View metadata, citation and similar papers at core.ac.uk brought to you by CORE

provided by Elsevier - Publisher Connector

Nuclear Engineering and Technology 48 (2016) 1219e1229

Available online at ScienceDirect

Nuclear Engineering and Technology

journal homepage: www.elsevier.com/locate/net

Original Article Computer Modeling, Characterization, and Applications of Gunn in Radiation Environments

* Wafaa Abd El-Basit a, , Safaa Mohamed El-Ghanam a, Ashraf Mosleh Abdel-Maksood b, Sanaa Abd El-Tawab Kamh a, and Fouad Abd El-Moniem Saad Soliman b

a Research Laboratory, Physics Department, Faculty of Women for Arts, Science and Education, Ain-Shams University, Heliopolis, Cairo, Egypt b Nuclear Materials Authority, P.O. Box 530, Maadi, 11728, Cairo, Egypt

article info abstract

Article history: The present paper reports on a trial to shed further light on the characterization, appli- Received 25 January 2016 cations, and operation of radar speed guns or Gunn diodes on different radiation envi- Received in revised form ronments of neutron or g fields. To this end, theoretical and experimental investigations of 30 March 2016 oscillating system for outer-space applications were carried out. Radiation ef- Accepted 19 April 2016 fects on the transient parameters and electrical properties of the proposed devices have Available online 24 May 2016 been studied in detail with the application of computer programming. Also, the oscillation parameters, power characteristics, and bias current were plotted under the influence of Keywords: different g and neutron irradiation levels. Finally, shelf or oven annealing processes were Domain Excess Field shown to be satisfactory techniques to recover the initial characteristics of the irradiated Gamma Dose devices. Microwave Oscillator Copyright © 2016, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society. This Mobility is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ Neutron Fluence licenses/by-nc-nd/4.0/). Shelf Annealing Transferred Electron Devices

1. Introduction type of , on the design of the device and on the operating conditions. Accordingly, the radiation stability The electrical properties of semiconductor devices are of diodes is sometimes determined by the degree of defor- greatly influenced by irradiation, i.e., both the forward- and mation of the forward (IeV) characteristics and sometimes reverse-electrical (IeV) characteristic curves are changed. by the changes in reverse characteristics [1e5]. Transferred However, the magnitude of those changes depends on the electron devices (TEDs), sometimes called Gunn diodes,

* Corresponding author. E-mail address: [email protected] (W. Abd El-Basit). http://dx.doi.org/10.1016/j.net.2016.04.009 1738-5733/Copyright © 2016, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1220 Nuclear Engineering and Technology 48 (2016) 1219e1229

(A) 3.00E+015 Neutron fluence, n/cm Initial 9.0x10 5.0x10 2.00E+015 1.2x10

1.00E+015 Average velocity, (m/s)

0.00E+000 02468101214 Applied electric field, (kV/cm)

(B) (C)

Data 4.0 2.80E+015 Data Linear fit Exponential fit 2.60E+015 3.6 2.40E+015

2.20E+015 3.2 2.00E+015 Applied field, (kV/cm) 1.80E+015

2.8 /s) (m velocity, Average

1.60E+015 2.4 1.40E+015 1E9 1E10 1E11 1E12 1E13 1E14 1E15 1E12 1E13 1E14 Neutron fluence, (n/cm ) Neutron fluence, (n/cm 2)

Fig. 1 e Average velocities. Calculated average velocity as a function of (A) applied electric field and (B) applied field. (C) Average velocity as a function of neutron fluence.

