Anomalous temperature dependence of photoelectron charge and spin mobilities in p+-GaAs

0.61 MB·English

by  F. Cadiz

Anomalous temperature dependence of photoelectron charge and spin mobilities in
p+-GaAs.
F. Cadiz,∗ D. Paget, and A.C.H. Rowe
Physique de la mati`ere condens´ee, Ecole Polytechnique, CNRS, 91128 Palaiseau, France
E. Peytavit and S. Arscott
Institut d’Electronique, de Micro´electronique et de Nanotechnologie (IEMN), University of Lille,
5 CNRS, Avenue Poincar´e, Cit´e Scientifique, 59652 Villeneuve d’Ascq, France
1 (Dated: June9, 2015)
0
2 Theeffectofanelectricfieldonthespatialchargeandspinprofilesofphotoelectronsinp+-GaAs
is studied as a function of lattice and electron temperature. The charge and spin mobilities of
n
photoelectrons are equal in all conditions and exhibit the well known increase as the temperature
a
islowered. Itisshownthatthisisrelated mainlytotheelectron statisticsratherthanthemajority
J
holestatistics. Thisfindingsuggeststhatcurrenttheoreticalmodelsbasedondegeneracyofmajority
8 carriers cannot fully explain theobserved temperaturedependenceof minority carrier mobility.
2

]
Understanding the mechanisms which limit the mi- ensures that recombination at the interface is negligible.
l
al nority carrier charge mobility µe and spin mobility µs AsshowninFig. 1(a),aHallbarisphotolithographically
h in semiconductors is necessary for the correct design of etched into the active layer so that the lattice tempera-
- bipolar charge and spin devices. The limiting mecha- ture (T ) dependence ofthe majorityhole concentration
s L
e nisms are revealed in studies of the temperature depen- and mobility can be measured as shown in Fig. 1(b).
m dence of the average momentum relaxation time hτ i= The density of ionized acceptors is only weakly temper-
m
µ m∗/q where q is the absolute value of the electronic ature dependent for this doping level since the impurity
. e
at charge and m∗ is the effective mass. Here τm =τm(ε)= band andthe valence band are mergedinto a continuum
m a(T)εp is dependent on the electron’s kinetic energy, ε, of states [5, 6]. The hole mobility at room temperature,
- and the notation hτmi indicates an average over all elec- µh =202cm2V−1s−1, as well as its ∼TL1/2 temperature
d trons. The exponent p depends on the process which dependencebelow100Kareingoodagreementwithpre-
n limits the mobility [1] and this energy dependence re- vious reports on similarly doped GaAs [6, 9, 10].
o
sults in a temperature dependence of τ given, in the
c m
nondegenerate case, by Spin-polarized photoelectrons were generated by a
[
tightly-focussed circularly-polarizedCW laser excitation

1 (1/e half width of 0.6 µm, energy 1.58 eV) in a setup
v τ ∝a(T).T−p (1) described elsewhere [11]. A maximum excitation power
m
5
of 0.01 mW produces a non degenerate photoelectron
05 where kB is Boltzmann’s constant and T is the temper- concentration of ∼ 5×1014 cm−3 in the steady state.
2 ature. Te was monitored from the high energy tail of the spa-
0 The electron mobility in p-type GaAs features a com- tially homogenous luminescence spectrum, which is ob-
. pletely different temperature dependence than that of tained using a multimode optical fiber placed in the im-
6
majority electrons in n-GaAs for a similar doping level age plane. As shown in Fig. 2(a), taken at a low elec-
0
5 [2–4]. A number of possible reasons for this have been tric field of E = 200 V/cm, Te significantly differs from
1 discussed in the literature, including carrier freezeout at T . Furthermore, Fig. 2(b) shows that without caus-
L
: highholeconcentrations[5,6],screeningofionizedimpu- ing intervalley transitions [12, 13], T can be increased
v e
rities [7] and increasing hole degeneracy as temperature by applying higher electric fields. The lines in Fig.
