IMPATT oscillators with enhanced leakage current

Solid-State

Electronics.

1975, Vol. IX. pp. I-I?.

IMPATT

Pergamon

Precs.

Prmted in Great Britain

OSCILLATORS WITH ENHANCED LEAKAGE CURRENT* P. E. COTTRELL

IBM System

Products

Division,

Essex Junction.

Vermont

05452, U.S.A.

and J. M. BORREGO and R. J. GUTMANN Electrophysics

and Electronic

Engineering

Division, Rensselaer

York (Received 7 December Abstract-The behavior of IMPATT experimentally evaluated by irradiating current was induced in diffused junction 1OOnsec pulses of 10 MeV electrons. decreases and the frequency of oscillation is developed which correlates well with 1.

1973; in revisedform

INTRODUCTION

*This work is in part composed from a dissertation submitted by P. E. Cottrell to the Eiectrophysics and Electronic Engineering Division of Rensselaer Polytechnic Institute, Troy, New York in partial fulfillment of the requirements for the Ph.D. degree and was partially supported by the Defense Nuclear Agency through the Air Force Cambridge Research Laboratories, Bedford, Mass., under Contract FI96828-72-C-0112. 18. No. I-A

Troy,

New

20 March

1974)

the elevated junction temperatures of high power IMPATT diodes of up to 50O”K, bulk generation leakage current on the order of 0. I A/cm’ is expected in silicon devices. Also leakage current of 0.1 A/cm’ or more can be expected in a GaAs Schottky diode operating at this temperature from minority carriers going over the potential barrier lowered by the high electric field. This paper is concerned with the experimental characterization and large signal circuit modeling of the effect of leakage current on the RF performance of IMPATT diodes. In the experimental evaluation, operating diodes were irradiated with 1OOnsec pulses of IOMeV electrons produced by a linear accelerator. This radiation creates a photo or leakage current which is proportional to the rate of absorbed energy from the radiation (radiation dose rate) and the sum of the volume of the depletion region and the region from which carriers can reach the depletion region before recombining. A silicon (Diode A) and a GaAs (Diode B) X-band, diffused junction, 0.5 W diode were tested in a waveguide cavity with an the silicon external Q, Q<,,, of 100. In addition, diode was tested in a modified cavity with a Qcxt of 2000. The diode RF output power, frequency and voltage were monitored before, during and after the radiation pulse. An extension of Mouthaan’s[3,4] large signal model was used to predict IMPATT diode performance with leakage current. The model consists of identifiable circuit elements and in simplified form

current

SSE Vol.

Institute,

oscillators with enhanced leakage current has been operating diodes with transient ionizing radiation. Leakage GaAs and silicon X-band IMPATT diodes by irradiation with With increasing leakage current, the oscillator RF power increases. A large signal circuit model of the IMPATT diode experimental measurements.

has been shown to have important effects in IMPATT (impact ionization avalanche transit time) oscillators. Decker, et a/.[11 studied the effect of excess majority carriers in the avalanche region caused by injecting ‘ohmic’ contacts. Minority carriers from the metal-semiconductor contact are injected into the diffused region of an IMPATT diode, move through that region and are swept across the depletion region causing an increase in the leakage current. It was shown that for high bias current densities, effective leakage currents of 6 per cent of the bias current reduced the peak diode output power by ninety per cent. Misawa[2] considered the effect of minority carrier storage in the diffused region of an IMPATT diode. Carriers generated by avalanche multiplication diffuse backwards from the avalanche region into the heavily doped diffused region due to high carrier concentration gradients. These carriers are released later during the IMPATT cycle and act as a large effective leakage current. Leakage current as small as 0.2 per cent of the bias current was shown to reduce the diode efficiency by half. Moreover, at Leakage

Polytechnic

12181, U.S.A.

I

P. E. COTTRELL, J. M. BORREGO and R. J. GUTMANN

2

can be easily evaluated without a digital computer. It can be used to predict diode output power with leakage current without explicit knowledge of the RF circuit if the cw characteristics of the diode with insignificant leakage current are known. If the variation of RF circuit impedance as a function of frequency is also known it can be used to determine the oscillation frequency shift as a function of leakage current. The paper is arranged as follows: section 2 outlines the experimental method used to determine the diode output power and oscillation frequency with enhanced leakage current and section 3 gives the results for the GaAs and silicon X-band IMPATT diodes. In section 4, the device model with enhanced leakage current is derived and the method of evaluation described. The correlation and discussion of theoretical and experimental results is made in section 5. Section 6 summarizes the results of this work. 2.

