Temperature Behavior of Thin Film Varactor 

By Richard X. Fu 

ARL-TR-5905 January 2012 

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ARL-TR-5905 January 2012 

Temperature Behavior of Thin Film Varactor 

Richard X. Fu

Sensors and Electron Devices Directorate, ARL 

Approved for public release; distribution unlimited. 
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Temperature Behavior of Thin Film Varactor

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Richard X. Fu

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14. ABSTRACT

The low loss varactor (voltage tunable capacitor) would revolutionize the wireless communication, sensing, and detecting 

industries. Temperature behavior plays a critical role in barium strontium titanate (BST) thin-film varactors. In this report, the 

behaviors of resonant frequency as a function of test time were investigated and discussed. The temperature behaviors of both

metal organic deposition (MOD) and pulsed laser deposition (PLD) thin-film varactors were studied from –30 to 80 °C. The 

temperature coefficients of thin-film varactors were modeled and calculated.

15. SUBJECT TERMS

MOD, PLD, BST thin film, varactor

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Richard Fu

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iii

Contents 

List of Figures iv

1. Introduction 1

2. Experimental Approach 1

3. Results and Discussion 2

3.1 Resonant Frequency as a Function of Test Time ............................................................2

3.2 Temperature Behavior of MOD Thin-film Varactor .......................................................5

3.3 Temperature Behavior of PLD Thin-film Varactor ........................................................6

4. Conclusions 8

5. References 9

List of Symbols, Abbreviations, and Acronyms 10

Distribution List 11
iv

List of Figures 

Figure 1. PLD varactor’s frequency as a function of time. .............................................................3

Figure 2. Capacitance as a function of test time. ............................................................................3

Figure 3. Frequency as a function of time (0 °C, 50 V). ................................................................4

Figure 4. Frequency as a function of time (0 °C, 100 V). ..............................................................4

Figure 5. MOD samples: (a) percentage of tuning of capacitance, (b) capacitance, and (c) Q 

of the varactor as a function of temperature at 2 GHz and DC bias voltages up to 100 V. ......6

Figure 6. PLD samples: (a) percentage of tuning of capacitance, (b) capacitance, and (c) Q 

of the varactor as a function of temperature at 2 GHz and DC bias voltages up to 100 V. ......7
1

1. Introduction 

In wireless communication, systems should operate over multiple frequency bands and provide 

an enhanced signal-to-noise ratio. These goals can be achieved by having electronic tunability in 

the radio frequency (RF) part of the radios. Electronic tuning is the ability by which electronic 

devices operate over a wide frequency range. It can allow a single filter to tune over multiple 

frequency bands, a voltage tunable oscillator (VTO) to accommodate a wide range of frequencies 

for the synthesizer, and a scanning antenna to position a beam, on command, anywhere within its 

sector of operation. Traditionally, electronic tuning has been achieved through ferrite or 

semiconductor diodes. Commercially available ferrite products are expensive and bulky. Also, 

the power consumption of these devices is prohibitive. Further, semiconductor junction diodes 

are restricted in their range of linear response to input power. For high frequency applications, 

semiconductor-based technology for products like electronic scanning antennas is also very 

expensive. 

These limitations in existing solutions have paved the way for new approaches to address lowcost electronic tuning. One of the most promising approaches is the use of tunable dielectric 

materials. The existence of low loss voltage tunable dielectric materials would revolutionize the 

industry of microwave components and antennas. “Tunable” refers to the ability to change 

dielectric constant by applying an electric field. This ability in the microwave component field 

enables a single component to operate over multiple frequencies by simply changing the input 

voltage. The low power consumption in operating devices fabricated from these voltage tunable 

dielectrics is an additional benefit. Varactors are voltage tunable capacitors in which the 

capacitance is dependent on a voltage applied. Temperature behavior plays a critical role in thinfilm varactors (1–5). In this report, we investigate a test method for determining the temperature 

behavior of thin-film varactors, discuss the relaxation time to a stable state, and provide the 

experimental results. 

2. Experimental Approach 

Strain-relieved and epitaxially grown barium strontium titanate (Ba1-XSrXTiO3 or BST) 

(x = 0.3‒0.6) films on (100) magnesium oxide (MgO) were prepared by metal organic deposition 

(MOD) and pulsed laser deposition (PLD) (6). 

MOD has the advantages of ease of composition adjustment and small capital cost. The main 

features of this process are room-temperature chemical precursor solution preparation, short 

preparation time, readily available precursors, high stability, and compatibility with 

semiconductor-fabrication technology. The BST MOD precursors selected as the source of the 
2

solution are Ba(thd)2 trietherdiamine adduct [(C32H62N2O7)Ba], Sr(thd)2 trietherdiamine adduct 

[(C32H62N2O7)Sr], and Ti(O-IPr)2(thd)2 (all from Advanced Technology Materials, Inc.). The 

spin-coated films were baked on hot plate with 350 °C for 10 min and finally crystallized films 

were formed under 750 °C for 1 h. 