i
X is lowered [8]. The correct determination of p, and thus 2(b) are predictions based on a simple balance equation
r the role and importance of each of these phenomena, re- 3/2k [T (E)−T (0)] = qv Eτ for the power delivered
B e e d E
a mains uncertain since it is not clear whether the lattice, totheelectrongasbytheelectricfield. Here,T (0)isthe
e
hole or electron temperature should be used in Eq. 1. electronic temperature at zero electric field, v =µ E is
d e
Hereweexperimentallymeasurepina3µmthick,car- thedriftvelocityandτ theenergyrelaxationtime. The
E
bon doped p-GaAs active layer (NA = 1018 cm−3) and data is well explained by an energy independent energy
demonstratethecrucialroleofthephotoelectrontemper- relaxationtime ofτ =1.2 ps and τ =1.5ps for initial
E E
ature,Te inEq. 1. Theinterfacebetweentheactivelayer electron temperatures of Te(0) = 40 K and Te(0) = 92
and the S.I. GaAs substrate is a 50 nm thick GaInP epi- K, respectively. These values are an order of magnitude
layerthatconfinesphotoelectronstothe activelayerand larger than values measured at 300 K [12], consistent
with a significant decrease of the energy relaxation rate
at lower temperatures due to less efficient phonon scat-
tering. Note that under similar electric fields, resistivity
∗ [email protected] measurements in the dark show that the hole tempera-
2
FIG.1. (a) SEMimage ofthep-GaAshallbarusedtostudy
both minority and majority carrier transport. Also shown
is a 3D representation of a measured electron density profile FIG.2. (a)Normalizedluminescencespectrafordifferentlat-
when an electric field is applied. (b) Concentration of ion- tice temperatures. Fits of the high energy tail of the spectra
ized acceptors and majority hole mobility as a function of (shown by thicker lines) are used to estimate the electronic
lattice temperature, as found from resistivity and Hall effect temperature. (b)Measuredelectronictemperatureasafunc-
measurements. tion of applied electric field for different values of the elec-
tron temperature at zero electric field. The increase of Te
a function of E is well explained by simple energy balance
ture (T ) remains unchanged and that T ≈ T . This is considerations which assume an energy-independent energy-
h h L
not surprising since the photogenerated hole concentra- relaxation time of 1.5 ps (dotted line) and 1.2 ps (solid line)
for each case.
tion is much smaller than N .
A
The minority carrier mobility µ is determined by
e
imaging the spatial dependence of the luminescence,
whichisproportionaltotheelectronconcentrationn[11]. sity profile yields an estimate for µ . At T = 300 K,
e L
Fig. 3 shows sections ofthese imagesalong the direction µ = 1560 cm2V−1s−1, in excellent agreement with the
e
of the electric field for T = 15 K (see movie attached theoretical value of 1643 cm2V−1s−1 at similar doping
L
as an ancillary file). Drift of the electrons in the applied predicted by Bennett [15] and with the existing experi-
electric field leads to a significant change of the profiles mentaldata[2,9,10,16]. Thespinmobilityµ wasmea-
s
which are well approximatedby the 2-dimensional diffu- sured using a similar approach by placing a circularly-
sion result [3] polarized excitation and a quarter wave plate followed
by a linear polarizer at the reception, thus yielding the
n(x)∝eµeτeExK0 (µeτeE)2+4Deτe x , (2) pisrothfielecoofntcheentsrpaitniocnonofceenletcratrtoionnssof=spni+n−±,nw−i,thwhaeqreuann±-
2D τ
"p e e #
tization axis along the direction of light excitation [11].
The equation for s is similar to Eq. 2 where D and τ
where D and τ are the electron diffusion constant and e e
e e
arereplacedbytheirspincounterpartsD andτ . Using
lifetime, respectively, and K0 is a modified Bessel func- s s
the predetermined value of the spin lifetime, τ [14], an
tion of the second kind. In a nondegenerate electron s
estimation of µ is possible.
gas the Einstein relation, D = [k T /q]µ , is valid so s
e B e e
that the only fitting parameter in Eq. 2 is the µ τ The results aresummarizedinFig. 4. The chargeand
e e
product. An independent time resolved photolumines- spinmobilitiesasafunctionofT forafixedelectricfield
L
cence characterization of the sample was made in or- of200V/cmareshowninFig. 4(a). Itisfirstfoundthat
der to measure τ as a function of electron temperature µ and µ equal within experimental error at all tem-
e e s
[14], so that a fit of Eq. 2 to the luminesence inten- peratures,thus verifyingpredictions fora nondegenerate
3
matic increase of mobility, with both electron and spin
mobilities being described by a T−4.3 power law.
