Donor and acceptor impurity states in N-polar wurtzite InGaN staggered quantum wells: Built-in electric field effects

Donor and acceptor impurity states in N-polar wurtzite InGaN staggered quantum wells: Built-in electric field effects

Physica E 58 (2014) 43–47 Contents lists available at ScienceDirect Physica E journal homepage: www.elsevier.com/locate/physe Donor and acceptor im...

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Physica E 58 (2014) 43–47

Contents lists available at ScienceDirect

Physica E journal homepage: www.elsevier.com/locate/physe

Donor and acceptor impurity states in N-polar wurtzite InGaN staggered quantum wells: Built-in electric field effects Congxin Xia a,b,n, Heng Zhang b, Jiao An b, Shuyi Wei b, Yu Jia a,n a b

International Laboratory for Quantum Functional Materials of Henan, Zhengzhou University, Zhengzhou, Henan 450001, China Department of Physics, Henan Normal University, Xinxiang, Henan 453007, China

H I G H L I G H T S

G R A P H I C A L

 The hydrogenic impurity states are investigated in N-polar wurtzite InGaN staggered QWs.  The influences of the built-in electric fields are obvious on impurity states in the QWs.  The stepped barrier height can tune effectively acceptor impurity states in the QWs.  The stepped barrier height is insensitive to donor impurity states in the QWs.

Under the influences of the built-in electric field, the stepped barrier height can tune effectively acceptor impurity states in the N-polar InGaN staggered quantum wells.

art ic l e i nf o

a b s t r a c t

Article history: Received 27 September 2013 Accepted 12 November 2013 Available online 23 November 2013

Based on the effective-mass approximation, the hydrogenic donor and acceptor impurity states are investigated theoretically in the N-polar wurtzite (WZ) InGaN staggered quantum wells (QWs). Numerical results show that the built-in electric field, the stepped barrier height and well size influences are obvious on impurity states in the staggered QWs. Moreover, the stepped barrier height can tune effectively acceptor impurity states, while it is insensitive to donor impurity states in the staggered QWs. In particular, the calculated results indicate that the built-in electric field can induce the donor and acceptor binding energies of impurities located at zi ¼Lw and  Lw become insensitive to the variation of the well width, respectively. & 2013 Elsevier B.V. All rights reserved.

Keywords: Impurity N-polar InGaN Staggered quantum wells

A B S T R A C T

1. Introduction In recent years, wurtzite (WZ) III–V nitrides semiconductor alloys and heterostructures have attached much attention due to their extensive applications in electronics and optoelectronic devices, such as laser diodes (LDs) and light emitting diodes (LEDs) [1–3]. Moreover, in the process of devices fabrication, the major epitaxial growth direction is the positive c-direction of the hexagonal WZ III-nitrides crystal corresponding to (0 0 0 1) or Gapolar surface. However, studies show that the strong built-in

n

Corresponding authors. Tel.: þ 86 371 67739336; fax: þ86 371 67767758. E-mail addresses: [email protected] (C. Xia), [email protected] (Y. Jia).

1386-9477/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physe.2013.11.012

electric fields are induced by the spontaneous and piezoelectric polarizations in the Ga-polar WZ GaN-based heterostructures [4,5], which reduces significantly the electron–hole recombination rate and optical gain of these heterostructures. In addition, in the Ga-polar heterostructures, the direction of the built-in electric field is also reversed with respect to the p–n junction depletion field, thus leading to a wider depletion region and the higher turnon voltage threshold [6,7]. These above factors degrade the performances of GaN-based optoelectronic devices. In order to improve the efficiency of WZ GaN-based electronic and optoelectronic devices, more recently, the studies of N-polar WZ GaN-based QWs have attached much interesting because the direction of the spontaneous and piezoelectric polarizations is reversed from that of Ga-polar counterpart [8–10]. Moreover, in

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the N-polar WZ GaN-based heterostructures, the polarization acts in the same direction as the depletion and the depletion region is thus reduced, which is expected to lead to a lower turn-on voltage for the N-polar p–n junction. It has also been reported that Indium incorporation along N-polar WZ InGaN is higher than that of Gapolar crystal case under the similar growth conditions [8,11,12]. In addition, recent studies have also proven that the built-in electric field and the electron–hole recombination rate can be tuned effectively by the stepped barrier layer in the Ga- and N-polar WZ InGaN staggered QWs structures [13–15]. Thus, it is very interesting to study the electron and impurity states in the N-polar WZ InGaN staggered QWs. It is well known that impurity states play an important role in semiconductor electronic and optoelectronic devices [16]. Recently, the donor impurity states have been investigated theoretically in the Ga-polar WZ InGaN staggered QWs [17,18]. However, to our knowledge, there are few studies involved on impurity states in the N-polar WZ InGaN staggered QWs. Therefore, in order to gain insight into the impurity states in the N-polar WZ InGaN staggered QWs, in this work, the hydrogenic donor and acceptor impurity states are studied in the N-polar WZ InGaN staggered QWs. According to previous studies on the WZ InGaN staggered QWs [17,18], the N-polar WZ GaN/InxGa1 xN/InyGa1 yN/GaN staggered QWs theoretical model is characterized as the size 1/Lw1/Lw2/1, where the Lw1 and Lw2 are well widths in the staggered QWs. Following the theory of Ref. [4], the expressions of the built-in electric field in the N-polar WZ InGaN staggered QWs are the same as that of Ref. [17–19], and the direction is reverse to that in the Ga-polar case. Moreover, the impurity energies are also calculated by means of the variational method within the effective mass approximation [17,20]. All material parameters are also taken from Ref. [17].

