Tunnelling current in Schottky diodes containing InAs quantum dots

Superlattices and Microstructures 50 (2011) 164–172

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Tunnelling current in Schottky diodes containing InAs quantum dots N. Hamdaoui a,⇑, R. Ajjel a, B. Salem b, M. Gendry c a

Laboratoire d’énergétique et de transfert thermique et massique (LETTM), Ecole supérieur des Sciences et de la Technologie Hammam Sousse, Université de Sousse, Sousse 4011, Tunisia Laboratoire des Technologies de la Microélectronique (LTM), UMR CNRS, CEA-Grenoble, 17 Rue des Martyrs, F-38054 Grenoble, France c Institut des Nanotechnologies de Lyon, INL-CNRS, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69134 Ecully, France b

a r t i c l e

i n f o

Article history: Received 22 November 2010 Received in revised form 3 April 2011 Accepted 18 May 2011 Available online 30 May 2011 Keywords: Current transport mechanism Schottky diode InAs quantum dots

a b s t r a c t Current transport mechanism in Schottky diode containing InAs quantum dots (QDs) is investigated using temperature-varying current–voltage characteristics. We found that the tunnelling emission has obvious effects on the I–V characteristics. The I–V–T measurements revealed clear effects of QDs on the overall current flow. Field emission (FE, pure tunnelling effect) was observed at low temperature and low voltages bias region. The zero-bias barrier height decreases and the ideality factor increases with decreasing temperature, and the ideality factor was found to follow the T0-effect. When the reverse bias is varied, the ideality factors of Schottky barriers exhibit oscillations due to the tunnelling of electrons through discrete levels in quantum dots. The traps distributed within InAlAs layer can also act as a transition step for reverse bias defect-assisted tunnelling current which can phenomenologically explain the decrease of the effective barrier height with measurement temperature. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The use of quantum dots (QDs) in semiconductor devices such as laser, photodetector, and future dynamic memories [1], requires a detailed understanding of the physical properties determining the exchange of charge carriers between the QDs and the host material. Moreover, the efficiency of luminescence from QD laser structures depends on the capture of carriers within the QDs and the ⇑ Corresponding author. E-mail address: [email protected] (N. Hamdaoui). 0749-6036/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.spmi.2011.05.013

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minimisation of non-radiative recombination channels within the QD and the surrounding matrix via defects at heterointerfaces [2]. A good understanding of the electron transport in the dark is, however, crucial for the quantum dot infrared photodetector (QDIP) design and optimisation, because it contributes to the detector noise and determines the operating temperature [3–5]. Memory devices based on QDs, which allow storage of information by means of single charge carriers, are an ambitious challenge so far. Of central importance for such applications is the localisation energy, which limits the retention and, therefore, the storage time, due to thermal and tunnel escape [6]. Much work has been done on the transport and optical properties of InAs/GaAs and InGaAs/GaAs QDs structures [7–10]. Some studies have been devoted to the optical and electrical properties of the InAs/InAlAs nanostructures grown on InP [11–15]. However, the carrier transport mechanism in such QDs is less understood. The aim of this work is to analyse in detail the electron emission process in the dark for InAs/ InAlAs grown on an InP substrate. This sample was studied by a combination of photoluminescence (PL), and I–V–T experiments. By correlating the analyses of these measurements, we were striving to more clearly describe the tunnelling effects in a quantum dot structure. Field emission dominated the current mechanism at low temperature, especially at low voltage. Owing to the presence of deep level impurities in the InAlAs material barrier, the decrease of the effective barrier height with measurement temperature can be described by a two-step defect-assisted tunnelling process. 2. Results and discussions The investigated sample was grown on an n+ doped InP (0 0 1) substrate by solid source molecular beam epitaxy (SSMBE). It consists of a 0.4-lm thick In 0.52Al0.48 As (InAlAs) buffer followed by 0.9 nm of InAs. InAlAs buffer surface preparation and InAs growth conditions are adjusted to favour dot-like rather than wire-like islands [16]. Since the sample is designed for electrical characterisation, the buffer was Si doped at 3  1016 cm3. The InAs thickness of three monolayers (ML) is just above the 2D/ 3D growth mode transition detected by reflexion high electron energy diffraction at 2.5 ML. Then, a 10-nm thick non-intentionally doped (n.i.d.) InAlAs layer, a 170-nm thick Si-doped InAlAs layer at 3  1016 cm3 and a 20-nm thick n.i.d. InAlAs layer were grown. Schottky contacts were fabricated by evaporating 20 nm of gold (Au) onto InAlAs through a contact mask. The back ohmic contact was formed with Au–Ge–Ni alloy on the n+ substrate. Details of the growth process and atomic force microscopy (AFM) images of the InAs QDs are published elsewhere [16,17]. We note that the