EXPERIMENTAL

METHOD

Leakage current generated In order to experimentally evaluate the response of IMPATT diodes to enhanced leakage current it is necessary to induce a known leakage current in the diode and to measure the diode response. Leakage current was induced by irradiating operating IMPATT diodes with IOOnsec pulses of 10 MeV electrons. The radiation source used was the Air Force Cambridge Research Laboratories linear accelerator. The 10 MeV electrons are able to penetrate the 0.17 in. aiuminium cavity wail and the diode with little energy loss. The 100 nsec pulse length was shorter than the diode’s thermal time constant of about 1 psec. By varying the accelerator peak injector current, radiation dose rates of IO” to 4 x lo9 rads/sec were achieved with little shift in beam energy. The accelerator was operated in the signal pulse mode (one pulse per data point) so that the total accumlated dose received by the diode did not exceed five thousand rads. The absolute level of radiation dose rate was use of thermoiuminsecent determined by dosimetry[S] inside the diode cavity. The diode leakage current due to radiation is given by I, = qKjV

(1)

where q is the electron charge, K is the number of ionized pairs generated per rad per cm), + is the radiation dose rate in radslsec and V is the effective charge generation volume. This effective volume is essentially that volume from which

charge carriers can reach the depletion layer before recombining. This includes all the depletion layer volume and the volume associated with one diffusion length of the appropriate carrier to either side if the minority carrier lifetime is much less than the radiation pulse length. The minority carrier diffusion length for the diffused and the substrate regions of the diodes is difficult to evaluate with an) accuracy. However, in these heavily doped region\ the minority carrier lifetimes are at most I nsec fat both GaAs and silicon. This low lifetime corre\ponds to minority carrier diffusion lengths of le\s than 0.5 pm. If the depletion layer volume (on the order of several microns wide and easier to obtain with precision) only is taken ax the effective volume, the estimate will be no more than 20 peg cent low. Thus the effective volume was taken a\ V=AW,

(2)

where A is the diode cross-sectional area and W, the depletion layer width. The radiation source was calibrated directly in radsisec or absorbed dose rate. It i4 well known [6,7] that on the average, pair creation due to ionzing radiation uses energies of 3.6eV and 4.6eV per pair for silicon and gallium arsenide respectively and thus density of electron-hole pairs generated, K, is 4 x IO” pairs/rad/cm’ in silicon and 7.2 x lOi pairs/rad/cm’ in gallium arsenide. The diode area, A, and total depletion width, Wi, were found by evaluation of the diodes’ current and capacitance variation with reverse bias voltage and are given in Table I. The leakage current for the dose rates used in testing can now be calculated using the depletion volume and equation (1). Although accurate direct measurement of diode leakage current due to the IOMeV electron radiation could not be achieved due to unavoidable noise sources caused by beam current pick up and radiation generated Table.

I. IMPATT

diode parameters Diode A Silicon

Material

77 0.7

v,, (VI N (cm’ X IO’“) A (cm’ x 10~‘)

Diode B &IA\ 64 I .2 ( I ,2’)

I .6

2.2 (2m’)

WT(pm)

4.0

W, (pm) Wdbm) a' (V ') v, (cm/set

7.4 0. 14 0.95

2.7 (I.75 I.95 oz? 0.7

*Data

I .h x IO’)

provided

by the manufacturer.

IMPATT

oscillators

leakage paths in the diode bias circuit, a check was made on the calculated results by measurement of the current due to radiation at bias voltages somewhat below breakdown. After systematic calibration of noise signal, and with a compensating calculation of carrier multiplication, the actual radiation generated diode current was obtained from the measurements. The calculated and measured results are presented in Table 2. While we believe that the calculated values are more correct and certainly form a more consistent set, the error measured data indicates that no excessive exists. RF power and frequency The IMPATT diodes were mounted in a waveguide cavity of the post and disc type@] for characterization and radiation testing. During testing, the entire cavity was in a vacuum chamber which was evacuated to a pressure of less than 3 x 10 5 mm of mercury. Thus, a reduction in circuit Q due to ohmic loading of the RF cavity caused by air ionization was avoided[9] and no significant shunt d.c. current path caused by radiation ionized air was formed. The output signal was carried by X-band waveguide through a glass pressure window to the RF measuring circuit shown in Fig. 1. The IMPATT diode in the RF cavity was tuned by 7 SLIDING SHORT