results show that whether the built-in electric field is considered or not, the donor binding energy has a maximum with the variation of impurity position, and the peak position is localized inside the In0.15Ga0.85N well layer in the staggered QWs. The reason is that the electron wave functions are mainly confined inside the In0.15Ga0.85N well layer in the N-polar WZ InGaN staggered QWs considering or ignoring the built-in electric field effects. Moreover, Fig. 1 also shows that the built-in electric field can induce the peak of the donor binding energy shifts toward left in the staggered QWs. This is because the direction of the built-in electric field is along the (0 0 0 1) positive direction in the N-polar WZ InGaN staggered QWs, and thus it pushes the electrons shift toward left in the staggered QWs. In Fig. 2, the ground-state donor binding energy is investigated as a function of Indium composition y in the N-polar WZ In0.15Ga0.85N/InyGa1  yN staggered QWs. It can be seen from Fig. 2(a) that when the built-in electric field is considered, the donor binding energy is insensitive to the variation of Indium content y in the QWs for any impurity position case. This behavior is the results of competition effects between the built-in electric field and the stepped barrier height in the staggered QWs. When Indium content y is increased, the effective band gap of InyGa1  yN layer is decreased and thus quantum confinement is reduced in the QWs. On the other hand, the strength of the built-in electric field is also increased when Indium content y is increased, which pushes the electrons shift towards the left side of the QWs. In addition, Fig. 2(a) also shows that the donor binding energies of impurities located at zi ¼  Lw and Lw/2 (curves AF and BF) are larger than that of impurities located at other positions (curves CF, DF and EF). This is because the electrons are pushed towards the

2. Numerical results and discussions To understand the impurity properties in the N-polar WZ InGaN staggered QWs, we have calculated the hydrogenic donor and acceptor impurity binding energies as functions of impurity position, stepped barrier height and well width in the N-polar WZ InGaN staggered QWs considering and ignoring the built-in electric field effects cases. In Fig. 1, the ground-state donor binding energy is investigated as a function of impurity positions zi in the N-polar WZ In0.15Ga0.85N/InyGa1  yN staggered QWs. Numerical

Fig. 1. The ground-state donor binding energy Eb as a function of impurity positions zi in the N-polar WZ In0.15Ga0.85N/InyGa1  yN staggered QWs with the well width Lw ¼Lw1 ¼ Lw2 ¼ 2.0 nm and different Indium compositions y. The curves AF and BF, A0 and B0 are for Indium compositions y¼ 0.02 and 0.08 considering and ignoring the built-in electric field, respectively.

Fig. 2. The ground-state donor binding energy Eb as a function of Indium composition y in the N-polar WZ In0.15Ga0.85N/InyGa1  yN staggered QWs with the well width Lw ¼Lw1 ¼ Lw2 ¼ 2.0 nm and different impurity positions zi. The curves AF(A0), BF(B0) CF(C0), DF(D0) and EF(E0) are for the impurity positions zi ¼  Lw1,  Lw1/2, 0, Lw2/2, and Lw2, respectively. The figures (a) and (b) are for considering and ignoring the built-in electric field cases, respectively.

