Barrier height enhancement and temperature dependence of the electrical characteristics of Al Schottky contacts on p-GaAs with organic Rhodamine B interfacial layer

Superlattices and Microstructures 52 (2012) 470–483

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Superlattices and Microstructures

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . co m / l o c a t e / s u p e r l a t t i c e s

Barrier height enhancement and temperature dependenceof the electrical characteristics of Al Schottky contacts onp-GaAs with organic Rhodamine B interfacial layer

Murat Soylu a,⇑, Fahrettin Yakuphanoglu b

a Department of Physics, Faculty of Sciences and Arts, Bingol University, Bingol, Turkeyb Department of Physics, Faculty of Sciences and Arts, Firat University, Elazig, Turkey

a r t i c l e i n f o

Article history:Received 20 January 2012Received in revised form 10 April 2012Accepted 28 May 2012Available online 5 June 2012

Keywords:Inorganic semiconductorOrganic compoundElectrical parametersTemperature effect

0749-6036/$ - see front matter � 2012 Elsevier Lthttp://dx.doi.org/10.1016/j.spmi.2012.05.022

⇑ Corresponding author. Tel.: +90 4262132550; fE-mail address: [email protected] (M. Soyl

a b s t r a c t

In this work, two types of Schottky barrier diodes (SBDs) with andwithout Rhodamine B interfacial layer, were fabricated and mea-sured at room temperature in order to investigate the effects ofthe Rhodamine B interfacial layer on the main electrical parame-ters. It was seen that the barrier height (BH) value of 0.78 eV calcu-lated for the Al/Rhodamine B/p-GaAs device was higher than thevalue of 0.63 eV of the conventional Al/p-GaAs Schottky diodes. Ithas been observed that the Rhodamine B film increases the effec-tive BH by influencing the space charge region of GaAs. The maindiode parameters such as the ideality factor (n) and zero-bias BHof SBD with Rhodamine B interfacial layer were found to bestrongly temperature dependent and while the BH decreases, theideality factor increases with decreasing temperature. It has beenconcluded that the temperature dependent characteristic parame-ters for Al/Rhodamine B/p-GaAs SBDs can be successfully explainedon the basis of thermionic emission (TE) mechanism with Gaussiandistribution of the barrier heights.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The Schottky diode is a fundamental component in solid state electronics and has received exten-sive attention over the decades since the pioneering work of Mott and Schottky in 1938. The intrinsicpotential barrier or Schottky barrier in this type of device constitutes a rectifying contact and its

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M. Soylu, F. Yakuphanoglu / Superlattices and Microstructures 52 (2012) 470–483 471

properties underpin various areas of application [1]. For that reason, there is a vast number of reportsof experimental studies of metal/semiconductor systems [2–5]. The performance and reliability of aSchottky contact is influenced by the interface quality between the deposited metal and thesemiconductor surface. It is well known that there are considerable interest in the electrical andphotoelectrical properties of polymeric and nonpolymeric organic compounds [6–8]. Due to the sta-bility of nonpolymeric organic compounds, they have been employed particularly in electronic devices[9–11]. Campbell et al. [12] have used organic thin film to introduce a controlled dipole layer at thesemiconductor/organic interface and thus change the effective Schottky barrier height. They reportedthat the effective Schottky barrier could be either increased or decreased by using organic thin layeron inorganic semiconductor.

Gallium Arsenide (GaAs) has intrinsic electrical properties superior to silicon, such as a direct en-ergy gap, higher electron mobility, a high breakdown voltage, chemical inertness, mechanical stability,and lower power dissipation [13,14]. GaAs Schottky diode is an attractive research area for GaAs basedmetal semiconductor field effect transistors (MESFETs) for high speed circuits and optoelectronic de-vices. Many experimental ways to enhance the GaAs Schottky barrier height have been tried in recentyears to reduce the reverse bias leakage current and increase cut-in voltage. One of the ways is to placea wide band gap interlayer such as Si–Ge–B or AlAs between the metal gate and the GaAs semiconduc-tor. To obtain the interlayer, it needs an extra molecular beam epitaxy (MBE) deposition process[15,16].

In the present study, we will fabricate Rhodamine B based organic-on-inorganic Schottky device bynon-vacuum spin coating method and reference diode. By evaluating the electrical properties of thedevices, we will investigate the effects of Rhodamine B interlayer on conventional metal/semiconduc-tor. The aim is to study the suitability and possibility of organic-on-inorganic semiconductor contactbarrier diodes for use in barrier height modification of p-GaAs metal–semiconductor (MS) diodes. Inaddition, we will investigate the effect of temperature on the Al/Rhodamine B/p-GaAs device.