TO

BIAS

Table. 2. Calculated

and measured

leakage

Calculated Measured Dose rate leakage leakage (rads/sec X IO’) current (mA) current (mA)

Diode A

Diode B

0.2 0.5

0.082 0.21

I4

0.58

4.0

1.7

0.12 0.29 0.74 I.5

0.3 0.95 I.5 3.4

0.2 0.64

0.19 0.68

1.o

I.1

2.3

2.4

means of a calibrated sliding short, slide screw tuner, and if necessary by changing the post and disc diameters. During tuning, the RF power was measured through a directional coupler with the X-band thermistor mount and a power meter. The frequency of oscillation and RF spectrum were monitored with a spectrum analyzer. The diode output power during the radiation pulse was monitored using a crystal detector calibrated with the RF power meter shown in Fig. 1. Also shown is a waveguide frequency discriminator[lO] used to measure the RF output frequency shift during the radiation pulse. The outputs of the RF measurement apparatus provided

CIRCUIT

DIODE -

IN CAVITY

-

SCREW

TO POWER

---_

THERMISTOR

METER

MATCHED LOAD

VARIABLE

1 I

I

ATTENUATOR

I

‘0

I ISOLATOR

I +

&O

CR0

(

PHASE SHIFTER -

MAGIC

-

TEE

current

I

RF DETECTOR

Fig. 1. RF measurement

apparatus.

I MAGIC

-

TEE

-

P.

4

E.

COTTRELL,

.I. M.

BORREG~

and K. .I. GLI~‘MNN

9352

Coax~aicable Fig. 2. IMPATT

the necessary readouts on either d.c. meters or oscilloscopes to completely characterize the IMPATT cw characteristics and response to the 100 nsec radiation pulse. The d.c. bias current was supplied by a variable voltage power supply through the circuit shown in Fig. 2. The circuit provides a method of measuring the diode bias voltage change during the radiation pulse and has a 300 R source impedance up to a frequency of 50 MHz. This is necessary to assure a bias circuit pulse impedance high enough so that the bias current remains constant during the radiation pulse. 3.

EXPERIMENTAL

RESULTS

The RF power, oscillation frequency and bias voltage were measured for the silicon and GaAs diodes in the nominal Q cavity and for the silicon diode mounted in the high Q cavity for various bias currents and radiation dose rates. Results indicate that the radiation induced leakage current decreases the diode output power and increases the frequency of oscillation. Figure 3 gives typical output of the measurement apparatus for a 100 nsec radiation pulse. The diode output power returns to its original level within 50 nsec following the radiation pulse, indicating the absence of significant carrier trapping. The apparent delay between pulses is merely due to differences in triggering in dual beam oscilloscopes. In fact no measureable delay exists between the radiation pulse and onset of the diode response. Figures 4 and 5 give the diode output power in the nominal Q cavity for the silicon and GaAs diodes during the radiation pulse for various dose rates and bias currents. The fitted curves are used later to facilitate comparison with the theoretical

diode bias circuit.

results. Figure 6 gives similar results for the silicon diode in the high Q cavity which exhibits output power saturation at high bias currents with no radiation. The change in frequency due to the radiation pulse is given in Figs. 7 and 8 for diodes A and B in the nominal Q cavity. The data given is the difference between the measured frequency during the radiation pulse and the cw frequency at the bias current shown. Again. the fitted curves are for later theoretical correlation. The frequency shift of the silicon diode mounted in the high Q cavity was so small that the change in cw frequency with bias current obscured the data for all except the highest bias current. The frequency shift during the radiation pulse is reduced by a factor of about 3 in the high Q cavity compared to the frequency shift for the same diode in the nominal Q cavity. 500 1

Dose

rate

(rads

40

53

/set

Y IO’)

1 30

BIOS

60

current,

70

80

mA

Fig. 4. Output power vs bias current for various radiation dose rates, diode A in the nominal Q cavity.

