Optical band-gap of Zn3As2

Optical band-gap of Zn3As2

Solid State Communications, Vol. 32, pp. 687—690. Pergamon Press Ltd. 1979. Printed in Great Britain. OPTICALBAND-GAP OF Zn3 As2 J. Misiewicz and J.M...

321KB Sizes 24 Downloads 206 Views

Solid State Communications, Vol. 32, pp. 687—690. Pergamon Press Ltd. 1979. Printed in Great Britain.

OPTICALBAND-GAP OF Zn3 As2 J. Misiewicz and J.M. Pawlikowski Institute of Physics, Wroclaw Technical University, 50-370 Wroclaw, St. Wyspiañskiego 27, Poland (Received 18 June 1979 byL. Hedin) Absorption measurements of single Zn3 As2 crystals were made at temperatures 5, 80 and 300 K. Free-carrier absorption is interpreted in the simple classical model. Interband absorption shows contributions from Urbach-like excitations. The direct optical gap has been estimated as 0.99 eV at 300 K, 1.09 eV at 80K and 1.11 eV at 5 K. The linear dependence of band-gap on temperature 1 was found in the range 80—300 K with dEg/dT = 4.55 x i0~eVK 1. INTRODUCTION

easily noticed, especially at 300 K. The most probable reason of this high a-level is the free-carrier absorption

ZINC ARSENIDE Zn 3 As2 is a relatively uninvestigated p-type semiconducting compound of A”B” group. Its energy-band structure as well as other properties are not known at present. Theoretical calculations have been described in band-structure [1] however they are based on a simplified crystal structure and performed without including the spin-orbit interaction. The funda. mental energy-gap Eg was investigated at 300K and estimated as equal to 0.93 eV (absorption measurements [2]) and 0;99 eV (thermoreflectance [3J), while values closed to 1.0 eV were obtained for thin.film specimens [4]. M estimate ofEg below 100 K, E~= 1.1 eV [5] is also given, Preliminary results of the absorption edge of Zn 3 As2 at the temperatures 5.80 and 300 K have been shown in [6] and this paper presents a simple analysis of the absorption mechanism near the fundamental absorption edge and an estimate of the energy gap at the F point of this compound.

effect. The adjustment to the empirical formula described by e.g. Zawadzki [8] 2 +b (1) a = aX was made where the factor a is interpreted in a simple theory neglecting collision effects and is given by: e3N a = 4~2 ~2 ((ji) (m*)2)_l (2)

,

where N is a free-carrier concentration, (p) and (m*) are the mean values of mobility and effective mass of carriers, respectively, and other symbols have the usual meaning. The mean values obtained experimentally of a, N and p are given in Table 1. Taking also the value of the refractive index near the fundamental absorption edge, n = 3.53 [9] the values of m* were estimated from equation (2) and shown in Table 1. It should be noted that the values of carrier concentration and mobifity might be somewhat in error because we do not know exactly the transport phenomena in Zn3 As2 yet. Next, the free-carrier absorption and the flat “back-

,

,

2. RESULTS AND DISCUSSION Zn3 As2 specimens of approximate thickness 0.3 mm cut from single crystals (obtained by gas-transport method in closed space) were mechanically polished and then etched in 5% bromine solution in alcohol. Final smallest thicknesses were equal to 40—70 pm. Transmission measurements and computations of the absorption coefficient a were performed as in [6]. For measurements of the reflectivity of thick samples specialThe reflectance equipment described in [7] were used. carrier concentrations and mobilities in the samples measured were obtained by standard d.c. Halleffect method in low magnetic fields.

ground” were subtracted from the results measured and new values/plots of the absorption coefficient (denoted by a’) were analysed. They are listed in the inset of Fig. The 1. evident absorption tails below the fundamental edges are shown. Their origin is unknown at present (being, probably, connected in part with the high they doping 3), however, of material, of the order cm have shapes according toof the1018 well-known Urbach rule —

a(h~~, T)

=

a 0 exp

Figure 1 shows typical spectral plots of a for Zn3 As2. High absorption levels below the fundamental edge are 687

where

kT

(3)

688

OPTICAL BAND-GAP OF Zn3 As2

Vol. 32, No.8

Table 1. Values of the Zn3 As2 parameters Quantity

3) a (m N (m3) (p) (m2Vsec~) (int> (m 0) h~0 (eV) Eg(±0.02)(eV)