5

(c)

PL Intensity (arb.units)

4

(d) 3

(b)

2

(a) 1

(e)

0 0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Energy (eV) Fig. 1. Photoluminescence spectrum of the investigated sample at 10 K.

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T =10 K PL Intensity (arb. units)

4

150 mW

3

37 mW 7.5 mW

2

1.5 mW 1

0 0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

Energy (eV) Fig. 2. Photoluminescence spectra at 10 K of the InAs QDs as a function of the excitation power.

histogram of the dot heights obtained with AFM measurements reveals a broad height distribution centred at 1.5 nm with a full half maximum (FWHM) of 0.6 nm (see the inset of Fig. 1 in [17]). 2.1. PL The investigated sample was first characterised by PL measurement. Fig. 1 displays the PL spectrum measured at T = 10 K and under an excitation power density of about 150 mW/cm2. A structured PL band is observed between 0.9 and 1.4 eV. The spectrum can be fitted with five Gaussian peaks labelled (a)–(e) with FWHM = 50 meV. These peaks were confirmed to be the ground states and excited states luminescence by the use of PL measurement as a function of the excitation power. The data are presented in Fig. 2, which shows the spectra recorded at 10 K with varied excitation density between 1.5 and 150 mW/cm2. As the excitation power increases, we observe a relative saturation of (a) and (b) peaks while the intensity of peaks (c) and (d) increase notably, and new peak (e)

log (Dark current) (A)

1E-3

78 K 88 K 100 K 140 K 160 K 200 K 220 K 240 K 260 K 300 K

1E-4

1E-5

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Voltage (V) Fig. 3. Forward I–V–T characteristics.

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appear. This behaviour can be the signature for excited levels (c)–(e) related to the ground states (a) and (b) of InAs QDs with heights varying by monolayer fluctuations. Indeed, in such QD systems the excited states are expected to be filled at higher excitation powers when the fundamental ones are saturated. Weber et al. showed that the structure of the PL is mainly related to various dot heights corresponding to an integer number of monolayer and also to excited states [17]. 2.2. I–V–T 2.2.1. Forward I–V properties Fig. 3 shows a typical plot of forward I–V behaviour as a function of measurement temperature. For V in the 0.2–0.6 V range, the low temperature I–V curves become closer to each other, which indicates some contribution of tunnel current. Thermionic emission also began to dominate at higher temperature with medium bias. Under fairly high temperature, the spreading resistance effect prevailed. The data may be fitted to the general equation including thermionic emission (TE) and thermionic field emission (TFE) as below [18]:

    V qV 1  exp  E0 kT   qE00 E0  E00 coth kT sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qh Nd E00 ¼ 2 m er e0