IMPATToscillators

500 r

Dose Dose

rote

(radslsec

rate

(rods

/set

x IO91

x IO’)

14

ZeK,

0.5

/;j’, o-3

0

//

0

o-95

,J

/o’2

I.5

3.4

40

50

60

70

/

// -.J’

/i

40

50

BIOS

60

current,

70

rote

(rods

Bias

current,

mA

shift during the radiation A in the nominal Q cavity.

pulse,

diode

mA

Fig. 5. Output power vs bias current for various radiation dose rates, diode B in the nominal Q cavity.

Dose

Fig. 7. Frequency

/set

20 Dose

rote

(rads/sec

x10’)

r

x log)

0.95

Zero

/

0 0

/

60

0

o 0.3

0 /

OL’!do BIOS

Fig. 8. Frequency 30 BIOS

40 current.

xl

60

510 6io current,

;o

mA

shift during the radiation in the nominal Q cavity.

pulse, diode B

mA

Fig. 6. Output power vs bias current for various radiation dose rates, diode A in the high Q cavity.

The voltage across the IMPATT diode during the radiation pulse was measured to monitor the change in bias current through the diode. The net change in diode current was found in all cases to be less than 2 mA. In no case could the change in bias current have caused an RF output power reduction of more than five percent of the measured decrease at the highest bias current and of more than 10 per

cent at the lowest bias current at which diodes were tested. The change in frequency of oscillation due to the decrease in bias current was less than 10 per cent of the measured frequency shift at the maximum bias current used for both diodes and at worst 30 per cent for the lowest bias current for which data is presented. 4.

THEORETICAL

Complete model In this section

DIODE

an extension

MODEL

of the large signal,

P. E. COTTRELL, J. M. BORREGOand R. J. GUTMANN

6

IMPATT model proposed by Mouthaan[3,4] will be used to characterize the IMPATT diode with leakage current. The model derived is circuit oriented. that is composed of identifiable circuit elements. With this approach, the large signal effects of leakage current can be easily evaluated and interpreted without obscuring the device physics. A one sided Read [ I I] structure is assumed and the resulting equation which describes the avalanche region particle current and its limitations is well established[l2-141

The component is

of avalanche

current

at frequency

w

L(t)

(8)

= iI sin (wt) - i2 cos (wt)

where i, = 21,M

xk

(3) and where I,, is the avalanche particle current, I, is the leakage current, 6 is the effective ionization rate, W,, is the avalanche width, and u, is the saturated carrier drift velocity. The effective ionization rate, is described by 6 = cu,,+ cu’E,,

(4)

where E,, is the RF electrical field in the avalanche region and LY’is the derivative of the ionization rate with respect to the electric field. If the time dependent voltage across the avalanche region is a single frequency sinusoid. V,,(t) = V,, sin wt

(5)

the steady state, avalanche particle current I,,(t) can be found by solving equation (3) with (4).

(IO)

I.

The total current in the conduction current due to between two parallel plates the displacement current voltage

drift region L(t) is the a space charge moving at constant velocity and due to a time varying

i,,(r) = I,$++e !~,,~“rl~,,l’

MWT<, X cos (kwt) + k2 sin (kwt)

I

M

where

I

is

the

multiplication

l-w \ 1 I~ ” cxcldx , u!,, is the normalized

J

factor

II

(‘3 M=

J,M

Id(r) = - ii sin (wt) - LCOS (wt) + Cd %

avalanche

0 ! t region voltage L’,,= (Y’V,,/WT~~.r,, is the avalanche transit time r,, = W,,/u\,and the 1;s are modified Bessel functions of the first kind. When the bias current i is supplied by a current source it is independent of the RF voltage and can be found by considering the d.c. component of the avalanche current

i =

where Wd is the length of the drift region, Cd is the drift region capacitance and Vd is the voltage across the drift region. Substituting the fundamental component of I,(t) into equation (I 1)

(7)

(12)

where

i, =

_

ii

sin (WTd)

+

iz

SinZ

~

2 OTd i-i 2 t

SinZ 3 sin (07~) i 2 > i4= i, + 120 07d 0 2

J

(13)

(14)

