 2

(0i -70/32)2 02(6

02(0,+/002) ' 202(202+/0/32-0,)

D =02(0,-/002)

Here

0, 0f 30U0^

02 20U 26\ '

f'(exp02-l)+^exp02

Pt

nil

155

0308-6968/79/050155 + 06 $01-50/0

0 = cor is the transit angle, T is the transit time,

t m

T,

n Of T7 0 T1

Ou — til — ~ 1 — 7e evos

e is the permittivity of semiconductor material, ju is thehole mobility, vos is the average charge velocity in thesource plane, a is the small-signal conductivity of thesource, /0 is the constant current density, co is the angularfrequency, and A^ is the concentration of shallow donors.

For the open-circuit mean-square noise voltage and shot-noise measure Mfi when Iu = 0, we have

(2)

(3)Tli \Nt{u>)\*

4kT0Af

where k is the Boltzmann constant, To is the referencetemperature, normally 290° K, /?,(co) is the active resist-ance of the diode and A/is the frequency band.

For the Ipi we have8

f2 _1 Pi ~ 1 + 1-2

(4)

when delay injection from the electric field in the sourceplane is absent (0O = 0) a nd

1 PI

when 0O = TT/2, where 0O = COTJ is the delay angle of injec-tion from the electric field, rz is the delay time, and

0. = exp/0o = coeex

For the case 0O =̂= 0, from eqns. 2—4, and for large valuesof the capture coefficient of holes in traps, a we have

qI0Ldt(\ -T?J) [ (1 - exp (0,) cos 0ft)2 + exp(20,-)sin0ft]

2A:roe2co2(exp0)-l) 1 -sin

2 COS 0o+

(5)

where ^ is the carrier charge, L is the distance from thesource to drain and

Vi = , - 0 , - 1 )

is the space-charge parameter, which is connected with thecarrier velocity in the source plane by the expression

exp 0,- — 1

where

2pa2Nt2 c?pl + co2

Note that when the traps are absent (ft = 1) the expressionfor M^ reduces to the results obtained in Reference8 forthe case 0O = 0.

For example, in the case of small-signal injection and0 i = O (high field) from eqns. 3 we have

Mn =, ( 1 - c o s 0/30

kT0eu>3L ft 11 - cos 00! + 0sO sin 00!(6)

which coincides with the results of Reference 8 when0 i = l .

It is necessary to note that the presence of traps in thebase can essentially change the diffusion coefficient ofcurrent carriers and, therefore, the diffusion noise charac-teristics of the structure.

To use the field-impedance method of calculation20 forthe coefficient of diffusion D with traps we can obtain

D = (7)

where v is the velocity of injected carriers, Nt is the con-centration of holes captured at the trapping levels, r is thelifetime of injected carrier and Dp is the diffusion coeffic-ient of holes when traps are absent.

In the case of small-signal injection and of large valuesof the capture coefficient a we have18

Pt

and from eqns. 7

N++P = P0i

0i(8)

For the case of high-signal injection and or large values ofthe capture coefficient a.

N+ ~ Nt, pNt - > PtNt

and

+ (9)v ' ( l + 0 2 ) 2 ( l + c o V ) l + 0 2

When the traps are absent (0i = 02 = 1)

£>I(GO,0I) = Z)2(co,02) = Dp

For the thermal (diffusion) voltage fluctuation in open-circuit U^i we have

(10)

where

is the differential transfer impedance, s{x) is the timerequired for a point fixed in the carrier stream to drift

156 SOLID-STATE AND ELECTRON DEVICES, SEPTEMBER 1979, Vol. 3, No. 5

Table 1: Expressions for various quantities

' + 0 , - 1 2 (0,e » cos 0 + 0 sin 0 ee» — 0,-)

20 i d-+82

-, (0 2 f 2 0 , — 0 2 £ 2 ) e " ' + ( 0 2 — 0 2 £ 2 ) s i n 0 £ , — 2 0 , 0 £ , c o s 0 £ ,

\ e 1 , f l 2e « fl(I/ , + l/s)

2 + e2t7' + (flfff » - 0 , - s\nde'a')[ 20,- 0? + 0 2

[ 2(0,- -0 .e 0 ' cos0-0 sin0e0')A V* h + 1 !