2. Experimental details

SBDs were fabricated on p-type GaAs (Zn-doped) substrate with (100) orientation and a dopingagent of 1.7 � 1016 cm�3. The substrate was sequentially cleaned with trichloroethylene, acetoneand methanol and then rinsed in deionized water. The native oxide on the surface was etched in se-quence with acid solutions (H2SO4:H2O2:H2O = 3:1:1) for 60 s, and (HCI:H2O = 1:1) for another 60 s.After a rinse in deionized water a blow-dry with nitrogen, the ohmic contact of low resistance onthe back side of the sample was formed by evaporating of Ag at a vacuum of 10�6 mbar, followedby annealing at 370 �C for 5 min in nitrogen atmosphere. Then, the above procedures were also usedto clean the front surface before forming organic layer. After dividing to two pieces of substrate havingohmic contacts, Rhodamine B solution of 1 � 10�6 M in methanol was spin coated to the polished sur-face one of the substrates with the 1000 rpm (246 nm) spin speed for 1 min. The Rhodamine B is axanthene-type molecule. Since Rhodamine B has a conjugation in its structure, it is a good conductivecompound. Finally, circular dots with a diameter of approximately 2 mm of Al were then evaporatedthrough a molybdenum mask at a pressure of 2 � 10�6 mbar to form the Schottky barriers. Thus, ref-erence Al/p-GaAs and Al/Rhodamine B/p-GaAs Schottky barrier diode having interfacial layer were ob-tained. The current–voltage (I–V) and capacitance–voltage (C–V) measurements of the devices weremade using a 4200 SCS semiconductor characterization system. The structural properties of the filmwere investigated by Park System XE-100E atomic force microscopy (AFM). The surface morphologyand roughness of GaAs substrate were investigated using AFM. Fig. 1a and b shows three-dimensional(3D) AFM images of the GaAs substrate surface and the Rhodamine B film obtained using a Park Sys-tem XEI analysis software programming. The scan size of the image is 10 � 10 and 1 � 1 lm2, respec-tively. The surface roughness values of the GaAs and Rhodamine B film were found as �11–17 nm. Itmeans that the substrate surface is reasonably smooth. High flatness of the substrate surface causeshigh quality metal/semiconductor interface. A schematic cross-section of the Al/Rhodamine B/p typeGaAs structure and the molecular structure of the Rhodamine B are shown in Fig. 2.

Fig. 1. 3D AFM images of the native GaAs substrate surface and the Rhodamine B film.

Fig. 2. A schematic cross-section of the Al/Rhodamine B/p-GaAs structure.

472 M. Soylu, F. Yakuphanoglu / Superlattices and Microstructures 52 (2012) 470–483

3. Results and discussion

3.1. Analysis of Al/Rhodamine B/p-GaAs junction diode at room temperature

Fig. 3 shows energy level diagram of a metal–organic–semiconductor device with interfacial layerand interface states. In Fig. 3, Vp is the potential difference between the Fermi level and the top of thevalance band in the neutral region of p-GaAs, ws is the surface potential as a function of the appliedforward bias, Uorg is the work function of the organic material, w is the width of the depletion region,v is the electron affinity of the inorganic semiconductor. Vi is the potential drops across the interfaciallayer, U0 is the neutral level of the interface states measured from the top of the valance band.

Fig. 3. The energy level diagram of Al/Rhodamine B/p-GaAs junction.

-2 -1 0 1 2V (V)

1E-009

1E-008

1E-007

1E-006

1E-005

0.0001

0.001

0.01

Cur

rent

(A

)

(1) Al/p-GaAs(2) Al/Rhodamine B/p-GaAs

(1)

(2)

(1)

(2)

T=300 K

Fig. 4. The forward and reverse bias semi-logarithmic I–V characteristics of Al/p-GaAs and Al/Rhodamine B/p-GaAs diodes indark and at room temperature.