e
FIG. 3. The top panel shows the charge density profiles at
TL = 15 K for selected values of the electric field. Dotted
lines are fits obtained with Eq. 2 that give the µeτe product
forthechargedistribution. Thebottompanelshowsthesame
profilesatdifferentlattice(andelectronic)temperatureswhen
an electric field of 200 V/cm is applied. FIG. 4. (a) The measured electron (solid circles) and spin
(open circles) mobilities for an electric field of 200 V/cm as
a function of TL. Also shown (open squares) is the variation
of Te. (b) The fixed field, variable TL mobility data plotted
electrongasintheabsenceofspin-dependentmomentum
against Te shows a 1/Te variation at high temperatures, a
relaxationmechanisms[17]. ForTL >100K,µe variesas variation which is also found by varyingTe using theelectric
Tl−0.78 close to the 1/TL behaviour previously reported field only (i.e. fixed TL, variable field). The solid triangles
in this temperature range [2]. This exponent is reduced correspond to TL ≈ 30−40 K and an electricl field varying
to -0.25 for T < 100 K. Fig. 4(a) also shows a linear between 200−1300 V/cm. The solid and open squares cor-
L
variationofTe withTL above100Kfollowedbyaweaker respond to TL = 15 K and a variable electric field (50−800
variation at lower lattice temperatures. V/cm). At low Te a dramatic increase of the mobility is ob-
The fixed field, variable T mobility data are again served, with a 1/Te4.3 dependence. The inset of the bottom
L panel shows the expected dependence of rH (Eq. 3) on the
plotted in Fig. 4(b) (full and open circles), this time as
index p in Eq. 1.
a function of T . Above 100 K, a clear 1/T dependence
e e
is again observed, similar to that reported elsewhere [2].
In order to determine separately the temperature de-
This suggests that what really determines minority car-
pendences of the two factors in Eq. 1, p can be mea-
rier mobility is their own statistics, imposed by the light
sured using photoconductivity and photoHall measure-
excitation energy and power, rather than that of major-
ments. Using a defocused laser excitation to ensure that
ity carriers. This hypothesis can be tested by measuring
thephotoelectronconcentrationishomogeneousoverthe
the T dependence of the mobilities when T is varied
e e Hall bar, the ratio r = µH/µ of the Hall mobility µH
by changing the electric field (see Fig. 2(b)) while T is H e e e
L to the drift mobility of minority electrons can be found.
held constant. In this fixed T , variable field measure-
L p can then be determined using [18]
ment, the hole statistics do not change since T = T .
h L
The results of this measurement are also shown in Fig.
4(b), the solidtriangles correspondingto T ≈35K and Γ(5/2+2p)Γ(5/2)
L
r = (3)
the solid squares corresponding to TL = 15 K. For 100 H [Γ(5/2+p)]2
K < T < 200 K the mobility dependence is well fitted
e
by a T−1.3 law, close to that obtained in the fixed field, The result is r = 0.95 ± 0.25 at T = 15 K and
e H L
variable T case (circles). For T < 50 K there is a dra- r = 0.8±0.25 at T = 300 K, in agreement with the
L e H L
4
valuesclosetounityobtainedformajorityelectronsinn- and of their screening by valence holes. For T = 10 K
h
GaAs[19]. Usingthesevaluesandthegraphicalrepresen- the maximum amplitude of the potential fluctuations is
tation of Eq. 3 in the inset of Fig. 4(b), p is found to lie oftheorderof40meV[21]andwhilesomeattemptshave
betweenapproximately-0.5and0.5,inqualitativeagree- beenmadetoincludetheeffectsofscreeningontransport
ment with the predictions of the Brooks-Herring model [8, 20, 22], a complete description including the effect of
[20] for screened collisions by charged impurities. The disorder is still out of reach. This work shows that in
small value of p implies that the measured temperature developing these models, accounting for the hole distri-
dependences are mainly those of the prefactor a(T) in bution alone [8] cannot describe the observed tempera-
Eq. 1. ture dependence of the minority electron mobility since
The origin of the T dependence of the minority elec- significant variations are measured even when the hole
e
tron mobility is at present not understood. At the dop- temperature is constant. The inclusion of minority car-
ing levels considered here it is probable that the mobil- rierstatistics intheoreticalmodels is thereforenecessary
ity is determined by scattering off potential fluctuations tobetterunderstandminoritycarriermobilitiesindoped
caused by the random distribution of ionized acceptors semiconductors.
