Progress Report

TRIUMF Experiment 938

"Muonium Formation and Ionization in Semiconductors and Insulators"

Group: µSR in Solids Spokesbeings: J.H. Brewer & V.G. Storchak Beam Request: M15 - 48 shifts

Introduction & Beam Time

On implantation into semiconductors and insulators, muons can bind electrons to form hydrogen-like centres known as muonium - essentially a light isotope of hydrogen, which may be studied with great sensitivity and selectivity using muon spin rotation/relaxation techniques (including applied electric field). Determination of the electronic structure of these centres, their ionization temperatures and their binding energies, will provide unique information on electron capture and loss processes and, by inference, on the electrical activity of hydrogen impurities. In experiment E938 we proposed to study mechanisms of electron capture into different states by positive muons in semiconductors and insulators, as well as electron loss by thermal ionization or by ionization in electric fields.

In the original E938 proposal (July 2002) we requested, and were allocated, 36 shifts of surface muon beam time in 2002-2003. In Schedule 102, 12 shifts on M15 have been successfully delivered; the remaining 24 shifts on M15 are expected to be delivered in Schedule 103 just before the July 2003 EEC meeting. Thus our quota of EEC-approved beam time will be exhausted by the end of Schedule 103.

We are therefore submitting the present progress report with a request for 48 shifts (four standard weeks) on M15 to be scheduled before the end of the next two beam periods.

Progress and Status Report

In Experiment 775 ("Electron Transport in Insulators, Semiconductors and Magnetic Materials") we developed a new method for investigating electron transport in nonmetals on a microscopic scale by measuring the effect of applied electric fields on delayed muonium formation (DMF). As an outcome of E775, it is now well-established that the incoming µ⁺ leaves behind an ionization track of liberated electrons and ions - in fact, these products may determine much of the subsequent behavior of muons and muonium in insulators and semiconductors.

Recent progress in the study of atomic centers in matter has led to realization that isolated H/Mu atoms may have an electrical activity of their own. Therefore it is important to understand different possible mechanisms for electron capture and loss by positive centers.

Muonium in semiconductors is commonly discussed citePatterson88 in terms of the lowest electronic states or long-lived metastable states without explicitly considering the details of how these states are formed. Only recently have we begun to examine the muonium formation processes in detail with experiments designed to modify the final stages of muon implantation and thermalization. Specifically, we have sought to probe interactions between the muon and the carriers released during its implantation, particularly the initial capture of an electron to form an atomic muonium defect state. In µSR experiments one accumulates the necessary statistics into a time spectrum that reveals the spin polarization of positive muons stopped in the sample. Each incoming 4 MeV muon leaves behind an ionization track of excess electrons and ions liberated during the µ⁺ thermalization process. Experiments in insulating citeStorchak95,Storchak96,Storchak99 and more recently in semiconducting media (Si citeStorchak97 and GaAs citeEshchenko99) have shown that the ionization track products are very close to the thermalized muon. (The characteristic distance is about 10^-5 - 10^-6 cm.) Some of the excess electrons generated in the end of the µ⁺ track are mobile enough to reach the thermalized muon and form the muonium atom.

The phenomenon of sl delayed muonium formation described above implies that as the electron approaches the muon it may be captured initially into a highly excited muonium atom with macroscopic-sized orbits, it viz. a weakly bound metastable precursor of the ground state. Such a weakly bound state (WBS) may produce an extremely shallow level in the gap; thus it would be susceptible to ionization, either thermally or by an electric field. Both the ionization temperature and the characteristic electric field in this case will be significantly less than those required to ionize deep states. In particular, the characteristic electric field is expected to be much less than atomic scale electric fields (~10⁹ V/cm).

