Effect of Layers Thickness and Temperature on Electronic Transport of Nanostructures Infrared Detectors

Effect of Layers Thickness and Temperature on Electronic Transport of Nanostructures Infrared Detectors

Nassima Benchtaber, Abdelhakim Nafidi, Samir Melkoud, Meriem Benaadad, Driss Barkissy

Laboratory of Condensed Matter Physics and Nanomaterials for Renewable Energy Department of Physics Faculty of Sciences Ibn Zohr University

Agadir, Morocco

Abstract We report here the effect of layers thickness and temperature on electronic transport of nanostructure by calculation of band structure of two superlattices SL1 InAs(d1)/Gasb(d2) of type II and SL2 HgTe/CdTe of type III for infrared detection application. These studies were done using the envelope function formalism. We calculated the energy of carriers as a function of layers thickness, the ration d1/d2 and the temperature. The calculated density of states and Fermi level energy shows that temperature generated transitions from quasi bidimensional (Q2D) to three dimensional (3D) in the two SL. The later occurred near 20 K in the p type SL1 and near 84 K in SL2 with p type to n type conductivity transition. We found

In order to determine the effect of layers thickness and temperature on electronic band structure of these superlattices we have calculated the band structure, band gap energy , the cutoff wavelength and the density of state and we found that SL1 and SL2 are mid infrared detector materials.

1. THEORY OF BAND STRUCTURE

   The dispersion relation for electrons, light and heavy holes bands is written as [9,10]:

   cos [k (d d )] cos(k d ) cos(k d ) 1 [( 1 )

   that these SL are mid infrared and terahertz detectors. The electronic transport parameters calculated here are necessary

   for the design of infrared photo-detectors.

   z 1 2

   k 2 1

   1 1 2 2 2

   p (r 2)]sin(k d ) sin(k d )

   KeywordsSuperlattices nanostructures; mid infrared detector; density of state; semiconductors; band structures.

   4k1k 2 r

   1 1 2 2

   (1)

   1. INTRODUCTION

      Infrared detection can be used in a wide range of areas, including remote sensing, astronomy, medicine, surveillance and defense … Many of these applications, require high sensitivity on a specific band of wavelengths, use infrared systems based on semiconductors [1].

      The requirements of the next generation of infrared systems, which are mainly high performance, large bay sizes and high temperature operation, have led to intensive research in industry and academia [2]. This, coupled with the

      With kz and kp(kx,ky) the wave vector in the growth

      direction and in-plane of the superlattice and 1, 2 refet to the layers of the SL.

      The two samples studied here are SL1 InAs(d1=21 Ã…)/GaSb(d2=24 Ã…) and SL2 HgTe (d1= 45 Ã…)/ CdTe(d2=48 Ã…) with periods d= d1+d2= 45 Ã… and 93 Ã… and the ratio d1/d2= 0,875 and 0,9375, respectively. So the period of SL2 is the double of that of SL1 with the same ratio d1/d2 near 0.9.

2. RESULTS AND DISSCUSSION

   20 40 60 80

   continued development of new growth technologies, has

   Ekz=0

   0 k /d

   encouraged researchers to study alternative materials suitable for these infrared systems [3].

   The infrared detectors based materials are III-V and II-VI semiconductors, The objective of this paper is to study the two type of theses materials superlattice type II (SL1) wich was Proposed by Mailhiot and Smith [4] in 1987, InAs / GaSb is a stress layer system with Type II band alignment, in which

   600

   E (meV)

   E (meV)

   400

   200

   HHkz=/d

   1

   E

   E

   kz=/d 1

   k =

   E2 z

   SL2

   T=21,88 K

   h

   h

   kz=0 1

   600

   400

   200

   the InAs conduction band is located under the GaSb valence band. As a result, the super-network may have a smaller band gap than any of its components [5]. Electrons and holes tend to reside in different places; electron layers in InAs,and holes in GaSb. And the superlattice type III (SL2) The peculiarity of

   1

   0

   -200

   HH1z

   Eg=201,43 meV

   kz=/d 1

   h

   h

   0

   -200

   this type of superlattice is related to the inversion of light particle bands in HgTe compared to that of CdTe [6]. The energy difference of the peaks of the heavy-hole bands, estimated to be zero [7] but found to be as low as 40meV by magneto-optical measurements [8].

   20 40 60 80

   d2 (Ã…)

   Figure 1: Calculated bands energy of electrons (Ei), heavy-hole (HHi), and light-hole (hi) subbands calculated at 21.88 K, in the first Brillouin zone as a function of the barrier thickness d2 of (CdTe).