PLD provides excellent target stoichiometry transfer of complex oxide ceramics to high-quality 

thin films. During this process, the focused output (laser fluence of 1.9 J/cm2) of a short-pulse 

(full width at half maximum [FWHM] of ~20 ns) excimer laser was used to flash-evaporate a 

target. The rapid heating and evaporation of the solid target by the laser resulted in the formation 

of an energetic plasma plume, which was transported through an ambient gas (200 mTorr O2) to 

the surface of a 5-cm away heated substrate (770 °C) (1, 3, 4).

The temperature behavior of thin-film varactor was done in Delta 9028 temperature-controlled 

chamber. It has electric heating and nitrogen cooling provided by a liquid nitrogen tank. The 

sample and its fixture were installed within this chamber. For each temperature change, the 

sample sits in the chamber at least 45 min before measurement. There is a “warming” period in 

the data collection process, during which one applies bias voltages of 0, 50, 100, 50, and 0 V,

correspondingly. After the bias voltage returns to 0 V, the system is ready for measurement. 

3. Results and Discussion 

3.1 Resonant Frequency as a Function of Test Time 

After each bias voltage switch, I found that the resonant frequency of the varactor was 

continuously changing. As an example, resonant frequency as a function of test time for a PLD 

varactor is shown in figure 1. The test was done at a temperature of 0 °C and a bias voltage of 

0 V. An exponential decay behavior is observed. Figure 2 shows calculated capacitance as a 

function of test time. 
3

0 200 400 600 800 1000 1200

2126

2128

2130

2132

2134

2136

2138

2140

2142

2144

2146 Fig. 1 Frequency as a Function of Time

Data: Data9_B

Model: ExpDec2 

 

Chi^2 = 0.0976

R^2 = 0.9957

 

y0 2128.66954 ±0.21644

A1 8.91471 ±0.44021

t1 8.56808 ±1.01393

A2 6.36259 ±0.31665

t2 203.76521 ±29.35305

Frequency (MHz)

Time (sec)

Figure 1. PLD varactor’s frequency as a function of time. 

1.22

1.23

1.24

1.25

1.26

1.27

1.28

1.29

0 200 400 600 800 1000 1200 1400 Cp (pF)

Time (sec)

Figure 2. Capacitance as a function of test time. 

The time behavior of resonance frequency at 50 V (switched from 0 V) and 100 V (switched 

from 50 V) are different. The results are shown in figures 3 and 4, respectively. An exponential 

increase for both measurements is observed. 
4

0 100 200 300 400 500

2210

2212

2214

2216

2218

2220

2222

2224 Fig. 3 Frequency vs. Time (0 C, 50V)

Data: Data1_B

Model: ExpDec2 

 

Chi^2 = 0.00216

R^2 = 0.99989

 

y0 2222.44566 ±0.11907

A1 -6.88194 ±0.13579

t1 13.3594 ±0.50237

A2 -5.56013 ±0.08132

t2 189.09373 ±12.68359

Frequency (MHz)

Time (seconds)

Figure 3. Frequency as a function of time (0 °C, 50 V). 

0 100 200 300 400 500

2310.0

2310.5

2311.0

2311.5

2312.0

2312.5

2313.0

2313.5

2314.0

2314.5 Fig.4 Frequency vs. Time (0 C, 100 V)

Data: Data4_B

Model: ExpDec2 

 

Chi^2 = 0.00214

R^2 = 0.99761

 

y0 2314.58577 ±0.17979

A1 -2.52092 ±0.12364

t1 280.79956 ±47.29236

A2 -2.11079 ±2.67642

t2 9.54924 ±6.41098

Frequency (MHz)

Time (seconds)

Figure 4. Frequency as a function of time (0 °C, 100 V). 

Figures 1, 3, and 4 indicate that if one takes the data at different times after the bias voltage 

switch, the data would be different. For example, there was an 8–25% tuning difference between 

one set of data taken immediately after it was switched to the desired bias voltage versus one that 

was taken after waiting 5 min. 

It was found that these plots could be fitted by a second-order exponential decay function: 

Frequency = y0 + A1 exp (–t/t1) + A2 exp (–t/t2), (1) 
5

where t is the time, and t1 and t2 are time constants. Fitted parameters are also shown in 

figures 1, 3, and 4, respectively—the fitting is very good. All three R2

’s are better than 0.998. 

The second-order exponential fitting suggests that there exist two processes. Both have 

exponential decay (or increase) behaviors. The time constants of these two processes are around 

10 and 220 s. 

If the BST thin-film varactor sits in the environmental chamber for a long time, the temperature 

(a measure of random translation motion) of the crystal lattice, sample, and chamber all become 

equal. As observed, when applying a bias voltage, a lattice shift or displacement of the BST 

crystal structure would occur. The crystal structure would go back to normal (no distortion) once 

the bias voltage was removed (from 50 to 0 V). The shifted or displaced structure would exhibit 

a higher energy than the normal structure. The extra energy would then transfer to the lattice 

vibration energy. Thus, the vibration temperature would be higher than the random translational 

temperature. Thus, the first process necessary is the relaxation of the sample from vibration to 

translation. This relaxation process causes the local temperature increase (and higher frequency 

reading). 