Weakly Bound Muonium State in Semiconductors: Electronic Structure

In semiconductors with low electron effective mass and high dielectric constant, an electron and a positively charged center can form a hydrogen-like weakly bound state with macroscopic-sized orbits. In particular in GaAs, the binding energy of such a shallow donor is U ~ 7 meV while its characteristic radius a ~ 8 x 10^-7 cm citeAnimalu77. The electric field required to ionize this shallow state is estimated to be E_i ~ 5 kV/cm in close agreement with the characteristic field found to prohibit formation of Mu⁰_BC in GaAs citeEshchenko99. Therefore, formation of Mu⁰_BC in GaAs was suggested to proceed through an intermediate weakly bound Mu state citeEshchenko99,Eshchenko02.

One may estimate the ionization energy from the temperature dependence of the muonium signal, but existing data are insufficient to give good numbers, yielding an estimate of 200-400 meV in GaAs, and even cruder for GaP. Ionization probabilities are typically treated as simple activated processes with energies equivalent to the defect level depth below the conduction band.

Ionization by an external electric field is a different matter. Assuming that the precursor is a weakly bound quantum state with an extended orbit, an increasing electric field will bias the Coulomb potential until this state is eventually never formed. Such a process may be considered "preemptive ionization" of this weakly bound Mu state. The characteristic electric field E_{i required to ionize this state can be estimated by equating the bias across the orbit, 2 e Ei a, to the binding energy citeKnox63. Electric field ionization can thus directly measure the binding energy of a shallow state.}

If the formation of WBS has general validity, the binding energy as well as the characteristic radius of the electron orbit (and therefore the characteristic electric field) of this intermediate weakly-bound Mu state formed on initial capture should scale with the electron effective mass and dielectric constant of the host. Here we present experimental evidence that formation of the final (deep) Mu state in GaP also proceeds through an intermediate weakly-bound (shallow) Mu state. The characteristics of this shallow Mu state are found to be in good agreement with those expected for a hydrogen-like atom within the effective mass approximation. Comparing the characteristic fields required to prohibit formation of the muonium ground state in GaAs and GaP demonstrates that they scale with the electron effective mass and dielectric constant of the host very much as expected for initial electron capture into the n=1 orbital of a hydrogen-like state associated with a positive muon.

Electric field experiments were carried out using an alternating field technique which prevents charge accumulation at the contact interface and associated reduction of the field in the sampleciteEshchenko99. The time scale of this screening depends on electrode interface properties and the rate of carrier generation by the muon beam. For our GaP sample and a typical beam intensity (5 x 10⁴ s^-1) we found charge accumulation effects to be negligible for switching periods less than 20 seconds.

The electric field dependence of the diamagnetic asymmetry in GaP is shown in Fig. 1, along with that observed in semi-insulating GaAs. Less detailed measurements in GaP at T = 20 K give virtually the same electric field dependence as at T = 100 K.

The large difference in electric field dependences for GaP and GaAs -- the characteristic electric fields differ by an order of magnitude (about 50 kV/cm in GaP it vs. about 5 kV/cm in GaAs) - cannot be attributed to ionization of the final (deep) muonium states. First, the electric field strength is 4-5 orders of magnitude less than atomic fields. Second, both muonium centers in GaP have hyperfine constants extremely close to those for their counterparts in GaAs citeKiefl85. Therefore we conclude that it is not ionization of the final Mu state which is observed in either case, but rather field ionization of a weakly-bound precursor to a deep muonium final state.

beginfigure[htb] begincenter epsfigfile=gap_gaas_e.eps,width=10cm endcenter caption Electric field dependences of the diamagnetic asymmetry in a transverse magnetic field of H = 51 G for semi-insulating GaAs (10 K, open circles) and GaP (100 K, filled squares). In both cases the temperature is well below that causing ionization of Mu in zero electric field. labelfig:1 endfigure

We argue further that this weakly-bound muonium state is well described within the effective mass approximation of the hydrogen-like model commonly used for shallow donors citeAnimalu77. Specifically, in that model the characteristic electric field for ionization, estimated by equating the bias across the orbit to the binding energy citeKnox63, may be expressed as