~

I

I I

I

300K 9.1 x i0~ 5.1 x 1023 85x104

80K 6.5 x iO’5 3.8 x 1023 328x104

5K 4.8 x lO~ 3.5 x 1023 624x104

~0.1 0.90 0.99

~0.05 0.94 1.09

~O.04 0.95 1.11

I

300K 80K 5K

C-)

1500 ~00 500

~J ~

G 0.6 0.7 0.8 0.9 1.0 1~w(eV)

I

1.1

Fig. 1. Typical absorption curves of Zn3As2 near fundamental edge. Inset shows the plots without the free.carriers and flat “background” absorptions. 0o 2kT tg h he-.,,, U

=

and a 0, 00, hw0, and hi4, are constants. The fit of equation (3) to the experimental data is presented in Fig. 2. Also shown in Fig. 2 are theoretical curves obtained from (1). exponential Distinct dissimilarities between the room-temperature plot and those at lower temperatures are shown; at 300 Kone exponent is sufficient to describe the Urbach edge while at both 5 and 80K two exponents give the good fit to the points between fundamental edge and free-carrier absorption plot. First exponents (at lower energies) at 5 and 80K cover the region of “background” absorption which may be due to, in our opinion, two reasons: the relatively low quality of the single crystals measured and the residual scattered light. Well-visible precipitations and non-homogeneities were locally observed by an electron microscope. Physically speaking, this absorption background is caused by the effect of additional photon absorption and/or scattering at these crystal-structure imperfections and diffuse scattering at the semiconductor—air interface. At 300 K the “back-

ground” absorption is masked by higher free-carrier absorption. Similar phenomena were observed e.g. for

ZnTe [10]. and300 factor 0.13 The lx~is best atand 80also fit K,isto and obtained obtained 0.016 being fore and=and 0.008 equal = 1.82 at to at50.94eV) 0.9 K. 300K, The ateV) 0.31 300, at 5 K. 0.94 K The changes parameter 0.82 eV (a(2) set at 80K, = (a~’~ 0.31, 1.82, hw~ 0.95 h~A$~ =eV and =eV 0.9 0.90 ateV 80K and next to ~ = 0.016, hw~1’~ = 0.95 eV) at 5 K, characterising Urbach rule (notations the transitions as in Fig. 2). described These a by variations the are often expected for Urbach-like edges (see e.g. [11]). Hence, the residual parameter sets (a, 1iwo) at Sand 80 K describe the absorption “background” mentioned above. We started to fit the fundamental part of the absorption edge at room temperature to the simple parabolic-, spherical- and two-band model of nondegenerate semiconductor because, on the one hand, lack of reliable theoretical band-model calculations (band parameters) and, other, Zn3 As2 a wide gap semiconductor and on thisthe simplicity may be isused in the first approximation. The well-known formula has



been used for direct band-to-band transitions in the absence of electron—hole interactions: 312IH~,v(0)I2(h~) _Eg)V2 a’hi~.,= nh (2m~) = A (hid Eg)1 /2,

(4)

taking A = const in the range of the fundamental edge. ~ (0) is the optical matrix element at k = 0. A deviation of this model from the experimental data could be expected only at higher photon energies, and the corrections according to the Kane band model [121 should be introduced at that time. The best fit is obtained for the energy gap (Eg) listed in Table 1. As shown, Eg (300 K) obtained in this way is in good agreement with the thermoreflectivity data [3] Hence, a similar procedure was also used at lower temperatures, neglecting the degeneracy and Burstein—Moss shift which is smaller than the experimental errors. Theoretical curves from (4) are also shown in Fig. 2. .