* l I'I +

£, - ( 0 , cos0 + 0£, sin0) ! L ( 0 2 + edl) sin.20 + (/sin 0£,0 00 , 0

0so . „ . , , n . ,. , & \ t>la2 , , . , . . , , I wso" i c - .(0£, cos0 + 0, sin0) + e ( 0 ; + d 1 % \ ) — Q $\\ cos 0 + (h sir

0 0 0 , | | 0 0

S/\4 — As sin 20

eteued2(el —et)(e

2 + 0 2 i(ff2 + 04

O sin2 20)

An 02 [ f i ( 0 , + 0£20so cos0 + 0,0 s o sin 0) + 0 j o sin 20(0SO0?2 sin 0 — 0£2 — 0,0SO cos 0) ] — 0 , /

/4'7 d2Quri(B2 + 04

O sin2 20)

4 8 0 2 [ f i ( 0 ,0 s o cos0 — 0 ^ 2 + 0£2 + 0^20s o s in0)—0 2O sin 20(0, + 0£20so cos 0 — 0SO0, sin 0) ]

1 + —1—.1 1 A'20 2 [ (20 2 -

A'9 ~i—'~~T

Al0 ^ ^202[(202 -dt)

2 + 9

et(2e2-el)

20 2 [ (20 2 - 0 , ) 2 +

from the source contact (JC = 0) to the point x (Reference 20) D _ (fii ~ 1 ) r D _ 2(j32 — \)T

S(x) =\X -4-dxJo v (x)

The expressions for the ^,(0,0,), Ax — A n , K1 0 , K'IO areThe transit-time T is equal to S(I). From eqns. 7-10 for indicated in Table 1, wherethe thermal noise measure we can obtain

Mt, = B = l +elo cos 20o,ol/2.-(w)|A/ exp(0,)-0, .-l

exp 0j

+J52 + 0S

4O s in 2 20 O

/ = 0i —dpidso cos 0o — 0 i0 s O sin 0O )

where h = 6idso cos 0O - 0 j 3 j ( l - 0 s O s in0 o ) ,

SOLID-STATE AND ELECTRON DEVICES, SEPTEMBER 1979, Vol. 3, No. 5 1 5 7

~9t) C0S ^02 ~~ 1)

-v48 exp (02 -0 f ) s i n00 2

K20 = Ag + exp (02 —Ot) x (^io s i n #02 —I)

—An cos 0j32

We note that, when the traps are absent (ft = 1), theexpressions for Mti reduce to the results given in References8 and 19 for the case 0O

= 0. For example, when v, ju, Dand P = I/qv are constant, from eqns. 7—11 it is easy toobtain

Mtl =PLq2PpT

2

e2kTn(12)

which coincides with the results of Reference 19. In thecase of 01 = 0 (high-field) from eqns. 7—11 we have

2qI0Dp\\-sin vd'J

kT0eco2(\ - cos 0 + 0sO sin 0)(13)

which coincides with the results of Reference 8.Besides, for the noise measure, corresponding to the

maximum value of differential negative resistance (d.n.r.)we obtain

M.T\ M\1-48

T\

for the small-signal injection, and

\T2

(14)

(15)

for the high-signal injection, where

= 6-

e2kT0

3 Discussion

After obtaining the results in eqns. 5—15 it is possible toinvestigate the dependence of noise characteristics onvarious parameters. The analysis of exprs. 5 and 11 showsthat the decrease of noise measure is possible in the small-signal injection case within certain restricted regions ofthe parameters 0, fa(Nt) and a. Moreover, the decrease ofnoise measure is greater, the larger the coefficient ofcapture a and concentration of traps Nt.

The peculiarity of expr. 6 consists in the inverse depen-dence of Mfx on the parameter fa. From eqns. 6, Mfx

approaches zero when the transit angle 0 = (2ir/fa)n (n =1, 2, 3 . . . ). However, simultaneously, the active negativeresistance Rx also approaches zero. By increasing thespace-charge parameter r}h i.e. near to the space-chargelimited (s.c.l.) condition (17,--»• 1), it is possible essentiallyto decrease the fluctuations of current and, therefore,reduce the shot-noise measure. The shot noise, like thediffusion-noise measure is directly proportional to thedensity of constant current and inversely proportional tothe square of the frequency.

As shown in Reference 18, the existence of empty trapsresults in a delay in degenerative feedback due to possiblecapture of injected holes by the traps during the drift andfollowing re-emission into the valence band. This delay ofcurrent with respect to the field provides the increase inmagnitude of the active negative resistance R1 with simul-taneous decrease of the possible range of transit angles. Inresults, the noise measure can be decreased.