have been a topic for active research since 1965 [6,7].The 2. Materials and methods Gunn is a unique component. Even though it is called a diode, it does not contain a positiveenegative diode 2.1. Computer modeling junction. The Gunn diode can be termed a diode because it has two electrodes. It depends upon the bulk material To study the radiation effects on the output characteristics of properties rather than that of a positiveenegative junction. the transferred electron device, a computer model has been The Gunn diode operation depends on the fact that it has a developed (by the authors) in order to solve the transient voltage-controlled [8]. A possible appli- characteristics of the diode such as charge carrier mobility, cation of these diodes involves satellites and military com- domain excess potential, and the outside domain electric munications where radiation tolerance is desired. Damage field. In addition, the waveforms of current density value as a in GaAs devices results from the displacement of lattice function of time for the oscillating diode were obtained under atoms and their subsequent migration and trapping to form the influence of different neutron fluence (4) levels. All the stable and metastable defects. These defects lead to a pro- analyses of the domain behavior of GaAs devices are based on nounced change in both the static and dynamic character- its velocityefield (y-E) characteristics [8e13]. Among them, the istics, but not necessarily in the same way. In addition, Thim [8] model was chosen to be used for this study, where: different defects may arise from various radiation types, h i h i 1 flux rates, and energies. ¼ ð Þ¼ $ þ $ð = Þ4 $ þð = Þ4 y y E m1 E yV E Eo 1 E Eo (1) The principal effect of high energy neutrons on GaAs is to produce defect clusters, which act as trapping where y:velocity;m1: measure of how quickly an electron can 2 and scattering centers for free carriers. In turn, the move through a metal or semiconductor; ¼ 8,000 cm /V.s; E: ¼ effect of these clusters on the device characteristics can applied field in kV/cm; yv: valley velocity and Eo 4.0 kV/cm. be modeled by a carrier removal rate and a fluence- For current calculations, one considers a uniformly doped dependent effective mobility describing the decrease in GaAs diode to which an electric field is applied, which biases it carrier mobility and the reduction in the effective carrier to the negative differential mobility region. Any disturbance in concentration. the field will grow and thus produce a high field domain. In the Nuclear Engineering and Technology 48 (2016) 1219e1229 1221

(A) (B) 7

8,000 ) 6 /cm /V.s) 5 6,000 4

4,000 3

2 Carrier mobility, (cm mobility, Carrier 2,000 Data Data 1 Exponential fit Exponential fit Carrier(x10 concentration, 0 0 1E9 1E10 1E11 1E12 1E13 1E14 1E15 1E8 1E9 1E10 1E11 1E12 1E13 1E14 1E15 Neutron-fluence, (n/cm ) Neutron fluence, (n/cm )

(C) 2.5 )

/cm 2.0

1.5

1.0

0.5 Data Exponential fit Carrier concentration, (x10 Carrier concentration, 0.0 1E9 1E10 1E11 1E12 1E13 1E14 1E15 Neutron fluence, (n/cm )

Fig. 2 e Calculated mobility and concentration. (A) Calculated mobility. Calculated concentration for (B) electrons and (C) holes as a functions of neutron fluence.

low field region, the total current will be due to conduction where, mo and no are the preirradiation values of the carrier current and displacement current in this region, while the mobility and carrier concentration, respectively; m and n are

field Eo(t) does not vary in the longitudinal direction. This the postirradiation values. implies that the charge density is uniform and equal to the Using these definitions, one can express the neutron- charge concentration, Po. Hence, the total current induced carrier removal and mobility changes by: ¼ $ð $4Þ density J(t) is given by: n no 1 a (6)

JðtÞ¼Po$yoðtÞþε$dEoðtÞ=dðtÞ (2) ¼ =ð þ $4Þ m mo 1 b (7) The first term of the above equation represents the con- where the values for the degradation parameters a and b have duction current, where yo(t) is the drift velocity and the second been determined for n-type epitaxially grown GaAs as [8]: ε term represents the displacement current, where is the 2 4 0:77 permittivity of GaAs. Finally, the magnitude of the domain a cm ¼ 7:2 10 ðnoÞ (8) potential at any instant (t) can be given as [14]: Zþ∞ 2 6 0:64 b cm ¼ 7:8 10 ðnoÞ (9) ð = Þ DVðtÞ¼ DEðx; tÞdx ¼ DVð0Þ$e t td (3) ∞ Fig. 1 shows the average velocity as a function of applied field yeE curve, plotted at different neutron fluence (4) where, DV(0) is the magnitude of the initial disturbance po- values (Fig. 1A), from which the dependence of both the tential which was chosen to be equal to 0.025 V, and td is the applied field (Fig. 1B) and average velocity (Fig. 1C) were decay or growth time of the device. plotted as a function of neutron fluence. It is clear that the 4 The effect of neutron fluence ( ) on the carrier mobility (m) average velocity curves have a negative slope over a broad and effective carrier concentration (n) have been determined range of intermediate field values, which is a necessary e by a number of researchers [15 17]. It is reported that the condition for the existence of negative resistance. Finally, main degradation parameters representing carrier removal empirical equations concerning the obtained data could be rate (a) and mobility (b) are defined as: deduced as: a ¼ð1=noÞ$ðdn=d4Þ (4) E ¼ Ei þ B1$ð4Þ (10)