I ¼ IS exp

ð1Þ ð2Þ ð3Þ

Here m is the effective mass of electrons in the semiconductor, er e0 is its permittivity, N d is the donor concentration. The pre-exponential factor IS is a complicated function of temperature, barrier height and other semiconductor parameters. At low temperature, the case of field emission (FE, pure tunnelling effect) corresponds to a straight line of:

    qV vs V ln I 1  exp  kT with no sensitivity to temperature. At relatively higher temperatures, the TFE becomes prevailing and there usually is a smooth transition from FE, through TFE, to pure TE. For our cases, we noticed that typically TE dominated at room temperature. The ratio E00 =kB T can be used as a measure of the relative importance of TE and tunnelling. For example, FE tunnelling can be expected for E00 =kB T  1, TFE tunnelling process takes control for E00 =kB T  1, and TE transport will dominate for E00 =kB T  1. At low temperature, and especially in the low bias regions, however, I–V–T indicated insensitivity to the temperature. The plots of:

    qV vs V ln I 1  exp  kT show little deviation from linear variation as in Fig. 4. The plots in Fig. 4 start to deviate slightly from the straight line at high-T which is typical TFE dominant current transport characteristic. We calculated the zero-bias space charge (SCR) width. The calculated SCR width is W = 0.43 lm. Comparing this with the thickness of the InAlAs cap of 0.4 lm, it is clear that the electrons tunnelling from the QD will contribute to the current flow. The current magnitude of the QD sample is around two orders of magnitude higher at low bias region than the same sample without quantum dots [19]. We attribute this fact to the effect of tunnelling injection in QD structure and to indicate that the QDs are the cause of the tunnelling current. The high density of electrons in QDs has a strong probability of tunnelling penetration. The tunnelling injected electrons from the QD contributed to the whole electrons flow which then led to a higher current. These all imply that FE played a key role in low-T and low-V regions.

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ln(I/(1-e(-qV/kT))

-11

-12

78 K 100K 140K

-13

-14

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Voltage (V) Fig. 4. Plots of ln [I/1  e(qV/kT)] vs V.

The following analysis was restricted to temperature above 160 K where linear regions in the log I– V characteristics can be clearly seen (Fig. 3). A gradual shift of the I–V characteristics towards a higher voltage is observed with decreasing temperature, which is in agreement with the thermionic emission diffusion (TED) equation at forward bias ðV P 3kT=qÞ:

 I ¼ IS exp

qV nkT

 ð4Þ

where V is the applied voltage, q is the electronic charge, kT is the thermal energy and IS is the saturation current defined by

qu  IS ¼ AA T 2 exp  b0 kT

ð5Þ

and where A is the diode area, A⁄⁄ is the Richardson constant (10.1 A K2 cm2) and ub0 is the zero-bias Schottky barrier height. The ideality factor n defined as

n¼

  q d ln V kT dI

ð6Þ

is introduced to describe the deviation of the experimental I–V data from the ideal TED theory. Using Eq. (6), the ideality factor n of the diode at different temperatures was evaluated from the slopes of the linear region of the semi-log I–V curve. Using Eq. (5), the zero-bias barrier height ub0 was determined from the saturation current IS , obtained from the intercept of the extrapolated linear region with the current axis at V = 0. The values of ub0 and n are plotted as a function of temperature in Fig. 5. The barrier height decreases whereas the ideality factor increases with decreasing temperature. For an ideal Schottky diode, the barrier height should increase as the temperature is decreased, following the band gap variation with temperature [20]. The temperature dependence of the ideality factor can reveal the conduction mechanism of a Schottky diode. In a Schottky diode following a non-perfect thermionic-emission model, the ideality factor increase as the temperature decreases, a phenomenon generally known as the T0-effect [21,22]. In its general meaning, it can be connected either with the lateral inhomogeneity of the barrier heights or with the domination of the thermionic field emission (TFE) at low temperatures [23,24].

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1.7

0.8

1.6

Ideality Factor

1.4

0.6

1.3 0.5

1.2 1.1

Barrier Height (eV)

0.7

1.5

0.4

1.0 140

160

180

200

220

240

260

280

300

0.3 320

Temperature (K) Fig. 5. Variation of the ideality factor and zero-bias barrier height with temperature.