E_i = 1over 4 e^5over hbar^4 m_*^2over epsilon^3 = left(m_*over mright)^2 1over epsilon^3 times left( 1.9times 10^9 hboxrm V/cm right) ,

where e is the electron charge, m_* is the effective mass of the electron and epsilon is dielectric constant of the medium. The ratio ${m_*^2/epsilon^3}$ makes $E_i$ in semiconductors about 5 orders of magnitude less than atomic-scale electric fields. In the case of GaP, with effective electron mass $m_* = 0.17 m$ and dielectric constant $epsilon = 10.7$, the predicted characteristic field is $E_i = 50$ kV/cm, in very good agreement with the experimental value. Comparison with GaAs ($m_* = 0.067 m$ and $epsilon = 12.9$) where $E_i = 5$ kV/cm citeEshchenko99 allows us to conclude that the electric field required to ionize this weakly-bound Mu state scales with the electron effective mass and the dielectric constant of the host as expected for a hydrogen-like state.

The characteristic radius of the electron orbit within this model, beginequation a = hbar^2over e^2 cdot epsilonover m_* = mover m_* epsilon a_0 , labelradius endequation is $0.28times 10^{-6}$ cm and $0.83times 10^{-6}$ cm in GaP and GaAs, respectively. These values are about 2 orders of magnitude bigger than the Bohr radius $a_0$. This fact makes the use of the hydrogen-like model justified as both electron effective mass and dielectric constant are essentially macroscopic characteristics of the medium.

The binding energy of such a weakly-bound state, beginequation U = e^4over 2hbar^2 m_*over epsilon^2 = m_*over m 1over epsilon^2 times left( hboxrm 13.6 eV right) labelbind_en endequation is 23 meV and 7 meV for GaP and GaAs, respectively. Both the shallow donors and excitons in GaAs have a binding energy near 7 meV citeAnimalu77 in good agreement with the hydrogen-like model. In GaP, the exciton binding energy is 21 meV citeZhang90, again close to the estimate from the hydrogen-like model. In both semiconductors, the estimated binding energies for the precursor to the deep Mu$^0$ state imply that this precursor state should be relatively easy to ionize thermally.

A possible scenario consistent with the current experimental results is that muonium in GaP is formed it via electron transport from the muon's track, as seen in many insulators citeStorchak95,Storchak96,Storchak99 and semiconductors citeStorchak97,Eshchenko99. As the electron approaches the muon, they initially form a weakly-bound paramagnetic muonium atomic-like state with a macroscopic-sized orbit of about $a sim 100a_0$, and hence very weak hyperfine interaction, as a precursor to the final deep-level muonium ground state. The lifetime of the precursor state is estimated to be less than a few nanoseconds, based on observation of a coherent precession signal from the final Mu ground state.

In conclusion, our $mu$SR experiments in an electric field imply that Mu formation in GaP (as well as in GaAs) proceeds through a weakly-bound intermediate muonium state. Comparing the results in GaP and GaAs we find that the characteristic electric field for ionization of this precursor state scales with the electron effective mass and dielectric constant of the medium as modeled for a hydrogen-like effective-mass state. Since there is nothing particularly special about muonium with respect to $e^-$ capture, we suggest that electron capture by other deep-donor impurities may also proceed through a similar shallow-donor-like intermediate state.

Magnetic Freezeout of Electrons into Muonium Atoms in GaAs

Here we present our studies of the magnetic field effects on shallow impurity (hydrogen-like) states in semiconductors.

In spite of intense studies, the behaviour for comparable Coulomb and magnetic interactions remains an unsolved problem even for the hydrogen (or muonium, Mu = $mu^+ e^-$) atom with the simplest form of Hamiltonian. Difficulties arise because this Hamiltonian is nonseparable, the Coulomb symmetry being broken by the action of an external magnetic field of different symmetry but similar strength. Due to the absence of an exact solution for this problem, certain approximations have been made at low and high magnetic fields; thus the correspondence of energy states between the low-field and high-field limits has attracted considerable attention.