IMPATToscillators

7

and 7d = Wd/ve. With the addition of the displacement current through the avalanche capacitance, C,, a complete steady state, circuit model for operation of an IMPATT diode at angular frequency o has been derived and is shown in Fig. 9(a). Although the model is complicated, it is instrucive to see what effect each current generator has on IMPATT diode operation. Current generator iI increases in value with increasing leakage current and represents an ohmic loss in the avalanche region. Current generator iz represents the avalanche inductance of the IMPATT diode which decreases slightly with increasing leakage current. The negative resistance of the circuit is derived from generator ii. Its value decreases with increasing leakage current and thus reduces the RF voltage and output power. Current generator i4 decreases the capacitive susceptance of the diode with increased leakage current. This has the effect of increasing the frequency of oscillation with increasing leakage current. In the case of the leakage current approaching zero, this circuit model is identical to the circuit model derived by Mouthaan[4]. In the small signal case with leakage current the model reduces to that of Sanderson and Jordan[lS].

can be truncated for k > 1 with little loss of accuracy. With some algebraic manipulation equations (7), (9), (lo), (13) and (14) become

Approximate model Simplification of the model can be easily achieved by assuming a leakage current much smaller than the bias current while retaining the large RF voltage level. Since Zk(x) > L+,(x) the summation terms in the expressions for the current generators of the model decrease at least as fast as (kw~,M/2) ~I. For reasonable values of normalized avalanche voltage, avalanche transit time and leakage current the current generator expressions

Further simplification can be achieved for reasonable physical parameters and operating conditions. The displacement current through the junction capacitance is much greater than the reactive currents produced by avalanche dynamics. Elimination of the reactive current generators give the circuit shown in Fig. 9(b). Thus, the simplified model consists of only one active element with the parameters given by equations (IS), (lg), (20), and

z= Z,MZ$2V,)

(15)

i, = 2Z/3 cos 4 sin 4

(16)

iz = 2Z/3 co? 4

(17)

i, = 2Z/3 cos 4

sin C-1 2 sin

(-1 WTd 2

w7L ( 2

(18)

41

i4 = 2Z/3 cos 4

(19)

WTd

(-) 2 where

cot 4 =-

MWT” 2

(20)

and p=- Z1(2U”) Z0(2v, )’

(21)

(21). 0 +

V V

I

Fig. 9(a). Complete

IMPATTdiode

I

0

circuit

model.

Fig. 9(b).

Simplified

IMPATT

4 diode circuit

model.

8

COTTRELL,

P. E. The models

derived

do not account field

by

the

saturation

RF

voltage

approximation calculation

They

and

as

thus.

power

depletion

width

rate precludes

the

of the change in d.c. diode voltage

of the ionization

due

to rectification

of the RF current

variation

of

However,

the principal

ionization

on the performance oscillation

rate

by the nonlinear

with

effects

held. current

of IMPATT

diode

parameters

are well described

electric

of leakage

Fig. IO. Simplified RF circuit model

by these large signal

models. Evaluation

of the simplified

X-band

silicon

the simplified

complete output

model (Fig. 9(b)) and

model (Fig. 9(a)) was carried

the complete show

model power

IMPATT

model

for

out for a

diode.

Results

in agreement

prediction

at leakage

of the

current

At

higher

densities to the

leakage

the difference increasing

truncated

from

equation

influence

of

the complete

quently.

diode

RF

below

bias

I

the predict

large due terms

The

measured diode

the

leakage

current

buildup

of the avalanche

timing

is not

agreement

particle

a

causes

current

maintained.

and thus optimum

These

results

arc

in

with those of Misawa[l6]. (‘OMPARISON

OF

In order calculate diode

with

RF

enhanced

sary to consider connected in

output

leakage

obtained

from

10

inductance.

L.,

where R,

the

to

in the nominal

package

resistance,

is represented

and R, I-

by

correctly with

predicts

The package capacitance

C,, was neglected

expected

inductance

current

almost

series

resonant

with

the diode

L,

is

capacitive

Once the microwave diode performance can he predicted ties

measurement impedance function

for

condition.

at which

circuit impedance

according a given

diodes

or theoretical of

a

diode

Unfortunately

IMPATT typical

of frequency

is known.

to the derived structure

and

at the frcquenare

prediction oscillator

is extremely

model

most

useful,

of the RF circuit

difficult.

as a In this

and for

as no saturation

the

the silicon Compari-

diode

current

and

for the silicon

nominal Q cavity

Q cavities

and

power-

saturation levels fat

This is to be

effects except for leakage agreement

measured

output

of output

for the power

for the model.

quantitative

KF

.A\ can be

between

power- with

the

Icakage

diode

in both the high and

GaAs

diode in the nominal

is quite good.

