The diffusion of P, As and Sb in high-purity Ge was studied between 600 and 920C. Secondary ion mass spectrometry and spreading resistance profiling were used to determine the concentration profiles of the chemically and electrically active dopants. Intrinsic and extrinsic doping conditions resulted in a complementary error function and box-shaped diffusion profiles, respectively. These profiles revealed enhanced dopant diffusion under extrinsic doping. Accurate modelling of dopant diffusion was achieved on the basis of the vacancy mechanism; taking account of singly negatively charged dopant-vacancy pairs and doubly negatively charged vacancies. The results (tables 14 to 16) could be described by:

As:     D (cm2/s) = 3.2 x 101exp[-2.71(eV)/kT]

P:     D (cm2/s) = 9.1 x 100exp[-2.85(eV)/kT]

Sb:     D (cm2/s) = 1.67 x 101exp[-2.55(eV)/kT]

The activation enthalpy decreased with increasing atomic size of the dopants. This was attributed to differences in the binding energy of the dopant-vacancy pairs.

Intrinsic and Extrinsic Diffusion of Phosphorus, Arsenic and Antimony in Germanium. S.Brotzmann, H.Bracht: Journal of Applied Physics, 2008, 103[3], 033508

 

Table 13

Diffusion of Ga in Ge

   

Temperature (K)

D (m2/s)

827

1.3 x 10-22

870

6.6 x 10-22

922

1.0 x 10-20

923

1.6 x 10-20

983

1.4 x 10-19

1040

1.3 x 10-18

1045

1.2 x 10-18

1094

7.7 x 10-18

1097

1.1 x 10-18

1144

3.7 x 10-17

1189

1.4 x 10-16

 

Table 14

Diffusivity of As in Ge

Temperature (C)

Donor Concentration (/cm3)

D (cm2/s)

640

1.3 x 1017

3.2 x 10-14

640

2.3 x 1019

3.4 x 10-14

680

1.9 x 1017

1.5 x 10-13

680

3.6 x 1019

1.9 x 10-13

730

5.0 x 1017

8.8 x 10-13

730

2.5 x 1018

1.1 x 10-12

730

5.7 x 1019

7.7 x 10-13

770

1.1 x 1018

3.1 x 10-12

770

6.5 x 1019

2.2 x 10-12

820

1.1 x 1017

9.5 x 10-12

820

5.8 x 1019

9.6 x 10-12

868

8.8 x 1017

3.2 x 10-11

868

3.0 x 1019

4.5 x 10-11

920

1.3 x 1018

1.1 x 10-10

920

8.6 x 1018

1.3 x 10-10