Fig. 4 shows forward bias semi-logarithmic I–V characteristics of the Al/p-GaAs and Al/RhodamineB/p-GaAs Schottky diodes at room temperature and in the dark, and not in vacuum. It is shown thatthe saturation current in these semi-logarithmic plots decreases by organic compound Rhodamine B.As clearly seen from Fig. 4, the Al/Rhodamine B/p-GaAs inorganic/organic semiconductor (IO) hetero-junction structure exhibits a good rectifying behavior. The weak voltage dependence of the reverse-bias current and the exponential increase of the forward-bias current are characteristic propertiesof rectifying interfaces. The current curve in forward bias quickly becomes dominated by series resis-tance from contact wires or bulk resistance of the organic material and inorganic semiconductor, giv-ing rise to the curvature at high current in the semi-log I–V plot. This indicates that the leakage currentof the Al/Rhodamine B/p-GaAs IO Schottky device decreases in significant rate in respect to that of MSreference Schottky diode.


The current (I) through a SBD at a forward bias (V), according to thermionic emission (TE) theory, isgiven by Rhoderick and Williams [17]

I ¼ I0 expqðV � IRsÞ

nkT

� �ð1Þ

where, I0 is the reverse saturation given by

I0 ¼ AA�T2 exp � qUb

kT

� �: ð2Þ

From Eq. (1), the ideality factor n can be written as

n ¼ 1a¼ q

kTdV

dInðIÞ

� �: ð3Þ

Eq. (1) shows that the logarithmic plot of I/[1 � exp(�qV/kT)] vs. V (Fig. 5) is linear and I0 is ob-tained from the y-axis intercept at zero voltage. Where q is the electron charge, V is the definite for-ward biasing voltage, A is the area of the contact, A⁄ is the effective Richardson constant, k is theBoltzmann’s constant, T is the absolute temperature, Ub is the barrier height and n is the ideality fac-tor. The values of Ub and n were determined from the intercept and the slopes of the forward bias ln(I)vs. voltage (V) plot, respectively. The barrier height and ideality factor values of 0.696, 0.783 eV and1.521, 1.593, respectively, for this reference Al/p-GaAs and Al/Rhodamine B/p-GaAs Schottky diodeshave been obtained from the forward bias I–V characteristics. It has been observed that ideality factorremains almost constant while barrier height of Al/Rhodamine B/p-GaAs structure increases about0.087 eV with respect to Al/p-GaAs at room temperature. The values of Ub are the effective valuesand do not take into account the image-force lowering. It should be known that Ub is the contact po-tential barrier that exists at the interface between the organic and inorganic layers, i.e. at the Rhoda-mine B/p-GaAs interface. The obtained barrier height of the Al/Rhodamine B/p-GaAs device is higherthan that of Al/p-GaAs Schottky diodes [18,19]. This suggests that the organic Rhodamine B layer mod-ifies the electrical properties of the p-GaAs Schottky diode by influencing the space charge region ofthe inorganic substrate [20]. The studies in literature have shown that effective Schottky barrier couldbe either increased or decreased by using organic thin layer on inorganic Si semiconductor [21–26]. Itis evaluated that the interface properties of the diode are passivated by using organic layer surface toreduce the interaction between metal and inorganic. Indeed, modification of semiconductor surfacesby molecules can lead to the changes in the electronic properties of the metal–semiconductor devices.

V (V)

1E-008

1E-007

1E-006

1E-005

0.0001

I/(1-

exp(

-qV

/kT

)) (A

)

Al/Rhodamine B/p-GaAsAl/p-GaAs

0.1 0.2 0.3

Fig. 5. Plots of I/[1�exp(�qV/kT)] vs. V of the Al/p-GaAs and Al/Rhodamine B/p-GaAs diodes.


It has been observed that the chalcogen passivation reduces the surface band bending on n-GaAs, andon the other hand, the band bending on the surfaces of p-GaAs increases. The change in barrier heightcan qualitatively be explained by an interface dipole, induced by the chalcogen passivation [27].

There are several effects, which cause deviations of the ideal behavior and must be taken into ac-count. These effects can be interface states and series resistance and these are important parametersfor the diode performance. These parameters cause a downward curvature in the I–V characteristics athigher forward bias values. In such a case, Cheung’s method can be used to obtain the barrier height,ideality factor and series resistance. Cheung’s functions are expressed by [28]

dVdðln IÞ ¼

nkTqþ IRs ð4Þ

HðIÞ ¼ V � nkTq

� �ln

I

AA�T2

� �ð5Þ

HðIÞ ¼ nUb0 þ IRs ð6Þ

Eq. (4) should give a straight line for the data in the downward curvature region of the forward biasI–V characteristics. Thus, the slope and y-axis intercept of the plot of dV/d(ln I) vs. I will give n and Rs