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left edge of the In0.15Ga0.85N layer of the QWs due to the built-in electric field effects. However, one can see from Fig. 2(b) that when the built-in electric field is ignored, the trends of the donor binding energy are obviously different from that considering the built-in electric field effects case. The calculated results show that with increasing Indium content y of InyGa1  yN layer, the donor binding energies are decreased when the impurities are located at zi ¼  Lw and Lw/2 (curves A0 and B0); while the donor binding energies are increased for the impurity positions zi ¼0, Lw/2 and Lw (curves C0, D0 and E0). This is because when Indium content y increases, the band gap of InyGa1  yN layer increases and the stepped barrier height decreases in the QWs. Thus, the electron wave function distributions shift toward right side when Indium concentration y increases in the N-polar WZ In0.15Ga0.85N/InyGa1  yN staggered QWs ignoring the built-in electric field effects case. Therefore, we can conclude from Fig. 2 that the effects of the built-in electric field and stepped barrier have an obvious influences on electronic and impurity states in the N-polar WZ InGaN staggered QWs. To further address quantum size effects on the donor impurity states in the N-polar WZ InGaN staggered QWs, in Fig. 3, the donor binding energy is investigated as a function of the well width Lw in the N-polar WZ In0.15Ga0.85N/In0.04Ga0.96N staggered QWs considering different impurity positions zi. Numerical results of Fig. 3 (a) show that when the built-in electric field is considered, the donor binding energies of impurities located at zi ¼ 0, Lw/2 and Lw are decreased when the well width Lw is increased (curves CF, DF and EF). The reason is that when the well width is increased, the electron–impurity distance is increased, and then the electron– impurity Coulomb interaction and the donor binding energy are

Fig. 3. The ground-state donor binding energy Eb as a function of the well width Lw ¼ Lw1 ¼Lw2 in the N-polar WZ In0.15Ga0.85N/In0.04Ga0.96N staggered QWs for different impurity positions zi. The figures (a) and (b) are for considering and ignoring the built-in electric field, respectively. The curves have the same meaning as in Fig. 2.

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decreased. In addition, for the impurity located at zi ¼  Lw/2 (curve BF), the donor binding energy increases slowly when the well width Lw increases (Lw o2 nm); however, it decreases sharply when the well width is larger (Lw 42 nm). The reason can be given as follows. When the well width increases first, the electron wave function can be much more localized inside the In0.15Ga0.85N layer, thus the donor binding energy increases; however, when the well width increases continuously, the electron–impurity Coulomb interaction and the donor binding energy decrease. In particular, we can find from Fig. 3(a) that for the impurity located at zi ¼  Lw (curve AF), the donor binding energy is insensitive to the variation of the well width and has the largest value compared with the other impurity cases. This is because the electrons are shifted towards the left edge of the QWs due to the built-in electric field effects, and then the well width has an unobvious influence on the electron–impurity distance and Coulomb interaction. In addition, it can also found from Fig. 3(b) that the donor binding energy decreases when the well width Lw increases for any impurity position zi for any impurity case. This is because the electron wave function distributes mainly inside the In0.15Ga0.85N well layer when built-in electric field effects are ignored. Now we turn to study the hydrogenic acceptor impurity states in the N-polar WZ InGaN staggered QWs. In Fig. 4, the acceptor binding energy is calculated as a function of impurity positions zi in the Npolar WZ In0.15Ga0.85N/InyGa1 yN staggered QWs with and without the built-in electric field. Numerical results show that the acceptor binding energy has a maximum value with the variation of impurity position for any case. Moreover, Fig. 4 also shows that when the builtin electric field is considered, the impurity position of peak for low Indium composition y is located in the In0.15Ga0.85N layer; however, for high Indium composition y, it is located in the InyGa1 yN layer. This can be explained as follows. The built-in electric field is increased when Indium content y is increased in the N-polar WZ InGaN staggered QWs. Therefore, under the influence of the built-in electronic field, the holes are confined inside the In0.15Ga0.85N well layer when Indium composition y is low; however, the holes are confined inside the InyGa1 yN barrier layer when Indium composition y is high. On the other hand, we can also see from Fig. 4 that when the built-in electric field effect is ignored, the impurity position of peak is located at the In0.15Ga0.85N layer for any Indium composition y case in the QWs. This is because quantum confinement effects make the holes wave function be distributed mainly inside the In0.15Ga0.85N well layers in the N-polar WZ InGaN staggered QWs when the built-in electric field is ignored. These results show that the impurity positions and stepped barrier have remarkable influences on the acceptor binding

Fig. 4. The ground-state acceptor binding energy Eb as a function of impurity positions zi in the N-polar WZ In0.15Ga0.85N/InyGa1  yN staggered QWs with the well width Lw1 ¼ Lw2 ¼2.0 nm and different Indium compositions y. The curves have the same meaning as in Fig. 2.

