The two-band model predicts that is roughly constant across direct-gap III-V…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Semiconductor physics and devices

Solid State Physics, Ch Semiconductors: masses, statistics, defect levels and mobility

Problem

The two-band

\mathbf{k}\cdot\mathbf{p}

model predicts that

m^*/E_g

is roughly constant across direct-gap III-V semiconductors with the conduction minimum at

\Gamma

: across InSb, InAs, GaSb, InP and GaAs (with

E_g

ranging from

0.17

1.42\,\mathrm{eV}

) the ratio lies between

0.047

and

0.082\,\mathrm{eV^{-1}}

. The ternary alloy In

_{0.53}

_{0.47}

As is a direct-gap semiconductor with its conduction minimum at

\Gamma

and

E_g=0.75\,\mathrm{eV}

300\,\mathrm{K}

. ((a)) Use the quoted range of

m^*/E_g

to bracket the electron effective mass of In

_{0.53}

_{0.47}

As. ((b)) The measured value is

m^*=0.041\,m_e

. State whether it falls inside the estimated bracket.

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