2.2.2. Reverse bias I–V properties The reverse bias current shows a sharp increase with increasing reverse bias as presented in Fig. 6, this behaviour is similar to the tunnelling current observed in heavily doped GaAs diodes [25]. The deviation of n from unity in Schottky diodes is mainly associated with the occurrence of the tunnelling current component [20]. We should note here that this deviation of n from unity can be also attributed to the influence of the recombination current by the presence of defect that acts as carrier-recombination centres. Therefore, an analysis of n provides information on emission processes in structures with QDs [26]. The ideality factor in the case of a reverse bias is determined by the equation [27]:

    e I expðeV=kTÞ dV d ln kT expðeV=kTÞ  1

ð7Þ

1E-4

Dark Current (A)

nðVÞ ¼

78 K 88 K 100 K 140 K 160 K 200 K 220 K 240 K 260 K 300 K

1E-5

1E-6

-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

Voltage (V) Fig. 6. Reverse I–V–T characteristics.

-1.0

-0.5

0.0

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As the reverse bias increases, the ideality factor grows, and peaks appear in curves n (V) as shown in Fig. 7, which points to a resonance character of the tunnelling current. Resonance tunnelling processes are a characteristic feature of charge carrier transport in double-barrier structures of reduced dimensionality and are due to the quantization of the energy spectrum of electrons or holes in the region confined between the barriers. As the reverse bias increases, the energy levels of electrons in the QD layer, in turn, reach a resonance with the quasi-Fermi level in the metal. In this case, the probability of tunnelling through the Schottky barrier and, hence, the ideality factor must increase, which is actually observed in our experiments. The period of oscillations in curves n (V) is reproduced sufficiently well at various temperatures. The average period is DV  350 mV. Assuming that the QD layer is introduced in the middle of the diode base and neglecting the band bending due to the potential of the ionised impurity in the diode base, one can estimate the energy gap between the electron levels in InAs nanoclusters at DE  e D2V  175 meV. This value is in a reasonable agreement with the value of the energy gap between s and d levels of electrons determined by DLTS measurements [13]. We have studied the temperature and field dependence of the reverse current (Fig. 8). We found two regimes; in the high temperature region, the activation energy ranges from 0.52 to 0.78 eV when the bias is changed from 3.5 to 0.5 V. In the low temperature region, the activation energy is in the range 0.19–0.37 eV. Several escape routes for the dark current electrons are possible since the structure includes three electron levels in the QDs and large number of defects in the InAlAs layers. Consequently, the activation energies deduced from the dark current measurement will be an effective value including all these escape route [28]. The decrease of the barrier height with the increase of the reverse bias is caused by thermionic-field emission which becomes dominant over the thermionic emission. For the temperature dependence of the reverse current activation energy, a continuous smooth lowering of the barrier height with measurement temperature may be interpreted as a consequence of direct tunnelling. Indeed, as the measurement temperature decreases, the direct tunnelling current, which is temperature independent, becomes dominants over thermionic current. The activation energy of the total current therefore decreases with measurement temperature. In our case, the clear appearance of two slopes probably infers to another mechanism. As a result of the large number of defects found in InAlAs layers, a two-step defect-assisted tunnelling process can phenomenologically well describe this behaviour. Similar behaviour has been experimentally observed in InAs/ GaAs [29,30] and InGaAs/GaAs [31] quantum dot infrared photodetectors. Defect-induced sequential resonant tunnelling due to significant level of growth defects in Si-doped QD sample is shown in their quantum dots systems.

2.5

Ideality Factor

300 K 200 K 100 K 2.0

1.5

1.0

1.0

1.5

2.0

2.5

3.0

3.5

Voltage (V) Fig. 7. Dependence of the ideality factor on the reverse bias.

4.0

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0.520.78 eV

-8.0

Log(dark current) (A)

-8.5

0.190.37 eV

-9.0

3.5V 3V 2.5V 2V

-9.5 -10.0

1.5V

-10.5

1V

-11.0 -11.5

0.5V 2

4

6

8

10

12

14

1000/T (K-1) Fig. 8. Temperature dependence of reverse current.

