Nuclear magnetic resonance of 31P in InP

Volume 31A, number 6

PHYSICS

NUCLEAR

MAGNETIC

LETTERS

23 March 1970

RESONANCE

OF

IN InP

*

M. ENGELSBERG and R. E. NORBERG Department of Physics. Washington University, St.Louis. Missouri, 63130. USA Received 2 February 1970 31P line width in an InP powder is found to be appreciably narrower than the theoretical dipolar The width. It is proposed that the effect arises from the nuclear pseudo-dipolar interaction.

We have performed pulsed and cw NMR experiments on 31P in a number of n and p-type InP powders. Various contributions [1] to the second moment of the resonance line were measured near 14 Mc/s and at temperatures between 78°Kand 300°K. The results were found to be independent of temperature and sample material. The dipolar contributions to the Van Vleck second moment can be calculated for the 31P resonance. One finds:

In P3’ SECOND DERIVATIVE OF ECHO 9O.~r.9090 PULSE SEQUENCE

2.4

~

TEUPERATURE 78K

2.0

12 —

(M21!)dipolar = 0.17 gauss2 (from other (M2JS)dipolar = 4.08 gauss2 (from 1131n and 1151n spins); total 2 and (M2)dipolar 4.25 gauss . The 31P free-induction decay observed at 78°K yielded a second moment (M2)decay = 2.0 ± ±0.1 gauss2, a factor of two smaller than (M2)~aoIar.We then turned to an echo technique, using a 9O-r-9O 90 pulse sequence (the notation indicates a second 90090°with pulse applied at to time with its phase shifted respect theT first 90°pulse). For r> 40 ~sec the In31P echo shows a well-resolved maximum at time 2T measured from the first pulse. Mansfield [1] has shown that, for a two spin system (no distinction is made between h131n and 1151n), such an echo signal R(t,T) (normalized to unity fort = = r = 0) satisfies: R

(T) =

-[d 2 R(tT)/dt 2 ItT

=

2

(M2 11+M2IS) - M4E

T(1)

for sufficiently small r. Here t is the time measured from the second pulse; M4e is a quantity related to the fourth moment of the resonance line and M2 = M211+ M2JS is the total seeond moment,

P

0

I

10

20

I

30

~

I

so

I

60

70

72(10-10 sec2) Fig. 1. The second derivative of the normalized 31P echo signal as a function of the square of the pulse separation.

2 for an 1 shows a plot with of R”(r) versus r InPFig. sample Zn-doped 2x1018 carriers/cm3. The intercept of the straight line corresponds to R”(0) = (M2)echo = M 2, in reasonable agreement 2jj+M2j~ with (M2)decay. 2.3 ±0.15gauss As an additional experimental check, the cw resonance was observed. The second moment was found to be (M2)cw = 2.0 ±0.1gauss2 in good agreement with the pulsed measurements. Since the three measurements of the total second moment disagree with (M2)~~lar, it was interesting to try to separately measure M211 and M2j~. Mansfield [1] has shown that the echo amplitude at time t T is given by R(t=r, T) = R(4~)= *

Work supported in part by the US Air Force Office of Scientific Research. 311

Volume 31A, number6

PHYSICS LETTERS

2, for sufficiently small T. A plot of = 1 ~M~A~r R(i-) versus T2 for our data shows the predicted ,-2 dependence for T < 40 ~isec with (M2IS)echo = = 2.10 ±0.08 gauss2. Finally a 90-T-l80 90 pulse sequence small should T the echo envelope forwas suchapplied. a pulse For sequence correspond to the decay arising from interactions among like spins only [2, 3]. The gaussian envelope observed for our InP echoes corresponds to (M211)echo = 0.12 ±0.01gauss2. The contribution from spins S to the powder second moment of the resonance of the spin I is given by: ~ 2 2

_____

M

215~

.

N5

.

—

(2)

2Bjtkr~,3k) frIv5r

where Aj?k and Bj~kcorrespond to the exchange and pseudo-dipolar interactions respectively [4, 5]. The last term in eq. (2) is an interference term which, for negative ~ can reduce the second moment from (M 2~tot~ ~dipoiar~ The reduction can be particularly significant if (M2IS)dipolar 31P. Taking >> >> as is the and caseassuming in In our~ observed (M2IS)echo, that A and .~ are non-zero for nearest neighbors only, we obtain a quadratic equation for B which has real roots provided IA/h~~2.5 kc/sec and, consequently, -6.8 kc/sec ~B/h ~ -1.2 kc/sec.

312

A ratio of B/A ~, 1 implies that the electronic wave function in the solid is largely non-s over the valence and/or conduction bands. The relatively large paramagnetic shift re15InPchemical resonance is conported the ‘ non-s character of the sistent [6,7] with afor largely valence electron wave function near the indium nuclei. In addition, the calculated [8] p-like ~ conduction band lies unusually close to the s-like ~ band. We thank Drs. J. Broerman, K. Luszczynski, and R. Sundfors for their interest and assistance.

4 -6

it~+i)~J~~sh r~,k+ +

23 March 1970

References 2. andRev. R.E.Norberg, Phys. Rev. 154 1. W.W.WarrenJr. P. Mansfield, Phys. 137 (1965) 961. (1967) 277. 3. M. E. Emshwiller, E. L. Hahn and D. Kaplan, Phys. Rev. 118 (1960) 414. 4. N. Bloembergen and T. J. Rowland, Phys. Rev. 97 (1955) 1679. 5. N. Bloembergen and P.P. Sorokin, Phys. Rev. 110 (1958) 865. 6. H. eds. LUtgemeier, R. K. Wlllardson Z. Naturforschg. and A. G. Beer 19a(Academic (1964) 1297. 7. R. L. Mieher, in: Semiconductors and semimetals, Press, 1966) Ch. 7. 8. F. H. Pollak, C. W. Higginbotham and M. Cardona, Proc. Intern. Conf. on Physics of semiconductors,

Kyoto, 1966; J. Phys. Soc. Japan 21, Suppi. 1966.