Properly from eqns. 7 under the condition of a constantvelocity of charge carriers, an increase in the concentrationof traps decreases the effective coefficient of diffusion ofholes. Because the diffusion noise is primarily connectedwith the thermal motions of current carriers in drift re-gions, it is reasonable, that because of the capture ofcarriers, that part of the diffusion noise which takes partin the thermal motions, is decreased. Secondly, as thedynamic negative resistance is increased in absolute value,the injected carriers are 'cooled' more in the alternatingfield and smaller 'noising'.

For high-signal injection (i = 2), when traps are practi-cally completely filled, their action is only to limit flowingcurrent. The charge of the traps simply adds to the chargeof shallow donors. In this case, the increase in the resultingpositive charge q(ND + Nt) provides the decreases in thefield at the emiter and magnitude of active negative resist-ance R2 and the transit angles, where \R2\ > 0. As a con-sequence the noise measure can be increased.

The numerical estimates have been carried out fortypical silicon injection transit-time diodes with a distanceof 5 x 10~6 m from the source to the drain and an area of1-25 x 10~8 m2 made of material of a specific resistivity0-04 fim and hole mobility 0-045 m2/Vs.

Calculations have been carried out for the parameters:T = AT, aPt ̂ 5 x 109 s"1, ND = 1 -25 x 1021 m~3, Dp ^0-12 m/s, 0! = 0 2 = 2 . The numerical estimates show thatin the transit-angle regions when negative resistance exists,the fluctuation noise measure Mfi is always less than ther-mal. With the increase of the capture coefficient a in trapsthe noise measure decreases (Fig. 1), but the frequencyband where it takes place narrows and is displaced to lowerfrequency (Figs. 2, 3).

For example, when Io = 10s A/m2, fa = 1, (Nt = 0),0 = 6, Mi =Mfl +Mtl 2il3-5dB and for the fa = 5,0 = 2 , M i ^ 2 d B .

The noise measure in the case of small-signal injectiondecreases monotonically with the increase of the concen-tration of traps Nt in a narrow region of the parametersNt(fa) and Pt. Then the noise inevitably increases roughly

102 10° 7 1 i o 2

ocPtx5x10 s102 10° 7,102

<XPtx5xK) s

Fig. 6 Total noise measure M = Mf2 + Mt2 as a function ofcapture coefficient a of the parameter 0, = 1 + Nt/Pt

a Current contact, when dso » 1b Field contact, when 0S0 « I.9

158 SOLID-STATE AND ELECTRON DEVICES, SEPTEMBER 1979, Vol. 3, No. 5

due to amplified fluctuation phenomena arising from thecapture of charge carriers in the traps and subsequentthermal release to the corresponding band (Fig. 4).

CO

2~

2 A 6 89,rad

b

Fig. 2 Total noise measure Ml as a function of transit angle 6for various values of the parameter 0, for the current-contact casea Io = IO5 A /m 2

b Io = IO5 A / m ' = 0

co 1 f lTJ 18

2 4 69, rad

a

10 2 A 6 8 109, rad

Fig. 3 Total noise measure M, as a function of transit angle dfor various values of the parameter 0, for the field-contact case

Io = 10s A/m2

a For the case 0O = 0b For the case 0O = 7r/4

100 A/cm 2

y =70 A /cm 2

The dependence of noise measure Mx of the transitangle 6 for the case when v, n, D and P are constant, areindicated in Fig. 5.

For high-signal injection, with the increase of the con-centration of traps (j32) the noise measure M2 - Mf2 + Mt2

increases (Fig. 6) and the frequency band where it takesplace narrows and is displaced to lower frequency.

Finally, it is necessary to note that the possibility ofdecreasing the noise measure and accordingly the noisecoefficient by the trapping of space charge in some range ofthe 6, (3,- and a is an urgent issue for the design of low-noise microwave devices.

U r -

12

10

OD•o .