It is suggested that in bulk semiconductors the presence of an external magnetic field enhances the binding energy of the impurity atom citeYafet56. The point here is the effect of competition between the magnetic energy and the Coulomb energy. The characteristic Coulomb interaction arises from a charged impurity center with binding energy expressed by equation (refbind_en). The strength of a magnetic field $H$, on the other hand, may be characterized by the shift of the band edge due to the field, it i.e. the zero-point energy of the lowest Landau level, given by beginequation 1over 2 hbar omega_c = ehbarover 2m^*c H . labelLan endequation The comparison of (refbind_en) and (refLan) can also be interpreted in terms of the two kinds of orbital radius, it i.e. the effective Bohr radius expressed by Eq. (refradius) and the cyclotron radius beginequation l = left( hbar c over eH right)^1/2, labelcyc endequation respectively. Yafet it et al. citeYafet56 showed that when the magnetic field is strong enough that ${1over 2}hbaromega_c$ is comparable or larger than $U$, a considerable compression of the electronic wave function of the atomic state occurs because its orbital radius tends to decrease in accordance to (refcyc) as the field is increased. This shrinkage of the wave function in turn causes the electron to be affected by a stronger binding of the attractive Coulomb potential, and thus results in an increase of the ionization energy. This effect can be observed as a decrease in the number of conduction carriers being frozen out of the lowest-order conduction band Landau level onto localized states, with a binding energy that increases with magnetic field.

However, in semiconductors with shallow donor levels the impurity band merges with the conduction band at comparatively low impurity concentration, thus masking the effect of electron localization citeEdwards95. This is because of the overlap of electronic wave functions situated on neighboring impurity sites due to an increased effective Bohr radius [see (refradius)].

Also in bulk semiconductors, the phenomenon of the metal-insulator transition is typically studied using "electrical" techniques (such as measurements of magnetoresistance or Hall coefficient, see it e.g. citeEdwards95). In particular, an increase of the Hall coefficient at low temperatures in high magnetic field in InSb citeKeyes56 was interpreted in terms of the magnetic freezing out effect citeYafet56. In these experiments, however, the conclusion about electron localization is made indirectly, based on measuring the properties of electrons "left delocalized" and thus available for conduction.

Although the metal-insulator transition is essentially a collective phenomenon, its study on the level of the elementary act of electron localization is important for understanding of this effect.

In this regard the technique of muon spin rotation/relaxation/resonance ($mu$SR) has made a significant contribution in clarifying the process of formation and the electronic structure of isolated states of the muonium atom (see section 2.1). Of relevance to the present work is the fact that electrons (and holes) created during the process of muon implantation and thermalization are available for interaction and capture, irrelevant of temperature or doping. The phenomenon of sl delayed muonium formation described in section 2.1 implies that as the electron approaches the stopped muon it may be captured initially into a weakly bound muonium state. In particular, studies of GaAs and GaP imply validity of the effective mass approximation within the hydrogen-like model as a description of the weakly-bound muonium states formed on initial capture of an electron by a thermalized positive muon.

The phenomenon of formation of this weakly bound muonium center may serve to model the process of free electron capture (or electron localization) by an attractive center, thus modeling a metal-insulator transition in a solid. Delayed muonium formation it via capture of a free electron by a positive muon gives an opportunity to study the elementary act of a metal-insulator transition. These studies are carried out in the extremely dilute limit of a single impurity in the sample (in $mu$SR techniques one follows the behavior of every muon one at a time) thus avoiding complications related to impurity-impurity interactions and formation of an impurity band.

Here we present preliminary results of our study of magnetic freezing out of electrons into muonium atoms in GaAs in magnetic fields up to 7 T.