   (b)

   (b)

   Ekz= 1	E =316 meV g	Ekp=
   		1
   		SL1
   		T = 5K
   HHkz= d 1 hkz= 1	HHkz= d 2	hkp= 1	HHkp= 1
   		HHkp= 2

   Ekz= 1	E =316 meV g	Ekp=
   		1
   		SL1
   		T = 5K
   HHkz= d 1 hkz= 1	HHkz= d 2	hkp= 1	HHkp= 1
   		HHkp= 2

   1000

   6

   m)

   m)

   750

   SL2 SL1

   SL2 SL1

   E (meV)

   E (meV)

   500 5

   EF

   250

   4

   0

   -0,06

   -k-0(,Ã…04-1)

   -0,02 0,00 0,02

   k0,(0Ã…4-1)

   0,0

   0 100 200 300

   T(K)

   p

   p

   z

   z

   Figure 2. Band structures of the SL1 along the kz and kp directions at 5 K

   This study is done using the envelope function formalism and a various parameters like valence band offset, Kane matrix elements and effective masses of the layers.

   Figure 1 show the band structure of the SL2. We plotted

   Figure 3. (a) Band gap energy of the SL1 and SL2 as function of temperature (b) the cutoff wavelength of the two samples SL1 and SL2 as function of temperature.

   In figure 3 (b) we have calculated the cutoff wavelength for the SL1 and SL2, using the following formulate [11-12]:

   the energy as function of layer thickness d2 of the barrier

   (nm)

   1240

   (2)

   CdTe. We found that if d2 increases the width of the bands and the band gap deceases. Our theoretical band gap energy is Eg=E1-HH1= 201.43 meV at 21.88 K.

   Figure 2 shows the calculated band structure of SL1 along the wave vectors kz and kp directions at the T=5K. This SL1 is semiconductor type p with a positive band gap energy Eg=316 meV. Along kp the first conduction sub-band E1 and first light hole suband p increases with kp. whereas HH1 and HH2 decreases. Along kz, the observed week widths of subands (7.5 meV for E1, 6.4 meV for HH1 and 8 meV for p) indicated a week coupling between the HgTe quantum wells. So, the parallel electronic transport governs in the plane of this superlattice.

   (a)

   (a)

   The band gap energy Eg as function of the temperature for SL1 and SL2 is shown in Figure. 3 (a). When the temperaure increases the energy band gap decreases for SL1 and increases for SL2.

   Eg(meV)

   Eg(meV)

   300

   SL1

   SL2

   SL1

   SL2

   250

   E

   E

   g

   g

   c (eV )

   We found that when the temperature increases the cut off wavelength of SL1 decreases and that of the SL2 increases.

   In order to test the effect of layer thickness on the band structure we have calculated and plotted the energy band gap as a function of layer thickness at three temperature (5,77 and 300K) for SL1 Figure 4 (a) and (21.9,150 and 300k) for SL2 respectively Figure 4 (b).

   We found that for SL1 at fixed temperature and if the thickness d2 increases Eg decreases goes to zero and became negative accusing transition conductivity from semiconductor to semi metal. When the temperature increases, at given d2 the gap decreases and the critical thickness of the transition goes to higher d2c.

   (a)

   Eg(meV)

   Eg(meV)

   400 SL1

   T=5 K T=300 K

   T= 77 K

   T=5 K T=300 K

   T= 77 K

   200

   0

   200

   0 100 200 300

   T(K)

   0 20 40 60 d2

   80 100 120

   Eg(meV)

   Eg(meV)

   400

   200

   T=21,99 K T=150 K

   T= 300 K

   T=21,99 K T=150 K

   T= 300 K

   SL2

   (b)

   with our calculated band gap Eg(300 K) = 245.15 meV.

   In figure 5 (a) the cut off wavelength c decreases when the temperature increases and for a given temperature it decreases when d1/d2 increases.

   In figure 5 (b) the cut off wavelength c decreases when the temperature increases and for a given temperature it decreases when d1/d2 increases. In the investigated temperature range of 4.2 K to 300 K, 5060 nm c 6300 nm, situates this sample in the mid infrared region.