—£,=10

w 1 2 3 A 5 6 7 8 99 , rad

Fig. 5 Total noise measure Mi as a function of transit angle 0for various values of the parameter 0, (/0 = 10s A/m2) whenv, M, D and P are constant

12

10

-5-543

log ftFig. 4 7b fa/ nowe measure Mx as a function of the parameter 0,for various current values

6 = = 0

9, rad

Fig. 6 Total noise measure M = Mf7 + Mtl as a function oftransit angle 6 for the various values of the parameter 02 = 1 +(dt/e2)(exp62 - 1 ) + (6t/du)expd2.I0 = 2 X IO6 A/m2

SOLID-STATE AND ELECTRON DEVICES, SEPTEMBER 1979, Vol. 3, No. 5 159

4 References

1 WRIGHT, G.T.: 'Small-signal characteristics of semiconductorpunch-through injection and transit-time diodes', Solid-StateElectron, 1973, 16, pp. 903-912

2 WRIGHT, G.T., and SULTAN, N.B.: 'Small-signal design theoryand experiment for the punch-through injection transit-timeoscillator',/Z>/d, 1973, 16, pp. 535-544

3 CHU, J.L., PERSKY, G., and SZE, S.M.: 'Thermionic injectionand space-charge limited current in reach-through p*-n-p*structures',/. Appl. Phys., 1972,43,pp. 3510-3515

4 COLEMAN, D.J., and SZE, S.M.: 'A low-noise metal-semicon-ductor-metal (msm) microwave oscillator', Bell Syst. Tech. J.,1971, 50, pp. 1695-1699

5 SZE, S.M., COLEMAN, D.J., and LOYA, A.: 'Current transportin metal-semiconductor-metal (msm) structures', Solid-StateElectron, 1971, 14, pp. 1209-1218

6 CHU, J.L., and SZE, S.M.: 'Microwave oscillations in PNPreach-through BARITT diodes', ibid., 1973,16, pp. 85-91

7 RUEGG, H.W.: 'A proposed punch-through microwave negative-resistance diode', IEEE Trans., 1968, ED-15, pp. 577-585

8 TAGER, A.S.: 'Field-injection transit-time diodes with a negativedynamic inpedance', Izv. VUZ Radioelektron, 1974, 17, pp.3 18

9 TAGER, A.S., SULIMOV, V.B., and MAL'KOVA-KHAIMOVA,N.Ya.: 'Small-signal characteristics of injection-transit diodes(ITDs) with a positive differential charge-carrier mobility',Radiotekh & Elektron, 1975, 20, pp. 387-396 (English Trans-lation in Radio Eng. & Electron Phys., 1975, 20, pp. 108-116)

10 SNAPP, C.P., and WEISSGLAS, P.: 'On the microwave activityof punchthrough injection transit-time structures', IEEE Trans.,1972,ED-19,pp. 1109-1118

11 SNAPP, C.P., and WEISSGLAS, P.: 'Experimental comparison ofsilicon p*-n-p + and Ci-n-p* transit-time oscillations', Electron.Lett., 1971, 7, pp. 743-744

12 NICOLET, M.A., BILGER, H.R., and ZIJLSTRA, R.J.J.: 'Noisein single and double injection currents in solids. Pt. 1' Phys.Status Solidi, 1975, 70, pp. 9-45. 'Pt. 2', ibid., 1975, 70, pp.415-438

13 HAUS, H.A., STATZ, H., and PUCEL, R.A.: 'Noise measure ofmetal-semiconductor-metal Schottky-barrier microwave diodes',Electron. Lett., 1971, 7, pp. 667-669

14 FIKART, J.L.: 'AM and FM noise of BARITT oscillators'',IEEE Trans., 1974, MTT-22, pp. 517-523

15 LEE, C.A., and DALMAN, G.C.: 'Local-oscillator noise in asilicon Vt-n-p* microwave diode source', Electron. Lett., 1971, 7,pp. 565-566

16 CHRISTIE, J., and STEWART, J.A.C.: 'Comparison of metal-n-p+ and p+-n-p+ Baritt small-signal noise measures', ibid.,1973, 9, pp. 553-555

17 BJORKMAN, GUNNAR, and SWAPP, C.P.: 'Small-signal noisebehaviour of companion p+-n-p + and p+-n-v-p* punchthroughmicrowave diodes', ibid., 1972, 8, pp. 501-503

18 ROBSON, P.N.: 'Low-noise-microwave on using transferredelectron and BARITT devices', Radio & Electron. Eng., 1974,44, pp. 553-567

19 HARUTUNIAN, V.M., and BUNIATIAN, V.V.: 'The influenceof capture of the injected current carriers on the characteristicsof Baritt diodes', Solid-State Electron, 1977, 20, pp. 491-497

20 SHOCKLEY, W., COPELAN, J.A., and JAMES, R.P.: 'Quantumtheory of atoms, molecules, solid state' (Academic press, 1966),p. 537

160 SOLID-STATE AND ELECTRON DEVICES, SEPTEMBER 1979, Vol. 3, No. 5