Our experiments in electric field citeEshchenko02 have shown that formation of the Mu$^0_{rm BC}$ ground state in GaAs proceeds through a weakly-bound intermediate state with a binding energy of about 7 meV. A reverse process of Mu$^0_{rm BC}$ ionization may then take place not necessarily from the ground state but may include thermal ionization from intermediate weakly bound states. Muonium centers in semiconductors typically ionize above several hundred Kelvin; the Mu$^0_{rm BC}$ signals are not observed above roughly 150-200 K in GaAs citePatterson88. In our sample the relaxation rate of the Mu$^0_{rm BC}$ signal becomes faster than $10^8$ MHz at about 160 K and thus Mu$^0_{rm BC}$ is unobservable at higher temperature. Ionization of Mu$^0_{rm BC}$ in GaAs is accompanied by an increase in the diamagnetic fraction, as shown in Figure 2. The diamagnetic signal in GaAs is normalized to that in Ag in order to take into account effects of the finite time resolution of the spectrometer (it is known that in Ag 100% of the polarization is diamagnetic). The data are normalized at every temperature point.

beginfigure[thb] begincenter epsfigfile=GaAs_1-7.ps,width=6cm, angle=-90 endcenter caption Temperature dependences of the diamagnetic polarization (ionization curves) in semi-insulating GaAs in magnetic fields of 1 T (circles) and 7 T (triangles). labelfig:2 endfigure

One can notice a clear difference between the two data sets: the ionization curve measured in a magnetic field of $B = 7$ T (triangles) is shifted with respect to that measured in $B = 1$ T (circles) by about 10 K to higher temperatures. This shift of the ionization temperature probably indicates an increase of the binding energy of a weakly-bound precursor to the Mu$^0_{rm BC}$ ground state, according to the model of Yafet it et al. citeYafet56. Indeed, in GaAs in a magnetic field of $B = 1$ T the dimensionless parameter beginequation gamma = hbaromega_cover 2R_y = left( a^*over l right)^2 labelgamma endequation is still much less than 1, while $gamma sim 1$ in $B = 7$ T. According to calculations of the characteristic radius of the weakly-bound hydrogenic donor state in GaAs as a function of $gamma$ citeYafet56 one may expect a reduction of $a^*$ by about 5% in a magnetic field of $B = 7$ T. As $R_ysim (a^*)^{-2}$ one would expect an increase of the binding energy by about 10%.

One may argue that the decrease of the diamagnetic fraction is a result of dephasing in the diamagnetic signal formed by ionization of Mu$^0_{rm BC}$: muonium atoms ionize after a mean lifetime $tau$, thus causing a dephasing $deltaphi sim 2pideltanutau$, where $deltanu$ is the difference between the precession frequencies of Mu$^0_{rm BC}$ and the "bare" muon. This effect may explain a reduction of the diamagnetic polarization in low magnetic field. A magnetic field of about 1 T, however, sets up the high field limiting case ( $A ll gamma_{mu}B$) with muonium frequencies positioned symmetrically about the diamagnetic signal at $nu_{Mu^0_{rm BC}} = nu_{mu}pm A/2$ citePatterson88, where $A$ is the hyperfine constant of Mu$^0_{rm BC}$. Above this field the difference in precession frequencies $deltanu$ is independent of magnetic field; thus, the dephasing associated with a Mu$^0_{rm BC}$ precursor state cannot explain the reduction of the diamagnetic polarization at high magnetic field.

This reduction of the diamagnetic fraction may, however, be explained by magnetic freezing out of free electrons into muonium atom energy levels when the characteristic energy of the lowest-order conduction band Landau level becomes comparable to the binding energy of the weakly bound muonium atom. Within the hydrogenic model, an estimate of the magnetic field required for ${1over 2}hbaromega_c$ to match $R_y$ for the ground state of the weakly bound muonium atom in GaAs yields beginequation B_0 = e^3 m^* c over hbar epsilon^2 = (m^*/m)^2over epsilon^2times B_aapprox 6.7 hboxrm T , labelB endequation where $B_aapprox 2.2times 10^5$ T is the atomic scale magnetic field.