   The effective masse is obtained by the expression below [13]:

   i j

   i j

   1 1 2E

   0

   0 20 40 60 d2 80 100 120

   ( m* )ij

   kij 2 k k

   , (3)

   Fig.4. (a) Eg as a function of d2 at three temperatures SL1 (T=5, 77 and 300K) (b) Eg as a function of d2 at three temperatures SL2 (T=21.99, 150 and 300K)

   The SL2 is semiconductor with gap energy positive. At fixed temperature when d2 increases the energy band gap decreases.

   Our calculated band gap is 316 meV in agreement with

   The second derivation of Figure 2 along kp allow us the determination of the effective masse at the Fermi wave vector kF.

   For the determination of the dimensionality of the carriers charges in the SL we calculated the superlattice ith mini-band, with an energy width E=Eimax- Eimin, the density of states (DOS) can be written as [14,15]:

   0 for Ei E Ei

   the measured 300 meV for SL1 in [16]. In the SL2 the

   min max

   observed Eg agreement.

   = 244.1 meV of f H.S. Jung et al. [17] is in good

   i DOS

   1. m*

      2 2

      kz (E) otherwise

      (4)

      d1= 0,87 d2

      d1= 2 d2

      d1= 3 d2

      d1= 4 d2

      d1= 0,87 d2

      d1= 2 d2

      d1= 3 d2

      d1= 4 d2

      SL1

      SL1

      The summation of Eq.(4) gives the total density of states

      300 as:

      DOS DOS

      DOS DOS

      (E) i

      (E)

      (5)

      c m)

      c m)

      200

      100

      Figure 6 shows the calculated density of states versus energy for E1, HH1 and p mini-bands at 21.9 K for the SL2. At 21.88K, the Fermi level energy is on HH1 so the conductivity is quasi-bidimensional.

      0

      0 100 200 300

      T(K)

      3×1019

      (eV-1 cm-3)

      (eV-1 cm-3)

      2×1019

      2mm** 22 d

      E

      E

      SL2

      F T=21.88K

      h

      h

      1

      d1= 0,93 d2

      d1= 2 d2

      d1= 3 d2

      d1= 4 d2

      d1= 0,93 d2

      d1= 2 d2

      d1= 3 d2

      d1= 4 d2

      SL2

      SL2

      300

      c m)

      c m)

      200

      DOS

      DOS

      1×1019

      E

      E

      1

      1

      1

      HH

      100

      0

      0 100 200 300

      T(K)

      Figure 5: (a) The cut-off wavelength c as function of the temperature for various d1/d2 in the SL1. (b) The cut-off wavelength c as function of the temperature for various d1/d2 in the SL2

      0

      -20 0 20 220 240 260 280 300

      E (meV)

      Figure 6: Density of State of the investigated superlattice SL2 at T=21.88K.

      800

      (a)

      E1

      Figure 7 (b) shows that the position of the Fermi level energy EF, indicate p type and quasi bidimentional (Q2D) holes gas at 21.9 K. A similar Figure, at 300 K, showed n type and 3D electrons gas in the investigated superlattice.

      600

      E

      E

      E (meV)

      E (meV)

      2D F

      400

      200

      SL1

      E

      E

      3D F

      HH1

      p

      At Tinv= 84 K, the conductivity of this semiconductor sample change from p-type at low temperatures to n-type at high temperatures. Using the calculated effective mass and the concentrations of electrons from [16], the energy of Fermi level EF is constant for T < Tinv and increases linearly at high temperatures. These means a transition of the carriers charges from quasi bidimensional to three-dimensional.

      Our calculated gaps are in agreement with photoluminescence and transport measurements of H. J. Haugan et al. [16] and with H.S. Jung et al. [17].

      T

      T

      0

      c

      300

      E ) (meV)

      E ) (meV)

      200

      EF (Q2D)

      EF (Q2D)

      100

      100 200 300

      1

      1

      T (K)

      EF (3D)

      E

      EF (3D)

      E

      SL2

      (b)

      SL2

      (b)

      Eg/2

      Eg/2

      300

      200

      100

3. CONCLUSION

We investigate the effects of layers thickness and temperature on the electronic band structures and transport parameters in two nanostructure superlattice type II and type

III. We have calculated the energy band gap; the effective masses the density of state and the Fermi level. We deduce the variation of the band gap and the cut-off wavelength as a function of the temperature and d1/d2. We calculated the density of states and the Fermi level as a function of temperature. We found that temperature generated transitions from quasi bidimensional holes (Q2D) to three dimensional electrons (3D) for SL1and also p type to n type conductivity respectively for SL2.