[1] R. A. Smith, Semiconductors (Cambridge University [13] N. Okamoto, H. Kurebayashi, T. Trypiniotis, I. Farrer,
Press, Cambridge, 1978). D. A. Ritchie, E. Saitoh, J. Sinova, J. Masek, T. Jung-
[2] K.Beyzavi, K.Lee, D.M.Kim,M.I.Nathan,K.Wren- wirth, and C. H. W. Barnes, Nature Materials 13, 932
ner,andS.L.Wright,Appl.Phys.Lett58,1268 (1991). (2014).
[3] D.Luber,F.Bradley,N.Haegel,M.Talmadge, M.Cole- [14] F.Cadiz,P.Barate,D.Paget,D.Grebenkov,J.P.Korb,
man,andT.Boone,Appl.Phys.Lett88,163509(2006). A. C. H. Rowe, T. Amand, S. Arscott, and E. Peytavit,
[4] F. Schultes,T. Christian, R. Jones-Albertus, E. Pickett, J. Appl.Phys. 116, 023711 (2014).
K. Alberi, B. Fluegel, T. Liu, P. Misra, A. Sukiasyan, [15] H. S. Bennett,J. Appl.Phys.92, 4475 (2002).
H.Yuen,et al., Appl. Phys.Lett 103, 242106 (2013). [16] R. K. Ahrenkiel, D. J. Duniavy, D. Greenberg, H. C.
[5] S.Kim,C.Son,S.Chung,Y.Park,E.Kim,andS.Min, Schlupmann, Hamaker, and H. F. MacMillan, Appl.
Thin Solid Films 310, 63 (1997). Phys. Lett 51, 776 (1987).
[6] M. L. Lovejoy, M. R. Melloch, and M. S. Lundstrom, [17] Y. Qi, Z. G. Yu, and M. E. Flatte, Phys. Rev. Lett 96,
Appl.Phys.Lett 67, 1101 (1995). 026602 (2006).
[7] W. Walukiewicz, J. Lagowki, L. Jastrzebski, and [18] R. S. Popovic, Hall effect devices (Institute of Physics
H.Gatos, J. Appl.Phys.50, 5040 (1979). Publishing, Bristol, 2004).
[8] T.Kaneto,K.Kim,andM.Littlejohn,Phys.Rev.B47, [19] D.Look,C.E.Stutz,J.R.Sizelove,andK.R.Evans,J.
16257 (1993). Appl. Phys.80, 1913 (1996).
[9] C. M. Colomb, S. A. Stockman, S. Varadarajan, and [20] D. Chattopadhyay and H. J. Queisser, Rev. Mod. Phys.
G. E. Stillman, Appl.Phys.Lett 60, 65 (1992). 53, 745 (1981).
[10] E. S. Harmon, M. L. Lovejoy, and M. R. Melloch, Appl. [21] A.L.Efros, Y.S.Halpern,andB.I.Shklovsky,Proceed-
Phys.Lett 63, 536 (1993). ings ofthe International Conference on Physicsof Semi-
[11] I. Favorskiy, D. Vu, E. Peytavit, S. Arscott, D. Paget, conductors, Warsaw 1972 (Polish Scientific publishers,
and A. C. H.Rowe, Rev.Sci. Instr.81, 103902 (2010). Warsaw, 1972).
[12] T. Furuta, H. Taniyama, and M. Tomizawa, J. Appl. [22] D. N. Quang, N. N. Dat, and D. V. An, Phys. Lett. A
Phys.67, 293 (1990). 182, 125 (1993).