The fr-equency

shifts measured

during the radia

tion pulse are more than an order of magnitude than can be predicted reactance

are GaAc

show that the theory

variation

except

were considered

predicted

susceptance.

operating

seen.

with

and the

current

shown at the highest hias current

case

package

leakage

the silicon diode in the high Q cavity.

in this

the

current

and measured

the

hias current

effects

previ-

power

respectively.

power with no leakage current

the

of RF

cavity

of Fig. 9(a)

This is shown

1.

I I-13 for the silicon and

diode in the high Q cavity.

jX, (0).

since

with

cry’,WI\

assumptions

model with no leakage model

data1 171.

[ IX]. The value of the

the prediction

diode

bias. The

( W,,. W,,) were

coctlicient.

and

circuit

circuit.

reverse

are listed in Table

in Figs.

diodes

work

W,

of the diode current

width

son of the predicted

parasitic

circuit

model IMPATT

in

data.

width

and Haddad’s

parameters

discussed

complete

depletion

with

region

it is neces-

represents

the total

microwave

diode of the

en-

given

from published

and total

of the ionization

parameters

Using

plotted

with

A. W,,. W,,. CY’ and r, were

Schroeder

The derivative above

to

subse-

described

development

current.

the equivalent

to the microwave

Fig.

the

power

AND

RESLITS

to use the theoretical the

the

variation

ously

THEORETIC-\L

EXPISRIhIENT.41~

A

and drift

Mouthaan’s 5.

by

taken from Goedhloed‘s

premature

performance

by evaluation

avalanche

due to the finite leakage current.

used

and,

This procedure

were determined and capacitance

the peak to peak avalanche

were

impedance

or calculated

area

of

fixed.

current.

characteristics

,4.

of

is reduced

circuit

is justified

either

output current

the diode

leakage

Appendix

power

leakage

RF

Evaluation

current

RF

The diode parameters

current

summation

model.

determine hanced

up to

in results become

insignificant

(6) shows that with the d.c. component

current Also,

or

the diode

with

the

levels

current

work.

with

per cent of the bias current densities of 500 A/cm’or less.

GUTMlNh

R. .t.

[ 141 are not modeled. The use of a linear

modulation

typical

and

of the d.c. electric

swing

such

BORREGO

M.

here have limitations.

for perturbation

effects

J.

during the radiation

I,C tuned circuit

less

from the change in the diode pulse using

:I

simple

model. This simply means that the

IMPATT

9

oscillators

500 r

Leakage 400

current

(mA)

/

-

Zero

Data Theory

---

300% i al

i

a,

zoo-

z a

5 a

:

::

60

40-

IOOzo-

BIOS

current,

mA

Leakage

400

current

(mA)

/

”

/,

40

30

Fig. 1 I. Comparison of theoretical and experimental variation of output power with bias current, diode A in the nominal Q cavity.

Doto ---Theory

alas

Fig. 13. Comparison of theoretical variation of output with bias current, Q cavity.

alas

current,

mA

nominal

Q

cavity.

waveguide cavity tends to stabilize the frequency of the diode with a rapidly varying reactance with frequency. For small frequency deviations, Ao, from the angular frequency oo, the RF circuit reactance can be expressed as X(o)

= X(w) + X’(w,,)Aw

50

60

mA

and experimental diode A in the high

where X,,(w,J is the cavity reactance at the cw oscillation frequency and X’(w) is the rate of change of cavity reactance with frequency. Since the diode susceptance is largely due to junction capacitance it can, to first order, be considered linear with frequency. Using the fact that the diode reactance is approximately equal in magnitude to the lead reactance, wL,, the fractional oscillation frequency shift can be found from the circuit

AW -= WI,

Fig. 12. Comparison of theoretical and experimental variation of output power with bias current, diode B in the

current.

AXz, X‘l 3 + X’(& T

(22)

where AXd is the change in diode reactance due to the enhanced leakage current and XI is the diode reactance with no leakage current. The theoretical curves shown in Figs. 14 and IS have been calculated using equation (22) developed from the RF circuit model shown in Fig. IO and a value of X’/L calculated from one frequency shift data point taken at one radiation dose rate and RF output power level for each diode. The resulting values ranged from 10-30. It can be seen that indeed the diode frequency shift due to enhanced leakage current is proportional to the change in diode reactance and that the proportionality constant is on the order of 10. Although the equivalent

P. E. COTTRELL, J. M. B~RREGO and

I0

lated

40

current

Leakoge

(mA)

