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\title{Mercury Cadmium Telluride}
\author{ Athula Herat\\
	\\
	Department of Physics \\
	University of Cincinnati \\
	Cincinnati, Ohio 45221\\[1em]}
\date{Dec 4, 95 }
\maketitle


\begin{abstract}
 Mercury-Cadmium-Telluride is a very useful and widely used IR detector material.In this review some of the important physical properties of  this material has been considered. Among the properties discussed are the lattice structure, Energy Band Structure, Optical properties,  Carrier life time , and other electrical properties. 
\end{abstract}

\newpage

	Infrared sensors are used to detect, and measure thermal heat radiation emitted from objects.  In late 1950's semi-conductor alloys consisting of III-V, IV-V, and II-VI materials were introduced in IR detectors.  HgCdTe which is an alloy consisting of II-VI compounds has currently become the most widely used IR detector material.



\section{Lattice Properties}

	The II-VI compounds, HgTe and CdTe both crystallize in the zincblende cubic structure.  This structure consists of two face centered cubic sub-lattices that are displaced by one another by  (1/4 $a_0$, 1/4$a_0$, 1/4$a_0$) along the body diagonal as shown in Fig.(1). Here A denotes cations consisting of 2 valance electrons, and B denotes anions with six such electrons. The crystal bonding is mainly covalent, but there could be some ionic bonding  due to the difference in the nuclear charges of A and B.  In an alloy as in the case of HgCdTe two different species of cations are involved, with each one being distributed randomly over the cation lattics sites in the crystal. Therefore in general this material is denoted by $Hg_{1-x}Cd_xTe$, where x denotes the mole factor of CdTe.


\begin{figure}
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\caption{Zincblende crystal lattice structure[1]}
\label{}
\end{figure}


	As in the case of most known semi-conductor materials the Brillouin zone  of this structure is a truncated octahedron.

	The lattice constant $(a_0)$ of HgCdTe depends on the x, and they obey Vagards law to a high degree of accuracy, except for an extremely small non-linearity between x vs. $a_0$ . $a_0$ varies from approx. 6.485 A to 6.460A as x  is varied from 0.0 to 1.0.  The density varies from $5.55 g/cm^3$ to $7.55g/cm^3$ as x is varied from 0.0 to 1.0.

\section{Energy Band Structure}
	
	The band structure near the $\Gamma$ point(k=0) for three different values of the band gap is shown in figure 2. The valence band in this material have a maximum at the center of the Brillouin zone with relatively large effective electron mass. The conduction band has a minimum at the zone's center with relatively small effective mass. 
	
	HgCdTe is an alloy whose bandgap may be tuned during manufacture. This results from the dependence of the energy gap on the operating temperature and x. It has been reported that the analytic expression for this dependence can be given as[3]. 

$E_g = -0.295 + 1.87 x - 0.28^2 + (6 - 14 x + 3 x^2)(10-4)T + 0.35 x^4$.

where   $E_g$ = energy bandgap in electron volts
	T = temperature in Kelvins

	Due to this reason  all semiconductor alloys have a variable cutoff wavelengths over a wide spectrum. The $Hg_{1-x}Cd_xTe$ alloy systems can cover the greatest range that varies from less than $1 \mu m$ to greater than $30 \mu m$.

\begin{figure}
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\caption{Band structure near $\Gamma$ - point of $Hg_{1-x}Cd_xTe$ for selected values of direct-gap energy[2]}
\label{}
\end{figure}



 
\section{Electron Mobility}

The electron Hall mobility vs. Temperature curve is shown in Figure 3. The rapid drop of mobility with increasing temperature(greater that 50K) is due to the dominance of lattice scattering mechanism at higher temperatures.  At lower temperature the mobility varies very little with T, and this could be explained by scattering by a single charged ionized impurity having an equal population to that of extrincic electron concentration.  

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\caption{Temperature dependence of the electron Hall mobility in $Hg_{1-x}Cd_xTe$ as a function of composition[2]}
\label{}
\end{figure}


\section{Optical Absorption edge}

	Figure 4 shows the dependence of the optical absorption coefficient upon photon energy for several compositions. The edges are very steep as expected of a direct-gap semiconductor. This plot again illustrates the fact that these alloys  provide continously variable cutoff wavelengths over a wide spectrum.


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\caption{Optical absorption coefficient as a function of composition in $Hg_{1-x}Cd_xTe$ at room temperature[2]}
\label{}
\end{figure}



\section{Excess-Carrier Lifetime}

	The lifetimes of optically excited, excess electrons and holes are among the most important parametrs of an intrinsic infrared detector material, since they control the magnitude and frequency response of the signal. When developing detector material one tries to achieve longest carrier life times  in order to get the maximum detectivity. But this is limited due to the radiative, and Auger recombination processes. When limited by these intrinsic recombination processes the life time of both excessive electrons and hole are equal. The lifetimes of electrons(and Holes) limited by the recombination processes can be given by the well-known Shockley-Read expression

$\tau =\tau_n (P_0 + P_1/n_0 + P_0) + \tau_p (n_0 + n_1/ n_0 + p_0)$

where $n_o$ and $p_0$ are the equilibrium electron and hole concentrations, $n_1$ and $p_1$ are exponential functions of the energy level of the recombination centers, and $\tau_n$ and $\tau_p$ are constants.
A plot of excess carrier lifetime vs. temperature is shown in Figure 5. 

\begin{figure}
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\caption{Excess-carrier lifetime vs. temperature in an n-type sample of $Hg_{0.77}Cd_{0.23}Te$ [1]}
\label{}
\end{figure}

\section{Referrences}

[1]  Semiconductors and Semimetals, edited by R.R. Willardson and A.C. Beer (Academic, New York) Vol. 5.

[2] Semiconductors and Semimetals, edited by R.R. Willardson and A.C. Beer (Academic, New York) Vol. 18.

[3]  The Infrared and Electro-Optical Systems Handbook, edited by W.D.Rogatto (SPIE Optical Engineering Press, Washington) Vol. 3.


[4]  Solid State Physics, N.W. Ashcroft and N.D. Mermin(Holt, Rinehart and Winston, New York)


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