¼ ð ð = Þ= 4Þ ¼ þ : $ð4Þ b mo d 1 m d (5) E Ei 0 27407 (11) 1222 Nuclear Engineering and Technology 48 (2016) 1219e1229

(b) Carrier concentration (Fig. 2B and 2C) 0.4 ð4=t1Þ n ¼ no þ A1$e (16) /V.s) 2 0.2 20 3 20 3 ð4=2:0839 E14Þ n 10 cm ¼ no 10 cm þ 5:89348$e (17)

0.0 and

P ¼ P þ A1$eð4=t1Þ (18) –0.2 o Neutron fluence, n/cm

Differential mobility, (m mobility, Differential Initial P 1020 cm3 ¼ 0 þ 1:923651$eð4=6:9657 E13Þ (19) –0.4 5.00x10 1.20x10 where m and mo: carriers mobility before and after irradiation; p 020406080100120140 and po: holes concentration before and after irradiation; n and

Time, (psec) no: electron concentration before and after irradiation and A1's: constants for each equation. Fig. 3 e Calculated instantaneous change of differential By differentiating Eq. (1), the differential mobility (md) can mobility, plotted at different neutron fluences. be obtained. Fig. 3 shows the change in differential mobility, plotted at different neutron fluences. As the neutron fluence is increased, the mobility begins to be more positive. Up to a y ¼ y þ B2 eð4=tÞ (12) i fluence level of 1.2 1014 neutrons/cm2, the average mobility becomes nearly positive and thus any existing domain will be y ¼ y þ : ð4=1:33378 E14Þ i 1 7414 E15 e (13) decayed. where Ei: initial value of applied field (E and Ei are given in The domain excess potential was plotted at different

V/cm); B1andB2: constants of the equation and yi: initial neutron fluencies (Fig. 4), applying Eq. (3). By contrast, Fig. 4B value of average velocity (y and yi are given in m/s). shows the dependence of domain excess potential on neutron The carrier mobility and concentration dependencies on fluence. The maximum domain excess potential DV(t)is neutron fluence have been calculated applying Eqs. (6 and 7). shown to decrease with increasing the neutron fluence and it Both the mobility and concentration of carriers remain unin- approximately reaches zero level at a neutron fluence of about 14 2 fluenced with irradiation up to fluence of around 1 1012 1.20 10 neutrons/cm . Finally, empirical equations were neutrons/cm2. For higher neutron fluencies (4), a sharp deduced as: decrease was noticed in both cases, as shown in Fig. 2. The DVðtÞ ¼ DVðtÞ Bð4Þ (20) following empirical equations could be deduced using the i exponential fit: DVðtÞ¼0:71678 0:04752ð4Þ (21)

(a) Carrier mobility (Fig. 2A): where DV(t)i is the initial value of domain excess potential, and B is the constant of the equation. ¼ þ $ ð4=t1Þ Fig. 5 illustrates the change of the maximum domain m mo A1 e (14) e excess field (Ed Eo) and the outside domain field (Eo)with ¼ þ ; : $ ð4=1:23687 E14Þ time. As the applied voltage across the diode is increased m mo 4 858 0577 e (15) with time (Fig. 5A), the change of domain excess field (EdeEo) 2 where m and mo are given in cm /V.s. was increased up to its maximum value at the instant

(A) (B)

0.35 Neutron fluence, n/cm 0.30 Data 0.30 Initial Linear fit 3.0x10 0.25 0.25 5.0x10 1.2x10 0.20 0.20 0.15 0.15

0.10 0.10 Domain excess potential, (Volt) potential, excess Domain 0.05 (Volt) potential, excess Domain 0.05

0.00 0.00 0 20406080100120140 1E9 1E10 1E11 1E12 1E13 1E14 1E15 Time, (psec) Neutron fluence, (n/cm 2)

Fig. 4 e (A) Calculated instantaneous change of domain excess potential and (B) domain excess potential plotted at different neutron fluences. Nuclear Engineering and Technology 48 (2016) 1219e1229 1223

(A) (B) 0.6 18 2 Neutron fluence, n /cm 16 Initial 9.0x1011 14 13 0.4 5.0x10 12 1.2x1014 10 ), kV/cm ), o , kV/cm