for Al/Rhodamine B/p-GaAs structure at room temperature (Fig. 6). Using the n values determinedfrom Eq. (3) and data of the downward curvature region in Eq. (4), a plot of H(I) vs. I according toEq. (5) will also give a straight line with y-axis intercept equal to nUb0 with the BH value (Fig. 6). Then,by using Eqs. (3)–(5), the barrier height, the ideality factor and Rs were obtained as 0.673 eV, 2.01 and2.34 kX, respectively. The value of series resistance indicates that the series resistance is a current-limiting factor for this structure. The series resistance influences the current mostly at the high voltageregion, whereas at the very low region of about V 6 3kT/q [49], the line is non-linear. Only the regionabove V P 3kT/q and below the important effect of the series resistance, is assumed to behave accord-ing to the TE model, and thus it is anticipated that in this region the slope might represent an idealdiode behavior. Thus, I–V measurements at low tensions enable the main diode parameters, especiallyn to be obtained more reliably. Thus, the deviation from ideal behavior is surrounded by both the highideality factor and the limited linearity region of the I–V curves.

C–V curves of Al/Rhodamine B/p-GaAs device were plotted at different frequencies (Fig. 7). The va-lue of the capacitance is increasing in forward bias till a point where it reaches a maximum value. Thehigher values of capacitance at low frequencies are attributed to the excess capacitance resulting fromthe interface state density which is in equilibrium with the semiconductor that can follow the alter-nating current (a.c.) signal. Whereas, at higher frequencies, the capacitance is not dispersive and thus,

0 0.1 0.2 0.3 0.4Current (A)

0.2

0.4

0.6

0.8

1

dV/d

In(I)

1.2

1.6

2

H(I)

(A)

H(I)-IdV/dln(I)-I

Rhodamine B/p-GaAs

Fig. 6. Experimental dV/dln(I) vs. I and H(I) vs. I plots of Al/Rhodamine B/p-GaAs diode.

V (V)

0

2E-010

4E-010

6E-010

8E-010

1E-009

C (F

)

Al/Rhodamine B/p-GaAs ↓10 kHz

1 Mhz

↓50 kHz

100 kHz

- 10 kHz- 50 kHz- 100 kHz- 200 kHz- 300 kHz- 400 kHz- 500 kHz- 600 kHz- 700 kHz- 800 kHz - 900 kHz- 1 Mhz

-2 -1 0 1 2

Fig. 7. Capacitance C vs. V plots of Al/Rhodamine B/p-GaAs diode at various frequencies and at room temperature.


the interface states in equilibrium with the semiconductor do not contribute to the capacitance, be-cause the charges at the interface states cannot follow the fast a.c. signal. Therefore, the total capac-itance is equal to the sum of space-charge capacitance and interface capacitance at low frequencies,while at higher frequencies the total capacitance arises mostly from the space-charge capacitance.Measurement of the depletion region capacitance under forward bias is difficult because the diodeis conducting and the capacitance is shunted by a large conductance. However, the capacitance canbe easily measured as a function of the reverse bias. The capacitance of a rectifying contact can alsovary due to defects in semiconductor and the presence of deep lying impurities in the depletion region.The defects act either as traps or as recombination centers in the semiconductors, depending on thecapture cross section of the electrons and holes. Traps reduce the semiconductor free carrier densitywhereas recombination centers introduce generation–recombination currents in rectifying devices.

As seen in Fig. 8, Rs vs. V curves of Al/Rhodamine B/p-GaAs device were plotted at different frequen-cies. As can be seen in Fig. 8, the Rs values were quite sensitive to applied bias voltage and the series

-2 -1 0 1 2V (V)

0

4000

8000

Rs

(ohm

)

Al/Rhodamine B/p-GaAs

100 kHz

1 Mhz

200 kHz300 kHz

Δf =100 kHz

Fig. 8. The series resistance profile of Al/Rhodamine B/p-GaAs diode at various frequencies and at room temperature.


resistance gives a peak about 0.20 V depending on the frequency and disappears at sufficiently highfrequencies. Also, the peak magnitude increases with the decreasing frequency and shifts toward po-sitive biasing voltage. The voltage and frequency dependencies of Rs are attributed to the particulardistribution density of interface states and interfacial insulator layer. The change in Rs becomes ratherimportant in the depletion and accumulation regions. The voltage dependence of Rs is the result ofvoltage-dependent charges such as interface trapped charge.