It is worth noting that $B_0$ is about 5 orders of magnitude less than the magnetic field required to affect the vacuum ground state of a muonium or hydrogen atom in the same manner. Accordingly, the characteristic electric fields required to ionize a muonium atom in GaAs and GaP is about 4-5 orders of magnitude less than atomic scale electric fields. It is therefore more consistent that ionization of Mu$^0_{rm BC}$ (either thermally or by electric field) takes place from the weakly bound muonium state rather than from the deep state.

In conclusion, we have used $mu$SR techniques in high magnetic field to detect magnetic freezing out of a free electron into atomic energy levels of the weakly bound muonium atom. Using this effect one may be able to model an elementary act of the metal-insulator transition in doped semiconductors.

beginthebibliography99

bibitemPatterson88 B.D. Patterson, sl Rev. Mod. Phys., bf 60, 69 (1988).

bibitemStorchak95 V.G. Storchak, J.H. Brewer and G.D. Morris, sl Phys. Rev. Lett., bf 75, 2384 (1995).

bibitemStorchak96 V. Storchak, J.H. Brewer and G.D. Morris, sl Phys. Rev. Lett., bf 76, 2969 (1996).

bibitemStorchak99 V.G. Storchak, J.H. Brewer, G.D. Morris, D.J. Arseneau, and M. Senba, sl Phys. Rev., bf B59, 10559 (1999).

bibitemStorchak97 V.G. Storchak, S.F.J. Cox, S.P. Cottrell, J.H. Brewer, G.D. Morris, D.J. Arseneau, and B. Hitti, sl Phys. Rev. Lett., bf 78, 2835 (1997).

bibitemEshchenko99 D.G. Eshchenko, V.G. Storchak and G.D. Morris, sl Phys. Lett., bf A264, 226 (1999).

bibitemAnimalu77 A.O.E. Animalu, it Intermediate Quantum Theory of Crystalline Solids, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1977.

bibitemEshchenko02 D.G. Eshchenko, V.G. Storchak, J.H. Brewer and R.L. Lichti, sl Phys. Rev. Lett., bf 89, 226601 (2002).

bibitemKnox63 R.S. Knox, it Theory of Excitons, Academic Press, (1963).

bibitemKiefl85 R.F. Kiefl, J.W. Schneider, H. Keller, W. Kundig, W. Odermatt, B.D. Patterson, K.W. Blazey, T.L. Estle, and S.L. Rudaz, sl Phys. Rev., bf B32, 530 (1985).

bibitemZhang90 X. Zhang, K. Dou, Q. Hong and M. Balkanski, sl Phys. Rev., bf B41, 1376 (1990).

bibitemYafet56 Y. Yafet, R.W. Keyes and E.N. Adams, sl J. Phys. Chem. Solids, bf 1, 137 (1956).

bibitemEdwards95 sl Metal-Insulator Transitions Revisited, eds. P.P. Edwards and C.N.R. Rao, Tailor & Francis, London, Bristol, 1995.

bibitemKeyes56 R.W. Keyes and R.J. Sladek, sl J. Phys. Chem. Solids, bf 1, 143 (1956); R.J. Sladek, sl J. Phys. Chem. Solids, bf 5, 157 (1958).

endthebibliography

Conclusions

Our experiments reveal that electron capture into a weakly bound state may be a general route for muonium formation in semiconductors. We found the electronic structure of this state; the results imply validity of the effective mass approximation within the hydrogen-like model as a description of the weakly-bound precursor states formed on initial capture of an electron by a thermalized positive muon. Our experiments in high magnetic field point to the possibility of studying electron localization into WBS it via magnetic freezeout. This finding opens up the possibility to study the elementary act of a metal-insulator transition in a wide variety of materials.