-E 8 o d 2 E

(E Neutron fluence, n/cm 0.2 6 Initial 11 4 9.0x10 5.0x1013 2 1.2x1014 0.0 0 020406080100120 020406080100120 Time, psec Time, psec

Fig. 5 e Calculated instantaneous change of excess domain field due to neutron exposure.

corresponding to the maximum excess potential (threshold 2.2. Electrical characteristics point). After this instant, the domain excess field decreased as DV(t) was decreased. From Fig. 5B, it is clear that the 2.2.1. Choice of devices outside domain field (Eo) increased with increasing time up In order to obtain complete data about the effects of radia- to a certain instant, then decayed with time. Moreover, it is tion on the and microwave characteristics of noticeable that Eo is slightly influenced with increasing the TED, its behavior was studied in detail under different neutron fluencies. Finally, Fig. 6 shows the dependence of operating and irradiation conditions. A commercial fixed the calculated current density (Eq. 2)ontimeattwo CW (continuous wave) GaAs Gunn diode, different neuron fluencies (Fig. 6A). The dependence of the MA49618 was selected for this experiment, where its elec- ¼ ¼ current density on different neutron fluencies is shown in trical characteristics are: VOp 12 V; IOp 80 mA; ¼ ¼ Fig. 6B. Frequencymin 9.00 GHz; Frequencymax 10.5 GHz; and ¼ Powermin 5.0 mW. ð4=t1Þ JðtÞ¼JoðtÞþA1$e (22) 2.2.2. Gamma irradiation ð Þ ¼ ð Þ þ : $ ð4=1:04725 E14Þ J t J t i 5 87112 e (23) A g irradiator, belonging to the National Center for Radiation 2 Research and Technology of Egypt, was used during the where J(t) and J(t)i are given in A/mm . The decrease in the current value can mainly be attributed course of the present study. It is a Gamma Cell-220, which is a to the fact that the dielectric growth time constant increases Co-60 irradiator manufactured by Atomic Energy of Canada due to a decrease in the negative conductivity and the do- Limited for use in an unshielded room. As shown in Fig. 7, the mains do not have time to form before they drift out of the unit consists basically of an annular source permanently device. enclosed within a lead shield, a cylindrical drawer up or down

(A) (B) 9 Neutron fluence;n/cm2 8 Initial 8 Data ) ) 5.0x10 Exponential fit 7 1.20x10 7 6

5 6 4 5 3 Current density, (A/mm Current density, (A/mm 2 4 1 0 3 0 40 80 120 160 200 240 280 320 360 1E13 1E14

Time, (psec) 2 Neutron fluence, (n/cm )

Fig. 6 e Calculated instantaneous change of external current density. Plotted at (A) different neutron fluencies and (B) dependence of current density on neutron fluence. 1224 Nuclear Engineering and Technology 48 (2016) 1219e1229

Fig. 7 e Overall view of Gamma Cell 220.

along the source centerline. The drawer has a chamber for thermal annealing implies elevated temperatures. Other carrying samples to be irradiated from outside. Samples up to types of annealing are also possible where the device may be approximately 15 cm in diameter and 20 cm in height can be subjected to a symmetrical high-frequency electromagnetic accommodated in the chamber. An electrically powered digi- field or bias temperature stressing. tal timer automatically raises the drawer at the termination of a sample irradiator. Time can be preset either automatically to 2.3.1. Self/shelf annealing a maximum of 999.9 hours or to a manual operation position. Irradiated samples were left on a shelf, at room tempera- Finally, the samples were irradiated with ascending gamma- ture, while plotting their electrical characteristics periodi- doses of up to 12 kGy, at a rate of 0.35 Gy/s. Reference do- cally. Measurements were carried out up to the recovery simeters were always applied for irradiation quality control saturation conditions, where no more annealing effect was adjustment. noticed.

2.3. Annealing of radiation damage 2.3.2. Isochronal/oven annealing The temperature of the irradiated sample has been raised up The annealing of radiation damages in semiconductor de- to different levels (to 60 C, 80 C, and 100 C) for different vices usually follows one of three different approaches: annealing times (0.5 hours, 1.0 hours, 1.50 hours, 2.0 hours, rapid annealing; slow annealing; or thermal annealing 2.5 hours, 3.0 hours, 3.5 hours, and 4.0 hours). For each [18]. Rapid annealing is usually performed at high temper- annealing time step, the sample was left to cool down to ature where it takes little time for the device to recover. room temperature. Its electrical characteristics were then Slow annealing proceeds at room temperature. By contrast, measured.