The interface states and interfacial layer between the metal/semiconductor structures play animportant role in the determination of the characteristic parameters of the devices. The density ofthe interface states is determined by using equations given in Ref. [29]. The density of the interfacestates (Nss) of the Al/p-GaAs Schottky diode (�1012 eV�1 cm�2 at 300 K) is lower than that of Al/Rho-damine B/p-GaAs Schottky diode (�1013 eV�1 cm�2 at 300 K). The interface state density for Al/p-GaAsdiode corresponds to that of states present in the interface between Al and p-GaAs, whereas, Nss valueof Al/Rhodamine B/p-GaAs Schottky diode corresponds to interface between organic layer and p-GaAs.

The current transport across a Schottky junction is interest of material science and device physics.Generally, the SBD parameters are determined over a wide range of temperatures in order to under-stand the nature of the barrier and the conduction mechanism. In order to get further insights into themechanism of current transport through the Al/Rhodamine B/p-GaAs contact, the I–V measurementswere performed at different temperatures in the range of 297–423 K. Fig. 9 shows the semi-logarith-mic plot of the I–V curves of the Al/Rhodamine B/p-GaAs diode at various temperatures.

Figs. 10 and 11 show the variation of the ideality factor and barrier height as a function of temper-ature, respectively. The barrier height decreases and the ideality factor increases significantly withdecreasing temperature as can be seen in these figures. That is, more electrons have sufficient energyto overcome the higher barrier when temperature increases and then, BH increases with temperatureand bias voltage. Furthermore, a linear correlation between the experimental zero-bias BH Ub0 and theideality factor n has been obtained utilizing Tung’s pinch-off model [30] by Schmitsdorf et al. [31].Fig. 12 shows an example of this plot for Al/Rhodamine-B/p-GaAs SBD. A linear relationship betweenthe Ub0 and n values in Fig. 12 is an indication of the barrier irregularity and can be explained bylateral inhomogeneities of the BHs [31]. A homogeneous BH of approximately 1.107 eV was obtainedfrom the extrapolation of the least-square linear fitting to data to n = 1 (Fig. 12).

The Richardson plot is drawn to obtain the barrier height in another way. Eq. (2) can be rewrittenas

V (V)

1E-009

1E-008

1E-007

1E-006

1E-005

0.0001

0.001

I (A

)


423 K413 K393 K373 K353 K333 K313 K297 K

↓

↓

↓

-2 -1 0 1 2

Fig. 9. Semi-logarithmic plots of both forward and reverse current vs. applied voltage at different temperatures.

280 320 360 400 440T (K)

1

1.2

1.4

1.6

Idea

lity

fact

or, n

ExperimentTheory (Eq. 17)

Al/Rhodamine B/p-GaAs device

Fig. 10. Temperature dependence of the ideality factor for the Al/Rhodamine B/p-GaAs Schottky barrier diode in thetemperature range of 297–423 K. The continuous curve shows the estimated value of the ideality factor using Eq. (17) withq2 = �0.858 and q3 = �0.064 V.

280 320 360 400 440T (K)

0.7

0.8

0.9

1

1.1

1.2

Bar

rier

hei

ght (

eV)

0.6

0.8

1

1.2

Φf b

(eV

)

ExperimentTheory (Eq. 16)

Φ Ib0(I-V)

= (-7.362x10-4) T + 1.368Φfb

Fig. 11. Temperature dependence of the zero-bias BH UIb and flat band BH Uf

b for the Al/Rhodamine B/p-GaAs Schottky barrierdiode in the temperature range of 297–423 K. The closed circles represent the estimated value of UJ

b using Eq. (16) with rs0

0.216 eV, respectively.


InJ0

T2

� �¼ InA� � qUj

b0

kTð7Þ

Fig. 13 shows the In(J0/T2) vs. 1000/T plot. The experimental data show a bowing at low temperatureand yielding an activation energy of 0.273 eV. Similarly, a Richardson constant value of3.33 A K�2 cm�2 for Rhodamine B/p-GaAs SBD was obtained from the intercept at the ordinate. Thisvalue is 22.34 times lower than the theoretical value of 74.4 A K�2 cm�2 for holes in p-GaAs. The devi-ation in the Richardson plots may be due to the lateral inhomogeneity of barrier heights and potentialfluctuations at the interface that consist of low and high barrier areas [8,32–35]. It can be explained byassuming the effects of the image-force, the effect of tunneling current through the potential barrier,

0.8 0.9 1 1.1Ideality factor, n

1

1.2

1.4

1.6

Bar

rier

hei

ght

(eV

)

Φeff = -2.117 n + 3.224

Φhom = 1.107 eV


Fig. 12. Plot of the zero-bias BH UIb vs. ideality factor (n) at the investigated temperature range.