3. Conclusions In conclusion, we have studied InAs/InAlAs/InP QDs by use PL, and I–V–T measurements. We found that tunnelling emission from the QDs has a significant influence on the current–voltage spectra. Relative higher current was observed due to the higher tunnelling probability of electrons from the QD. The phenomenon of oscillations of the ideality factor in the case of a reverse bias in Schottky diodes with QDs may serve as a basis for the development of a new method of electron spectroscopy of energy levels in systems with reduced dimensionality. The presence of tunnelling sets limits on the magnitude of the electric field allowable in the junction region above which the dark current becomes prohibitively large. In our device, we find that tunnelling is the dominant source of leakage over a wide range of applied voltages. The limitation set on electric field has a significant impact on the capabilities and design consideration for several device applications. References [1] A. Marent, T. Nowozin, J. Gelze, F. Luckert, D. Bimberg, Appl. Phys. Lett. 95 (2009) 242114. [2] D.G. Deppe, H. Huang, in: H. Morkoç (Ed.), Advanced Semiconductor and Organic Nano-Techniques, Part I, Academic Press, San Diego, 2003, p. 367. [3] S. Chakrabarti, A.D. Stiff Roberts, P. Bhattacharya, S. Gunapala, S. Bandra, S.B. Rafol, S.W. Kennerly, IEEE Photon. Technol. Lett. 16 (2004) 1361. [4] W. Zang, H. Lim, M. Taguchi, S. Tsao, B. Movaghar, M. Razeghi, Appl. Phys. Lett. 86 (2005) 191103. [5] J. Szafraniec, S. Tsao, W. Zhang, H. Lim, M. Taguchi, A.A. Quivy, B. Movaghar, M. Razeghi, Appl. Phys. Lett. 88 (2006) 121102. [6] C.M.A. Kapteyn et al, Appl. Phys. Lett. 76 (2000) 1573. [7] M. Geller, E. Stock, C. Kapteyn, R.L. Sellin, D. Bimberg, Phys. Rev. B 73 (2006) 205331. [8] S.W. Lin et al, J. Appl. Phys. 100 (2006) 043703. [9] A. Schramm, S. Schulz, C. Heyn, W. Hansen, Phys. Rev. B 77 (2008) 153308. [10] O. Engstrom, M. Kaniewska, Nanoscale Res. Lett. 3 (2008) 179. [11] R. Ajjel, M. Baira, M. Gassoumi, H. Maaref, B. Salem, G. Brémond, M. Gendry, Semicond. Sci. Technol. 21 (2006) 311. [12] R. Ajjel, M. Baira, H. Maaref, B. Salem, G. Bremond, M. Gendry, Semicond. Sci. Technol. 20 (2005) 514. [13] N. Hamdaoui, R. Ajjel, H. Maaref, B. Salem, G. Bremond, M. Gendry, Semicond. Sci. Technol. 25 (2010) 065011. [14] W. Lei, Y.H. Chen, Y.L. Wang, X.Q. Huang, C. Zhao, J.Q. Liu, B. Xu, P. Jin, Y.P. Zeng, Z.G. Wang, J. Cryst. Growth 286 (2006) 23. [15] M. Hjiri, F. Hassen, H. Maaref, B. Salem, G. Bremond, O. Marty, J. Brault, M. Gendry, Physica E 17 (2003) 180. [16] J. Brault, M. Gendry, G. Grenet, G. Hollinger, J. Olivares, B. Salem, T. Benyattou, G. Brémond, J. Appl. Phys. 92 (2002) 506. [17] A. Weber, O. Gauthier-lLafaye, F.H. Julien, J. Brault, M. Gendry, Y. Désieres, T. Benyattou, Appl. Phys. Lett. 74 (1999) 413. [18] F.A. Padovani, K. Stratton, Solid State Electron. 9 (1966) 695. [19] J.K. Luo, H. Thomas, S.A. Clark, R.H. Williams, J. Appl. Phys. 74 (1993) 11. [20] S.M. Sze, Physics of Semiconductor Devices, second ed., Wiley, New York, 1981.

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