OPTICAL BAND-GAP OF Zn3As2

Vol. 32, No. 8 16~s

160( -

-

i~

Zn3As2 A—24

-

Zn3As2 A—24

“°~-

i~oo- 300 K

800

80K

~~~wEg)~”2

-

100(

1000

-

800

6(1

-

-

i

~~EgX2_1

-

-

\ c~exp( 600 -N 400

689

kT

6

600



exp

kT

.

1

~‘‘._~

cC_exp( 6

400

~-

~)-2/~~••~

200

200 cC.-(hc$~

-

0 U6

6

I

I

I

I

07

08

0.9

10

o.~

I

o.7

08

09

I

1.0

11

12

16a -

140

-

1200-

Zn 3As2 A-24 5K

100

oC-(1co-Eg~

800

600

~—exp 6

400

kT

cC-.exp

200006

(4)J_ 4. (4) ~n~-nc~0

I 07

I 08

kT

I 0.9

1.0

1.1I 1~~(eV)—*

12

Fig. 2. The fit of theoretical plots (solid lines) to the experimental data (points) at 300K (a), 80K (b) and 5 K (c). Parameters of fit are described in the text. Not all measurement points are marked (every third) to clarify the Figure.

As shown in Fig. 1, the fundamental absorption Additional measurements performed by the waveedge rises rather sharply. It can suggest an excitonic length modulation method [7] show the linear edge slightly broadened by internal potential fluctudependence of Eg on temperature in the range of 80— ations. This question, however, cannot be answered 300K with dEg/dT = —4.55 x l0~eVK’. without further investigations at higher photon energies (absorption coefficients).

690

OPTICAL BAND-GAP OF Zn3As2 E C.B.

Vol. 32, No. 8

hw = E~.It does not appear possible to identify these mechanisms unambiguously and more precisely due to the lack of prior band-structure calculations and full data of carrier transport mechanisms.

Eg

~

A

Acknowledgements assistance optical measurements. of Dr. P. Becla We Weand greatly are M.Sc. alsoappreciate indebted J. Wrobel to the for Dr. F. Krolicki for preparing good crystals. The work was supported by the “UNITRA” under contract 55/77 PR-3, IM-132.

B



REFERENCES V B.

Fig. 3. The outline of schematic band-model proposed for Zn3 As2 at the F point. The dashed line drafts the density-of-states tail.

3. CONCLUSIONS In conclusion we can say that quite a good fit was obtained in three parts of the absorption spectrum. The long-wave absorption can be explained in the models of free-carriers and “background” absorption processes and the fundamental edge by those of direct interband transitions. The experimental points between the above mentioned mechanisms are very well fitted by the Urbach rule for transitions to the density-of-states tail in the conduction band. The schematic two-band diagram of Zn3As2 at the F-point is outlined in Fig. 3. Transition “A” represents excitations from the valence band to the density-of-states2~4~ tail while in conduction band direct band-tostarting from hware = hw’~ band transitions indicated by “B”, starting from

1. 2.

PJ. Lin-Chung,Phys. Rev. 188, 1272 (1969). W.J. Turner, A.S. Fischler & W.E. Reese, Phys. Rev. 121,759(1961). 3. MJ. Aubin & J.P. Cloutier, Canad. J. Phys. 53, 1642 (1975). 4. J.M. Pawlikowski & P. Becla, Acta Phys. Pol. A47, 721 (1975); J.M. Pawlikowski & T. Borkowska, OpticaApplicata 4, 31(1974). 5. Unpublished data, cited by L.G. Caron, M.J. Aubin & J.P. Jay-Germ, Solid State Commun. 23, 493 (1977). 6. J.M. Pawlikowski, J. Misiewicz, B. Sujak-Cyrul & j• Wrobel,Phys. Stat. So!. (b) 92, K123 (1979). ~ P. Becla, Z. Gumienny & J. Misiewicz, Optica Applicata 9 (1979), in press. 8. W. Zawadzki,Adv. Phys. 23,435 (1974). 9. J. Misiewicz, Ph.D. Thesis, Wroclaw Technical University (1979), unpublished. ~ W. Wardzynski & M. Kwietniak, Proc. Nation. Symp. on Semicond. Compounds, Jaszowiec 1976, Prace IF PAN, 74, 180 (1977), (in Polish). 11. See e.g. A.S. Davydov.Phvs. Stat. So!. 27,51 (1968); J .A. Gaj & The Khoi Nguyen, Phys. Stat. Sol. (b), 83,&K133 (1977) and Phys. V.P. Mushinskij, L.I. K149 Palaki V.V. Chebotaru, Stat. So!. (b) 83, (1977). 12. E.O. Kane,J. Phys. Chem. Solids 1,249 (1957).