1000/T (K-1)

-17.2

-16.8

-16.4

-16

-15.6

In(J

0/T

2 )

2 2.4 2.8 3.21000/T (K-1)

-56

-52

-48

-44

-40

-36

-32

ln(J

0/T

2)-

q2 σ2 /[

2(k T

)2 ]


Φb=0.273 eV,

A*=62.01 AK-2cm-2

↑→

←↓

2.4 2.8 3.2 3.6

Fig. 13. Richardson plot of the ln(J0/T2) vs. 1/T and modified Richardson plot, ½lnðJ0=T2Þ � ðq2r2s0=2k2T2Þ vs: 1000=T�, and its

linear fit for the Al/Rhodamine B/p-GaAs Schottky diode according to Gaussian distribution of the barrier heights.


the effect of recombination in the space charge region appearing at low voltage and the variation ofthe charge distribution near the interface [35].

As seen in Fig. 11 the reduction in BH is 278 meV in the investigated temperature range. In order topoint out the factors influencing the barrier height lowering and the increase in ideality factor withdecreasing measurement temperature, the effect of image force lowering can be considered at firstsight. The barrier lowering due to the image force effect is given by Rhoderick and Williams [17]

DUimf ¼q3Na

8p2e3s

� �Ub0 � V � n� kT

q

� �� 1=4

ð8Þ


where n = (kT/q)[In(Nv/Na)] is the energy difference between the fermi level and the top of the valenceband, V is the applied bias voltage, es is the permittivity of GaAs, Nv(=1.45 � 1015 T3/2 cm�3) is thedensity of the states at the valence band and Na(=2.5 � 1016 cm�3) is the ionized acceptor density ofp-GaAs. The values of DUimf found by using Eq. (8) are 26 meV at 297 K and 28 meV at 423 K. Thesevalues of DUimf point out that the influence of the barrier lowering due to the image force on Ub0 isnearly constant in the investigated temperature region and the image force effect alone cannotaccount for the decreasing of the barrier height with decreasing temperature. The increase in the ide-ality factor with decreasing measurement temperature might be due to image force lowering [17,36]

1nimf¼ 1� 1

4q3Nd

8p2e3s

� �14

Ub0 � V � n� kTq

� ��34

ð9Þ

The ideality factors found by using Eq. (9) are 1.008 and 1.006 at 297 and 423 K, respectively. Thesevalues also show that the observed variation in the ideality factor cannot be explained by the imageforce lowering. Thus, image force lowering effect is also insufficient and so fails to explain the ob-served changes in BH and n.

If the current transport is controlled by thermionic field emission (TFE) theory, the relationship be-tween the current and voltage can be expressed by Rhoderick and Williams [17]

J ¼ J0 expVE0

� �ð10Þ

E0 ¼ E00 cothqE00

kT

� �ð11Þ

E00 ¼qh2

Na

m�es

� �1=2

ð12Þ

where E00 is the characteristics energy, which is related to the transmission probability,h = 6.626 � 10�34 j.s, m⁄ = 0.45 (m⁄ is the effective mass of holes), es = 13.1e0 for GaAs [37] and yieldvalues of E00 = 1.17 � 10�3 and 3.7 � 10�3 eV (at 297 K and 423 K, respectively). According to the the-ory, field emission (FE) becomes important when E00iikT/q, whereas TFE dominates when E00 � kT/qand TE is crucial if E00hhkT/q. The value of kT at 297 K is equal to 2.56 � 10�2. Since E00 is lower thankT for the lowest temperature in this work. Therefore, neither FE nor TFE contributes significantly tothe current. The ideality factor n is related to E00 according to Rhoderick and Williams [17]

ntun ¼qE00

kTcoth

qE00

kT

� �¼ E0

kTð13Þ

The ideality factor for tunneling according to Eq. (13) is obtained as 1.007 at 297 K. This value is toolow to explain our measured value (n = 1.593) at 297 K. As a result, the possibility of the FE and TFEcan ruled out. As was anticipated by Horvath [38] it can be represented the theoretical temperaturedependence of ideality factor for the case when the current through Schottky junction is dominatedby the TFE. The experimental temperature dependence values of ideality factor are not in agreementwith the curve obtained with the values of E00 in the temperature range of 297–423 K. This case is con-nected with local enhancement of electrical field which can also yield a local reduction of the BH [38].

