Haynes - Shockley experiment

Haynes - Shockley experiment

In the Haynes - Shockley experiment, a piece of semiconductor gets a pulse of holes, induced by voltage or a short laser pulse.

To see the effect, we consider a n-type semiconductor with the length "d". We are interested in determining the mobility of the carriers, diffusion constant and relaxation time. In the following, we reduce the problem to one dimension.

The equations for electron and hole currents are:

:j_e=-mu_n n E-D_n frac{partial n}{partial x}

:j_p=+mu_p p E-D_p frac{partial p}{partial x}

where mu=eeta D is mobility, Einstein relation states: v=mu E.

We consider the continuity equation:

:frac{partial n}{partial t}=frac{-(n-n_0)}{ au_n}-frac{partial j_e}{partial x}

:frac{partial p}{partial t}=frac{-(p-p_0)}{ au_p}-frac{partial j_p}{partial x}The electrons and the holes recombine with the time au.

We define p_1=p-p_0 and n_1=n-n_0 so the upper equations can be rewritten as:

:frac{partial p_1}{partial t}=D_p frac{partial^2 p_1}{partial x^2}-mu_p p frac{partial E}{partial x}-mu_p E frac{partial p_1}{partial x}-frac{p_1}{ au_p}

:frac{partial n_1}{partial t}=D_n frac{partial^2 n_1}{partial x^2}+mu_n n frac{partial E}{partial x}+mu_n E frac{partial n_1}{partial x}-frac{n_1}{ au_n}

Let us consider the part with the gradient of the electric field. Laplace equation states:

: ho=-epsilon epsilon_0 frac{partial^2 U}{partial x^2}= epsilon epsilon_0 frac{partial E}{partial x}

:frac{partial E}{partial x}= frac{ ho}{epsilon epsilon_0}=frac{e_0 ((p-p_0)-(n-n_0))}{epsilon epsilon_0}

Introducing n_2=p_1+n_1 and n_3=p_1-n_1<, we rewrite the initial equations with the new parameters.

:frac{partial n_2}{partial t}=D_p frac{partial^2 n_2}{partial x^2}-mu_p p frac{partial E}{partial x}-mu_p E frac{partial n_2}{partial x}-frac{n_2}{ au_p}

:frac{partial n_2}{partial t}=D_n frac{partial^2 n_2}{partial x^2}+mu_n n frac{partial E}{partial x}+mu_n E frac{partial n_2}{partial x}-frac{n_2}{ au_n}

These two equations are coupled and can be combined:

:frac{partial n_2}{partial t}=D^* frac{partial^2 n_2}{partial x^2}+mu^* E frac{partial n_2}{partial x}-frac{n_2}{ au^*},

kjer so D^*=frac{D_n D_p(p+n)}{p D_p+nD_n}, mu^*=frac{mu_nmu_p(p-n)}{pmu_p+nmu_n} in :frac{1}{ au^*}=frac{pmu_p au_p+nmu_n au_n}{ au_p au_n(pmu_p+nmu_n)}.Considering n>>p or p ightarrow 0 (that is a fair approximation for a semiconductor with only few holes injected), we see that D^* ightarrow D_p, mu^* ightarrow mu_p and frac{1}{ au^*} ightarrow frac{1}{ au_p}. The semiconductor behaves as if there were only holes traveling in it.

The final equation for the carriers is:

:n_2(x,t)=A frac{1}{sqrt{4pi D^* t e^{-t/ au^*} e^{-frac{(x+mu^*Et-x_0)^2}{4D^*t

This can be interpreted as a delta function that is created immediately after the pulse. Holes then start to travel towards the electrode where we detect them. The signal then is Gaussian curve shaped.

Parameters mu, D and au can be obtained from the shape of the signal.

:mu^*=frac{d}{E t_0}

:D^*=(mu^* E)^2 frac{(delta t)^2}{16 t_0}

References

*Wang:"Solid State Electronics"


Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

  • Organic field-effect transistor — OFET based flexible display An organic field effect transistor (OFET) is a field effect transistor using an organic semiconductor in its channel. OFETs can be prepared either by vacuum evaporation of small molecules, by solution casting of… …   Wikipedia

  • Diffusion current — Contents 1 Introduction 1.1 Diffusion current versus drift current 1.2 Carrier Actions of Diffusion Current 2 Derivation of diffusion current …   Wikipedia

  • Шокли, Уильям Брэдфорд — Уильям Брэдфорд Шокли англ. William Bradford Shockley Шокли в 1975 году Дата рождения: 13 февраля 1 …   Википедия

  • 1956 — This article is about the year 1956. Millennium: 2nd millennium Centuries: 19th century – 20th century – 21st century Decades: 1920s  1930s  1940s  – 1950s –  1960s   …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”