A polar plane refers to families of planes where each plane is not electrically neutral, and therefore as you 'move' between neighboring planes the (ionic) charge density changes the sign (and thus forming a dipole between each plane).

Consider rock salt structure as a simple example. Each {001} plane has the same amount of Na+ and Cl- ions and is neutral and therefore it is a non-polar plane. However, the {111} planes consist entirely of a single ion type, and therefore dipoles are formed between parallel planes and it is thus polar.

GaN has a more complex structure but if you look at this schematic

http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/Articleimage/2012/CP/c2cp40998d/c2cp40998d-f1.gif

You can see that the c-planes are not neutral, whereas the m plane has: 4 Ga3+ ions, each shared at the corner between 6 unit cells, so a total of 4/6 3+ charges, and 2 N3- ions that are each shared between 3 unit cells, so a total of 2/3 3- charges. Therefore this plane is charge neutral and non-polar. It's not always straightforward to see.

The polarity I describe above has nothing to do with n/p doping. Sometimes (but not commonly), the type of doping may be referred to in a sense of polarity, which basically means what is the sign of the free carriers. It is more in the context of a sign, which may also relate to the sign (polarity) of the Hall voltage. Again, this has nothing to do the polarity of the crystal planes.

Polar Semiconductor: example - GaN when grown on c-plane (0001 direction). Noncentrosymmetric III-N compound semiconductors like GaN, AlN, InN etc. consists of sequential bilayers which are made up of cations and anions respectively, which leads to polar faces. i.e. for GaN these closely spaced hexagonal layers are made up of Ga and N. Due to this lack of inversion symmetry, a large polarization charge (sheet charge of opposite polarity) will build up on two surfaces (top surface and basal surface) in GaN like materials. This polarization charge is very large (generally > 1013 cm-2) which leads to very high electric field (~ in MV) in III-N materials. Depending upon the growth one can end up with either Ga-face or N-face GaN with opposite polarity. Two parts: intrinsic part of polarization is know as spontaneous polarization and polarization due to mechanical stress is called as piezoelectric polarization.  

A polar plane refers to families of planes where each plane is not electrically neutral, and therefore as you 'move' between neighboring planes the (ionic) charge density changes the sign (and thus forming a dipole between each plane).

Consider rock salt structure as a simple example. Each {001} plane has the same amount of Na+ and Cl- ions and is neutral and therefore it is a non-polar plane. However, the {111} planes consist entirely of a single ion type, and therefore dipoles are formed between parallel planes and it is thus polar.

GaN has a more complex structure but if you look at this schematic

http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/Articleimage/2012/CP/c2cp40998d/c2cp40998d-f1.gif

You can see that the c-planes are not neutral, whereas the m plane has: 4 Ga3+ ions, each shared at the corner between 6 unit cells, so a total of 4/6 3+ charges, and 2 N3- ions that are each shared between 3 unit cells, so a total of 2/3 3- charges. Therefore this plane is charge neutral and non-polar. It's not always straightforward to see.

The polarity I describe above has nothing to do with n/p doping. Sometimes (but not commonly), the type of doping may be referred to in a sense of polarity, which basically means what is the sign of the free carriers. It is more in the context of a sign, which may also relate to the sign (polarity) of the Hall voltage. Again, this has nothing to do the polarity of the crystal planes.

Semipolar and non-polar semiconductors: As mentioned in my previous answer, GaN like materials having large polarization charge on both surfaces which results in a very high electric field in hetero-structure devices(AlGaN/GaN, AlInN/GaN, InGaN/GaN etc). In some devices we can utilize this strong electric field, however in some cases (like LED, LASER etc) it will deteriorate the device performance. So to increase the efficiency of light emitting devices, one would prefer reduced/zero polarization charge in III-N semiconductor materials. 

When III-N materials are grown on m-plane (11bar00) or a-plane (112bar0) they are called non-polar semiconductors. These materials when grown on (112bar2) plane they are called as semi-polar material. Please see the attached image.

http://www.jst.go.jp/EN/seika/01/seika17_image03.gif

Classification of semiconductors into non-polar, semi-polar, polar semiconductors is based on the amount of ionicity in the chemical bond; ionicity depends on the electro-negativity (EN) difference. The non-polar semiconductor, e.g. diamond, Si, Ge, has a covalent bond with EN difference, say, < 0.5. Elemental semiconductors (C, Si, Ge) consist of one atom; hence, are necessarily covalent and non-polar. III-V compound semiconductors (GaAs, InP, GaN) have EN difference between the anions and the cations; hence have necessarily partly ionic bond and are slightly (EN = 0.4-0.9) or moderately (EN = 1-1.3) polar. II-VI compound semiconductors (ZnS, CdTe) have even higher ionicity and have a mixture of covalent and ionic bonds, i.e. are more polar. Ionic compounds have EN > 2.3, and are not semiconducting. 

Gourab Dutta Sir can you tell the relation between polar /non polar nature with crystal defects.