The term ‘‘flat band’’ derives from the zero curvature of the potential across the Schottky barrier.The influence of lateral inhomogeneities on the evolution of current–voltage characteristics is re-moved by using the flat-band barrier height Uf

b instead of the zero-bias barrier height (Ub0). Theflat-band barrier height is given by [33,39]

Ufb ¼ nUb � ðn� 1Þ kT

q

� �ln

Nv

Nd

� �ð14Þ

where Nv is the effective density of states in the valance band. A plot of the flat-band barrier height Ufb

as a function of the temperature is displayed in Fig. 11. Ufb is always larger than zero-bias barrier

height Ub0 and it increases with decreasing temperature in the 297–423 K range. A linear fit is usedto fit the points in the range of 297–423 K in order to determine the y-axis intercept which gives


the value of barrier height at absolute UfbðT ¼ 0Þ. Furthermore, the temperature dependence of the

flat-band barrier height can be expressed as [33]

Fig. 14accordi

UfbðTÞ ¼ Uf

bðT ¼ 0Þ þ aT ð15Þ

where UfbðT ¼ 0Þ is the flat-band barrier height extrapolated to zero temperature and a is the temper-

ature coefficient of UfbðT ¼ 0Þ. In Fig. 11 the fitting of the Uf

bðTÞ data to Eq. (15) yieldsa = �7.62x10�4 eV K�1 in the 297–423 K range. The value of a is in very close agreement with the va-lue of�4.7 � 10�4 eV K�1 for Cu/n-GaAs [40],�2.3 � 10�4 eV K�1 for Pt/n-GaAs [41],�7 � 10�4 eV K�1

for Al/n-GaAs [42].The decrease in the barrier height with a decrease in temperature can be explained by the lateral

distribution of BH if the barrier height has a Gaussian distribution of the barrier height values over theSchottky contact area with the mean barrier height ( �Uj

b0) and standard deviation (rs0). The standarddeviation is a measure of the barrier homogeneity. The Gaussian distribution of the BHs yields the fol-lowing expression for the BH [43–47]

Uap ¼ �Ujb0 �

qr2s0

2kTð16Þ

1=napðTÞ � 1 ¼ �q1ðTÞ ¼ �q2 þqq3

2kTð17Þ

where, Uap and nap are apparent barrier height and apparent ideality factor, respectively, q1, q2 and q3

are the voltage coefficients that may define the voltage deformation of the barrier height distribution,Since the Uap depends on the distribution parameters �Uj

b0 and rs0 and temperature, the decrease of theapparent zero-bias BH is affected by the existence of the interface inhomogeneities and this effect be-comes more significant at low temperatures. On the other hand, the abnormal increase in nap comesup mainly due to the bias coefficients (q2 and q3) of the mean barrier height and the standard devi-ation. The plot of Uap vs. q/2kT (Fig. 14) should be a straight line yielding �Uj

b0 and rs0 from the inter-cept and slope, respectively. The values of 1.705 and 0.216 eV for �Uj

b0 and rs0, respectively wereobtained from the least-square linear fitting of the data. Furthermore, as can be seen from Fig. 11,the experimental results of Uap (denoted by open squares) fit very well with Eq. (16) (denoted byclosed circles), with the same parameters. Also, the correction to the experimental data has been madeusing Eq. (16). The standard deviation is a measure of the barrier homogeneity. The lower value of rs0

corresponds to a more homogeneous barrier height. It is seen that the value of rs0 = 0.216 eV is small

12 14 16 18 20(2kT)-1 (eV)-1

0.7

0.8

0.9

1

Φap

p (e

V)

-0.4

-0.2

0

(n-1

-1)

Φapp=[-4.696x10-2(2kT)-1+1.704]

(n-1-1)=[-6.431x10-2(2kT)-1+0.858]


. Zero-bias BH UJb and the [(1/n) � 1] vs. 1/2kT plots and their linear fits for the Al/Rhodamine B/p-GaAs Schottky diode

ng to Gaussian distribution of the barrier heights.


compared to the mean value of �Ujb0 and it indicates larger inhomogeneities at the interface of our Al/

Rhodamine B/p-GaAs Schottky structure. But, it is found that is not small compared to the value ofrs0 = 0.105 eV for CrNiCo/n-MBE GaAs Schottky contact [48]. According to this result, it can be say thatinterfacial TF (Rhodamine B) thickness, inhomogeneities in the composition of the TF layer and non-uniformity of interfacial TF layer charges can cause barrier inhomogeneities.