HH1

p

HH2

HH3

HH1

p

HH2

HH3

In the investigated temperature range, the cut-off wavelength were (3.92 m<c<5.92 m) and (5.06 m c

0 0 6.30 m) in the SL1

and SL2, respectively. These SL are

0 100

T(K)

200 300

medium infrared detectors (MWIR).

REFERENCES

Figure 7: (a) The subbands energy at as a function of temperature and Fermi level energy transition from 2D to 3D for SL1 and (b) from 2D to 3D for SL2.

We calculated the Fermi levels using the following formulate in the SL1

E

E

2 (ki )2

1. A.Rogalski, Infrared Detectors, Gordon and Breach Science Publishers, Amsterdam, 2000.

2. P.R. Norton, Infrared detectors in the next millennium, Proc.SPIE 3698 (1999) 652665.

3. E. D. Palik, ed., Handbook of Optical Constants of Solids (Elsevier, 1998).

4. D. L. Smith, C. Mailhiot, J. Phys. Rev. Lett. 58 (1987) 1264-1267.

5. R. Dingle, A. C. Gossard, et W. Wiegmann, Direct Observation of Superlattice Formation in a SemiconductorHeterostructure, Phys.

   EF HH1

   F

   2m

   2m

   * HH1

   (6)

   Rev. Lett. 34, 1327 – 1330 (1975).

6. G. Bastard, Theoretical investigations of superlattice band structure

   with k2 D (2p)1/ 2 and k3D (32 p)1/ 3

   F F

   and in the SL2:

   in the envelope function approximation, Phys.Rev. B 25, 7584

   7597 (1982).

7. J. T. Cheung, G. Nizawa, J. Vac. Sci. Technol. A4(4), 101 (1986). [8] G Bastard, Phys., Rev. B 25 (1982) 75847597.

E

E

(7)

HH1 EF F EHH1

2 k2

2m

2m

*

*

F2D with k

HH1

2 k2

2m

2m

*

*

F3D with k

E1

F2D

F3D

(2p)1/ 2 for p type

(32 n)1/3 for n type

1. G. Bastard, Teoretical investigations of superlattice band structure in the envelope-function approximation , Phys. Rev. B 25:7584, 1982.

2. D. Barkissy, A. Nafidi, A. Boutramine, H. Charifi, A. Elanique, M. Massaq, Electronic properties of GaAs/AlAs Nanostructure superlattice, J. Low Temp. Phys. 182-185, 2016.

3. Boutramine, A. Nafidi, D. Barkissy, M. Bellioua, A. Khalal, Correlation between electronic bands structure and

   As chown in figure 7 (a) the sub-bands energy at as a

   function of temperature and Fermi level transition from 2D to 3D of the sample SL1. We found that kF2D and kF3D are bi- dimensional and tridimensional Fermi wave vector respectively. When the temperature increases, the Fermi level energy is constant (bi-dimensional gas) until Tc= 22 K. After it increases accusing a tridimensional holes gaz.

   magneto-transport properties of nanostructure type II superlattice for terahertz detection, Superlattices and Microstructures, Volume

   127, March 2019, Pages 151-156A.

4. D. Barkissy, A. Nafidi, A. Boutramine, E. Y. El Yakoubi, H. Chaib, Investigations in electronic quantum transport of quasi two dimensional InxGa1-xAs/InP nanostructure superlattice for infrared detection, Superlattices and Microstructures, Volume 127, March 2019, Pages 54-60

5. S. Perkowitz, R. Sudharsanan, K. A. Harris, J. W. Cook, Jr., J. F. Schetzina, and J. N. Schulman, Effective mass in an n-type HgTe- CdTe superlattice, Journal Phys. Rev. B 36, 9290,1987.

6. H.-S. Cho, Density of states of quasi two one and zero dimensional superlattice, J. Vac. Sci. Technol. B Microelectron. Nanom. Struct. 7: 13-63, 1989.

7. M. W. Prairie , R. M. Kolbas, a general derivation of the density of states function for quantum wells and superlattices, Journal Superlattices and Microstructures, Vol. 7, No. 4, 1990.

8. H.J. Haugan, S. Elhamri, B. Ullrich, F. Szmulowicz, G.J. Browna,

   W.C. Mitchel, J. Crys. Growth. (2009) 1897-1900.

9. H.S. Jung, P. Boieriu, and C.H. Grein, p-Type HgTe/CdTe Superlattices for Very-Long Wavelength Infrared Detectors, Journal of Electronic Materials vol. 35: no. 6, 13411345, 2006.