Future Plans and Beam Time Request for 2003-2004

Muonium Formation and Ionization in Semi-Insulating GaAs

We propose to complete our experiments with semi-insulating GaAs in high magnetic field in order to better understand the effect of electron freezeout. First we would like to measure the magnetic field dependence of the diamagnetic fraction in the middle of the ionization curve (see Fig. 2). Our next plans are to combine experiments in high magnetic field with electric field. As we expect a magnetic field of several Tesla to increase the binding energy of WBS, we should observe an increase in the electric field required to prevent Mu$_{rm BC}$ formation in high magnetic field. In other words, we should observe a less steep increase of the diamagnetic fraction with electric filed as we increase the magnetic field. We request 12 shifts for these experiments.

Mu Formation & Ionization in GaAs with Different Impurity Concentrations

All our experiments in GaAs so far were carried out using semi-insulating samples where Mu$_{rm BC}$ is readily formed at low temperatures. Having in mind the effect of electron freezeout into WBS of Mu atom we propose to carry out experiments in high magnetic field (up to 7 T) in a set of GaAs samples deliberately doped with Cr. The results of our recent PRL citeEshchenko02 indicate that an addition of $n_{rm Cr}=3times 10^{16}$ cm$^{-3}$ significantly increases the diamagnetic fraction at low temperatures. This gives us a possibility to reduce this diamagnetic fraction (or even get rid of it) in high magnetic field. The most convincing result we can expect is to carry out freezeout experiment in a sample with a concentration of impurities that causes a complete absence of the Mu$_{rm BC}$ signal at low $T$ which we can then recover at high magnetic field. For this purpose we request 24 shifts to measure the magnetic field dependence of the diamagnetic and Mu$_{rm BC}$ fractions in 3-4 GaAs samples with Cr concentration from $5times 10^{15}$ cm$^{-3}$ to $10^{17}$ cm$^{-3}$.

Muonium Formation and Ionization in InSb

The group III-V semiconductor InSb is known to possess the lowest electron mass and the highest dielectric constant among all common semiconductors. Therefore it is expected to have the lowest binding energy for the WBS of the muonium atom. In our case that means that we will be able to move from the condition where the Coulomb interaction is comparable to the magnetic interaction to the condition where the magnetic interaction is an order of magnitude higher than the Coulomb interaction in the highest magnetic field available at TRIUMF (about 7 T).

We propose to carry out experiments in InSb in high magnetic field, for which we request 12 shifts. This will give us a possibility to compare our results with theoretical expectations.

Thus in total we request 48 shifts to be allocated before the end of the Summer 2004 beam period. For these experiments we need high magnetic field, therefore we request this beam time to be allocated on M15 with the it HiTime apparatus.

After completion of these experiments, we anticipate that we will report back to the EEC with a request for additional beam time.

Experiment 938 Publications

1. D.G. Eshchenko, V.G. Storchak, J.H. Brewer and R.L. Lichti, "Influence of Impurities on Short Range Electron Transport in GaAs", sl Phys. Rev. Lett., bf 89, 226601 (2002).

2. V.G. Storchak, D.G. Eshchenko, R.L. Lichti and J.H. Brewer, "Weakly Bound Muonium State in GaP", sl Phys. Rev., bf B67, 121201 (2003).

3. D.G. Eshchenko, V.G. Storchak, S.P. Cottrell and S.F.J. Cox, "Excited Muonium State in CdS", sl Phys. Rev. B, submitted, 2003.

4. D.G. Eshchenko, V.G. Storchak, J.H. Brewer, S.P. Cottrell, S.F.J. Cox, E. Karlsson and R. Waeppling, "Ionization of a Shallow Muonium State in a Semiconductor", sl Physica, bf B326 , 120 (2003).

5. D.G. Eshchenko, V.G. Storchak, R.L. Lichti and J.H. Brewer, "Short Range Electron Transport in GaAs", sl Physica, bf B326 , 160 (2003).

6. V.G. Storchak, D.G. Eshchenko, R.L. Lichti and J.H. Brewer, "Weakly Bound Muonium State in a Semiconductor", sl Physica, bf B326 , 164 (2003).