R. J.

GUTM.~NN

by irradiation

energy irradiation

-

Data ---Theory

hole-electron The

high

current

during

current,

mA

Fig. 14. Comparison of theoretical and experimental frequency shift with leakage current, diode A in the nominal Q cavity.

diode

Comparison

power

as a function

show

good

for the GaAs

current

(ma)

diode

agreement 0.64 /

/

/

/

/

/

/

/

/

/

02

/’ /

BlQS

mA

current,

Fig. 15. Comparison of theoretical and experimental frequency shift with leakage current, diode B in the nominal Q cavity. of the disc and post waveguide

circuit

not been derived

from

analysis indicates

that the proportionality

obtained within

are

the

first principles,

reasonable[l9].

limits

of experimental

The

cavity

has

a simplified constants

agreement

is

error.

6. SUMMARY

The major an IMPATT in

RF

effect of enhanced

leakage

current

in

diode has been shown to be a decrease

power

oscillation.

and

Enhanced

an

increase leakage

in

frequency

current

of

the

and predicted

testing

RF

between

current and

experiment

and silicon diodes mounted The

high

results

cavity

are

effects

The

in

qualitative

dominate

measured

is proportional change

to the constant analysis

at the

oscillation predicted

due to enhanced

;I qualitative

in

for the silicon

leakage that is in

of

the RF

REFERENCES

,/’

/

parameter%

and leakage

a proportionality

with

current.

D. Decker. C. Nunn and H. Frost. IEEE ‘Trc~r~,\. Electron Deuices ED-l& 141 (1971). 3 ‘1‘. Misawa, Solid-Sr. Electrorl. 13, 1369 (1970). -. 3. K. Mouthaan. Phil. Rcs. Rrp. 25. 31 (1970). IEEE Trctns. MicrowcIw Theorq cutd 4. K. Mouthnan, Techniques. MTT-IX, 853 (1970). 5. T. Cameron. N. Suntharalingam and C;. Kcnncy. ThermolL~minescrnt Dosimetry. University of Wi\consin Press (1968). E#ect.s ;,I Srmic.orltllrc.to,- Drricuc. 6. Larin, Radiution Wiley, New York (1968). 7. C. Klein, J. uppl. Phvs. 39. 3029 (1968). 8. T. Misawa and N. D. Kenyon, IEEE Trtrns. Microwctoe Theory urtd Techniques MTT-18. 969 (1970). 9. R. Chaffin. IEEE 7’run.s. Nucleur Science NS-1X. 436 (1971). fEEE Tmm. Microwc~w Theory md IO. R. Mohn. Techniques MTT-11. 263 (1963). I I. W. T. Read, Bell Spst. Tech. J. 37. 401 (IY%). Lee,J. uppl. Phys.41, 1743 (1970). 12. R. KuvasandC. 13. J. Nigrin. Proc. IEEE 60, 916 (1972). and G. Haddad. IEEE Proc. 61. 153 14. W. Schroeder (1973). and A. Jordan, Solid-St. Electron. IS. 15 A. Sanderson 140 (1972). Electron. 13. 1363 (1970). 16. T. Misawa, So/id-St. and G. Haddad, IEEE Prw. 59, 1245 17. W. Schroeder (1971). Solid-Sf. Eleclron. 15. 635 (1972). 18. J. Goedhloed, Ph.D. di\s. Rensselaer Polytehnic lnstiI9 P. Cottrell, tute. Troy. New York (1973). I

/’

with

diodes were

circuit.

/

/

shift

reactance

current

-Data ---Theory

of bia\

currents.

the

leakage

or

of this model were derived

but saturation

bias

frequency

the

region

from

of a model proposed

electrical

Q cavity.

of

pulse.

leakage

agreement

in

pairs

photo

of measured

theory

mounted

depletion

and structural

non-destructive

higher Leokaqe

to include electrical

diode\.

the nominal

distribution

effects in IMPATT

for evaluation

agreement

the a

the radiation

diode\ The high

the semiconductor.

ionized

by an extension

by Mouthaan necessary

in

the

creating

current

characterized

from

field

sweep

volume

Leakage

The

ionizes a uniform

electric

depletion

IMPATT electrons.

