Electronic effect on the debye temperature of N-type silicon

Solid State Communications, Vola27, pp. 6364. Prin~d in Great Brit~i’n.

0038-1098/78/0708—0063

$02.00/0

© Pergamon Press Ltd. 1978.

ELECTRONIC EFFECT ON THE DEBYE TEMPERATURE OF N-TYPE SILICON Robert W. Keyes IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, U.S.A. and Nobuyoshi Kobayashi Department of Physics, University of Tokyo. Hongo 7, Tokyo 113, Japan (Received 12 April 1978 by J. Tauc) Analysis of recently published measurements of the specific heat of heavily doped n-type silicon reveals a dependence of the Debye temperature on doping.

3)

THE THEORY of the effect of on the the elastic elastic constants of semiconductors1 andelectronic measurements constants of heavily doped n-type silicon2 both predict that the Debye temperature of silicon will depend on doping.3 Kobayashi, et al. ~ have recently published a comprehensive set of measurements of the specific heat of a series of eleven phosphorusdoped silicon samples spanning the range of donor concentrations from 3 x l0~Cm’3 to 1020 em’3. The authors of reference 4 reported a single value for Oo, the Debye temperature, that fitted the specific heat measurements on all samples. In view of the established effect of doping on the elastic constants it seems appropriate to look for a variation of B~with donor concentration. A re-examination of the original data with values of Oo being determined from (C/T) vs T2 plots separately for each sample suggests that 8D is decreased by heavy doping. The derived values of 8o are given in Table I. These results, with an estimate of the errors in the determination of 8~,and information presented in an earlier publication on the same subject3’5 are plotted in Fig. I. A tendency for to be smaller in heavily doped samples is evident. As has also been found for, germanium, the effect of doping is appreciably larger than the effect predicted by the theory and by the measurement of the elastic constants.1’3 The magnitude of the electronic effect on the elastic constants of the heavily doped multivalley semiconductors silicon and germanium is well established by theory and experiment. The elastic Debye temperature can be calculated in the usual way. Although the elastic and thermal Debye temperatures are in satisfactory agreement for the pure semiconductors, doping apparently produces a greater reduction in the thermal 8o than in the elastic 80. The source of the excessively large effect of doping on the thermal Oo is not clear.

0

650

2

j~l8 I

N (cm— 1Q19 2 5 I

1020

I

oo c

2

THERMAL THERMAL

D ELASTIC

640

0

~

630

-

620

I

0

2

4 I06N1”3(cm’~)

-

Fig. 1. The Debye temperature of silicon as a function of donor concentration, after Table 1. ((>) Values presented m an earlier work are also shown (0, thermal ~ 0, elastic 0D).~ The solid line shows the depression of the elastic ~according to the theory ~f fl~~nj~ effect in the elastic constants of a multivalley semiconductor.1

Acknowledgement We thank W. Sasaki, S. Ikehata, and S. Kobayashi for their cooperation.

63

64

ELECTRONIC EFFECT ON THE DEBYE TEMPERATURE TABLE 1. 4 AL.

VALUES OF

Vol. 27, No. 2

8~ DERIVED FROM THE DATA OF KOBAYASHI, ET

Sample

Donor Concentration (lO1tcm3)

1

96

630

2

24

630

3

16

630

4

8.9

623

5

6.7

640

6

4.5

651

7

2.6

640

8

2.3

647

9

1.7

640

10

0.53

638

11

0.34

640

REFERENCES KEYES R.W., in Solid State Physics, vol. 20 (Edited by SEITZ F.,TURNBULL D., & EHRENREICH H.) Academic Press, New York (1967)p.37. 2. -

HALL J.J., Phys. Rev. 161, 756 (1967).

3.

KEYES R.W., Phys. Rev. 812, 2539 (1975).

4.

KOBAYASHI N., IKEHATA S., KOBAYASHI S. & SASAKI W., Solid State Commun. 24, 67 (1977)

5.

FLUBACHER P., LEADBETTER A.J. & MORRISON J.A. HEINIGER F. & PAOLI A., to be published.

Phil. Mag. 4, 295 (1959); HEDGCOCK FT.,