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binding energies approach to the same value for the impurity positions B0 and C0 (curves A0 and E0), as expected. This is because when Indium content y approaches to the value 0.15, the staggered QWs will become a single QW. Thus, compared with the donor binding energy results Fig. 2, the calculated results indicate that the Indium composition y effects are much more obvious on the acceptor impurity states in the staggered QWs. In order to understand the well width influence on the acceptor impurity states, Fig. 6 presents the acceptor binding energy as a function of the well width Lw in the N-polar WZ In0.15Ga0.85N/ In0.04Ga0.96N staggered QWs for different impurity positions zi. One can see from Fig. 6(a) that when the built-in electric field is considered, the acceptor binding energy decreases with increasing the well width Lw when the impurities are located at zi ¼  Lw,  0.5Lw and center (curves AF, BF and CF). The main reason is that the increase of the well width induces the hole-impurity distance increase and thus the Coulomb interaction is decreased. In particular, Fig. 6(a) also shows that when the impurity is located at zi ¼ Lw case (curve EF), the acceptor binding energy has a rapid increases and then becomes insensible when the well width Lw 42 nm, which is interesting to understand quantum size effects on the impurity states in the QWs. This behavior can be understood as follows. When the well width Lw is large, the built-in electric field dominates the hole wavefunction distribution and pushes holes towards the right edge of the QWs. Thus, one can conclude from Fig. 6 that quantum size effects should be considered to optimize the performances of WZ GaN-based electronic and optoelectronic devices.

Fig. 5. The ground-state acceptor binding energy Eb as a function of Indium composition y in the N-polar WZ In0.15Ga0.85N/InyGa1  yN staggered QWs with the well width Lw1 ¼Lw2 ¼ 2.0 nm and different impurity positions zi. The figures (a) and (b) are for considering and ignoring the built-in electric field cases, respectively. The curves have the same meaning as in Fig. 2.

energy, which may be interesting to tune the hydrogenic acceptor impurity properties in the N-polar WZ InGaN staggered QWs. To further gain insight into the role of Indium composition y on hydrogenic acceptor impurity states, in Fig. 5, the acceptor binding energy is studied as a function of Indium composition y in the N-polar WZ In0.15Ga0.85N/InyGa1 yN staggered QWs. It can be seen from Fig. 5(a) that when Indium concentration yo0.08, the acceptor binding energies are decreased when the impurities are located at zi ¼  Lw,  0.5Lw and 0 (curves AF, BF and CF); however, the acceptor binding energies are increased when the impurities are located at zi ¼Lw and 0.5Lw cases (curves DF and EF). These behaviors can be explained as follows. When Indium content y is increased in the N-polar WZ In0.15Ga0.85N/InyGa1  yN staggered QWs (yo0.08), the energy gap of InyGa1  yN layer decreases and the strength of built-in electric field increases, the hole wave functions can penetrate easily into the InyGa1  yN layer. In particular, Fig. 5(a) also shows that when Indium concentration y40.08, the acceptor binding energy is insensible to the variation of Indium content y for any impurity case. The reason is that when Indium content y4 0.08 in the staggered QWs, the hole wave functions are much more confined inside the InyGa1  yN layer. In addition, Fig. 5(b) also shows that in the absence of the builtin electric field, when Indium concentration y increases, the acceptor binding energy decreases slowly for impurity positions zi ¼  Lw and  0.5Lw cases (curves A0 and B0); however, it is increased when impurities are located zi ¼0, Lw/2 and Lw (curves C0, D0 and E0). This is because the decrease of the barrier height of InyGa1  yN layer induces the holes shift towards the InyGa1  yN layer. Moreover, we can also see from Fig. 5(b) that when Indium concentration y approaches to the value of 0.15, the acceptor

Fig. 6. The ground-state acceptor binding energy Eb as a function of the well width Lw ¼ Lw1 ¼ Lw2 in the N-polar WZ In0.15Ga0.85N/In0.04Ga0.96N staggered QWs for different impurity positions zi. The figures (a) and (b) are for considering and ignoring the built-in electric field cases, respectively. The curves have the same meaning as in Fig. 2.

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3. Conclusion

References

In summary, our calculations show that impurity states are dependent highly on the built-in electric field, the stepped barrier height and well size in the N-polar WZ InGaN staggered QWs. Numerical results show that whether the built-in electric field is considered or not, the donor and acceptor binding energies have a maximum with the variation of impurity position in the staggered QWs. When the built-in electric field is considered, the stepped barrier height influence is insensitive (or obvious) to the donor (or acceptor) binding energy in the staggered QWs for any impurity case. However, when the built-in electric field is ignored, the stepped barrier height has the same influences on hydrogenic donor and acceptor impurity states in the staggered QWs. In particular, numerical results also show that the built-in electric field induces the donor (or acceptor) binding energy of impurity located at zi ¼Lw (or  Lw) become insensitive to the variation of the well width when the well width Lw 42 nm. These results may be useful to understand the hydrogenic impurity characteristics in N-polar WZ InGaN staggered QWs. Experimental studies for the hydrogenic impurity states in the QWs are still lacking at present. We hope that our calculation can stimulate further investigations of the related physics, as well as device applications of group-III nitrides.

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Acknowledgments This work was supported by the National Natural Science Foundation of China under Grant no. 11274280 and “973 project” (No.2012C13921300).