Corresponding author: Svetlana P. Kobeleva (kob@misis.ru)

We have analyzed phosphorus diffusion profiles in an In_{0.01}Ga_{0.99}As/In_{0.56}Ga_{0.44}P/Ge germanium structure during phosphorus co-diffusion with gallium for synthesis of the germanium subcell in multi-junction solar cells.. Phosphorus diffused from the In_{0.56}Ga_{0.44}P layer simultaneously with gallium diffusion into the heavily gallium doped germanium substrate thus determining the specific diffusion conditions. Most importantly, gallium and phosphorus co-diffusion produces two _{P} depth distribution in the specimen has been studied using two methods, i.e., the Sauer–Freise modification of the Boltzmann–Matano method and the coordinate dependent diffusion method. We show that allowance for the drift component in the coordinate dependent diffusion method provides a better _{P} agreement with literary data. Both methods suggest the _{P} tendency to grow at the heterostructure boundary and to decline closer to the main _{P} growth near the surface _{P} growth with the electron concentration, suggest that the negatively charged _{Ge}P complexes diffuse in the heterostructure by analogy with one-component diffusion.

Phosphorus and gallium and the main doping impurities in germanium and therefore the interest to their diffusion emerged from the very start of the germanium

There were many recent works on phosphorus diffusion in germanium. It was reported [_{P} in pure germanium depends on phosphorus concentration; later on this observation was confirmed [_{i}_{P} is an almost linear function of the phosphorus concentration. Later on box-shaped diffusion profiles were analyzed in the assumption that phosphorus diffusion in germanium occurs by vacancy diffusion mechanism with the formation of germanium vacancy _{Ge}P complexes in different charge states and the _{P}_{P} dependence is related with the charged vacancy concentration dependence on the electron concentration [

The development of multi-junction solar cell (^{3}^{5} compound base

The specimens were grown by MOS hydride epitaxy in a Veeco E450 LDM reactor in the form of (100) gallium doped germanium substrates (_{Ga} = 10^{18} cm^{-3}) and exposed to a phosphine gas flow at 635 °C for 2.5 min. Then the In_{0.56}Ga_{0.44}P buffer layer (1 min at _{0.01}Ga_{0.99}As layer (1.6 min at the same temperature) were deposited. The gallium, phosphorus and germanium profiles were measured by SIMS on a PHI-6600. As shown elsewhere [

The phosphorus diffusion coefficient _{P} was calculated using two methods, i.e., the Sauer–Freise modification of the Boltzmann–Matano method and [

(

_{L}^{21} cm^{-3}; _{R}^{17} cm^{-3} using the formula

_{P}

Phosphorus diffusion coefficient distribution in depth: (

The coordinate dependent diffusion method deals with two atom migration mechanisms, i.e., due to the concentration gradient (proper diffusion) and drift at the velocity

The diffusion coefficient and the drift velocity are calculated using one parameter (the average distance between adjacent sites λ) and two variables, i.e., the probability of vacant sites for jump φ(

^{2};

For the calculations λ was accepted equal to the germanium lattice parameter

The coordinate dependent diffusion calculated _{P} data are expectedly lower than the Sauer–Freise ones since we took into account the phosphorus atom drift component for their calculation. The only exclusion is a small portion in the hole conductivity region at the phosphorus distribution tail, but with account of the calculation inaccuracy in this region one can consider these results to be approximately equal, i.e., the drift component is negligible beyond the second

Figure

Phosphorus, gallium and free carrier concentration profiles in germanium: (_{P}; (_{Ga}; (

We did not take into account the concentrations of germanium vacancies (_{Ge}) and possible P–_{Ge} complexes due to their negligibility compared with the doping impurity concentration [

The element concentrations at the heterostructure interface exceed the density of states in the conduction band (_{С}) and in the valence band (_{V}) at the diffusion temperature, i.e., germanium is degenerate in this region and hence we calculated the electron and hole concentrations using the Fermi–Dirac distribution function [

_{C}_{1/2}(η), _{V}_{1/2}(–η – ε_{i}

where _{1/2}(η) is the Fermi integral having a value of approx. 1/2:

_{C} and _{V} are the conduction band bottom and valence band top, respectively, and

Numeric calculations of Eq. (3) were carried out using the Newton method. The origin of coordinates in Fig. _{0.56}Ga_{0.44}P/Ge heterostructure interface. The first

The electric field of the first _{Ge}P) complexes) and decelerate the diffusion of positively charged (P^{+}) atoms. The field of the second deeper _{P} growth near the first _{Ge}P complexes co-diffuses with gallium.

To analyze the diffusion coefficient dependence on material’s parameters we plotted _{P} vs _{P} ~ ^{3} [_{P} ~ ^{2} [_{i}_{i}^{18} cm^{-3} for

_{P} as a function of electron concentration: (

or (for the quadratic mechanism):

The regions in Fig.

It can be seen from Fig. _{P} data of this work are higher compared with literary data but in the region close to the intrinsic one the coordinate dependent diffusion method data agree well with earlier results [_{P} growth with _{Ge}P complexes.

The general _{P} growth with the concentration

In the hole conductivity region at the heterostructure interface _{P} grows with _{P} growth deceleration may be caused by a decrease in the overall vacancy concentration since Eqs. (5) and (6) were derived in the assumption of constant overall vacancy concentration. It should be noted that the phosphorus diffusion coefficient was first studied in this work for a hole conductivity region in germanium.

In the electronic conductivity region of the structure between the two _{P} depends on _{Ge}P complex deceleration by

The diffusion coefficient calculated as a function of a distance from the heterostructure interface using the Sauer–Freise modification of the Boltzmann–Matano method and the coordinate dependent diffusion method. It is shown that diffusion in a _{P} growth tendency closer to the first _{P} decline tendency moving away from the second _{Ge}P complexes with a charge of -1 or -2. The Sauer–Freise method overestimates _{P} whereas the coordination dependent diffusion method gives a better _{P} agreement with literary data. The latter is because the coordinate dependent diffusion method takes into account both the diffusion and the drift phosphorus atom diffusion components in germanium lattice. For two

The _{P} growth tendency with

The _{P} data for the hole region also shows the _{P} growth tendency with _{P} should be constant at phosphorus concentrations of below _{i}_{P} which is not valid for the heavily compensated _{P} dependence on _{P} data for the hole region also show the _{P} growth tendency with _{P} should be constant at phosphorus concentrations of below _{i}_{P} which is not valid for the heavily compensated _{P} dependence on

_{0.56}Ga

_{0.44}P/Ge heterostructure on diffusion of phosphor in germanium within the formation of multiple solar cells.

_{0,01}Ga

_{0,99}As/In

_{0,56}Ga

_{0,44}P/Ge heterostructures.