pairs throughout

continuously

BIOS

of operating

with 100 nsec pulses of 10 MeV

was

of

simu-

11

IMPATToscillators APPENDIX

Relationship between RF circuit output characterizution

A

impedance

ment of the oscillation starting current, oscillation frequency and RF output power at a known bias current can be used to determine the RF circuit impedance at frequency w. This has been done for the diodes used in this study and the results are given in Table 3. In general, the characteristics with enhanced leakage current can be predicted by a solution of the tuning conditions, [equation (Al)], the circuit model (Fig. 9(a)), and the constant current condition [equation (7)], for a given diode and operating point. This involves, however, the simultaneous solution of three coupled, transcendental equations with three unknowns. However, certain simplifications can be made. Since the diode reactance is largely passive junction capacitance, to first order the diode oscillation frequency can be considered constant as leakage current is varied. Thus, the terms WT,, and ~7~ in the active elements of the model can be replaced by constant transit angles 0, = OG-,, and &, = ti17~. This eliminates one variable (w) and one transcendental equation (X, = - X,) when calculating the diode operating characteristics with leakage current. Furthermore for small frequency deviations the real part of the RF circuit impedance can be considered constant and the value derived from the cw measurement previously described can be used to find the diode operating characteristics with leakage current. Solving the tuning condition for a fixed frequency and RF circuit resistance for the simple model with leakage current in Fig. 9(b) gives the following result for a diode with enhanced leakage current

and diode RF

The IMPATT model can be related to the RF circuit by solution of the tuning condition equationl4J Z,, = - Z,

= ~ (R,%+ R, + jX, ).

(Al)

When this expression is evaluated for the diode with no leakage current, the results relate the normalized avalanche voltage to the physically measurable oscillation starting current I,,.,,, and the bias current 1141

of RF where I..,,,,, is a function electrical and structural parameters, RF circuit impedance

frequency, the diode and the real part of the

(A3

where Q = [WC, (Rs + R, )J-‘.

(A4)

The reactive part of the circuit impedance determines the frequency of oscillation which in this case is independent of the RF voltage and bias currentf41

c,, - = cos $J P

This equation with equation (20) can be solved simultaneously with equation (15) for D, and M. The diode output power, P, with enhanced leakage current can now be calculated as it is proportional to the square of the normalized voltage. The RF output power P at a bias current I is

Measurement of the oscillation starting current and the frequency of oscillation for a diode with known electrical and physical parameters, therefore, determines the total load RF resistance, R, + R ,, and the load reactance X,,. The RF output power is given by[4]

P P,=

If the RF output power is also measured for a given bias current, the RF load resistance, R,. can be determined from equations (A?). (A3) and (A6). Thus, the measure3. Derived

and measured

((3%~) (2x1 Diode A Nominal Q Diode B Nominal Q Diode A High Q

tj”> (G 1

where P,, is a measured reference power at reference current I,, v,,
(A6)

Table.

(A7)

diode operating

parameters

I,,

P,,

R,_ + Rs

R,.

X0

(mA)

(mW)

(a)

(fl)

(fi)

IO.6

33.5

63

324

1.98

I.17

- 40.0

8.9

32.0

64

316

I.91

1.88

~ 25.8

9.8

22.5

44

68

I ,57

0.285

- 42.4

12

P. E. COITRELL, J. M.

BORREGO and R. J. GUTMANN

above calculation can be easily done by hand as only a few iterations are necessary to solve equations (A7) and (15). The calculated value of normalized avalanche voltage can now be used to find the values of the current generators, actual avalanche voltage. and the diode impedance. If the change in transit angle is small, the increase in oscillation frequency due to enhanced leakage current can now be calculated from the change in diode impedance if the variation of RF circuit impedance with frequency i\ known a\; the tuning condition must be still met. The model described by Fig. 9(a) and equations (7). (9). (10). (13) and (14) can be evaluated by iterative ~imultaneoux solution or by systematic evaluation. If again the frequency shift is considered small. the real part

of the RF circuit impedance is considered constant and the use of the transit angles 0,. and (Id simplify the calculation of diode impedance. Assuming the RF circuit resistance constant with frequency the value of the real part of the diode impedance with no leakage current can be matched to the calculated diode impedance with leakage current. The diode output power is then P = &I<,

*R,

(A%

where I,, is the total diode current. Again the oscillation frequency shift can be calculated from the tuning condition and the evaluated circuit model if the RF circuit impedance as a function of frequency is known. The above procedure is used in calculating the theoretical results presented in this paper.