(A) (B) 300 60

) Data 250 Ω 50 Exponential growth fit 200 40

150 30

Current, (mA) 100 Gamma-dose, MGy 20 Low field resistance, Low field ( Initial 50 0.005 10 2.70 3.90 0 0 02468101214 012345 Applied voltage, (Volts) Gamma-dose, (kGy)

Fig. 8 e (IeV) characteristic curves for GaAs Gunn diodes. (A) Plotted under the influence of different g dose levels and (B) the dependence of low-field resistance on g dose. Nuclear Engineering and Technology 48 (2016) 1219e1229 1225

(A) (B) 9.95 9.90 Data 9.90 Polynomial fit 9.85 9.85 9.80 9.80 9.75 9.75 9.70 Gamma-dose, kGy Initial Frequency, (GHz) Frequency, 9.65 1.0 (GHz) Frequency, 9.70 1.6 9.60 2.0 6.0 9.65 9.55 8.0 9.50 9.60 56789101112 024681012 Bias voltage, (Volts) Gamma-dose, (kGy)

Fig. 9 e Dependence of operation frequency of Gunn diode oscillator bias voltage. (A) Plotted at different g dose levels and (B) dependence of oscillation frequency on g dose.

3. Results and discussion 3.2. Microwave characteristics

3.1. Direct current characteristics 3.2.1. Oscillation frequency During the course of the study, frequency characteristics of During the present part of the work, the (IeV) characteristic the Gunn diode for a millimeter wave oscillator were investi- curves of the investigated Gunn devices were plotted before gated [19e21]. The dependence of the operating frequency and after exposure to ascending g dose levels. The state of (Fop) on the bias voltage is shown in Fig. 9A. It is clear that the the 370A curve tracer, manufactured by Tektronix, which frequency is a direct function of the g exposure (g) and it in- is a high-performance, general purpose interface bus- creases in a linear manner up to a total dose of 8.0 kGy (Fig. 9B). programmable digital-storage instrument, can provide For higher g doses, the effect was shown to be insignificant, static and dynamic characteristics which means that the radiation damage reaches saturation measurement. The instrument stimulates, measures, and level. The obtained dependence of the oscillation frequency displays the semiconductor characteristics of a variety of on g dose could be expressed in the manner shown in the two- and four-terminal devices. Fig. 8A shows the g irradi- following equation, where the polynomial fit could be ation effects on the (IeV) characteristics of Gunn devices expressed as: (TEDs). It is clear that there are two important regions of F ¼ F þ B $x þ B $x2 (27) interest in each curve. The first is below the threshold op opi 1 2 voltage (approx. 3.5 V), where the low field resistance (Ro)is 2 shown to increase with irradiation (Fig. 8B). The matter that Frequency ¼ 9:58686 þ 0:04804$ðgÞ þ ð0:00202Þ$ðgÞ (28) is mainly attributed to the decrease in both initial carrier The observed increase in frequency can be explained in the concentration (no) and carrier mobility (m1)withg exposure presence of the simplified equivalent circuit diagram of the is due to the carrier removal effect, and: Gunn diode oscillator (Fig. 10). The cavity parameters are represented by L, C, and R , while that for the diode is repre- R ¼ L=n $q$m $A (24) L o o 1 e sented by Rn (most of C is due to device capacitance). The where Ro: low-field resistance and L and A: length and operating frequency is determined by both the cavity and L/R cross-sectional area of the device, respectively. time constant, hence: Concerning the dependence of the low field resistance on the gamma-irradiation dose, an exponential relationship was obtained, where:

ðx=tÞ Ro ¼ Roi þ A$e (25)

ð4=3:65809Þ Ro ¼ 0 þ 15:35145$e (26)

The second region of interest is observed at voltage values above threshold levels (>3.5 V), and for g-doses below 3.90 MGy where negative resistance changes are mainly due to domain formation. Finally, for g-doses above 3.90 MGy, the devices lose their main feature as negative resistance devices Fig. 10 e Simplified equivalent circuit of a relaxation mode and behave as linear positive resistance devices. Gunn diode oscillator. 1226 Nuclear Engineering and Technology 48 (2016) 1219e1229