Fig. 14 also shows the [(1/n) � 1] vs. 1/2kT plot. According to Eq. (17), this plot should be a straightline that gives the voltage coefficients q2 and q3 from the intercept and slope, respectively. The valuesof q2 = �0.858 and q3 = �0.064 eV were obtained from this plot. Furthermore, the experimental re-sults of n in Fig. 10 can be seen to fit very well with Eq. (17), denoted by solid line, with the sameparameters. The linear behavior of [(1/n) � 1] vs. 1/2kT plot confirms that the ideality factor does in-deed denote the voltage deformation of the Gaussian distribution of the BH. It is clear from the Eq. (17)that when q3 becomes negative, it will be responsible for the increase in nap with a decrease in tem-perature. As q2 becomes also negative, we can conclude that the barrier height and its standard devi-ation are decreased as bias increases. These results reveal that a bias voltage obviously homogenizesthe BH fluctuation, i.e., the higher the bias, the narrower the BH distribution, which can be explainedthat image forces shift the effective barrier maximum deeper into the semiconductor when the biasvoltage increases.

As indicated above, the conventional activation energy ln(J0/T2) vs. 1/T plot has shown non-linear-ity at low temperatures. To explain these discrepancies, according to the Gaussian distribution of theBH, it can be rewritten

InJ0

T2

� �� q2r2

s0

2k2T2

� �¼ InA� � qUj

b0

kT: ð18Þ

Hence, modified Richardson plot [ln(J0/T2) � (q2rs02/2k2T2) vs. 1000/T] according to Eq. (18) should

also be a straight line with the slope and the intercept at the ordinate directly yielding the zero-biasmean barrier height �Uj

b0 and A⁄, respectively. As can be seen from Fig. 13 (denoted by open triangles),the modified Richardson plot has a quite good linearity over the whole temperature range correspond-ing to a single activation energy around �Uj

b0. By the least-square linear fitting of the data,Uj

b0 ¼ 1:691 eV and A⁄ = 62.01 A K�2 cm�2 are obtained. Meanwhile, this value of Ujb0 ¼ 1:691 eV is

approximately the same as the value of Ujb0 ¼ 1:705 eV from the plot of Uap vs. 1/2kT given in

Fig. 14, while modified Richardson constant A⁄ = 62.01 A K�2 cm�2 is in close agreement with the the-oretical value of A⁄ = 74.4 A K�2 cm�2. These results show that the temperature dependent I–V charac-teristics of Al/Rhodamine B/p-GaAs Schottky structure obey the Gaussian distribution of BHs as in thecase of CrNiCo/n-MBE GaAs [48], Ti/n-GaAs [49], despite the presence of Rhodamine B at the Al/p-GaAs interface. So, we can speculate that the lateral SB inhomogeneities are not only peculiar to theAl contacts on GaAs, but also other contact metals.

4. Conclusions

This work reported here proposes that modification of the interfacial potential barrier for metal/GaAs diodes has been achieved using a thin interlayer of the Rhodamine B. The Rhodamine B moleculeshould be considered, among other candidates, as a potential semiconducting non-polymer thin filmfor the novel MIS devices. The higher barrier height value of the device is ascribed to the physicalbarrier properties of Rhodamine B layer plus probable native oxide layer between the metal andthe inorganic semiconductor. The temperature-dependent I–V characteristics of the Al/RhodamineB/p-GaAs diode have been measured over the temperature range 297–423 K. It has been seen anincrease in ideality factor and decrease in apparent barrier height and significant deviations fromlinearity in the Richardson plots with a decrease in temperature for diode. The significant decreaseof zero-bias BH and the increase of the ideality factor decreasing temperatures cannot be caused bythe processes such as tunneling, generation–recombination currents, image-force lowering, etc. Thecase has been attributed to barrier inhomogeneities at the metal semiconductor interface. The mostlikely inhomogeneities are connected with Al–Rhodamine B–p type GaAs reaction phases and interfa-cial crystallography. Abnormal behavior in the temperature dependent ideality factor and the barrier


height in the Al/Rhodamine B/p-GaAs SBDs have been successfully cleared up accounting the TE theorywith a Gaussian distribution of the BH having spatial variations. In conclusion, it can be speculatedfrom the diode parameters obtained by I–V techniques that the spatial inhomogeneities of the SBHsare an important factor and could not be ignored in the analysis of temperature dependent electricalcharacterization of the Schottky structures.

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Barrier height enhancement and temperature dependence of the electrical characteristics of Al Schottky contacts on p-GaAs with organic Rhodamine B interfacial layer