The second process is the energy transfer from local higher temperature to the environmental

temperature (the cooling down process by nitrogen). It is suggested that the shorter time t1

constant belongs to local heating or cooling by environment and the longer time constant t2 fits 

into relaxation from vibration to random translation movements. 

I determined that one should wait 40 to 45 s before taking the measurement data. The reasons 

are (1) waiting 40 to 45 s reduces the error ranges of capacitance and tuning to less than 3% and 

6%, respectively, which is acceptable; and (2) 40 to 45 s is more than four times the shorter time 

constant (10), which corresponds to a 98% completion of the relaxation process, in other words, 

the error will be less than 2%. 

3.2 Temperature Behavior of MOD Thin-film Varactor 

The temperature behaviors of MOD thin films are shown in figure 5. The MOD samples have 

composition of 60.01 with tungsten doping on an MgO substrate. Figure 5a shows the tuning 

behavior of the MOD thin-film varactor. Tuning decreases as temperature increases. Figure 5b

shows capacitance variation as a function of temperature. Note that there is a significant change 

in capacitance at a 0-V bias; however, the capacitance changes at a 50- and 100-V bias are 

minor. The temperature coefficient of MOD varactor is –1230 ppm at a 50-V bias and 154 ppm 

at a 100-V bias. Figure 5c shows the Q variation. 
6

Figure 5. MOD samples: (a) percentage of tuning of capacitance, 

(b) capacitance, and (c) Q of the varactor as a function of 

temperature at 2 GHz and DC bias voltages up to 100 V. 

3.3 Temperature Behavior of PLD Thin-film Varactor 

The temperature behaviors of PLD thin films are shown in figure 6. The PLD samples have 

composition of 60.01 with tungsten doping on an MgO substrate. Figure 6a shows the tuning 

behavior of the PLD thin-film varactor. Tuning decreases as temperature increases. Figure 6b 

shows capacitance variation as a function of temperature. The temperature behaviors are similar 

(c)

(a)

(b)
7

to those of the MOD thin films. The temperature coefficient of PLD varactor is 2600 ppm at a 

50-V bias and 604 ppm at a 100-V bias. Figure 6c shows the Q variation. 

Figure 6. PLD samples: (a) percentage of tuning of capacitance, 

(b) capacitance, and (c) Q of the varactor as a function of 

temperature at 2 GHz and DC bias voltages up to 100 V. 

(c)

(a)

(b)
8

4. Conclusions 

Exponential decay or increase behavior is observed by the resonant frequency of a varactor as a 

function of test time. I determined that one should wait 40 to 45 s before taking the measurement 

data. 

The following are the results of temperature behaviors of thin film varactors: 

• The temperature coefficient of MOD thin film varactor is –1230 ppm at a 50-V bias and 

154 ppm at a 100-V bias. 

• The temperature coefficient of PLD varactor is 2600 ppm at a 50-V bias and 604 ppm at a 

100-V bias. 
9

5. References 

1. Kim, W. J.; Chang, W.; Qadri, S. B.; Pond, J. M.; Kirchoefer, S. W.; Chrisey, D. B.; 

Horwitz, J. S. Microwave Properties of Tetragonally Distorted Ba0.5Sr0.5TiO3 Thin Films. 

Appl. Phys. Lett. 2000, 76, 1185–1187. 

2. Slowak, R. et al. Graded Thin Film Composite Synthesized for the Superior Microwave 

Properties with Improved Temperature Stability. Integrated Ferroelectrics 1999, 24, 169–

179. 

3. Chang W.; Horwitz, J. S.; Carter, A. C.; Pond, J. M.; Kirchoefer, S. W.; Gilmore, C. M.; 

Chrisey, D. B. The Effect of Annealing on the Microwave Properties of Ba0.5Sr0.5TiO3 Thin 

Films. Appl. Phys. Lett. 1999, 74, 1033–1035.

4. Chang W.; Gilmore, C. M.; Kim, W. J.; Pond, J. M.; Kirchoefer, S. W.; Qadri, S. B.; Chrisey, 

D. B.; Horwitz, J. S. Influence of Strain on Microwave Dielectric Properties of (Ba,Sr)TiO3

Thin Films. J. of Appl. Phys. 2000, 87, 3044–3049. 

5. Kozyrev A. B. Microwave Measurements of the Nonlinear Properties of Ferroelectric Film 

Planar Varactors. Electrotechnical University of Saint Petersburg, Saint Petersburg, Russia; 

1999. 

6. Fu, R. Unique Combination of Pulsed Laser Deposition (PLD) and Metal Organic 

Deposition (MOD) Technology to Produce High Tunability, Long-lifetime Barium Strontium 

Titanate (BST) Thin Films for Microwave Applications; ARL-TR-5671; U.S. Army Research 

Laboratory: Adelphi, MD, 2011.
10

List of Symbols, Abbreviations, and Acronyms 

ARL U.S. Army Research Laboratory 

BST barium strontium titanate 

Cp capacitance 

MgO magnesium oxide 

MOD metal organic deposition 

PLD pulsed laser deposition 

Pt platinum 

Q quality factor 

VTO voltage tunable oscillator 
11

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