(A) 11 10 9 8 7

6 Gamma-dose, kGy

Power, (dBm) Initial 5 1.0 4 1.6 2.0 3 6.0 2 56789101112 Bias voltage, (Volts)

(B) (C) 12.5 14

12.0 Data 13 Data Exponential decay fit Exponential growth fit 11.5 12

11.0 11

10.5 10

Power, (dBm) 10.0 9 Bias-voltage, (Volts) 9.5 8

9.0 7

8.5 6 0246810 012345678 Gamma-dose, (kGy) Gamma-dose, (kGy)

Fig. 11 e Dependence of output power of Gunn diode oscillator on bias voltage. (A) Plotted at different g dose levels, and dependence of (B) output power and (C) bias voltage on g dose.

. pffiffiffiffiffiffi ¼ þ $ ðx=tÞ T ¼ 1 Fop ¼ 2p LC þ L=Ro$M (29) Pout Pouti A e (30)

¼ ð ð Þ= : Þ where, M is the bias/threshold voltage ratio ( EB/ET). Power ¼ 4:672 þ 7:7813$e g kGy 11 02261 (31) Now, referring to the previously stated relationships for the radiation effects on the low field resistance and the ratio ðx=tÞ VB ¼ VBi þ A$e (32) M, it is clear that both Ro and M are increased by g exposure. As a result, and from Eq. (29), it is clear that a decrease in the time ðgðkGyÞ=6:29982Þ VB ¼ 3:54799 þ 2:61778$e (33) constant (T) occurs as a function of the increases in Ro and M.

Therefore, a corresponding increase will appear in the oscil- where Pout and Pouti: output power before and after g lation frequency. irradiation are given in (dBm); VB and VBi: bias voltage before and after g irradiation (given in V) and A and B: constants of 3.2.2. Effects on radio frequency output power the equation. The dependence of the radio frequency oscillator output The decrease in maximum peak output power can be un- power on the bias voltage was plotted under the influence of derstood from an inspection of the previously mentioned different g-dose levels (Fig. 11A). The power increased with equivalent circuit (Fig. 10). The condition for oscillation re- j j < bias voltage reached a peak value and then decreased slowly quires that Rn RL, and the fall off in power before failure is with increasing the bias voltage. As the devices are exposed to reached due to the following: g radiation, severe interruption occurs to their power char- acteristics. The maximum peak output power was decreased i. Since these devices are operated at a constant voltage, the (Fig. 11B), while the bias is shown to be shifted toward higher decrease in operating current that occurs with increased voltage values (Fig. 11C), resulting in an increase in the bias/ resistance results in a reduced output power, and threshold voltages ratio. Finally, the dependence of output ii. For n · L products below the optimum value, the efficiency power on g dose was plotted where an empirical equation was is decreased as n · L is decreased. An upper limit on output deduced as: occurs due to the fact that jRnj is increased with bias. This Nuclear Engineering and Technology 48 (2016) 1219e1229 1227

(A) (B) 12.0 11.5 9.64 Data linear fit 11.0 9.62 10.5 9.60 10.0 9.5 9.58 9.0 9.56 Power, (dBm) 8.5 Gamma dose, kGy Frequency, (GHz) Frequency, Initial 8.0 1.0 9.54 1.6 7.5 2.0 6.0 9.52 7.0 9.0 6.5 9.50 9.45 9.50 9.55 9.60 9.65 9.70 0246810 Frequency, (GHz) Gamma-dose, (kGy)

Fig. 12 e Dependence of output power of Gunn diode oscillator on frequency. (A) Plotted at different g dose levels, and (B) dependence of frequency on g dose.

can be demonstrated as follows: near breakdown, jRnj has samples, which were kept at room temperature, were tested the form: weekly, where the (IeV) characteristic curves of Gunn diode, plotted after irradiation and different shelf annealing periods j j ¼ $ $ Rn K Ro M (34) are shown in Fig. 13A. Fig. 13B shows the recovery percentage of the Gunn devices plotted as a function of self-annealing where, K is constant for large values of M. time, following Eq. (37). From this it is clearly noticed that Therefore, it can be seen that as EB is increased, M is for annealing times of more than around 12 weeks, the rate of increased, and if jRoj > RL, oscillation will cease and breakdown annealing was negligible, i.e., the saturation condition was can occur. Therefore, it can be seen from Eq. (34) that as Ro is almost reached. increased, with irradiation, the maximum allowable value of j j < M will be decreased if the condition that Ro RL is to be ðx=tÞ Y ¼ Yo þ A$e (37) satisfied. This in turn means that the maximum peak power output is decreased, since the allowable bias voltage must be Y ¼ 0:80386 þð0:27787Þ$eðtime;weeksÞ=1:99966 (38) reduced.

It is clearly shown in Fig. 12A that as the g-dose is where, Yo: is the ratio of the device current after to before increased, the same maximum power is caused at higher irradiation, and A: constant of the equation. frequency, which can be understood from Eq. (35), since this means that by increasing the g-dose, T will be decreased and, 3.3.2. Isochronal/oven annealing so, the frequency of oscillation will be increased. While for the The temperature of the irradiated devices has been raised up same dose, it is observed that the power will be decreased to 60 C, 80 C, and 100 C for different annealing times of 0.5 from the maximum value, due to the effect of the loading hours, 1.0 hours, 1.5 hours, 2.0 hours, 2.5 hours, 3.0 hours, 3.5 circuit. Finally, Fig. 12B shows the dependence of the oscilla- hours, and 4.0 hours, then each of the samples were left until tion frequency on g dose, where: room temperature was reached. The obtained data show that for the investigated three annealing temperature levels, the ¼ þ $ðgÞ Fosc Fosci B (35) maximum recovery percentages of 70%, 81%, and 91.5% were reported. Note that no more heat could be applied due to the ¼ : þ : ð ; Þ Fosc 9 51486 1 433E 2 g kGy (36) temperature operating range of the devices under test. Finally, the recovery percentage of the irradiated devices, under the where, Fosci: is the initial oscillation frequency of the oscillator, and B: constant of the equation. influence of 100 C, as an example, was plotted as shown in Fig. 13C, following the empirical equation:

3.3. Annealing of radiation damage 2 Y ¼ Yo þ B1$x þ B2$x (39)

To ascertain the behavior of the irradiated Gunn devices, their Y ¼ 0:49931 þ 0:24109$ðannealing time; hr:Þ electrical characteristics were plotted under two annealing þ ð : Þ$ð ; :Þ2 methods. 0 03455 annealing time hr (40)

3.3.1. Self/shelf annealing 4. Conclusion Primarily, self/shelf annealing is a technique in which the irradiated devices were left at air temperature (room level) The performance of a Gunn diode for a microwave oscillator and so may be cold-worked without strain-hardening. In this under the influence of neutron and g fields was investigated. respect, the electrical characteristics of the irradiated To this end, different empirical equations were deduced, 1228 Nuclear Engineering and Technology 48 (2016) 1219e1229

(A) 240

200

160

120 Current, (mA) 80 Initial Irradiated 4 Weeks 40 8 Weeks 12 Weeks 16 Weeks 0 024681012 Applied voltage, (Volts)

(B) (C) 1.0 0.85 0.9 0.80

0.75 0.8

0.70 0.7 0.65 0.6 Recovery percentage Recovery 0.60 percentage Recovery 0.5 0.55 Data Data Exponential fit Polynomial fit 0.50 0.4 024681012141618 01234 Annealing period, (weeks) Oven annealing time, (hours)

Fig. 13 e (IeV) characteristic curves of Gunn diode. (A) Plotted after irradiation and different shelf annealing periods, recovery percentages a function of (B) annealing period and (C) oven annealing time at 100C.

tested, and proved to be satisfactory in representing the State Univ. Novi Pazar Ser. A: Appl. Math. Inform. Mech. 3 behavior of a Gunn diode and its oscillation circuit. It was (2011) 27e34. shown that radiation influences the Gunn diode oscillator [3] M. Zdravkovic, A. Vasic, B. Cavric, R. Radosavljevic, K. Stankovic, Radiation induced noise level in solar cells, in: operation; the matter is mainly due to the reduction of carrier PIERS Proceedings, Kuala Lumpur, Malaysia, March 27e30, mobility, as a result of the introduced traps and reduction in 2012, pp. 1160e1164. the effective carrier concentration. As a result, the radiation [4] R. Katz, K. LaBel, J.J. Wang, B. Cronquist, R. Koga, S. Penzin, causes the oscillation frequency to increase and the output G. Swift, Radiation effects on current field programmable power and bias current to decrease. Higher g dose levels cause technologies, Nucl. Sci. IEEE Trans. 44 (1997) 1945e1956. the devices to lose their main feature as negative resistance [5] Z. Pavlovic, I. Manic, S. Golubovic, Effects of g-irradiation on devices and behave as a linear positive resistance device. electrical characteristics of power VDMOS , Facta Univ. Ser. Phys. Chem. Technol. 2 (2002) 223e233. Finally, oven and self-annealing processes were to shown to [6] A. Forster,€ J. Stock, S. Montanari, M.I. Lepsa, H. Lu¨ th, be acceptable techniques for devices to recover to their com- Fabrication and characterisation of GaAs Gunn diode chips plete initial characteristics. for applications at 77 GHz in automotive industry, Sensors 6 (2006) 350e360. [7] S.I. Domrachev, S.A. Alaverdjan, V.N. Skorokhodov, Conflicts of interest Application of a Gunn-diode current-pulse generator for of semiconductor lasers, Tech. Phys. 44 (1999) e The authors declare no conflicts of interest. 544 547. [8] H.W. Thim, Computer study of bulk GaAs devices with random one-dimensional doping fluctuations, J. Appl. Phys. e references 39 (1968) 3897 3904. [9] K.K. Thornber, Current equations for velocity overshoot, IEEE Electron Device Lett. EDL-3 (1982) 69e71. [10] T. Wang, K. Hess, Calculation of the electron velocity [1] K.G. Naik, S. Bhat, G. Sangeev, The effect of electron distribution in high transistors using an irradiation on BJTs and at elevated temperatures, ensemble Monte Carlo method, J. Appl. Phys. 57 (1985) Arch. Phys. Res. 4 (2013) 74e86. 5336e5339. [2] D. Nikolic, A. Vasic, I. Fetahovic, K. Stankovic, P. Osmokrovic, [11] N. Berg, H. Dropkin, Neutron displacement effects in behavior in radiation environment, Sci. Publ. epitaxial Gunn diodes, IEEE Trans. Nucl. 17 (2007) 233e238. Nuclear Engineering and Technology 48 (2016) 1219e1229 1229

[12] G.E. Brehm, G.L. Pearson, Effects of gamma radiation on Accelerators Spectrometers Detectors Assoc. Equip 362 (1995) Gunn diodes, IEEE Trans. Electron Devices 17 (2005) 338e343. 475e479. [18] M.I. Gorlov, D.A. Litvinenko, Annealing of radiation and [13] D.J. Widiger, C. Kizilyalli, K. Hess, J.J. Coleman, Two- electrostatic damages in semiconductor devices, Russian dimensional transient simulation of an idealized high Microelectronics 31 (2002) 295e304. electron mobility , IEEE Trans. Electron. Devices. [19] L.B. Lin, Z.J. Liao, Q. Liu, T.C. Lu, X.D. Feng, Effect of proton ED-32 (1985) 1092e1102. irradiation on electric properties in AlGaAs/GaAs [14] P.J. Price, On the flow equation in device simulation, J. Appl. heterostructure materials, Surface and Coatings Technology Phys. 63 (1988) 4718e4722. 158e159 (2002) 737e740. [15] I.C. Kizilyalli, K. Hess, Simplified device equations and [20] J. Huang, H. Yang, C. Tian, J.R. Dong, H.Y. Zhang, T.Y. Guo, transport coefficients for GaAs device modeling, IEEE Trans. Design and manufacture of planar GaAs Gunn diode for Electron Devices 34 (1987) 2352e2354. millimeter wave application, Chin. Phys. B 19 (12) (2010) [16] R.K. Parida, N.C. Agrawala, G.N. Dash, A.K. Panda, 127203-1e127203-5. Characteristics of a GaN-based Gunn diode for THz signal [21] Z. Greenwald, D.W. Woodard, A.R. Calawa, L.F. Eastman, The generation, J. Semiconductor 33 (2012) 084001e084007. effect of a high energy injection on the performance of mm [17] V. Eremin, Z. Li, Carrier drift mobility study in neutron wave Gunn oscillators, Solid-State Electronics 31 (1988) irradiated high purity silicon, Nucl. Instr. Meth. Phys. Res. A: 1211e1214.